JP2008299536A - Design program and design equipment - Google Patents

Abstract

An object of the present invention is to obtain an appropriate design specification using a correlated design specification.
For a plurality of physical specifications in a CAE model to be designed, a worst condition that causes the largest output fluctuation is obtained. Under these worst conditions, design specifications that can minimize the output fluctuation are obtained.
[Selection] Figure 1

Description

  The present invention relates to a design for obtaining design specifications that are low in sensitivity to variations in characteristics of a design target.

  Conventionally, in the design of various apparatuses, simulation using a model has been used to determine design specifications.

  For example, in the field of quality engineering, a technique called Taguchi method described in Non-Patent Document 1 is widely adopted. For determining circuit parameters, a method such as Patent Document 1 has been proposed. Furthermore, in the control system design, stability (robustness) against variations in physical specifications is important, and this robustness is described in Non-Patent Document 2 and the like.

JP 2000-293556 A "Introduction Taguchi Method" Kazuo Tatebayashi Published by Nikka Giren Publishers 2004 “Robust Control Performance and μ-Synthesis” Masayuki Fujita Magazine “System / Control / Information” Vol. 37, no. 2, pp. 93-101, 1993

  Here, Taguchi method is a technique that excludes design parameters with large interaction and focuses only on parameters having main effects. For this reason, even if there is a robust (optimal) solution in the interaction, it cannot be used. In the Taguchi method, there are three levels that can be assigned to one design specification in one experiment (design). Therefore, how to set the three level values is important, and a large part is left to the skill of the designer as to whether an appropriate solution can be obtained. In addition, it is difficult to obtain an optimum specification in one experiment, and usually several trials and errors are required.

  Furthermore, Taguchi Method uses an evaluation index called SN (Signal / Noise) ratio to adjust the rework cost (quality scale, loss function value converted to money) when a non-standard defective product comes out at the factory. The aim is to minimize. However, since the signal-to-noise ratio is a square evaluation using the variance value of characteristic fluctuations, it is assumed that a non-standard product is manufactured to some extent, and the cost for “rework” is low. appear.

  Further, H∞ control and μ synthesis are known as robust design methods for control systems, but the targets to which these control methods can be applied are linear systems or systems with small nonlinearity. In the field of quality engineering, unlike control system design, since the target hardware specifications are the design object, the design is generally a strong non-linear problem. In addition, the design specification has a certain settable range, which is also a non-linear problem. Therefore, it is difficult to apply the robust design method of the control system.

  The present invention is a design program for obtaining design specifications that are low in sensitivity to variations in characteristics of a design object, a procedure for setting a physical model for the design object in a computer, and a plurality of physical models in the set physical model. The setting procedure for setting the characteristic fluctuation range for the specifications, the evaluation procedure for evaluating the effect on output variation by varying the values of each physical specification within the set characteristic fluctuation range, and the evaluation The characteristic variation determination procedure for determining the characteristic variation of each physical specification that has the greatest effect on the output variation, and the optimization design calculation by mathematical programming for the physical model on the condition of the determined characteristic variation And performing an optimization calculation procedure for obtaining each design specification.

  Further, the optimization design calculation is designed so that the output fluctuation with respect to the characteristic fluctuation of the design specification is within a predetermined value, and that the output when the characteristic fluctuation of the design specification is zero matches the target value. It is preferable that the operation is a request.

  In addition, it is preferable that the evaluation procedure, the characteristic variation determination procedure, and the optimization calculation procedure are executed again using the design specifications obtained by the optimization calculation procedure.

  Further, the characteristic variation determination procedure uses a physical model to calculate a structured singular value by fixing one of a plurality of fluctuating physical specifications and changing another physical specification. It is preferable to determine the characteristic variation by repeating for each physical specification.

  In the optimization calculation procedure, it is preferable to perform optimization calculation using sequential quadratic programming.

  Further, the present invention is a design apparatus for obtaining a design specification that is low in sensitivity to characteristic variations of an object, and means for setting a physical model for the design object, and a plurality of physical specifications in the set physical model. Obtained by this evaluation, a setting means for setting the characteristic fluctuation range, an evaluation means for evaluating the influence on the output variation by varying the values of each physical specification within the set characteristic fluctuation width. , Characteristic variation determination means that determines the characteristic variation of each physical specification that has the greatest effect on output variation, and on the condition of the determined characteristic variation, the optimization design calculation is performed by mathematical programming on the physical model, And an optimization calculation means for obtaining each design specification.

  As described above, in the present invention, the value of each physical specification is varied within the set characteristic fluctuation range, and the characteristic fluctuation of each physical specification having the greatest influence on the output variation is determined. On the condition of the characteristic variation, optimization design calculation is performed on the physical model by mathematical programming, and each design specification is obtained. Therefore, since the positive interaction between the design parameters that has been excluded in the Taguchi method can be utilized, the robustness against variations can be improved.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

  The design program according to the present embodiment is basically executed by a general-purpose computer, and the general-purpose computer that executes the design program is a design apparatus. The design program is installed in a general-purpose computer, and is executed to perform various displays, etc., receives corresponding inputs, performs arithmetic processing, and outputs processing results.

  FIG. 1 shows the overall configuration of processing by the design program of this embodiment. First, the CAE model is set for a design object in consideration of its physical characteristics. Then, the design is performed so that the output variation Δy is within a predetermined value when the disturbance d is input and the variation occurs for a specific physical specification (which is also a design specification in the present embodiment). i)). Further, when there is no variation in the physical specifications, the condition is that the output y = y * (y * is the design target value of the output) (request (ii)).

  A flowchart of such processing is shown in FIG. First, CAE (Computer Aided Engineering) modeling is performed on the object (Step 1). This CAE model is a model in which each part of an actual target is mathematically expressed from its physical characteristics and an output is obtained when an input is given.

  For example, consider the stabilized power supply shown in FIG. In this circuit, the input terminal of the input voltage Vin is connected to the collector of the NPN transistor Q1, and the emitter of the transistor Q1 is connected to the output terminal of the output voltage Vout. One end of the resistor R1 is connected to the input end, and the other end of the resistor R1 is connected to the base of the transistor Q1. The collector of the NPN transistor Q2 is connected to the base of the transistor Q1. The emitter of the transistor Q2 is connected to the cathode of the Zener diode Zr1, and the anode of the Zener diode Zr1 is connected to the ground. A series connection of two resistors R2 and R3 is arranged between the output terminal and the ground, and a connection point of the resistors R2 and R3 is connected to the base of the transistor Q2.

  Therefore, a voltage obtained by dividing the output terminal voltage Vout by the resistors R2 and R3 is input to the base of the transistor Q2, and a voltage lower than the divided voltage by VBE2 is applied to the cathode of the Zener diode Zr1. Therefore, when the output voltage increases, a current flows through the Zener diode Zr1, the current flowing through the resistor R1 increases, the base voltage of the transistor Q1 decreases, and the output voltage Vout decreases. On the other hand, when the output voltage decreases, the current flowing through the resistor R1 decreases, the base voltage of the transistor Q1 increases, and the output voltage Vout increases. As a result, the output voltage Vout is stabilized.

  In such a stabilized power supply circuit, the gain of the transistor Q1 is hfe1, the base-emitter voltage is VBE1, the collector current IC1, the base current IB1, the emitter current IE1, the gain of the transistor Q2 is hfe2, the base-emitter voltage is VBE2, and the collector Assuming that the current IC2, the base current IB2, and the emitter current IE2, the currents of the resistors R1, R2, and R3 are IR1, IR2, and IR3, the voltage drop Vr of the Zener diode Zr1, and the resistor Rr, respectively, The following relational expression is obtained.

  And using this Formula (1), the CAE model which prescribes | regulates the relationship between a design item like Formula (2) and an output voltage is obtained.

  Next, the robustness is formulated (step 2). That is, it is formulated by the expression | Δy / d | <γ that the influence of the disturbance is not more than a predetermined value. Here, Δy is the output fluctuation, d is the disturbance input, and γ is the upper limit of the variation, and the robustness that the variation γ is minimized and the variation γ is smaller than the design requirement variation γ * (γ <γ *). (Request (i)).

  Next, a request for following the design target is formulated (step 3). In this example, y * = f (P, Δ = 0) is a condition. Here, y * is a design target value, f is a design target model equation, P is a design specification (p1, p2, p3,...), Δ is a design variation, and a variation Δ = 0 with respect to the design specification. In this case, the fact that the output matches the design target value y * is formulated as a request for following the design target (request (ii)).

  Next, mathematical design is applied to calculate design parameters that satisfy the requirements (i) and (ii) of steps 2 and 3 (step 4).

  Here, the relationship between the current I flowing through the stabilized power supply and the output voltage Vout is a linear relationship as is apparent from the equation (1), and the problem of designing the current and voltage (= control problem) is a linear problem. Can be obtained by H∞ control or the like.

  However, the relationship between the design specifications (resistance R and transistor amplification factor hfe) and the output voltage Vout is strongly non-linear as can be seen from Expression (2) obtained by modifying Expression (1). It is difficult to design this object by applying H∞ control or μ synthesis (for example, obtaining specifications for setting the nominal output voltage to 10 [V]).

  For example, in the stabilized power source shown in FIG. 3, the search range of design specifications is R1: 0.08 to 2.2 kΩ, R2: 1.2 to 56 kΩ, R3: 0.16 to 25 kΩ, hfe1: 15 of the transistor Q1. ˜300, hfe2 of the transistor Q2: 50 to 150, and three characteristic variations are set: ΔR2: −10 to + 10%, Δhfe1: −30 to 30%, Δhfe1: −30 to 30%. The design target value of the output voltage is 10V.

In this case, in step 2, the output variation is minimized under the worst condition (combination of the worst characteristic variations) that the characteristic variation (ΔR2, Δhfe1, Δhfe2) gives to the output voltage Vout. In this case, | (Vout−10V) / Id | <γ is set, γ is minimized, and γ <γ * is satisfied (requirement of robustness). Note that Id is a disturbance current.
[Request (i)]
| (Vout−10V) / Id | <γ → γ is minimized, and γ <γ * (3a)

The condition of step 3 is Vout (r1, r2, r3, hfe1, hfe2) = 10V (ΔR2 = 0, Δhfe1 = 0, Δhfe2 = 0) (request for design target follow-up).
[Request (ii)]
Vout (r1, r2, r3, hfe1, hfe2) = 10V (3b)
(ΔR2 = 0, Δhfe1 = 0, Δhfe2 = 0)

  When these two requirements are formulated in a block diagram, they can be expressed as shown in FIG. As described above, under the worst condition (combination of the worst characteristic variations) that the characteristic variation (ΔR2, Δhfe1, Δhfe2) gives to the output voltage Vout, the output variation γ is minimized and the variation is less than the target value (γ < γ *) and the characteristic variation is 0, Vout = 10V is a condition.

  Thus, since it is necessary to satisfy two requirements (request (i): Formula 3a, request (ii): Formula 3b) at the same time, by solving the request for robustness and the request for target tracking simultaneously, 2 Two requirements can be met. However, for example, in the field of mathematical programming, an effective method for solving both requirements simultaneously is not provided.

  Therefore, in this embodiment, the steps of FIG. 9 are applied. That is, the optimum solution is asymptotically obtained by alternately solving the step of obtaining the worst condition of the robustness requirement and the step of minimizing Equation (3a) and solving the constraint condition of Equation (3b).

[Process 1-First iteration]
In Process 1, a robust evaluation index called “structured singular value” is used in order to obtain the worst characteristic fluctuation. This is because, according to this index, the worst magnitude can be obtained in the transfer gain from the disturbance current Id to the output Vout (however, there is no dynamics in this object) in consideration of the physical structure of the object. . However, the condition that causes the worst characteristic fluctuation cannot be directly known from the structured singular value (only the worst gain is known).

  Therefore, in the present embodiment, one characteristic variation element, for example, the resistance R2 is set to a value (fixed value) under a certain variation condition, and the other two characteristic variations (Δhfe1, Δhfe2) are arbitrary values. Compute structured singular values. If this calculation is performed within the range of the upper and lower limits of the fluctuation of the resistance R2, what characteristic fluctuation value the resistance R2 takes will have the worst effect on the output (whether the structured singular value will be the maximum) Can know. The same applies to the other two characteristic fluctuations (Δhfe1, Δhfe2).

  A specific example is shown in FIG. In this example, hfe1 and hfe2 have a nominal value of 10, giving a variation of −30 to + 30%, and the resistor R2 has a nominal value of 1190Ω, giving a variation of −10 to + 10%, The robust performance value is calculated by fixing one and changing the other two. From the figure, it can be understood that the worst condition is that hfe1 and hfe2 are −30% and R2 is −10%.

  The structured singular value is applied to an object including dynamics in the field of control system design and represents the maximum gain of input and output in the frequency domain, but does not explicitly consider dynamics in the field of quality engineering. Therefore, the structured singular value in this embodiment is the worst value in DC gain excluding dynamics. Specifically, it is possible to calculate using, for example, the Robust Control Toolbox (trade name) of the control system design software Matlab.

[Process 2-First iteration]
In process 2, the design parameters are optimized under the worst condition obtained in process 1. For this reason, the SQP method (sequential quadratic programming) is applied.

  FIG. 11 shows the evaluation function and the constraint conditions expressed in equations (4a) and (4b), and the optimization problem expressed in a block diagram.

  As described above, each design specification that minimizes the variation | ΔVout / ΔId | in Δhfe1 = −30%, Δhfe2 = −30%, and ΔR2 = −10% is obtained with the above requirement (ii) as a constraint condition.

  If the design specifications are obtained in this way, the process returns to the process 1 again, and the worst condition is calculated as in FIG.

[Process 1-Repeat 2nd time]
The worst condition is obtained again with the design parameters obtained in the above process 2 (first iteration). The results are shown in FIG. It can be seen that the γ value representing the output variation is improved by 0.46 times compared to the case of FIG. 10 (first repetition).

  Thereafter, process 1 and process 2 are performed alternately until the γ value converges. That is, when the result of determination of γ <γ * in step 5 in FIG. 2 is Yes, convergence is determined, and the process ends.

  In this example, since there is almost no change from FIG. 12 after the third iteration, the design specifications in FIG.

  Table 1 shows the initial values and optimum values of the design specifications.

  FIG. 7 shows the result (frequency distribution) of the effects when using the optimum design specifications compared with the conventional method (Taguchi method).

[Step 6 in FIG. 2]
As described above, when the solution is obtained by minimizing the variation γ in Step 4 in FIG. 2, the variation γ may not be less than the target value γ * in Step 5.

  As described above, when the upper limit value γ of the output variation does not satisfy the design requirement (γ <γ *), the characteristic fluctuation range is reviewed (step 6 in FIG. 2). For example, although the cost is increased, it is conceivable to use parts with small variations. At this time, it can be determined from FIG. 12 how much variation should be selected for which component. That is, according to FIG. 12, it can be understood that even if the amplification factors hfe1 and hfe2 of the transistors vary, there is almost no influence on the variation of the output values. On the other hand, if the resistance R2 is changed to one with less variation, the effect is great. For example, as shown in FIG. 13, it can be determined that in order to reduce the output variation to 1/2, the resistance R2 variation should also be 1/2. Thus, according to the present embodiment, it is possible to obtain an improvement guideline for the target.

  If the design requirement is satisfied according to FIG. 13, the design is completed. However, when the magnitude of the characteristic variation is reviewed, the process returns to step 2 as shown in the flowchart of FIG. 2, and the design step is executed again. Also good. As a result, a more robust design result may be obtained.

[Influence of interaction]
The influence of the interaction between design specifications in the design of this embodiment will be described for each of the conventional method and this embodiment. Here, in order to make the explanation easy to understand, there are only two design parameters (control factors) R2 and R3 as shown in Table 2. Here, “e3” represents x1000. The assumed characteristic variation is the same as that described above with reference to FIG. In this design, only robustness is considered, and the constraint condition of the nominal output voltage: Vout = 10 [V] is not considered.

  First, as a conventional method, the result of obtaining the SN ratio with an appropriate mesh interval under the conditions in the table is shown in FIG.

  In FIG. 14, it can be seen that the R2 value (level) at which the SN ratio is optimum (maximum) differs depending on the strong interaction between the control factors R2 and R3, that is, the R3 value (level). For this reason, in the Taguchi method, as shown in FIG. 14, even if there is a combination of R2 and R3 with an optimum (maximum) SN ratio, it cannot be designed using R2 and R3.

  On the other hand, FIG. 15 shows the result of obtaining the maximum fluctuation amount (robust performance value) at the time of variation as the present embodiment under the conditions of FIG. It can be seen that there is a strong interaction as in FIG. The design results according to the present embodiment are indicated by the arrows in Table 3 and FIG. 15 (the starting point of the arrow is the initial design value, and the end point of the arrow is the optimum value after the design). It can be seen that an optimal (robust) combination of design specification values in which the interaction acts positively (synergistically) is required.

  As shown in FIG. 15, even when there is an interaction between the two design specifications, when the optimum value (the combination of the specifications that minimizes the maximum fluctuation amount) is unimodal, it is shown in Table 3. The initial value can be converged to the optimum value no matter where it is set. On the other hand, in the case of multimodality, it does not necessarily converge to a global optimum value. Therefore, in the case of multimodality, it is necessary to set the initial value to be close to the optimum value by using a method such as a Monte Carlo method or an experimental design method.

  Thus, according to the present embodiment, it can be seen that even when there is an interaction between design specifications (control factors), a more robust design than the conventional method is possible by utilizing this.

[Others]
Here, the structured singular values shown in FIG. 10 can be calculated when the design parameters (parameters) as shown in Expression (1) are expressed as linear coefficients. Therefore, for specifications (parameters) that cannot be expressed in a linear format, if Taylor expansion is performed under the design conditions (specification variation Δ = 0) as shown in Equation (5), and the primary approximation equation is targeted, good.

  Here, f (P, Δ): design object, P: design specification (parameter), Δ: variation in specification.

"Comparison with conventional examples"
(Problem of Taguchi method)
A case where the Taguchi method is applied to the stabilized power source shown in FIG. 3 described above will be described. The definition name and the type of characteristic variation are changed as appropriate.

  FIG. 4 shows the result of applying the Taguchi method using the L18 orthogonal table. The vertical dotted line is the selected level. The level with the highest S / N ratio is selected in each design specification, but in order to set the output voltage to Vout = 10 [V] when there is no characteristic variation (Δ = 0), R3 has a large effect of moving the average value. Aligned using the.

  FIG. 5A shows a result of obtaining a frequency distribution (calculating output voltage with a combination of all Δs (3 variations, 40 levels)) using the design parameters of the Taguchi method of FIG. FIG. 5B shows the results when the design specifications are appropriately adjusted for comparison (output voltage value Vout = 10 when there is no characteristic variation).

  On the other hand, the vertical dotted line in FIG. 6 is the level of the design specifications obtained by this embodiment. The solid line in the figure is the same as in FIG. FIG. 7 shows the result of obtaining the frequency distribution under the same conditions as the Taguchi method in the design specifications of the present embodiment.

  From FIG. 5, the design parameters determined by Taguchi method are more robust than the parameters determined appropriately, but from the comparison with this embodiment of FIG. 7, it is optimal in terms of output voltage variation width and standard deviation. It turns out that it is not a robust design. In fact, as shown in FIG. 6, the design specifications obtained in the present embodiment are greatly different from the optimum level indicated by the Taguchi method.

  The reason for this difference is that there is an interference “interaction” between design features in a stabilized power supply. The Taguchi method is a technique that eliminates design parameters with large interactions and focuses only on parameters that have main effects, so it cannot be used even if there are robust (optimal) solutions in the interactions. The presence of the interaction can be determined from the fact that the S / N ratio has a mountain shape or a valley shape in FIG. Moreover, the estimated value and the actual value of the optimum S / N ratio obtained from the factor effect diagram of FIG. 4 are shown in Table 4. It can also be seen from the fact that the improvement effect is deviated by 3 dB or more from the estimation.

  As is apparent from FIG. 4, in the Taguchi method, there are three levels that can be assigned to one design specification in one experiment (design). Therefore, how to set the three level values is important, but this is largely dependent on the skill of the designer.

  In addition, it is difficult to obtain the optimum specifications in a single experiment, and several trials and errors are required.

  Furthermore, the number of design parameters that can be assigned to an orthogonal table is limited to a maximum of seven (one for two levels), for example, when using an L18 orthogonal table, three levels can be set. Is done.

  Taguchi method uses an evaluation index called S / N ratio to minimize the rework cost (quality measure, loss function value converted into money) when non-standard defective products are produced at the factory. Yes. However, since the signal-to-noise ratio is a square evaluation using the variance value of characteristic fluctuations, it is assumed that a non-standard product is manufactured to some extent, and the cost for “rework” is low. (It is best that there is no defective product).

(Problems of robust control system design)
H∞ control and μ synthesis are known as robust design methods for control systems, but these control methods can be applied to linear systems or systems with small nonlinearity (for example, LPV: Linear Parameter Varing). System). In the field of quality engineering, unlike control system design, since the target hardware specifications are the design object, the design is generally a strong non-linear problem. In addition, the design specification has a certain settable range, which is also a non-linear problem. Therefore, it is difficult to apply the robust design method of the control system.

[Features of this embodiment]
In this embodiment, in the field of quality engineering for designing low-sensitivity (robust) specifications for target characteristic variations, a CAE model is used as a premise, and a problem formulation that reflects the physical structure is formulated. It is characterized by finding the optimum specifications by applying mathematical programming to the problem (Figs. 1 and 2).

  In particular, by reflecting the physical structure in the design, a positive interaction (synergistic effect) between design parameters (control factors) that has been excluded in the conventional method is utilized.

  Then, requirement (i): robustness: minimizing output variation under the worst condition (combination of worst characteristic variation) on output (evaluation index), requirement (ii): following design target: A solution that satisfies the two requirements of matching the output when there is no variation to the design target value is obtained.

  As a result, the positive interaction between the design parameters (control factors), which has been excluded in the prior art, can be utilized, so that it is possible to improve the robustness against variations compared to the conventional method (Taguchi method).

  In the conventional method (Taguchi method), the design specification level is left to the designer, and only three levels can be set (point design). In the present embodiment, the design specification and characteristics are set. It is possible to design in consideration of the entire range in which variation is possible (surface design).

  In the evaluation of robustness, the worst condition (condition in which the influence of the characteristic variation on the output is maximized), that is, the allowable error (absolute error) is used, so that it is easy to understand and quantitative evaluation / design is possible.

It is a figure which shows the structure of the process in embodiment. It is a figure which shows the flowchart of the process in embodiment. It is a figure which shows the structure of the stabilized power supply circuit which is a design object. It is a figure which shows the evaluation of each level by Taguchi method. It is a figure which shows frequency distribution of the output voltage by Taguchi method. It is a figure which shows the level employ | adopted in this embodiment. It is a figure which shows frequency distribution of the output voltage by this embodiment. It is the figure which made request | requirement (i) and (ii) in this embodiment a block diagram. It is a figure explaining the process of optimization by this embodiment. It is a figure explaining how to obtain the worst condition. It is a figure explaining the process of optimization calculation. It is a figure which shows the worst condition about the object by the design specification obtained by this embodiment. It is a figure explaining the design specifications which should be reviewed. It is a figure which shows the correlation of the item by Taguchi method. It is a figure explaining the optimization by this invention.

Explanation of symbols

  Q1, Q2 transistors, R1, R2, R3 resistors, Zr1 Zener diodes.

Claims (6)

A design program that requires low-sensitivity design specifications for variations in the characteristics of the design object.
On the computer,
A procedure to set up a physical model for the design object;
A setting procedure for setting the characteristic fluctuation range for a plurality of physical specifications in the set physical model,
An evaluation procedure that varies the values of each physical specification within the set characteristic fluctuation range and evaluates the effect on output variation,
Characteristic variation determination procedure for determining the characteristic variation of each physical specification having the greatest influence on output variation obtained by this evaluation,
Under the condition of the determined characteristic variation, an optimization calculation procedure is performed for the physical model by performing an optimization design calculation by mathematical programming to obtain each design specification,
A design program characterized by causing A design program according to claim 1,
The optimization design calculation requires that the output fluctuation with respect to the characteristic fluctuation of the design specification is within a predetermined value, and that the output when the characteristic fluctuation of the design specification is zero matches the target value. A design program characterized by being an operation to perform. A design program according to claim 2,
A design program characterized in that the evaluation procedure, the characteristic variation determination procedure, and the optimization computation procedure are executed again using the design specifications obtained by the optimization computation procedure. The design program according to any one of claims 1 to 3,
The characteristic variation determination procedure uses a physical model to calculate a structured singular value by fixing one of a plurality of fluctuating physical specifications and changing another physical specification. A design program characterized by determining characteristic fluctuations by iterating over specifications. A design program according to any one of claims 1 to 4,
In the optimization calculation procedure, a optimization program is used to perform optimization calculation using sequential quadratic programming. A design device that requires low-sensitivity design specifications for target characteristic variations,
A means of setting a physical model for the design object;
Setting means for setting the characteristic fluctuation range for a plurality of physical specifications in the set physical model,
An evaluation means for evaluating the influence on the output variation by varying the values of each physical specification within the set characteristic fluctuation range,
Characteristic variation determining means for determining the characteristic variation of each physical item having the greatest influence on the output variation obtained by this evaluation,
Under the condition of the determined characteristic variation, an optimization calculation means that performs optimization design calculation by mathematical programming on the physical model and obtains each design specification, and
The design apparatus characterized by having.