Bootstrap-based mean standard deviation threshold early warning method

Abstract

A Bootstrap-based mean standard deviation threshold early warning method, based on the measured data sample, the data sample of the early warning index is calculated, and then the Bootstrap method is used to expand the data sample of the early warning index, the mean and standard deviation of the data sample are integrated to obtain a single value set of the early warning threshold, and the appropriate early warning threshold is selected according to the early warning index distribution based on the measured data, so as to realize the fault early warning function of the gas turbine.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of triaxial gas turbine performance simulation, fault early warning and statistics, in particular to a method for obtaining early warning threshold. BACKGROUND

[0002] Correct and effective fault early warning is crucial for the healthy and efficient operation of the gas turbine, and the accuracy of the fault early warning is derived from the analysis and processing of the measured data of the gas turbine.

[0003] If a large amount of measured data of major faults occurring in the actual operation of the gas turbine can be obtained, and the early warning threshold can be directly formulated based on these large amount of fault data, it is the most ideal. However, major faults rarely occur in the actual operation of the gas turbine, and the experimental cost of the gas turbine is also difficult for ordinary people to bear, so for researchers studying fault early warning, fault data is often very rare and precious. SUMMARY

[0004] For such machines as the gas turbine that are difficult to obtain fault data, the present disclosure provides a Bootstrap-based mean standard deviation threshold early warning method, which obtains the early warning threshold based on normal data of the gas turbine, and achieves good early warning effect.

[0005] Specifically, it comprises:

[0006] According to the measured data, a statistical quantity is defined as an early warning index, and if the measured statistical quantity in the field operation process exceeds the early warning threshold, it indicates that the gas turbine has failed, and the field should have an early warning;

[0007] Based on the O-group measured data under typical working conditions (M-group 0.8 working condition data and N-group 1.0 working condition data), the sample of the O-group early warning index data is calculated;

[0008] The Bootstrap method (confidence of 99.7%) is used to expand the O-group early warning index data sample;

[0009] The mean and standard deviation of each group of early warning index data sample obtained by expansion are calculated;

[0010] The mean and standard deviation values are arranged in ascending order and divided into intervals in turn, and the frequency of the mean sample and the frequency of the standard deviation value in each interval are counted;

[0011] The threshold formula of the mean standard deviation threshold method is integrated according to each interval, and the single value of the early warning index threshold corresponding to each interval is obtained;

[0012] According to the distribution of the measured early warning index data, a suitable value is selected from the single value set as the early warning threshold.

[0013] Further, a statistical quantity, a gas path parameter fluctuation ratio r, is defined according to the measured data as the early warning index, which indicates the difference between the theoretical simulation value and the measured value of the gas turbine, and its meaning is that the difference between the simulation data and the actual data at the same time and the difference between the upper and lower limits of the simulation value under the influence of the fluctuation of the environmental conditions. Compared with the fixed threshold in the traditional early warning method, the denominator in the gas path parameter fluctuation ratio changes with the working condition and the initial environmental conditions, so it is more "flexible" than the fixed threshold in the traditional early warning method, and overcomes the defects of the fixed early warning threshold, and the r value is a dimensionless number, which is convenient for comparison between different parameters, and has good unity.

[0014] The specific calculation formula is as follows:

[0015]

[0016] In the formula:

[0017] Pm is the field measured data of a gas path parameter of any main component of the gas turbine at a certain working condition;

[0018] Ps is the parameter data obtained by simulation at a certain working condition;

[0019] Pmax is the simulation value of the parameter obtained by simulation when the environmental temperature and air pressure of a certain working condition are upper limit values;

[0020] Pmin is the simulation value of the parameter obtained by simulation when the environmental temperature and air pressure of a certain working condition are lower limit values;

[0021] Among them, the main components of the three-shaft gas turbine include low-pressure compressor, high-pressure compressor, combustion chamber, high-pressure turbine, low-pressure turbine and power turbine, and the gas path parameters refer to the inlet and outlet temperatures and pressures of these main components. The simulation value of the parameter is preferably obtained by using the Matlab / Simulink simulation method.

[0022] Further, the typical working conditions include 0.8 working condition and 1.0 working condition.

[0023] Further, the expansion of the early warning index data sample by using the Bootstrap method specifically includes:

[0024] By using the Bootstrap method, the confidence is 99.7%, and the O-group early warning index data, including M-group 0.8 working condition data and N-group 1.0 working condition data, are randomly sampled with replacement, O times are extracted from the O-group data in each sampling experiment, and a new data set composed of O-group data is formed;

[0025] The sampling experiment is repeated for several times to realize the simulation of various operation states of the gas turbine based on the original data in theory.

[0026] Further, the step of integrating the mean value and the standard deviation value of each interval according to the mean standard deviation threshold value method to obtain a single value set of the early warning threshold value includes the following specific methods:

[0027] The mean value of each interval is selected as the mean value of the interval.

[0028] The standard deviation value of each interval is calculated according to formula (2), wherein the numerator is the distribution frequency of the standard deviation value in the interval, the denominator is the sum of the distribution frequency of the mean value and the distribution frequency of the standard deviation value in the interval, multiplied by the standard deviation value distance of the interval and added to the lower limit of the standard deviation of the interval.

[0029]

[0030] The obtained mean value μ and standard deviation value σ are brought into formula (3) to obtain the integrated early warning threshold value TS of each interval:

[0031] TS = μ + 3σ (2).

[0032] Further, the method further includes the following steps:

[0033] The early warning threshold value is verified by using the fault data.

[0034] The method provided by the disclosure calculates the early warning index of the actual measurement data sample of the gas turbine with only single start-stop to obtain an initial data sample of the early warning index, uses the Bootstrap method to expand the data sample of the early warning index, and obtains a series of mean value data and standard deviation data; the mean value data and the standard deviation data are divided into intervals, integrated into a single value set of the early warning threshold value according to the threshold value formula of the mean standard deviation threshold value method, and finally, the appropriate early warning threshold value is selected according to the distribution of the early warning index obtained by the actual measurement data.

[0035] Compared with the prior art, the disclosure has the following beneficial effects: (1) the disclosure is extended on the basis of the mean standard deviation threshold value method and has sufficient theoretical basis; (2) the disclosure improves the reliability of the early warning based on a large amount of experimental data obtained by expanding the data sample; (3) the disclosure obtains a single value set of the early warning threshold value based on the sufficient expansion of the data, which is equivalent to an inherent property of the gas turbine, the property includes various operation states of the gas turbine, and only the corresponding early warning threshold value needs to be selected from the inherent property-single value diagram according to the r value histogram of the actual measurement data, so that the subsequent workload is greatly reduced. BRIEF DESCRIPTION OF DRAWINGS

[0036] The above and other objects, features and advantages of the present disclosure will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings in which like reference characters refer to like parts throughout the figures, exemplary embodiments of the present disclosure are shown.

[0037] Figure 1 An overall flow chart of the early warning method of the present disclosure;

[0038] Figure 2 A flow chart of the Bootstrap-based mean standard deviation threshold early warning method;

[0039] Figure 3 A flow chart of the calculation of the gas path parameter fluctuation ratio r;

[0040] Figure 4 A r value histogram of parameter T6;

[0041] Figure 5 A mean value histogram of parameter T6;

[0042] Figure 6 A standard deviation histogram of parameter T6;

[0043] Figure 7 A single value plot of the early warning threshold of parameter T6;

[0044] Figure 8 A plot of the early warning results of parameter T6 of the three-shaft combustion engine in normal state;

[0045] Figure 9 A plot of the early warning results of parameter T6 of the three-shaft combustion engine in fault state. DETAILED DESCRIPTION

[0046] Preferred embodiments of the present disclosure will be described herein below with reference to the accompanying drawings. Although preferred embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so as to make the present disclosure more thorough and complete, and to fully convey the scope of the present disclosure to those skilled in the art.

[0047] The present disclosure proposes a fault early warning method for gas turbines and other machines with insufficient field data, which can expand sample data and obtain a single value plot of the early warning threshold, an inherent property of the combustion engine, as shown in FIGS. 1 to 4. Figure 1 、 2

[0048] The mean standard deviation threshold early warning method of the present disclosure will be further described below with the low-pressure turbine outlet temperature T6 of a three-shaft gas turbine as a data sample.

[0049] ​1. Calculate the r value of the gas path parameter fluctuation ratio with the actual data of a gas turbine as the sample

[0050] In the data of a single start-stop of a three-shaft gas turbine, the 0.8 working condition data and the 1.0 working condition data of the three-shaft gas turbine with the most research significance were selected as the data sample for research. In the data sample, the 0.8 working condition data was 90 groups, the 1.0 working condition data was 681 groups, and the total data was 771 groups. The 771 groups of T6 data were brought into the calculation formula of the gas path parameter fluctuation ratio r, as shown in formula (1), and the calculation flowchart of r is shown in FIG. 1. The result is drawn into a histogram as shown in FIG. 2, the horizontal coordinate is the r value of the gas path parameter fluctuation ratio, and the vertical coordinate is the frequency of the r value. Figure 3 Figure 4

[0051] 2. Bootstrap method to expand the data sample

[0052] The Bootstrap method was used to sample the original data sample of 771 groups to expand the data sample. In each sampling experiment, the original data sample of 771 groups was randomly sampled with replacement for 771 times, and the gas path parameter fluctuation ratio r value was calculated after each sampling. Therefore, each experiment can obtain a group of 771 r value samples. In this embodiment, the expansion of the data sample was completed after 10,000 sampling experiments.

[0053] 3. Threshold integration

[0054] The mean and standard deviation of the r value obtained in the 10,000 experiments were calculated, and a histogram was drawn as shown in FIG. 3, where the horizontal coordinate is the mean and standard deviation of the gas path parameter fluctuation ratio r, and the vertical coordinate is the frequency. Figure 5 Figure 6 The mean and standard deviation of the obtained r value were divided into intervals, and both were set to 18 intervals, as shown in Table 1.

[0055] Table 1 Interval division and frequency table of mean and standard deviation of parameter T6 threshold integration

[0056]

[0057]

[0058] The mean and standard deviation of each interval were integrated. The obtained single value of the early warning threshold is shown in Table 1, and the corresponding early warning single value graph is shown in FIG. 4. When drawing the early warning threshold single value graph, the number of the mean frequency of each interval is used, and the early warning threshold value of each interval is used as the value for drawing.

[0059] Figure 7

[0060] ​​​​​Each integrated early warning threshold value represents various operating conditions of the engine, and each interval of the r value histogram of the measured data indicates various operating conditions of the engine in the experiment.

[0061] Further combined Figure 5 With Figure 6 , select the highest frequency of the number 10 mean interval corresponding to 4.1400 as the early warning threshold value.

[0062] To verify the accuracy of the early warning threshold value, the fault data and normal data are compared, and the verification result is as follows Figure 8 、 Figure 9 The results in the figure show that the early warning threshold value obtained by the method will not alarm when the three-shaft engine is working normally, and will alarm when the three-shaft engine fails, proving that the early warning threshold value is effective.

[0063] In summary, the present application can realize the early warning function accurately without false alarm when the three-shaft engine is working normally and without missing alarm when the three-shaft engine fails, has good early warning effect, and provides a new method for fault early warning of the three-shaft engine lacking sample data.

[0064] The above technical solution is only an exemplary embodiment of the present application, and for those skilled in the art, on the basis of the application disclosed application method and principle, various types of improvements or modifications can be easily made, and are not limited to the method described in the above embodiment, therefore the above described method is only preferred, and does not have limiting significance.

Claims

1. A Bootstrap-based mean-standard deviation threshold early warning method, comprising the following steps: Defining a statistical quantity as an early warning index according to measured data; Based on several groups of measured data under typical working conditions, calculating several samples of the early warning index, and using the Bootstrap method to expand the data samples of the early warning index; Calculating each group of early warning index data obtained in the expansion process to obtain its mean and standard deviation value; Dividing the obtained mean and standard deviation values into intervals to determine the mean distribution frequency and standard deviation value distribution frequency in each interval; Integrating the mean and standard deviation values in each interval according to the mean-standard deviation threshold method to obtain a single-value set of early warning thresholds; Selecting a corresponding value from the single-value set as the early warning threshold according to the distribution of the early warning index based on measured data; Selecting a gas path parameter fluctuation ratio r as the early warning index, and the calculation formula is as follows: (1) In the formula: Pm is the field measured data of an item of gas turbine main component gas path parameter under a certain working condition; Ps is the parameter data obtained by simulation under a certain working condition; Pmax is the simulation value of the parameter obtained by simulation when the ambient temperature and pressure of a certain working condition are upper limit values; Pmin is the simulation value of the parameter obtained by simulation when the ambient temperature and pressure of a certain working condition are lower limit values; The step of integrating the mean and standard deviation values in each interval according to the mean-standard deviation threshold method to obtain a single-value set of early warning thresholds, the specific method comprising: Selecting the mean value of each interval as the mean value of the interval; Calculating the standard deviation value of each interval according to formula (2), wherein the numerator is the distribution frequency of the standard deviation value in the interval, the denominator is the sum of the mean distribution frequency and the standard deviation value distribution frequency in the interval, multiplied by the standard deviation value distance of the interval and added to the lower limit of the standard deviation of the interval: (2) Bringing the obtained mean μ and standard deviation value σ into formula (3) to obtain the integrated early warning threshold TS of each interval: （3）。 2. The method of claim 1, wherein, The typical working conditions include 0.8 working condition and 1.0 working condition.

3. The method of claim 1, wherein, The expansion of the early warning index data samples using the Bootstrap method specifically comprises: Using the Bootstrap method with a confidence level of 99.7%, randomly sampling the O-group early warning index data, including M-group 0.8 working condition data and N-group 1.0 working condition data, with replacement, each sampling experiment extracts O times from the O-group data to form a new data set composed of O-group data; Repeating the sampling experiment several times to simulate various operating states of the gas turbine based on the original data in theory.

4. The method according to any one of claims 1 to 3, characterized in that, Further comprising the following steps: Using fault data to verify whether the early warning threshold is correct.

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