JPH07280603A - Machine abnormality determination method - Google Patents

Abstract

(57) [Summary] [Purpose] Providing a machine abnormality determination method that can perform accurate abnormality detection from machine state quantity measurement values without being affected by individual fluctuation ranges of normal and abnormal state quantities. To do. [Structure] The state quantity indicating the state of the machine is periodically measured from the output signal of the sensor installed in the machine, and the sample mean and sample variance are calculated from the sample of the state quantity under normal condition, abnormal condition, and monitoring. . From this calculated sample mean and sample variance, the test statistic of the difference between the population mean between normal and monitoring, and abnormal and monitoring, or the test statistic of the ratio of population variances is obtained.
The area surrounded by this test statistic on the t distribution or the F distribution is calculated, and the state characteristic value of the machine is obtained. When the state characteristic values under normal conditions and during monitoring are larger than the state characteristic values under abnormal conditions and during monitoring, it is judged as abnormal.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for determining an abnormality in an industrial machine such as a generator.

[0002]

2. Description of the Related Art Industrial machines such as generators perform rotary motions while generating heat and vibrations. In order to cope with abnormal situations such as excessive heat generation and vibrations, the temperature and vibrations of machines during operation, etc. Therefore, there is required a means for detecting the state characteristic value of the machine and monitoring the occurrence of an abnormality by the change of the state characteristic value.

The conventional state characteristic value is detected by measuring a state quantity such as temperature or vibration with a temperature sensor or a vibration sensor and using the measured value as a state characteristic value of a machine to determine an abnormality. . That is, in the conventional method,
The measured value of the state quantity such as temperature and vibration is used as it is as the state characteristic value of the machine, and it is compared with an arbitrarily set allowable value, and when it exceeds the allowable value, it is determined to be abnormal.

[0004]

However, in the actual measurement of the state quantity, for example, as shown in FIG.
Due to various factors, the measured value in the normal state momentarily shows a value close to that in the abnormal state, and conversely, the measured value in the abnormal state is the same as that in the normal state. And the state quantity measurement values are mixed and distributed. For this reason,
In many cases, the two cannot be completely separated by using an arbitrarily set allowable value, which is a factor that makes the machine abnormality determination inaccurate.

That is, FIG. 7 (a) is a state quantity time change curve in a normal state, in an abnormal state, and in a monitoring state when the variation range of the state amount in the normal state and the abnormal state is the same and the average value is different, The state quantity is periodically measured, and FIG. 2B is a plot of the state quantity measurement values during normal operation, abnormal operation, and monitoring on a number line. However, in this figure, when the allowable value is set to the value A, even if the machine is normal as shown in the monitoring time 1, some state quantities are erroneously determined to be abnormal because the amount exceeds the allowable value A. When the permissible value is set to the value of B, all the state quantities are smaller than the permissible value B, so that it is erroneously determined to be normal even if the machine is abnormal as shown in monitoring time 2.

On the other hand, in FIGS. 8 (a) and 8 (b), the time variation of the state quantity when the variation range of the state quantity in the normal state and the abnormal state is the same and the variance is different, and the state quantity is periodically measured. It shows the situation. In this figure, when the allowable value is set to the value of C, even if the machine is normal as shown at the time of monitoring 3, it is erroneously determined to be abnormal because some state quantities exceed the allowable value C. When the permissible value is set to the value D, even if the machine is abnormal as shown at the time of monitoring 4, all state quantities are smaller than the permissible value D, so that it is erroneously determined to be normal.

As described above, even when the average value or the variance of the state quantities at the time of normal and abnormal is different and the state quantity at the time of monitoring clearly indicates the abnormality of the machine, the state quantity at the time of normal and abnormal states is When the variation range of is the same, no matter what value the allowable value is set to, an erroneous determination will be made.

That is, unlike the conventional state characteristic value detecting method, the state characteristic values cannot be separated only by the arbitrarily set allowable values, and the state change of the machine cannot be detected accurately. There was a problem in that sufficient accuracy could not be obtained in determining the abnormalities.

The present invention has been made to solve the above problems, and an object thereof is to obtain an accurate state characteristic value of a machine from measured values of state quantities such as temperature and vibration. An object of the present invention is to provide a judgment method capable of judging a machine abnormality with high accuracy from a characteristic value.

[0010]

In order to solve the above-mentioned problems, the present invention collects state quantities indicating changes in the state of the machine for normal times and abnormal times, and monitors the state quantities of the machine over time during monitoring. Collected later, at the normal time of the collection,
Obtain the sample mean and sample variance for each sample of the state quantity at the time of abnormality and at the time of monitoring, and from these sample mean and sample variance, the test statistic of the difference between the population mean between normal time and monitoring time, and abnormal time and monitoring time or Calculate the test statistic of the ratio of population variances and use them as detection values that show the state characteristics, and compare the detection values with each other, and the detection values at the time of abnormality and at the time of monitoring are more than a predetermined ratio than the other detection values It was decided to be abnormal when it became very small.

The second means of the present invention is to obtain the difference between the population means on the t distribution in the test statistic of the difference between the population means for the normal time and the monitoring time and the abnormal time and the monitoring time obtained above. The area surrounded by the positive and negative values of the test statistic is used as the detected value indicating the state characteristic.

Further, the third means is a test statistic of the ratio of population variances on the F distribution in the test statistic of the ratio of population variances in the normal time and the monitoring time and the abnormal time and the monitoring time obtained above. The area surrounded by the numerical value and the reciprocal value is set as the detected value indicating the state characteristic.

On the other hand, the fourth means collects the state quantity of the machine under normal conditions, collects the state quantity of the machine over time at regular intervals during monitoring, and Obtain each normal distribution using each state quantity at the time of monitoring as a sample, compare this normal distribution with the normal distribution at every certain period at the time of monitoring to obtain the distance value between them, and this distance value is arbitrary The method for judging an abnormality when the allowable value set in (1) is exceeded is adopted.

The fifth means collects a plurality of kinds of state quantities such as temperature and vibration value from the machine at the same time and judges an abnormality based on the various kinds of state quantities.

[0015]

In the field of statistical analysis, it is known that the distribution of many phenomena fits well to the normal distribution, and the normal distribution is generally used as a model for many phenomena.

In the present invention, it is assumed that the distributions of the respective populations of the state quantities at the time of normal, abnormal, and monitoring of the machine are normal distributions, and the sample mean and sample for each sample obtained by measurement. The variance is determined, and the difference between the two population mean values or the difference between the two population variance values is tested for the state quantities under normal conditions and during monitoring, and abnormal conditions and during monitoring. Then, the test statistic of the difference of the population mean calculated by these tests or the test statistic of the ratio of the population variances are compared with each other, and the normal distribution at the time of monitoring is closer to the normal distribution at the abnormal time than at the normal time. At this time, it is determined that the state of the machine at the time of monitoring is abnormal.

In this method, the individual values of the state quantities at the time of normal, abnormal, and monitoring are not paid attention to, and the judgment is made by looking at the difference in the entire sample. The machine abnormality can be accurately determined without being affected by the range.

Further, like the second means or the third means, the area surrounded by the positive and negative values of the test statistic of the difference of the population mean on the t distribution, or the ratio of the population variance on the F distribution. If the area enclosed by the numerical value of the test statistic and the reciprocal value is calculated, the distance between the normal distribution of the entire sample at the time of monitoring and the normal distribution of the entire sample at the time of normal or abnormal can be expressed by a numerical value, making it easy to determine anomalies It becomes possible to do it.

On the other hand, when a sample when the machine is abnormal cannot be obtained, the distance value of the normal distribution between the samples at the time of normal operation and the sample at the time of monitoring is calculated as in the fourth means, and the distance value changes with time. It is possible to estimate the abnormality by monitoring the.

Further, if the fifth means is adopted, it is possible to make judgments for a plurality of kinds of state quantities at the same time, so errors due to sample fluctuations are reduced, and the accuracy of abnormality judgment can be improved.

[0021]

Embodiments of the present invention will be described below with reference to the accompanying drawings. FIG. 1 shows a measurement structure for detecting a state characteristic value of a machine, where 1 is a machine to be monitored, 2
Is a state quantity measuring device such as a temperature sensor and a vibration sensor. The state quantity measuring device 2 is arranged at a fixed position where changes in the state of the machine 1 are likely to occur, measures the state quantity indicating the state of the machine, and outputs it as a signal.

The output signal of the state quantity measuring device 2 is input to the AD converter 3, converted into a digital signal, and input to the arithmetic unit 4 such as a microcomputer. The arithmetic unit 4 is also configured to perform a state characteristic value detection process based on the output of the state quantity measuring device 2.

Next, the procedure for detecting the state characteristic value using the above measurement structure will be described. It should be noted that the processing means will be described here on the assumption that the distribution of the population of the state quantity during normal, abnormal, and monitoring of the machine is a normal distribution, that is, the population is a normal population.

Three samples {x11, x12, ..., x1N1}, {x11, x12, ...
21, x22, ..., x2N2}, {x31, x32,
......, x3N3}, each sample mean x
1, x2, x3, sample variances s1 ² , s2 ² , s3 ² , variances σ1 ² , σ2 ² , σ3 ² can be calculated by the following equation (1).

[0025]

[Equation 1]

Further, the probability density functions f1 (x), f2 (x), f3 of a normal distribution formed by the sample mean and the variance.
(X) can be calculated by the following equation (2).

[0027]

[Equation 2]

FIG. 2 (a) shows the case where the variation range of the state quantity measurement values in the normal state and the abnormal state is the same and the average value is different,
It is a schematic diagram which plotted the state quantity measurement value at the time of normal, abnormal, and monitoring on the number line. Further, FIG. 9B is an example in which the occurrence frequency of the state quantity is represented by a probability distribution (normal distribution) based on the equations (1) and (2). On the other hand, FIG. 2 (c)
Is a schematic diagram plotting on a number line in the case where the variation range of the state quantity measurement value in the normal state is the same as the variation range and the variance is different, and FIG. ) Is an example represented.

Here, as the number of samples increases, the distributions of FIGS. 2A and 2C approach the normal distributions of FIGS. 2B and 2D. , A sample of the state quantity at the time of abnormality and at the time of monitoring is represented by a normal distribution. As a result, it becomes unnecessary to process the individual values of the state quantity, and the entire sample can be processed only by its sample mean, sample variance, and variance. Due to the property of the normal curve of the equation (2), the variation range of the state quantity is from -∞ to + ∞ during normal operation, abnormal operation, and monitoring.

Next, let us consider expressing the distribution of the normal distribution at the time of monitoring, which is closer to the normal distribution at the normal time or at the abnormal time, by using a numerical value. Therefore, in the following, the case of performing the test of the difference between the two population means and the test of the difference between the two population variances are performed using the samples at the normal time and the monitoring time, and the samples at the abnormal time and the monitoring time. The processing procedure will be described separately for each case.

(I) Processing procedure when testing the difference between two population means: Using the samples at the normal time and the monitoring time, and at the time of the abnormal time and the monitoring time, the difference between the two population means is tested respectively. Describe how to do it. Generally, the population variances of the state quantities at the time of normal, abnormal, and monitoring are unknown, so the method of Welch's test will be used here.

A test statistic T13 of the difference between the population means of two samples at the time of normal and at the time of monitoring, and this test statistic T13.
The degree of freedom m13 of the t distribution that the distribution of follows can be calculated by the following equation (3). However, when m13 is not an integer, the nearest integer is defined as m13.

[0033]

[Equation 3]

In this equation (3), T13 is a numerical value representing the difference between the sample means x1 and x3, but the sample variance s1 ²
And s3 ² are normalized, the sample mean x1
And the difference between x3 and x3 is a constant value, the value of T13 becomes small when the values of s1 ² and s3 ² are large, and conversely, s1
^When the values of ² and s3 ² are small, the value of T13 is large. Therefore, T13 is a numerical representation of how close the normal distribution during normal monitoring is to the normal distribution during monitoring.

The probability density function ft (x) of the t distribution with the degree of freedom m13 can be calculated by the following equation (4).

[0036]

[Equation 4]

T13 in the equation (3) is a numerical expression of how close the normal distribution at the time of normal and the normal distribution at the time of monitoring are, but the distance between these two normal distributions. It would be convenient if T13 could be converted to a numerical value that varies between 0 and 1 in order to express. Therefore, the area D13 surrounded by the positive and negative values of the test statistic T13 on the t distribution having the degree of freedom m13 is calculated by the following formula (5).

[0038]

[Equation 5]

D13 is a numerical value representing the distance between the normal distribution during normal operation and the normal distribution during monitoring. Similarly, the test statistic T of the difference of the population mean between two samples at the time of abnormality and at the time of monitoring
23, the degree of freedom m23, and the probability density function ft (x) of the t distribution with the degree of freedom m23 are calculated, and the distance D23 between the normal distribution at the time of abnormality and the normal distribution at the time of monitoring is calculated.

The distances D13 and D23 thus calculated represent the distances from the normal distribution at the time of monitoring to the normal distribution at the normal time and at the abnormal time, respectively. Therefore, when the value of D13 is larger than the value of D23, that is, when the normal distribution at the time of monitoring is closer to the normal distribution at the abnormal time than at the normal time, it can be determined that the state of the machine at the time of the monitoring is abnormal.

This calculation method is suitable when there is a difference in the population mean of the state quantities in the normal state and the abnormal state, and a highly accurate result can be obtained regardless of the population variance in the normal state and the abnormal state.

(II) Processing procedure for testing the difference between two population variances Using the samples at the normal time and the monitoring time, and at the time of the abnormal time and the monitoring time, the test of the difference between the two population variances is performed. Describe how to do it.

The test statistic U13 of the ratio of the population variances of the two samples under normal conditions and during monitoring can be calculated by the following equation (6), and the distribution of this U13 has degrees of freedom (N1-1, N).
Follow the F distribution in 3-1).

[0044]

[Equation 6]

In this equation (6), U13 is a numerical value representing the ratio of the sample variances s1 ² and s3 ² . Sample mean x1
When x and x3 are equal, the centers of the normal distribution at the time of normal and the normal distribution at the time of monitoring match, but their shapes differ depending on the values of s1 ² and s3 ² . Therefore, U13 is a numerical representation of how similar the normal distribution during normal monitoring and the normal distribution during monitoring are.

Further, F of the degrees of freedom (N1-1, N3-1)
The distribution probability density function fF (x) can be calculated by the following equation (7).

[0047]

[Equation 7]

U13 in the equation (6) is a numerical representation of how similar the normal distribution in the normal state is to the normal distribution in the monitoring state.
There is no unit to represent the distance of two normal distributions, and 0 and 1
It would be convenient if U13 could be converted into a numerical value that varies between. Therefore, the area E13 surrounded by the numerical value of the test statistic U13 and the inverse numerical value on the F distribution having the degrees of freedom (N1-1, N3-1)
Is calculated by the following equation (8).

[0049]

[Equation 8]

E13 is a numerical value representing the distance between the normal distribution during normal operation and the normal distribution during monitoring operation. Similarly, the test statistic E of the ratio of the population variances of the two samples at the time of abnormality and at the time of monitoring
23 and the probability density function fF (x) of the F distribution with the degrees of freedom (N2-1, N3-1) are calculated, and the distance E23 between the normal distribution at the time of abnormality and the normal distribution at the time of monitoring is calculated.

The distances E13 and E23 thus calculated represent the distances from the normal distribution at the time of monitoring to the normal distribution at the normal time and at the abnormal time, respectively. Therefore, when the value of E13 is larger than the value of E23, that is, when the normal distribution at the time of monitoring is closer to the normal distribution at the abnormal time than at the normal time, it can be determined that the state of the machine at the time of the monitoring is abnormal.

This calculation method is suitable when there is a difference in the population variances of the state quantities under normal conditions and abnormal conditions, and highly accurate results can be obtained regardless of the population averages under normal conditions and abnormal conditions.

In the above, the method of detecting the state characteristic value of the machine and the method of determining the abnormality of the machine using the state characteristic value have been described. Next, using these methods, the abnormality determination of the machine is made by a specific numerical value. Here is an example.

As a first example, samples of the state quantity at the time of normal, abnormal, and monitoring obtained by measurement are {1,
2, 3, 5, 13}, {1, 9, 11, 12, 13},
In the case of {1, 8, 9, 12, 13}, the abnormality judgment is performed by the test of the difference between the two population means.

FIG. 3 (a) shows the distribution of the above sample plotted on a number line, and FIG. 3 (b) shows the same sample with a normal distribution. At this time, the sample size, sample mean, sample variance, test statistic, and degrees of freedom are
It becomes like the following formula (9).

[0056]

[Equation 9]

From this equation (9), the distance D13 = 0.7
6, D23 = 0.15 is obtained, and the value of D13 is larger than the value of D23, that is, the normal distribution at the time of monitoring is closer to the normal distribution at the abnormal time than at the normal time. Is determined to be abnormal. This determination is made in FIG.
Alternatively, it can be confirmed that it is appropriate from the distribution chart of (b).

As a second example, samples of the state quantity at the time of normal, abnormal, and monitoring obtained by measurement are {1,
6, 7, 8, 13}, {1, 2, 7, 12, 13},
In the case of {1, 3, 7, 11, 13}, an abnormality determination is made by testing the difference between two population variances.

FIG. 3 (c) shows the distribution of the above sample plotted on a number line, and FIG. 3 (d) shows the same sample with a normal distribution. At this time, the number of samples, the sample average, the sample variance, and the test statistic are as in the following Expression (10).

[0060]

[Equation 10]

From this equation (10), the distance E13 = 0.
25, E23 = 0.12 was obtained, and the value of E13 was E23.
Is larger than the normal distribution, that is, the normal distribution at the time of monitoring is closer to the normal distribution at the time of abnormality than at the time of normality, and therefore the state of the machine at the time of monitoring is determined to be abnormal. This judgment is shown in FIG.
It can be confirmed from the distribution chart of (c) or (d) that it is appropriate.

As a third example, the vibration amplitude value of the generator is measured by a vibration sensor, the difference between two population means is tested, and the difference between two population variances is tested.

FIG. 4 (a) shows the normal distribution of the sample at the normal time and the time of monitoring on the computer display, and FIG. 4 (b) shows the distance between the two normal distributions on the t distribution. And the area surrounded by the test statistics on the F distribution.

An example of using these methods to monitor the operating state of the machine by the computer continuously detecting the state characteristic value of the machine during the day and night will be described.

FIG. 5 is a flow chart for monitoring the operating state of the machine. In this figure, Step1
From (S1) to Step3 (S3), when normal or abnormal,
A sample of the state quantity at the time of monitoring is created, and the state characteristic value is calculated in Step 4 (S4) to Step 8 (S8).
In p9 (S9), abnormality determination is performed. Also, Step1
At 0 (S10), the state quantity measurement value with the oldest measurement time in the sample at the time of monitoring is excluded, and the state quantity at the time of monitoring is newly set to 1
The number of samples is measured and N3 samples are created, and the step is performed again.
The process from 4 (S4) is repeated. With such a processing procedure, even when the number of samples is large, the time interval for repeating the abnormality determination in Step 9 (S9) is shortened, and the state change of the machine can be continuously detected.

When the monitoring is performed by the above method, it is not necessary that the number of samples in each of the normal condition, the abnormal condition, and the monitoring condition is the same, but the larger the number of samples, the more accurate the determination result can be obtained.

In the above embodiment, the normal distribution distances between the normal time and the monitoring time, and the abnormal time and the monitoring time are calculated based on the three samples of the normal time, the abnormal time, and the monitoring time, and the normal distribution distances are calculated. When the normal distribution was closer to the normal distribution in abnormal conditions than in normal conditions, it was judged that the condition of the machine at the time of monitoring was abnormal. In many cases, it is not possible to obtain the distance, and the distance of the normal distribution at the time of abnormality and the time of monitoring may not be calculated.

In such a case, the normal state quantity of the machine is collected, the state quantity of the machine is periodically collected at regular intervals during monitoring, and the collected state quantities are sampled. As for each normal distribution. Next, the obtained normal distribution is compared with the normal distribution for each constant period during monitoring to obtain the distance value between the two, and the distance value is accumulated over a long period as shown in FIG. Monitor changes over time. Then, when the distance value exceeds an arbitrarily set allowable value, it is estimated to be abnormal and an abnormal signal is generated.
According to the above method, it is possible to accurately determine the abnormality of the machine even when the sample at the time of abnormality cannot be obtained.

Further, in the determination method of the present invention, all state quantities such as temperature and vibration have no unit and are detected as state characteristic values converted into numerical values varying between 0 and 1, so that the same time is detected. For multiple types of state quantities such as temperature and vibration measured for each state, the state characteristic value by the test statistic of the difference of population means or the state characteristic value by the test statistic of the ratio of population variances is detected, and these states are detected. An average value or a maximum value of the characteristic values may be calculated, and the abnormality determination may be performed based on the calculated value. As a result, errors due to sample fluctuations are reduced, and it is possible to perform machine abnormality determination with higher accuracy even when the number of samples is small.

[0070]

[Effects] As described above, according to the abnormality determination method for a machine of the present invention, the difference between the population averages of the normal state, the abnormal state, and the state quantity sample during the monitoring period is compared with the normal state and the monitoring period, and the abnormal state and the monitoring period. The test statistic of, or the test statistic of the ratio of population variances is calculated, and the normal distribution distance between normal time and monitoring and the normal distribution distance between abnormal time and monitoring are calculated. An accurate state characteristic value of the machine can be obtained without being affected by the variation range of each state quantity. Further, by making an abnormality determination based on the obtained state characteristic detection value, there is an advantage that the determination standard becomes highly reliable and the accuracy of the abnormality detection of the machine can be significantly improved.

[Brief description of drawings]

FIG. 1 is a block diagram showing a structure for measuring a state quantity of a machine in an embodiment.

2 (a), (b), (c), and (d) are schematic diagrams showing state quantity measurement values in a normal state, an abnormal state, and a monitoring state, respectively.

3 (a), (b), (c), and (d) are diagrams showing examples of state quantity measurement values during normal operation, abnormal operation, and monitoring, respectively.

FIG. 4A is a diagram showing a normal distribution of a sample at the time of normal and monitoring, and FIG. 4B is a diagram showing a distance between two normal distributions as an area on a t distribution and an F distribution.

FIG. 5 is a block diagram showing a flowchart for monitoring the operating state of the machine.

FIG. 6 is a chart showing an example of a machine abnormality determination based on a set allowable value.

7A and 7B are charts showing a conventional determination method.

8A and 8B are charts showing other conventional methods, respectively.

[Explanation of symbols]

 1 machine 2 state quantity measuring device 3 AD converter 4 arithmetic unit

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Hiroshi Yamaguchi 1703 Omachi Omura, Mure-cho, Kida-gun, Kagawa 66 (72) Inventor Koji Ono 15 672 Hatada, Ryonan-cho, Ayaka-gun, Kagawa (72) Inventor Hyoto Fumio 2-1226, Kaminocho, Takamatsu City, Kagawa Prefecture

Claims (5)

[Claims] 1. A state quantity indicating a state change of a machine is collected for each of a normal time and an abnormal time, and a state quantity of the machine is collected over time during monitoring, and the collected normal time, abnormal time, and monitoring time are collected. Obtain the sample mean and sample variance for each sample of the state quantity, and test the difference between the population mean between normal and monitoring, and abnormal and monitoring from the sample mean and sample variance. Calculate the statistics and use them as detection values that indicate the state characteristics, and compare the detection values with each other.When the detection value at the time of abnormality and at the time of monitoring becomes smaller than the other detection value by a predetermined ratio or more Machine abnormality determination method for determining. 2. A test statistic of a difference between population means on a t distribution in a test statistic of a difference between population means in a normal time and a monitoring time, and an abnormal time and a monitoring time, which are obtained by the determination method according to claim 1. A method for determining an abnormality in a machine in which the areas surrounded by positive and negative numerical values are detected values that indicate the state characteristics. 3. The test statistic of the ratio of the population variances on the F distribution in the test statistic of the ratio of the population variances in the normal time and the monitoring time and the abnormal time and the monitoring time obtained by the determination method according to claim 1. A method for determining an abnormality in a machine in which the area surrounded by the numerical value and the reciprocal value is the detected value that indicates the state characteristics. 4. A normal state quantity of a machine is collected, a state quantity of the machine is periodically collected at regular intervals during monitoring, and the collected state quantities at normal time and during monitoring are collected. The respective normal distributions are obtained by using as a sample, and the normal distribution at the normal time is compared with the normal distribution at constant intervals during monitoring to obtain the distance value between the two. Machine abnormality judgment method that judges abnormal when exceeding. 5. The method according to claim 1, wherein a plurality of types of state quantities such as temperature and vibration value are collected from the machine at the same time, and an abnormality determination process is performed based on the various state quantities. The method for determining the abnormality of the machine described.