JP2012190274A - Modelling device and method for the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a modelling device and a method for the same for constructing a more precise model even with insufficient input/output data by using a priori knowledge.SOLUTION: The modelling device S constructs a model of a system by deciding parameter value and includes: a restrictive condition input setting part 21 and a restrictive condition storage part 41 for setting a model as a mathematical expression including a time variable regarded as a continuous time and a priori information about a system obtained in advance as a restrictive condition; an evaluation operation part 13 for obtaining a result of evaluation of an evaluation function that evaluates a difference between achievement output data outputted when prescribed input data are inputted to the system as achievement input data and model output data outputted when the achievement input data are inputted to the model; and a model update decision part 14 for obtaining parameter value of the model so that the restrictive condition is satisfied and a result of evaluation becomes best.

Description

  The present invention relates to a modeling apparatus and a modeling method for creating a model of a system, and more particularly to a modeling apparatus and a modeling method that can use a priori information based on a priori knowledge.

  With the development of computers (computers) in recent years, computer-based simulation is used for designing a system control system. In order to incorporate a real-world system into a virtual world on a computer, it is necessary to describe the real-world system using a model that connects the real world and the virtual world in a form that can be handled by a computer. is there. This model is usually a mathematical model such as a differential equation, a difference equation, a transfer function, a state equation and a logical formula. Whether or not the simulation result accurately represents a real-world system is determined by the quality of the model (model accuracy), and the work of building this model is called modeling.

  The modeling methods are roughly classified into white box modeling and black box modeling, and there is a gray box modeling that compromises these white box modeling and black box modeling.

  This white box modeling is based on the so-called first principle, and is based on natural laws (first principles) such as physical laws and chemical laws governing the system to be modeled, and various physicochemical quantities. This is a method of modeling, and is called physical modeling when the target is a physical system. This method is effective when the system (target) is relatively small and natural laws such as the physical laws acting on this system are well understood. It becomes difficult to apply. In the case of a large-scale system, this large-scale system is divided into small subsystems, this method is applied to each subsystem, modeling is performed, and these are integrated into a large-scale system. May apply.

  Black box modeling considers a system as a black box without using natural laws such as physical laws and chemical laws, or a priori knowledge. This is a method of building a model according to the purpose (specification), and is called system identification in the field of control engineering. This is effective when the system is relatively large or complex, and the dynamic characteristics of the system cannot be described only by natural laws such as physical laws. Even if the same input / output data is given, the purpose of modeling ( Specifications) and models obtained by modeling engineers may differ, and there is room for subjective factors.

  Gray box modeling is a method that is positioned between white box modeling and black box modeling.For example, in addition to observed input / output data, natural laws such as physical laws are partially used in model construction. Used.

  Some systems that can be modeled can describe the basic behavior of the system in terms of equations of motion, such as an articulated robot (manipulator). In many cases, such as combustion furnaces and chemical plants with heat treatment and chemical treatment, it is difficult to derive the dynamic characteristics from the laws of nature, and black box is used for system modeling (system modeling). Modeling and gray box modeling are often used.

  In this black box modeling or gray-bock modeling, the model is constructed by using input / output data, so the quality of the model depends on the input / output data, and both the quality and quantity that enable highly accurate modeling It is desirable that sufficient input / output data is obtained in advance. However, in reality, the waveform and size (level) that can be input to an actual system are limited, and the experimental opportunities to collect these input / output data are limited. In many cases, sufficient input / output data cannot be obtained. Furthermore, noise is also present in input / output data collected from an actual system, and in some cases, this noise can have a significant negative impact on the modeling. Also, depending on the system, there may be a condition that the model should satisfy, such as persistently exciting (PE property) for the input signal. In such a case, for example, input / output data collection work, selection of input / output data range for modeling, selection of sampling interval, preprocessing such as removal of abnormal values (filtering), selection of model order, etc. The modeling work for constructing a highly accurate model often involves repeated trial and error, and much time and a relatively long time are required to complete the model. Thus, for example, Non-Patent Document 1 and Patent Document 1 disclose a technique for improving the accuracy of a model by supplementing a priori knowledge with system modeling.

  This non-patent document 1 discloses a technique for modeling a priori information regarding the sign and stability of a steady gain of a model as a constraint condition. However, not only the steady-state gain and stability, but also the range of the steady-state gain and the time constant are often restricted even in the case of a first-order lag system (a priori knowledge). Often). For this reason, in the technique disclosed in Non-Patent Document 1, a model satisfying these is not always obtained.

  The system identification method disclosed in Patent Document 1 is a method for improving the initial parametric model of the system by incorporating a priori knowledge of the system. First, the system is first optimized by optimization without constraints. The initialization model is generated based only on the test data information of the second, and secondly, the initialization model is optimized in the presence of the a priori knowledge constraint. That is, the initial parametric model of the system is a model including a plurality of parameters based on analysis of a plurality of input signals and a plurality of output signals (system test data information). Determining a set of constraints based on the a priori knowledge corresponding to the set of parameters of the system, and (b) the system based on the initial parametric model and the set of constraints determined in step (a) Performing constrained parametric optimization and generating an improved parametric model of the system, wherein the constrained parametric optimization in step (b) includes the plurality of input signals and the plurality of output signals. Is not included. However, in the system identification method disclosed in Patent Document 1, even if the value of the obtained model parameter is close to the value of the model parameter of the initial model, the dynamic characteristics of the model may not necessarily be close. In the optimization in the presence of a priori knowledge constraint, only the initial model is used as a norm, and the suitability for input / output data is not considered.

JP 2004-272916 A

Herbert J.A.F.Tulleken, Grey-box Modeling and Identification Using Physical Knowledge and Bayesian Techniques, Automatica, Vol. 29, No. 2, pp. 285-308 (1993)

  The present invention is an invention made in view of the above-mentioned circumstances, and its purpose is to use the a priori knowledge in a technique different from the Non-Patent Document 1 and the Patent Document 1, and thereby the quality and quantity. It is to provide a modeling device and a modeling method capable of constructing a model with higher accuracy even with insufficient input / output data.

  As a result of various studies, the present inventor has found that the above object is achieved by the present invention described below. That is, the modeling apparatus according to one aspect of the present invention is a modeling apparatus that constructs a model of a system by determining values of parameters of the model, and the model includes a time variable that is regarded as a continuous time. A constraint condition setting unit that sets a priori information about the system obtained in advance as a constraint condition, and is output from the system when predetermined input data is input to the system as actual input data An evaluation operation unit for obtaining an evaluation result of an evaluation function for evaluating an error between the actual output data and the model output data output from the model when the actual input data is input to the model; and the constraint condition setting unit In order to satisfy the set constraint conditions and the evaluation result calculated by the evaluation calculation unit is the best, Characterized in that it comprises a model computing unit for determining the value of Dell parameters.

  A modeling method according to another aspect of the present invention is a modeling method for constructing a model of a system by determining values of parameters of the model, wherein the model is a time variable that is regarded as a continuous time. A constraint condition setting step for setting a priori information on the system obtained in advance as a constraint condition, and output from the system when predetermined input data is input to the system as actual input data An evaluation calculation step for obtaining an evaluation result of an evaluation function that evaluates an error between the obtained actual output data and the model output data output from the model when the actual input data is input to the model; and the constraint condition setting An evaluation result that satisfies the constraint condition set in the step and that is calculated in the evaluation calculation step. There As will be best characterized by comprising a model calculation step of obtaining a value of the parameter of the model.

  In the modeling apparatus and modeling method having such a configuration, an error between the actual output data and the model output data is evaluated by the evaluation function, and the values of the model parameters are obtained so that the evaluation result is the best, and the model is constructed. Is done. Then, a priori information representing a priori knowledge is set as a constraint condition, and when the model is constructed, values of model parameters are obtained so as to satisfy the constraint condition. For this reason, the modeling apparatus and modeling method having such a configuration are different from the non-patent document 1 and the patent document 1, and by using a priori knowledge, the input and output of the quality and quantity are insufficient. Even with data, a more accurate model can be constructed.

  According to another aspect, in the above-described modeling apparatus, the a priori information is at least one of an upper limit value and a lower limit value related to a steady gain in the system.

  According to this configuration, a priori information regarding the steady gain is also taken into consideration as a constraint condition, and a system model that satisfies the a priori information regarding the steady gain can be constructed.

  According to another aspect, in the above-described modeling devices, the evaluation function has a weight for weighting an error between the actual output data and the model output data, and the weight is larger as the value is larger. When the evaluation result greatly influences, the value of the weight is relative to a section corresponding to the actual output data including noise of a predetermined threshold or more than other sections excluding the section. It is set so that it may become small.

  According to this configuration, the influence of the performance output data including noise of a predetermined threshold value or more on the evaluation result is reduced, and the system model can be constructed with higher accuracy.

  According to another aspect, in the above-described modeling apparatuses, the model calculation unit sets an initial value of the model parameter, and then performs an optimization method for obtaining the value of the model parameter, When obtaining a value, the initial value itself is treated as a parameter of the model.

  In general, in an optimization method in which an initial value in a model parameter is set and then the value of the model parameter is obtained, the accuracy of the model of the system constructed by this optimization method is often influenced by the initial value. . According to this configuration, since the initial value itself is also handled as an unknown parameter, a system model can be constructed with higher accuracy without being influenced by the initial value.

  According to another aspect, in the above-described modeling apparatuses, the model calculation unit obtains a value of a parameter of the model by a particle swarm optimization method (PSO).

  According to this configuration, it is possible to provide a modeling apparatus using PSO as an optimization method for obtaining the values of model parameters.

  In another aspect, in the above-described modeling apparatus, the model calculation unit obtains a parameter value of the model by a predetermined optimization method, and uses the obtained parameter value of the model as the Particle Swarm Optimization Method. It is characterized by adding to the initial value of.

  According to this configuration, since the parameter value of the model obtained by a predetermined optimization method determined in advance is also used as the initial value used for PSO, the PSO method can be calculated from the initial value obtained by adding a value closer to true. Since the process can be started, the system model can be constructed with higher accuracy without unnecessary search.

  Further, in another aspect, in the above-described modeling apparatuses, the model calculation unit, when performing update using the Particle Swarm Optimization Method, information on the sign of the steady gain, the range of the steady gain, the stability of the system, and At least one of the information on the unstable zero point of the system is used.

  According to this configuration, the PSO is updated using at least one of the sign of the steady gain, the range of the steady gain, the information on the stability of the system, and the information on the unstable zero point of the system. It is possible to construct a model of a system that satisfies at least one of them as a constraint without performing unnecessary search.

  The modeling apparatus and the modeling method according to the present invention are input / output data having insufficient quality and quantity by using a priori knowledge in a method different from that of Non-Patent Document 1 and Patent Document 1. Even more accurate models can be constructed.

It is a block diagram which shows the structure of the modeling apparatus in embodiment. It is a flowchart which shows schematic operation | movement of the modeling apparatus in embodiment. It is a flowchart which shows the setting operation | movement of the constraint conditions in the modeling apparatus of embodiment. It is a flowchart which shows the calculation operation | movement of the model in the modeling apparatus of embodiment. In a garbage incinerator, it is a figure which shows the change of the amount of steam generation when the speed of a dust feeder is changed in steps. It is a figure which shows the upper limit and lower limit of a step response as a constraint condition. It is a figure for demonstrating the step response in the model of the refuse incinerator modeled with the modeling apparatus of embodiment. It is a figure for demonstrating the step response in the model of the refuse incinerator modeled by the conventional method as a comparative example. It is a case where the constraint condition of a steady gain is considered, Comprising: It is a figure for demonstrating the step response in the model of the refuse incinerator modeled with the modeling apparatus of embodiment.

  Hereinafter, an embodiment according to the present invention will be described with reference to the drawings. In addition, the structure which attached | subjected the same code | symbol in each figure shows that it is the same structure, The description is abbreviate | omitted suitably.

  FIG. 1 is a block diagram illustrating a configuration of a modeling apparatus according to an embodiment. The modeling apparatus S of the embodiment is an apparatus for constructing a model of a system to be modeled by determining values of parameters of the model, and the model is a mathematical formula including a time variable regarded as a continuous time. A constraint condition setting unit that sets a priori information on the system obtained in advance as a constraint condition, and actual output data output from the system when predetermined input data is input to the system as actual input data And an evaluation calculation unit for obtaining an evaluation result of an evaluation function for evaluating an error from the model output data output from the model when the actual input data is input to the model, and set by the constraint condition setting unit The parameters of the model are such that the constraint condition is satisfied and the evaluation result calculated by the evaluation calculation unit is the best. A device and a model computation unit for determining the value of the data.

  For example, as shown in FIG. 1, such a modeling apparatus S includes a calculation unit 1, an input setting unit 2, an output unit 3, a storage unit 4, the calculation unit 1, an input setting unit 2, and an output unit. 3 and the storage unit 4 are configured to include a bus 5 that connects them to each other so that data can be exchanged between them.

  The input setting unit 2 is a device that inputs various commands such as calculation start instructions of the modeling device S and various data necessary for system modeling such as performance input / output data to the modeling device S. Such as a mouse. In the present embodiment, the input setting unit 2 includes a constraint condition input setting unit 21 that inputs and sets constraint conditions, a model order identification parameter input setting unit 22 that inputs and sets model orders and identification parameters, and optimization calculation parameters. An optimization calculation parameter input setting unit 23 for inputting and setting an evaluation function and an evaluation function input setting unit 24 for inputting and setting an evaluation function. These constraint conditions, model order, identification parameters, and optimization calculation parameters are set in the modeling device S by being stored in the storage unit 4 of the modeling device S so as to be used when modeling the system. .

  The constraint condition input setting unit 21 is for inputting model constraint conditions (a priori information) and setting them in the modeling apparatus S. The constraint condition is a condition to be satisfied by the model obtained by the modeling when the system is modeled. In the present embodiment, the constraint condition is given by a priori knowledge about the system to be modeled. The a priori knowledge is information obtained from the system by an arbitrary means, for example, information estimated by calculation from a system design value, a theoretical formula, or the like. For example, when the system is designed, For example, the information may be information empirically guessed in light of the above case, or may be information obtained by actually constructing a system, operating this actual system, and observing it. The obtained a priori knowledge is expressed (notation, description) in a format that can be handled by the modeling apparatus S, and used as a priori information.

In this embodiment, output data (output data obtained by calculation) output from a system when data that is a predetermined standard (reference) and a time-dependent standard input is given to the system as input data. And the actual output data observed by the system) are defined as the constraint conditions (time response constraint conditions). The reference input includes, for example, step input (step input), ramp input (ramp input), periodic input such as trigonometric function wave (for example, sin wave) and triangular wave, and frequency sweep waves (sweep wave, sweep wave). ) And the like. The time response constraint condition may be, for example, the output data itself, and may be, for example, the upper limit value and / or the lower limit value of the output data, and the time range may be set in addition to these. That is, when the input time point of the reference input is time 0, the output data from which time t _S to which time t _E is the constraint condition, or the output data from which time t _S to which time t _E It is set whether the upper limit value and / or the lower limit value are set as constraint conditions (0 ≦ t _S <t _E ). When this time response constraint condition is input and set, the constraint condition input setting unit 21 functions as a time response constraint condition input setting unit.

  A and / or B means at least one of A and B, and means A or B, or both A and B.

  In the present embodiment, the sign of the steady gain of the system and the range (upper limit value and lower limit value of the steady gain) are set as the constraint condition (steady gain constraint condition). When the steady gain constraint condition is input and set, the constraint condition input setting unit 21 functions as a steady gain constraint condition input setting unit.

  The model order unknown parameter input setting unit 22 is for inputting the order of the model and the identification parameter of the model and setting them in the modeling apparatus S. The model identification parameter is a parameter to be identified as an unknown parameter among the parameters in the model. The value of the model identification parameter is determined by an operation for creating a system model, which will be described later, whereby a system model is constructed. The order and identification parameters of these models are appropriately selected depending on the purpose of modeling, for example, for use in control system design or for use in simulation. In addition, the accuracy of the model, the quality and quantity of input / output data used for modeling, the information processing amount (calculation amount) of modeling, and the like may be taken into consideration.

The optimization calculation parameter input setting unit 23 is for inputting optimization calculation parameters and setting them in the modeling apparatus S. The optimization calculation parameter is an adjustment parameter required when performing the optimization calculation. In this embodiment, the optimization calculation parameter is a parameter necessary for the calculation of the PSO method because the PSO (Particle Swarm Optimization) method is used as an optimization calculation method as will be described later. P, the number of solution updates (repetition count) K, the initial value range, and w, c ₁ , and c ₂ in the equations described below. When the optimization calculation parameter is input, the order of the model and the number of identification parameters may be taken into consideration. For example, as the order of the model increases or as the number of identification parameters increases, the solution space to be searched for becomes wider. Therefore, it is preferable that the number P of particles p and the number of solution updates K are set large. .

  The evaluation function input setting unit 24 is for inputting an evaluation function and setting it in the modeling apparatus S. When the parameter value of the identification parameter is determined, the evaluation function is a value (evaluation value) that indicates the degree (model accuracy) of how well the model specified by this parameter value represents the system. This is the function to find. Only one evaluation function may be set in advance and may be incorporated in the program in advance, but in this embodiment, in order to evaluate the model more appropriately, it can be input from the evaluation function input setting unit 24. . Furthermore, for the convenience of the operator, in this embodiment, a plurality of evaluation functions are prepared in advance, and an evaluation function is selected by selecting from among the plurality of evaluation functions via the evaluation function input setting unit 24. Is set as input.

  The output unit 3 is a device that outputs the command and data input from the input unit 2 and the calculation result (system model) of the modeling apparatus S. For example, a display such as a CRT display, LCD, organic EL display, or plasma display A printing device such as a printer or a printer.

  The storage unit 4 includes a nonvolatile storage element such as a ROM (Read Only Memory) and an EEPROM (Electrically Erasable Programmable Read Only Memory), a hard disk, and the like that store data and programs, and a modeling program executed by the arithmetic unit 1 And a so-called working memory that temporarily stores data during execution of a control program and the like, and includes, for example, a RAM (Random Access Memory) that is a volatile storage element. The storage unit 4 functionally includes a constraint condition storage unit 41, a model order identification parameter storage unit 42, an optimization calculation parameter storage unit 43, an evaluation function storage unit 44, a model output storage unit 45, and an actual result. And a data storage unit 46.

  The constraint condition storage unit 41 stores constraint conditions, and the constraint condition input from the constraint condition input setting unit 21 is stored and stored in the constraint condition storage unit 41. In this embodiment, the constraint condition storage unit 41 includes a time response constraint condition storage unit 411 that stores time response constraint conditions and a steady gain constraint condition storage unit 412 that stores steady gain constraint conditions.

  The model order identification parameter storage unit 42 stores the model order and the identification parameter of the model, and the model order and the identification parameter input from the model order identification parameter input setting unit 22 are the model order identification parameter storage unit. 42 and stored.

  The optimization calculation parameter storage unit 43 stores optimization calculation parameters, and the optimization calculation parameters input from the optimization calculation parameter input setting unit 23 are stored and stored in the optimization calculation parameter storage unit 43. The

  The evaluation function storage unit 44 stores the evaluation function, and the evaluation function input from the evaluation function input setting unit 24 is stored and stored in the evaluation function storage unit 44. In the present embodiment, as described above, a plurality of predetermined evaluation functions are stored in advance, and one evaluation function is selected from the plurality of evaluation functions from the evaluation function input setting unit 24, and this selected Information indicating this is also stored in the evaluation function storage unit 44.

  The model output etc. storage unit 45 stores the model output calculated by the calculation unit 1, the evaluation result, and information on whether or not the constraint condition is satisfied in association with each other for a predetermined parameter value that defines the model. is there. In the present embodiment, the predetermined parameter value is a value given by the PSO method. In the present embodiment, the information indicating whether or not the constraint condition is satisfied is changed to an evaluation value indicating the evaluation result, and is stored in the model output etc. storage unit 45 as the evaluation result. Information on whether or not the constraint condition is satisfied is converted into an evaluation value indicating the evaluation result and stored in the model output etc. storage unit 45 as the evaluation result, so that when determining the value of the model parameter, It is only necessary to consider the evaluation result, and the process of determining the parameter value of this model is simplified.

  The record data storage unit 46 stores record data. The actual data is predetermined input data (actual input data) input (applied) to the system to be modeled, and output data (actual output data) output from the system by the input of this input data. The input data and the actual output data (actual input / output data) are stored in the actual data storage unit 43 in association with each other. The predetermined input data may be arbitrary data, for example, time-series data such as step-shaped input data, random input data, and pseudo-white series (for example, M series) data. Corresponding to this, the output data also becomes time series data. The predetermined input data is called identification input in the field of control engineering. The time series input data and time series output data may be one set or a plurality of sets. In the case of a plurality of sets, each set of time-series input / output data may be data obtained on the same day or data obtained on different days. Then, the modeling apparatus S may be configured such that the plurality of sets of time-series input / output data are appropriately selected from these during modeling.

  The calculation unit 1 includes, for example, a microprocessor and its peripheral circuits, and controls the input setting unit 2, the output unit 3, and the storage unit 4 according to the function according to the program, thereby controlling the entire modeling apparatus S. It is responsible for control, and a model of a system to be modeled is constructed by determining parameter values of the model. The calculation unit 1 functionally includes a model output calculation unit 11, a constraint condition evaluation unit 12, an evaluation calculation unit 13, and a model update determination unit 14.

  The model output calculation unit 11 inputs (applies) input data to the model of the system set by setting the model order, the identification parameter, and the optimization calculation parameter, thereby outputting the model output data (model output data). ). The obtained model output data is stored and stored in the model output storage unit 45.

  The constraint condition evaluation unit 12 evaluates whether the model output data obtained by the model output calculation unit 11 satisfies the constraint conditions. Information about whether or not the evaluated model output data satisfies the constraint condition is stored and stored in the model output etc. storage unit 45.

  The evaluation calculation unit 13 receives the actual output data output from the system when the predetermined input data determined in advance is input to the system as the actual input data, and when the actual input data is input to the model of the system. An evaluation result of an evaluation function for evaluating an error from the model output data output from this model is obtained. The obtained evaluation result is stored and stored in the model output etc. storage unit 45.

  The model update determination unit 14 updates the model of the system according to a predetermined update rule determined in advance, satisfies the constraint conditions set by the constraint condition input setting unit 21, and is calculated by the evaluation calculation unit 13. In order to obtain the best evaluation result, the value of the parameter in the system model is obtained to determine the system model.

  Such a modeling apparatus S can be configured by a computer such as a desktop personal computer or a notebook personal computer by mounting a program (software) of a modeling method.

  Note that the modeling apparatus S may further include an external storage unit 6 and a communication interface unit 7 indicated by broken lines in FIG.

  The external storage unit 6 stores data with a recording medium such as a flexible disk, a CD-ROM (Compact Disc Read Only Memory), a CD-R (Compact Disc Recordable), and a DVD-R (Digital Versatile Disc Recordable). An apparatus that performs reading and / or writing, such as a flexible disk drive, a CD-ROM drive, a CD-R drive, and a DVD-R drive. The communication interface unit 7 is connected to a communication network (network), and is a device for transmitting and receiving communication signals to and from other devices via this communication network.

  When each program is not stored, it may be configured to be installed in the storage unit 4 via the external storage unit 6 from a recording medium in which these programs are recorded, and a server computer ( You may comprise so that each program may be downloaded via a communication network and the communication interface part 7 from a not-shown. Further, data such as performance input / output data to be input to the modeling apparatus S in the system modeling operation is input to the modeling apparatus S via the external storage unit 6 by a recording medium storing the data. Alternatively, the data may be input to the modeling apparatus S via the communication network and the communication interface unit 7 from a server computer that manages the data.

  Next, the operation of the modeling apparatus in this embodiment will be described. FIG. 2 is a flowchart showing a schematic operation of the modeling apparatus in the embodiment. FIG. 3 is a flowchart showing the setting operation of the constraint condition in the modeling apparatus of the embodiment. FIG. 4 is a flowchart illustrating a calculation operation of a model in the modeling apparatus according to the embodiment.

  In the modeling apparatus S of the present embodiment, as schematically shown in FIG. 2, first, in step S11, a constraint condition is set, and then in step S12, the constraint condition is satisfied in order to construct a model, and The model is calculated by determining the values of the model parameters so that the evaluation result is the best. Subsequently, in step S13, it is determined whether or not the calculated accuracy of the model is within a predetermined allowable range. If the result of this determination is that the accuracy of the model is not within the allowable range (NO). Is returned to step S11. On the other hand, if the accuracy of the model is within the allowable range (YES), step S14 is executed, and the calculated model is output to the output unit 3 as a system model. It is output by the unit 3.

  Next, the step S11 will be described more specifically. In FIG. 3, first, in step S <b> 21, a constraint condition in the time response waveform (the time response constraint condition) is input from the constraint condition input setting unit 21 of the input setting unit 2, and the constraint condition storage unit 41 of the storage unit 4 stores the constraint condition. The time response constraint condition storage unit 411 stores and stores it. Thus, as will be described later, the constraint condition evaluation unit 12 of the calculation unit 1 uses the time response constraint condition stored in the time response constraint condition storage unit 411 so that the time response constraint condition is satisfied. Model is built.

  Hereinafter, for simplification of description, the case of a system with one input and one output will be described more specifically. Of course, the following description can be extended to a multi-input multi-output system without loss of generality.

First, for example, input / output data (input data U _data and output data Y _data ) is acquired as actual input / output data (actual input data U _data and actual output data Y _data ) from an actual system such as a combustion furnace plant. It is assumed that it is stored and stored in the storage unit 46. Since the model of the system is a continuous-time state space model expression or a continuous-time transfer function model expression including a time variable t that is regarded as a continuous time, the actual input / output data U _data and Y _data are continuous in time. It is preferable that the data is acquired at a shorter sampling interval so that the data can be seen. Here, for simplification of description, it is assumed that sampling is performed at intervals of 1 second (1-second cycle). The actual input / output data U _data and Y _data for t _max seconds from sampling start time 0 to time t _max are set to u (t) as an input value at time t seconds and y (t) as an output value at time t seconds. In this case, the following equations 1-1 and 1-2 are obtained, respectively.
U _data = [u (0) u (1)... U (t _max )] ^T (1-1)
Y _data = [y (0) y (1)... Y (t _max )] ^T (1-2)
Here, the superscript T is a symbol representing transposition.

Relates to an output data obtained when added normative input _{U r} of formula 2 to the system at _{t E} seconds from time 0 to time _{t E,} the upper limit during the period from time _{t S1} until time _{t E1 Y max} and the time _{t S2} If the lower limit Y _min from the time t _E2 to the time t _{E2 is} expressed by the expression 3-1 and the expression 3-2, the upper limit Y _max described by the expression 3-1 and the lower limit Y _min described by the expression 3-2 are constrained. It is given from the condition input setting unit 21 to the modeling apparatus S.
_{U r = [u r (0} ) u r (1) ··· u r (t E)] T ··· (2)
Y _max = [y _max (t _s1 ) y _max (t _s1 +1)... Y _max (t _E1 )] ^T (3-1)
Y _min = [y _min ( _{ts 2} ) y _min ( _{ts 2} +1)... Y _min (t _E2 )] ^T (3-2)
Here, u _r (t) is an input value at time t seconds, y _max (t) is an upper limit value of an output value at time t, and y _min (t) is an output value at time t. This is the lower limit of the value. Also, 0 ≦ t _S1 <t _E1 ≦ t _E , and 0 ≦ t _S2 <t _E2 ≦ t _E.

As a specific example of the normative input, the unit step input is U _r = [0 1 1... 1] ^T , and the unit impulse input is U _r = [0 1 0... 0] ^T. There also ramp input _is U r = [0 1 2 3 ···] T. Further, the normative input may be one type or a plurality of types.

Subsequently, in step S <b> 22, the constraint condition for the steady gain (the steady gain constraint condition) is input from the constraint condition input setting unit 21 of the input setting unit 2, and the steady gain constraint condition in the constraint condition storage unit 41 of the storage unit 4. It is stored in the storage unit 412 and stored. For example, when the steady gain G of the system is G _min ≦ G ≦ G _max , the lower limit value G _min and the upper limit value G _max are given from the constraint condition input setting unit 21 to the modeling device S. Thus, as will be described later, the constraint condition evaluation unit 12 of the calculation unit 1 uses the steady gain constraint condition stored in the steady gain constraint condition storage unit 412 so that the steady gain constraint condition is satisfied. Model is built.

  Next, the step S12 will be described more specifically. In FIG. 4, first, in step S <b> 31, the model order and the model identification parameter are input from the model order identification parameter input setting unit 22 of the input setting unit 2, and the model order identification parameter storage unit 42 of the storage unit 4 is input. Stored and memorized.

More specifically, in the case of the above-described one-input one-output system, for example, the continuous-time state space model expression for the system to be modeled is Expression 4 (Expression 4-1 and Expression 4-2). To do.
dx (t) / dt = Ax (t) + Bu (t) (4-1)
y _m (t) = Cx (t) + Du (t) (4-2)
Here, x (t) is an n-order state vector, y _m (t) is a model output (model output, calculated value by model), and A, B, C, and D are each n It is a constant matrix of row n columns, n rows 1 column, 1 row n columns, and 1 row 1 column. Here, for simplification of explanation, it is assumed that the system to be modeled is strictly proper, that is, D = 0.

  The model order is the value of n, and this value n is input from the model order identification parameter input setting unit 22 as the model order. In this example, it is assumed that n = 2, that is, a second order model whose model order is 2. The constant matrices A, B, and C may be in a predetermined format such as a controllable canonical form, but preferably have no redundant parameters. In this example, the constant matrices A, B, and C are assumed to be in an observable canonical form. Equations 5-1, 5-2, and 5-3 are obtained, respectively.

Here, a ₀ , a ₁ , b ₀ and b ₁ are unknown parameters that define the model. These unknown parameters of a ₀ , a ₁ , b ₀ and b ₁ are input from the model order identification parameter input setting unit 22 and designated as identification parameters. That is, to build a model of the system to be modeled is to obtain the values of the unknown parameters a ₀ , a ₁ , b ₀ and b ₁ designated as the identification parameters.

In addition, the solution of Formula 4 (Formula 4-1, Formula 4-2) and Formula 5 (Formula 5-1 to Formula 5-3) calculates | requires the continuous time transfer function model formula G (s) of Formula 6, That is, it is equivalent to obtaining the unknown parameters a ₀ , a ₁ , b ₀ and b ₁ in the continuous time transfer function model equation G (s) of Equation 6.
G (s) = (b ₁ s + b ₀ ) / (s ² + a ₁ s + a ₀ ) (6)

  Subsequently, in step S32, optimization calculation parameters are input from the optimization calculation parameter input setting unit 23 of the input setting unit 2, and are stored and stored in the optimization calculation parameter storage unit 43 of the storage unit 4.

More specifically, in the case of the above-described one-input one-output system, the unknown parameters (identification parameters) a ₀ , a ₁ , b ₀ and b ₁ are identified by, for example, PSO ( Particle Swarm Optimization) method is used. In this PSO method, a plurality of P particles p (particle groups) are randomly (randomly) dispersed in the solution space, and the particle groups dispersed in these solution spaces move in the solution space according to a predetermined update rule. This is a technique for searching for an optimal solution. When this PSO method is applied to this embodiment, the solution space is a coordinate space (in this example, a four-dimensional space) with unknown parameters (identification parameters) a ₀ , a ₁ , b ₀ and b ₁ as coordinate axes. Yes, the particle p is a point on the coordinate space represented by a four-dimensional vector, and the i-th particle p (i, k) among the P particles at the k-th update count is expressed by Equation 7. become.
p (i, k) = [a ₀ a ₁ b ₀ b ₁ ] ^T (7)

Hereinafter, [a ₀ a ₁ b ₀ b ₁ ] ^T of p (i, k) will be referred to as a parameter set as appropriate.

In such an optimization method, the number P of particles p (0 <i ≦ P), the number of updates K (0 <k ≦ K), and parameters (w, c ₁ , c ₂ described later) in a predetermined update rule are set. It is an optimization calculation parameter, and is input from the optimization calculation parameter input setting unit 23.

  Subsequently, in step S33, an evaluation function is input from the input setting unit 2 and set.

More specifically, in the case of the above-described one-input / one-output system, the evaluation function is, for example, the actual output data Y _data (= [y (0) corresponding to the actual input data U _data in this embodiment. ) Y (1)... Y (t _max )] ^T ) and the actual input data U _data in the model (in the above example, Expression 4 (Expression 4-1, Expression 4-2) and Expression 5 (Expression Model output data Y _i (= [y _i (0) y _i (2)... Y _i (t _max ) output from this model when input to 5-1 to 5-3) or 6) )] A function for evaluating an error from ^T ). Such an evaluation function J _i is given by, for example, Expression 8-1.
J _i = || W · (Y _i -Y _data ) || (8-1)
Here, || v || represents a so-called Euclidean norm of vector v, and | v || = v (v ^T v) when v is a vertical vector. W is a weighting matrix that determines which part of the output prediction error should be evaluated with importance, for example, a diagonal matrix.

Further, for example, the evaluation function J _i is an infinite norm given by, for example, Expression 8-2.
J _i = || W · (Y _i -Y _data ) || _∞ (8-2)
Here, || v || _∞ represents a so-called infinite norm (maximum norm) of vector v, and in the case of v = [v ₁ v ₂ ... V _n ] ^T , || v || _∞ = max (| v ₁ |, | v ₂ |,..., | V _n |).

For example, the evaluation function J _i is given by, for example, Expression 8-3.
J _i = || W · (Y _i -Y _data ) || ₁ (8-3)
Here, || v || ₁ represents a so-called 1-norm of vector v. When v = [v ₁ v ₂ ... V _n ] ^T , || v || ₁ = Σ | v _i |. However, Σ is the sum from i = 1 to i = n.

The evaluation function storage unit 44 stores, for example, such a plurality of evaluation functions J _i (Expression 8-1 to Expression 8-3), and inputs an evaluation function from the plurality of evaluation functions J _i. One evaluation function J _i is selected via the setting unit 24 and is input and set.

  Note that such an evaluation function J has a weight W for weighting the error between the actual output data and the model output data. The larger the value of the weight W, the greater the influence on the evaluation result by the evaluation function J. When given, the value of the weight W is set to be relatively smaller than the other sections excluding the section with respect to the section corresponding to the actual output data including noise of a predetermined threshold value or more. It's okay. Such an interval and its weight W and the other interval and its weight W are input and set, for example, from the optimization calculation parameter input setting unit 23 of the input setting unit 2. By configuring in this way, the influence of the actual output data including noise exceeding a predetermined threshold on the evaluation result is reduced, and the system model can be constructed with higher accuracy.

  Subsequently, in step S 34, the model output is calculated by the model output calculation unit 11 of the calculation unit 1 and stored in the model output etc. storage unit 45 of the storage unit 4.

More specifically, in the case of the above-described one-input one-output system, first, P particles p (i, 0) (update count k = 0, i = 0 to P), for example, 100 particles The initial value of the particle p (i, 0) (i = 0 to 100) is set randomly by generating a random number, for example. As a result, the value of each of the P parameter sets p (i, 0) is set. The initial value of the moving speed v (i, 0) of the i-th particle p (i, 0) is set to v (i, 0) = [0 0 0 0] ^T , for example.

Here, as a constraint, if it is known as a priori knowledge that the system to be modeled is a stable system, the i-th particle is in the range of a ₀ > 0 and a ₁ > 0. It is preferable that the initial value of p (i, 0) is set at random.

Further, as a constraint, when it is known as a priori knowledge that the steady-state gain in the system to be modeled is a positive value, the sign of b _{0 and} the sign of a ₀ are equal. That is, it is preferable that the initial value of the i-th particle p (i, 0) is set at random so that b ₀ × a ₀ > 0.

As a constraint, when it is known as a priori knowledge that there is no unstable zero point in the system to be modeled, the sign of b ₁ is equal to the sign of b ₀ , that is, , It is preferable that the initial value of the i-th particle p (i, 0) is set at random so that b ₁ × b ₀ > 0.

Also, as a constraint, if it is known as a priori knowledge that the steady-state gain in the system to be modeled is G _min or more and G _max or less, a ₀ × G _min ≦ b ₀ ≦ a ₀ The initial value of the i-th particle p (i, 0) is preferably set at random so as to satisfy × _Gmax .

  In this way, when setting the initial value of the i-th particle p (i, 0), it is possible to eliminate the waste of searching for an area where no solution exists by adding a constraint condition.

  By setting the values of P particles p in this way, one model is defined corresponding to one particle p. That is, one model is defined corresponding to the i-th particle p (i, 0). In the above example, 100 models are defined corresponding to each of the 100 particles p.

For the model defined in correspondence with the i-th particle p (i, 0) (in this example, the model represented by the equations 4 and 5 or the model represented by the equation 6) The actual input data U _data stored in the unit 46 is substituted to obtain model output data Y _i , and the obtained model output data Y _i is stored in the model output etc. storage unit 45 of the storage unit 4 as the i-th particle. It is stored in association with p (i, 0). For the calculation of the model output data Y _i , known control system simulation software, for example, MATLAB / Simlink of The Math Works, etc. is used. Thus, the model output is calculated for each of the P parameter sets p (i, k), and stored in the model output etc. storage unit 45 of the storage unit 4 in association with the parameter set p (i, k). Is done.

  Subsequently, in step S35, the constraint condition is evaluated by the constraint condition evaluation unit 12, and the evaluation result is stored in the model output etc. storage unit 45 of the storage unit 4 in association with the parameter set p (i, k). .

More specifically, in the case of the above-described one-input / one-output system, as in step S34, a predetermined model is used for the model defined corresponding to the i-th particle p (i, 0). The reference input U _r is substituted to obtain model output data Y _ri (= [y _ri (0) y _ri (1)... Y _ri (t _max )] ^T ) corresponding to the predetermined reference input U _r. It is done. Then, whether the model output data Y _ri corresponding to the obtained predetermined normative input U _r satisfies the constraints of the Code input is determined. For example, when the upper limit value Y _max between the time t _S1 and the time t _E1 and the lower limit value Y _min between the time t _S2 and the time t _E2 are set as constraints, the predetermined value Whether the model output data Y _ri corresponding to the reference input U _r is less than or equal to the upper limit Y _max between time t _S1 and time t _E1 and greater than or equal to the lower limit Y _min between time t _S2 and time t _E2 It is determined whether or not. As a result of this determination, the model output data Y _ri corresponding to the predetermined normative input U _r is not more than the upper limit Y _max from time t _S1 to time t _E1 and from time t _S2 to time t _E2 . If not more than the lower limit Y _min is between the model output data Y _ri corresponding to the predetermined norm input U _r is assumed that does not satisfy the constraint conditions, evaluation results of the constraints of the storage unit 4 model The output etc. storage 45 is stored in association with the i-th particle p (i, 0). In this way, the constraint condition is evaluated for each of the P parameter sets p (i, k), and the evaluation result is stored in the model output etc. storage unit 45 of the storage unit 4 in the parameter set p (i, k). Correspondingly stored.

In the above description, the constraint condition of the steady gain G is considered when setting the initial value of the particle p (i, 0). However, the lower limit value G _min and the upper limit value G _{max of} the steady gain G are set as the constraint condition. If the model output data Y _i corresponding to the actual input data U _data is not less than the lower limit G _{min and not} more than the upper limit G _max , the steady gain is determined. The constraint condition of G may be evaluated.

  Subsequently, in step S <b> 36, the evaluation value by the evaluation function is calculated by the evaluation calculation unit 13 and stored in the model output storage unit 45 of the storage unit 4.

More specifically, in the case of the above-described one-input one-output system, the evaluation value by the evaluation function J _i is given to the model defined corresponding to the i-th particle p (i, 0). The evaluation value of the evaluation function J _i is calculated and stored in the model output etc. storage unit 45 of the storage unit 4 in association with the i-th particle p (i, 0). Thus, the evaluation value by the evaluation function is calculated for each of the P parameter sets p (i, k), and the model output etc. storage unit 45 of the storage unit 4 corresponds to the parameter set p (i, k). It is memorized.

Here, as described above, when the evaluation result of the constraint condition is stored in the model output etc. storage unit 45 of the storage unit 4 in association with the i-th particle p (i, 0), the evaluation of the constraint condition is performed as described above. Although the result itself may be stored in the storage unit 45 such as the model output of the storage unit 4 in association with the i-th particle p (i, 0), in this embodiment, the evaluation result of this constraint condition is the evaluation function J. The evaluation value of _i is stored in the model output etc. storage unit 45 of the storage unit 4 in association with the i-th particle p (i, 0). For example, when the constraint condition is not satisfied, an evaluation value indicating that the evaluation is bad is stored in the model output etc. storage unit 45 of the storage unit 4 in association with the i-th particle p (i, 0). More specifically, for example, when the evaluation function J _i is configured such that the higher the evaluation is, the smaller the evaluation value is. If the constraint condition is not satisfied, for example, the model output data Y _i is the value A large evaluation value that cannot be obtained as is stored in the model output etc. storage unit 45 of the storage unit 4 in association with the i-th particle p (i, 0). Further, for example, in the case where the evaluation function J _i is configured such that the range of possible values is negative, if the constraint condition is not satisfied, a positive value (for example, a fixed value or a degree of deviation from the constraint condition). In accordance with the i-th particle p (i, 0) and stored in the model output etc. storage unit 45 of the storage unit 4. Such an evaluation function J _i is given by, for example, Expression 8-4.
J _i = tan ⁻¹ (|| W · (Y _i −Y _data ) ||) −π / 2 (8-4)

  Subsequently, in step S37, the model update determination unit 14 determines whether or not the update in the repetitive calculation of the optimization method has been completed. If the update has not been completed as a result of this determination (NO), On the other hand, when the process of step S38 is executed and the update is completed (YES), the process of step S39 is executed. The number of updates K may be any number, but in the PSO method, the number of updates is set to an appropriate number in consideration of the accuracy of the solution, the amount of calculation processing, and the like, for example, K = 100.

  In step S38, the model update determining unit 14 updates according to a predetermined update rule, and the process returns to step S34.

More specifically, in the case of the above-described one-input / one-output system, at the update time of the k-th (k = 0, 1, 2,..., K), The particle p having the smallest value of the evaluation function J is searched and is set as the first best evaluation particle p (best, k). For example, when the value of the evaluation function J _q of the q-th particle p (q, k) is the smallest at the k-th update time point, p (best, k) = p (q, k).

In the i-th particle p, the particle p having the smallest value of the evaluation function J from the 0th (initial value) to the (k-1) th time is searched, and the second best evaluation particle p (i, best) Is done. For example, when the value of the evaluation function J _i of the i-th particle p (i, r) is the smallest at the r-th update time, p (i, best) = p (i, r). When k = 0, each initial value itself is p (i, best) of each particle p.

Then, for example, according to the update rule given by Equation 9 (Equation 9-1 and Equation 9-2), the velocity and position of each particle p are determined and updated.
v (i, k + 1) = wv (i, k)
+ C ₁ R _1ik (p (i, best) −p (i, k))
+ C ₂ R _2ik (p (best, k) −p (i, k)) (9-1)
p (i, k + 1) = p (i, k) + v (i, k + 1) (9-2)
Here, w, c ₁ , and c ₂ are adjustment parameters, and are input and set as the optimization calculation parameters from the optimization calculation parameter input setting unit 23 as described above. For example, w = 0.9, c ₁ = 0.8 and c ₂ = 0.8. R _1ik and R _2ik are diagonal matrices, and the diagonal elements are random numbers that are uniformly distributed in the range of 1 to 0. The random value is not a fixed value, but a random value is used for each particle p and for each update k.

Here, as a constraint, if it is known as a priori knowledge that the system to be modeled is a stable system, the system is updated so as to fall within the range of a ₀ > 0 and a ₁ > 0. It is preferable. More specifically, when the updated particle p becomes a ₀ <0, it is updated to a point that internally divides a ₀ and 0 before the update as shown in Expression 10-1. That is, for a random number α of 0 to 1,
a ₀ (i, k + 1) = (1−α) · a ₀ (i, k) + α · 0 (10-1)
Here, for the i-th particle p, a ₀ (i, k + 1) is a ₀ after update, and a ₀ (i, k) is a ₀ before update. The speed v of the particle p, the portion v corresponding to _{a 0 (i, k + 1} ) for _{{a 0},} the formula 10-2.
v (i, k + 1) {a ₀ } = a ₀ (k + 1) −a ₀ (k) (10-2)

Further, as a constraint, when it is known as a priori knowledge that the steady-state gain in the system to be modeled is a positive value, the sign of b _{0 and} the sign of a ₀ are equal. That is, it is preferable to update so that b ₀ × a ₀ > 0.

As a constraint, when it is known as a priori knowledge that there is no unstable zero point in the system to be modeled, the sign of b ₁ is equal to the sign of b ₀ , that is, , B ₁ × b ₀ > 0 is preferably updated.

Further, as a constraint, if it is known as a priori knowledge that the steady-state gain in the modeling target system is in the range of G _min or more and G _max or less, a ₀ × G _min ≦ b ₀ ≦ It is preferable to update so as to satisfy a ₀ × G _max .

  In this way, when the particle p is updated, by adding the constraint condition, it is possible to eliminate the waste of searching for a region where no solution exists, and it is possible to search for a better solution faster.

Furthermore, when the identification parameter codes a ₀ , a ₁ , b ₀ , b ₀₁ are known as a priori knowledge as constraints, these identification parameters may be expressed in an exponential form. For example, if it is known as a priori knowledge that the transfer function of Equation 6 is stable and has no unstable zeros and the gain is negative, the sign of a _{0 and} the sign of a ₁ are positive, and , B ₀ and b ₁ must be negative, a ₀ = exp (λ ₀ ), a ₁ = exp (λ ₁ ), b ₀ = −exp (μ ₀ ), b ₁ = With exp (μ ₁ ), the parameter set of Equation 7 becomes p (i, k) = [λ ₀ λ ₁ μ ₀ μ ₁ ] ^T. Therefore, the solution is searched not in the coordinate space of the identification parameter [a ₀ a ₁ b ₀ b ₁ ] ^{T but in} the coordinate space of this parameter [λ ₀ λ ₁ μ ₀ μ ₁ ] ^T. By configuring in this way, arithmetic processing on the whole real number of −∞ <λ ₀ <+ ∞, −∞ <λ ₁ <+ ∞, −∞ <μ ₀ <+ ∞, −∞ <μ ₁ <+ ∞. It is possible to perform arithmetic processing without checking the sign and range.

  In this way, when updating by the PSO method, at least one of the sign of the steady gain, the range of the steady gain, the information about the stability of the system, and the information about the unstable zero point of the system may be used. . By configuring the modeling device S in this way, it is possible to construct a model of a system that satisfies at least one of these as a constraint without performing an unnecessary search.

  Thus, each of the P parameter sets p (i, k) is updated according to a predetermined update rule, and the process returns to step S34.

  On the other hand, in step S39, the model update determination unit 14 determines the value of the identification parameter set so as to satisfy the constraint condition and give the best evaluation value, and the model of this system is constructed. For example, in the above PSO method, a parameter set p (i, k) that satisfies the constraint condition and gives the best evaluation value is selected from the P × K parameter sets p (i, k). The value of the selected parameter set p (i, k) is determined as the value of the identification parameter that defines the model of the system to be modeled, and the model of this system is determined.

  As described above, in the modeling apparatus S and the modeling method according to the present embodiment, the error between the actual output data and the model output data is evaluated by the evaluation function J, and the values of the model parameters are obtained so that the evaluation result is the best. The model is built. Then, a priori information representing a priori knowledge is set as a constraint condition, and when the model is constructed, values of model parameters are obtained so as to satisfy the constraint condition. For this reason, the modeling apparatus S and the modeling method in the present embodiment use a priori knowledge in a method different from the above-mentioned Non-Patent Document 1 and Patent Document 1, and thus the input of the quality and quantity is insufficient. Even with output data, a more accurate model can be constructed.

Further, the modeling device S and modeling method in the present embodiment, in the system, at least one of the upper limit value G _max and the lower limit value G _min about constant gain G, the upper limit value G _max and a steady-state gain G in this embodiment The lower limit G _min is a constraint condition. For this reason, the modeling apparatus S and the modeling method according to the present embodiment can construct a model of a system that satisfies the a priori information regarding the steady gain G by adding the a priori information regarding the steady gain G as a constraint.

  Next, as an example, a case where a model of a waste incinerator (gasification melting furnace) is created using the modeling apparatus S in the embodiment will be described.

FIG. 5 is a diagram showing a change in the amount of steam generated when the speed of the dust feeder is changed stepwise in the refuse incinerator. FIG. 5A shows the speed of the dust feeder, the horizontal axis shows the elapsed time expressed in seconds, and the vertical axis shows the speed. FIG. 5B shows the steam generation amount, the horizontal axis shows the elapsed time expressed in seconds, and the vertical axis shows the steam generation amount. FIG. 6 is a diagram illustrating an upper limit and a lower limit of the step response as the constraint condition. The horizontal axis in FIG. 6 represents the elapsed time expressed in seconds, and the vertical axis represents the amount of steam generated. FIG. 7 is a diagram for explaining the step response in the model of the refuse incinerator modeled by the modeling apparatus of the embodiment. FIG. 7 (A) shows the speed of the dust feeder, its thick solid line shows the steam generation amount as a model output, and its thin solid line shows the steam generation amount as the actual data shown in FIG. 5 (B). Show. FIG. 7B shows a model step response (solid line), an upper limit step response Y _max (broken line) between time t _S1 and time t _E1, and a lower limit step between time t _S2 and time t _E2. The response Y _min (dashed line) is shown. FIG. 8 is a diagram for explaining a step response in a garbage incinerator model modeled by a conventional method as a comparative example. FIG. 8 (A) shows the speed of the dust feeder, its thick solid line shows the steam generation amount as a model output, and its thin solid line shows the steam generation amount as the actual data shown in FIG. 5 (B). Show. FIG. 8B shows a model step response (solid line), an upper limit step response Y _max (broken line) between time t _S1 and time t _E1, and a lower limit step between time t _S2 and time t _E2. The response Y _min (dashed line) is shown. FIG. 9 is a diagram for explaining the step response in the model of the refuse incinerator modeled by the modeling apparatus of the embodiment in consideration of the constraint condition of the steady gain. FIG. 9 (A) shows the speed of the dust feeder, its thick solid line shows the steam generation amount as a model output, and its thin solid line shows the steam generation amount as the actual data shown in FIG. 5 (B). Show. FIG. 9B shows a model step response (solid line), an upper limit step response Y _max (broken line) between time t _S1 and time t _E1, and a lower limit step between time t _S2 and time t _E2. The response Y _min (dashed line) is shown.

  In a garbage incinerator, when a dust feeder that supplies garbage to the incinerator is an input and the amount of steam generated in the incinerator is an output, as shown in FIG. As shown in FIG. 5 (B), the steam generation amount gradually increases with the start of operation of the dust supply unit and gradually with the stoppage of the operation of the dust supply unit. However, the noise is superimposed on the profile due to the influence of the disturbance, and the waveform is greatly disturbed. As a cause of this, for example, even if the speed of the dust feeder is constant, the amount of dust that is actually put into the incinerator by the dust feeder is not necessarily constant, and fluctuates, resulting in disturbance of the amount of generated steam. It is done. However, in actual waste incinerators (objects to be controlled for production facilities, plants, etc.), it is possible to obtain experimental input / output data to model waste incinerators, and garbage that can be thrown into waste incinerators. There are cases where the amount and the like are limited and only data including such noise can be acquired.

In such a garbage incinerator, as a priori information, when a unit step input is used to change the speed of the dust feeder in units of steps at time 0, the steam generation amount (step response) is: as shown in FIG. 6, the upper step response _{Y max} (dashed line, step response limit) of the period from time _{t S1} until time _{t E1} and the lower limit step response of the period from time _{t S2} to time _{t E2 Y min} It is assumed that it exists between (broken line and step response lower limit). Such a priori knowledge is usually understood from the experience of the operator who actually operates the waste incinerator and past data of the waste incinerator, but also from the design value of the waste incinerator. Sometimes understood. For example, the change in the amount of generated steam can be roughly calculated based on the fluctuation range in the calorie (heat amount) of the dust and the change in the amount of dust supplied when the dust feeder is changed by one unit.

  Note that such estimation calculation can be performed not only by a plant such as the garbage incinerator but also by various devices. For example, in a manipulator as a link mechanism, when the input torque is changed by one unit, the time response is determined from the parameters such as how much time the arm rotation speed changes and how much the arm rotation speed changes. Upper and lower limits can be roughly calculated.

  FIG. 7 shows the step response in the model of the refuse combustion furnace created by modeling the refuse combustion furnace with the modeling apparatus S of the present embodiment under the actual data shown in FIG. 5 and the constraint condition shown in FIG. . In the garbage combustion furnace model by the modeling apparatus S of this embodiment, the step response (steam generation amount) is a change in the actual steam generation amount shown in FIG. 5 (B) as shown in FIG. 7 (A). (Fitting), and as shown in FIG. 7B, the upper and lower limit constraints of the step response are satisfied.

  On the other hand, FIG. 8 shows the step response in the model of the refuse combustion furnace created by modeling the refuse combustion furnace by the conventional method under the actual data shown in FIG. 5 and the constraint condition shown in FIG. Compared with FIG. 7, the conventional garbage combustion furnace model does not match the actual steam generation change as much as the step response (steam generation amount) shown in FIG. 7. In particular, the model is to be matched with the actual output data of the part with a large disturbance surrounded by a broken circle in FIG. 8A. Therefore, in the step response shown in FIG. 8, the step response shown in FIG. Compared to the step response shown in FIG. 7, the fitting accuracy is lowered, which is a gentle rise. Furthermore, as shown in FIG. 8B, there is a portion that does not satisfy the upper and lower limit constraints of the step response. As a result, in the conventional method, a priori information such as changing the data section used for modeling again, preprocessing data such as filtering, or re-accomplishing actual input / output data, etc. It is necessary to repeat modeling work by trial and error until a model that satisfies the constraint conditions is created.

  However, the modeling apparatus S of the present embodiment reduces such modeling work as can be seen by comparing FIG. 7 and FIG.

Here, in the above-described modeling of the garbage combustion furnace, as shown in FIG. 6B, the step response is substantially settled (saturated) in 1200 seconds, so the time range of the constraint condition is 1200 seconds. It is separated. For this reason, the step response exceeds the upper limit of the step response, although it is at a level where there is no problem in practical use of the model in the portion exceeding 1200 seconds. Therefore, strictly, the upper and lower limit values of the steady gain G may be set as a constraint condition so that the step response does not deviate from the upper limit and the lower limit of the step response. That is, as described above, when it is known as a priori knowledge that the steady-state gain in the system to be modeled is G _min or more and G _max or less as a constraint condition, a ₀ × G _min ≦ b so as to satisfy ₀ ≦ _{a 0} × _{G max,} the initial value of i-th particle p (i, 0) is set at random, and, to satisfy _{a 0 × G min ≦ b 0} ≦ a 0 × G max It will be updated. By imposing such constraint conditions, the step response (steam generation amount) matches well with the actual steam generation change shown in FIG. 5B (fitting) as shown in FIG. 9A. In addition, as shown in FIG. 9B, the upper limit and the lower limit of the step response are satisfied, including the range exceeding 1200 seconds.

  In the above description, the speed of the dust feeder is input and the steam generation amount is output. However, the input / output relationship is not limited to this, and may be various relationships. For example, the input includes the amount of forced air, the amount of air supplied, the amount of burner oil, the opening of the steam valve, the amount of catalyst input, and the output includes the sand layer temperature, furnace temperature, boiler drum, etc. Examples include pressure, furnace pressure, oxygen concentration, carbon monoxide concentration, and NOx concentration.

  Although the modeling of the refuse incinerator has been described as an application example of the modeling apparatus S of the present embodiment, the modeling apparatus S of the present embodiment can perform various controls by using the operation amount as an input and the control amount as an output. It can be applied to target modeling. The modeling apparatus S of the present embodiment can be applied to, for example, modeling of a rolling mill, for example, by inputting a rolling position, a roll speed, and the like, and outputting an interstand tension, a plate width, a plate thickness, and the like. it can. Further, for example, the modeling apparatus S of the present embodiment can be applied to the modeling of a manipulator, and can input torque and the like, and can output arm speed and position and the like.

  In the above-described embodiment, when the parameter value of the model is obtained by an optimization method for obtaining the value of the model parameter after setting the initial value of the model parameter, the initial value itself is set to the value of the model. The modeling apparatus S may be configured to handle it as a parameter. In general, in an optimization method in which an initial value in a model parameter is set and then the value of the model parameter is obtained, the accuracy of the model of the system constructed by this optimization method is often influenced by the initial value. . For this reason, since the initial value itself is also handled as an unknown parameter, the system model can be constructed with higher accuracy without being influenced by the initial value.

  For example, in the above-described one-input one-output system, the model is constructed on the assumption that the initial state is 0 (zero vector). That is, it is considered that the input data is applied when the system to be modeled is in a set state (equilibrium state), and the input / output data such as the actual input / output data used for the model construction is the initial state. Is assumed to be 0.

In Expression 4, it is known that the behavior of the state x (t) generally becomes Expression 11.
x (t) = Φ (t) x (0) + ∫Φ (t−τ) Bu (τ) dτ (11)
Here, the integration interval is from 0 to t, and Φ (t) is referred to as a transition matrix and is expressed by Expression 12.
Φ (t) = exp (At)
^{= I + At + A 2 t} 2/2! + ^A 3 ^t 3/3! + ... (12)

By substituting the state x (t) represented by Equation 11 into Equation 4-2, Equation 13 is obtained. If the initial state x (0) = 0 is not satisfied, the output y _m (t) is the initial state x. It can be seen that it is affected by (0).
y _m (t) = CΦ (t) x (0) + C∫Φ (t−τ) Bu (τ) dτ + Du (t) (13)

  In an actual experiment for obtaining input / output data for constructing a model, for example, in a mechanical system such as a manipulator, the experiment can be started from a stationary state. In this case, the initial state is set to 0. Although it can be considered, for example, in a plant system such as a garbage combustion furnace or a chemical plant, an experiment must be performed during operation, the state is constantly changing, and the initial state is usually not zero.

  For this reason, as described above, it is preferable to handle the initial state itself as a parameter and construct a model.

More specifically, for example, in the case of the above-described system of one input and one output system, since the model order of the system to be modeled is second order in Expression 4 and Expression 5 or Expression 6, the initial state x (0) = [x ₁ x ₂ ] ^T. For this reason, the i-th particle p (i, k) of P particles is expressed by Expression 14 instead of Expression 7.
p (i, k) = [a ₀ a ₁ b ₀ b ₁ x ₁ x ₂ ] ^T (14)

In this case, the initial value of the moving speed v (i, 0) of the i-th particle p is set to v (i, 0) = [0 0 0 0 0 0] ^T.

  By setting such initial values, a system model is constructed by the same processing as described above.

In the above-described embodiment, the model parameter value is obtained by a predetermined optimization method determined in advance, and the obtained model parameter value is used in addition to the initial value of the PSO method. The device S may be configured. Examples of the predetermined optimization method include various optimization methods such as PSO method, least square method, and subspace method. When the least square method or the subspace method is used, a state space model expression or a transfer function model expression is obtained once in discrete time, and converted into a continuous time model. In the case of using the PSO method, a model that simply minimizes only the evaluation function may be obtained. In this case, J _i = || W (Y _i -Y _data ) || <ε (ε is You may preserve | save the particle | grain p used as the predetermined threshold). In the case of using this PSO method, the PSO method is used twice, that is, determination of an initial value and construction of a model. In general, in an optimization method in which an initial value in a model parameter is set and then the value of the model parameter is obtained, the accuracy of the model of the system constructed by this optimization method is often influenced by the initial value. . For this reason, even in the case of the PSO method, the range of random shaking is determined by trial and error. For this reason, in order to reduce the labor of trial and error and obtain an optimum model, it is desirable that the first model is fitted to the input / output data to some extent. In this configuration, since the parameter value of the model obtained by a predetermined optimization method determined in advance is also used as the initial value used for the PSO, the calculation processing of the PSO method is started from the initial value including a value closer to the true value. Therefore, the system model can be constructed with higher accuracy without performing unnecessary search.

  In order to express the present invention, the present invention has been properly and fully described through the embodiments with reference to the drawings. However, those skilled in the art can easily change and / or improve the above-described embodiments. It should be recognized that this is possible. Therefore, unless the modifications or improvements implemented by those skilled in the art are at a level that departs from the scope of the claims recited in the claims, the modifications or improvements are not covered by the claims. To be construed as inclusive.

S Modeling Device 1 Calculation Unit 2 Input Setting Unit 4 Storage Unit 11 Model Output Calculation Unit 12 Constraint Condition Evaluation Unit 13 Evaluation Calculation Unit 14 Model Update Determination Unit 21 Constraint Condition Input Setting Unit 22 Model Order Identification Parameter Input Setting Unit 23 Optimization Calculation Parameter input setting unit 24 Evaluation function input setting unit 41 Constraint condition storage unit 42 Model order identification parameter storage unit 43 Optimization calculation parameter storage unit 44 Evaluation function storage unit 45 Model output storage unit 46 Actual data storage unit

Claims (8)

In a modeling device for building a model of a system by determining values of parameters of the model,
The model is a mathematical formula that includes a time variable that is considered a continuous time;
A constraint condition setting unit that sets a priori information about the system obtained in advance as a constraint condition;
The actual output data output from the system when predetermined input data is input to the system as actual input data, and the model output data output from the model when the actual input data is input to the model. An evaluation calculation unit for obtaining an evaluation result of an evaluation function for evaluating an error;
A model calculation unit that satisfies the constraint condition set by the constraint condition setting unit and obtains the parameter value of the model so that the evaluation result calculated by the evaluation calculation unit is the best. Modeling equipment. The modeling apparatus according to claim 1, wherein the a priori information is at least one of an upper limit value and a lower limit value related to a steady gain in the system. The evaluation function has a weight for weighting an error between the actual output data and the model output data,
In the case where the weight has a greater influence on the evaluation result as the value is larger, the weight value is set to the interval corresponding to the actual output data including noise of a predetermined threshold value or more. The modeling apparatus according to claim 1, wherein the modeling apparatus is set so as to be relatively smaller than other sections excluding the section. When the model calculation unit obtains the value of the model parameter by an optimization method that obtains the value of the model parameter after setting an initial value of the parameter of the model, the model operation unit converts the initial value itself into the parameter of the model The modeling apparatus according to any one of claims 1 to 3, wherein the modeling apparatus is handled as: The modeling apparatus according to any one of claims 1 to 4, wherein the model calculation unit obtains a value of a parameter of the model by a Particle Swarm Optimization Method. 6. The model calculation unit according to claim 5, wherein the model calculation unit obtains a parameter value of the model by a predetermined optimization method, and adds the obtained parameter value of the model to an initial value of the Particle Swarm Optimization Method. The modeling device described. The model computing unit, when performing an update by the Particle Swarm Optimization Method, at least one of a sign of a steady gain, a steady gain range, information on the stability of the system, and information on an unstable zero point of the system The modeling apparatus according to claim 5 or 6, wherein one is used. In a modeling method for building a model of a system by determining values of parameters of the model,
The model is a mathematical formula that includes a time variable that is considered a continuous time;
A constraint condition setting step for setting a priori information on the system obtained in advance as a constraint condition;
The actual output data output from the system when predetermined input data is input to the system as actual input data, and the model output data output from the model when the actual input data is input to the model. An evaluation calculation step for obtaining an evaluation result of an evaluation function for evaluating an error;
A model calculation step for obtaining a parameter value of the model so that the constraint condition set in the constraint condition setting step is satisfied and the evaluation result calculated in the evaluation calculation step is the best. Modeling method.

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