CN115484146A - Self-adaptive early warning method for state parameters of gas turbine under time-varying working condition - Google Patents
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Abstract
The invention provides a self-adaptive early warning method for state parameters of a gas turbine under time-varying working conditions, which comprises the steps of firstly, carrying out nonlinear fitting on the state parameters of the gas turbine to be analyzed, which are obtained from a state detection system, and the power of the gas turbine, and finding out the nonlinear relation between the state parameters and the power of the gas turbine; then, performing Gaussian mixture distribution parameter estimation on the fitted residual error to obtain a probability distribution model of the residual error; and finally, setting upper and lower threshold limits according to a 3 sigma principle of mixed Gaussian distribution, thereby realizing the gas turbine state monitoring and early warning based on the measured parameters. The self-adaptive early warning method for the state parameters of the gas turbine under the time-varying working condition fully considers the influence of the complex working condition, is suitable for analyzing the monitoring and measuring parameters related to the working condition of the gas turbine, is not limited by the nonstandard working condition, realizes the monitoring and early warning of the state of the gas turbine under the complex working condition, and provides an effective means for identifying the abnormal state of the gas turbine.
Description
Technical Field
The invention belongs to the field of ship fault prediction and health management, and particularly relates to a self-adaptive early warning method for state parameters of a gas turbine under a time-varying working condition.
Background
The gas turbine is widely applied to the fields of aviation, ships, power generation and the like due to the advantages of quick start, stable operation, high heat efficiency and the like. However, because the structure is complex, the device can work in severe environments with high temperature, high pressure and high rotating speed for a long time, and various faults are easy to occur. Meanwhile, as the service time of the gas turbine is prolonged, the performances of various parts are liable to be degraded to different degrees, so that the overall performance of the gas turbine is reduced. Particularly, the gas turbine needs to be continuously started, stopped and switched to work conditions, so that the cyclic thermal load and the mechanical load borne by a high-temperature through-flow component are more complicated, and the problem of high-temperature fatigue failure is more and more prominent. Therefore, how to master the performance state of the gas turbine, especially the high-temperature through-flow component, and improve the existing maintenance guarantee mechanism under the condition of ensuring the safe operation of the gas turbine, so as to improve the reliability and the safety of the whole machine, is an important problem to be solved urgently in the field of the gas turbine.
The performance parameters of the gas turbine can represent the running state of the gas turbine, but the performance parameters cannot be measured, if the change of the performance parameters of the gas turbine can be estimated by monitoring the change of the measured parameters, the fault early warning can be given out in time at the early stage of the fault occurrence, the fault occurrence is effectively avoided, and the time and the cost for parking and maintaining are reduced. Most of the existing monitoring and early warning methods adopt a single invariable threshold value, and influence of complex working conditions on monitoring parameters is not considered, so that abnormity occurring when the gas turbine operates under the variable working conditions can not be effectively identified. The other monitoring and early warning methods are simply distinguished according to standard working conditions, only the monitoring and early warning are carried out on the gas turbine when the gas turbine operates under the standard working conditions, a large number of nonstandard working conditions exist during the operation of the gas turbine, and the methods lack universality.
Disclosure of Invention
In order to solve the technical problem, the invention provides a self-adaptive early warning method for state parameters of a gas turbine under a time-varying working condition, which monitors the state parameters of the gas turbine under the time-varying working condition through linear fitting and mixed Gaussian distribution and carries out self-adaptive early warning according to monitoring data.
The purpose of the invention is realized by the following scheme: a self-adaptive early warning method for state parameters of a gas turbine under time-varying working conditions comprises the following steps:
step 1: data acquisition and preprocessing: acquiring the state parameter data of the gas turbine acquired from a ship state monitoring system, and uniformly removing the data of the stop moment and abnormal points or null values generated due to sensor abnormality or other faults.
And 2, step: and (3) correlation analysis: and calculating the correlation coefficient of the state parameter of each measuring point and the power of the gas turbine by adopting a pearson correlation coefficient method. And then judging whether the correlation coefficient is larger than 0.5, if so, considering that the state parameter is related to the working condition, and if not, considering that the state parameter is not related to the working condition. And finally obtaining a state parameter list relevant to the working condition of the gas turbine and a corresponding correlation coefficient value.
And step 3: and (3) nonlinear fitting: firstly, taking the power of the gas turbine as an independent variable and the average value of the state parameters of the gas turbine as a dependent variable to carry out 2 times of nonlinear fitting, wherein the fitting formula is as shown in formula (1):
wherein p is a gas turbine state parameter, x is gas turbine power, k is a polynomial order, n is a total number of polynomials, a k Is the polynomial coefficient of the k-th term,
is a k-th term polynomial.
Calculating the difference value between the actual data and the numerical value of the corresponding fitting curve to obtain all residual errors r of 2 times of fitting; finally, the root mean square error R of the residual error is obtained RMSE And the mean absolute error R MAE And R is judged RMSE And R MAE If so, determining a final nonlinear fitting model, otherwise, adding a polynomial order and continuing to perform fitting analysis, wherein the polynomial order is added not more than 5 times in the process.
The non-linear fit model can be expressed as:
y’＝ax 5 +bx 4 +cx 3 +dx 2 +ex+f (2)
wherein y' is the state parameter data of the gas turbine, a, b, c, d and e are coefficients of a polynomial, and f is a constant term.
The root mean square error R RMSE And the mean absolute error R MAE The calculation formulas of (a) and (b) are respectively shown as formula (3) and formula (4):
in the formula (I), the compound is shown in the specification,
as fitting value, x i N is the actual value and the number of data points.
And 4, step 4: residual analysis: and (4) obtaining the residual data of the state parameters by calculating the difference value between the state parameter fitting data obtained in the step (3) and the state parameter actual data obtained in the step (1). Counting frequency distribution of residual data, and performing parameter estimation of a Gaussian mixture model based on an EM algorithm according to a distribution rule, wherein the formula is as follows (4):
Θ＝(θ 1 ,θ 2 ,…,θ k ) T (5)
in the formula, theta is a parameter estimation result of the Gaussian mixture model, and theta 1 As weight estimates, θ 2 As mean estimate, θ k And determining the residual error r to be subjected to normal distribution, two-dimensional Gaussian distribution or three-dimensional Gaussian distribution according to the parameter estimation result of the Gaussian mixture model.
Step 5, threshold setting: confidence region when the confidence rate is 99.7% according to the 3 sigma principle of two-dimensional Gaussian distributionIs meta [ R ] 1 ，R 2 ]Combining the nonlinear fitting model of the residual r obtained in the step 3 to obtain the final upper and lower threshold limits L of the state parameter down And L up The calculation formula is shown in formula (6) and formula (7):
L down ＝y’-R 1 (6)
L up ＝y’+R 2 (7)
the formula (6) and the formula (7) are input into the condition monitoring system and compared with the monitored condition parameters.
Step 6, monitoring and early warning: and respectively adopting normal state data T1 and abnormal data T2 of other navigation stages as test sets to verify the early warning method. And triggering an alarm when the state parameter of the gas turbine monitored by the monitoring system continuously exceeds the threshold range for 5 times.
Preferably, the state parameters of the gas turbine include pressure and temperature parameters.
Preferably, in step 4, when performing parameter estimation of the gaussian mixture model based on the EM algorithm, the number k of parameter estimation may be increased according to the requirement and the complexity of the gaussian mixture model.
Compared with the prior art, the invention has the following advantages:
the invention provides a self-adaptive early warning method for state parameters of a gas turbine under a time-varying working condition, which fully considers the influence of the complex working condition of the gas turbine, adopts a nonlinear fitting method based on least square, takes root mean square error and average absolute error as evaluation indexes, obtains the nonlinear relation between the average gas temperature and the power of the gas turbine, and takes the nonlinear relation as a reference value of the average gas temperature of the gas turbine under different working conditions. And judging a normal distribution model, a two-dimensional Gaussian mixture distribution model or a three-dimensional Gaussian mixture distribution model of the fitted residual error through probability statistical distribution analysis of the fitted residual error, realizing parameter estimation of the Gaussian mixture distribution based on an EM (effective rule) algorithm, setting upper and lower threshold limits according to a corresponding 3 sigma principle, and inputting a calculation formula of the upper and lower threshold limits into a state detection system as a basis for early warning. Because the threshold set according to the nonlinear fitting and the mixed Gaussian distribution changes along with the change of the working condition in a self-adaptive manner, the accurate monitoring and early warning of the state of the gas turbine can be realized in the full working condition range without judging whether the gas turbine is in the standard working condition in advance. Therefore, the early warning method provided by the invention can effectively identify the abnormal condition of the average value of the state parameters of the gas turbine and make timely and accurate early warning.
Drawings
FIG. 1 is a flow chart of a state parameter adaptive early warning method under a time-varying working condition of a gas turbine according to the present invention;
FIG. 2 is a time domain graph showing the correlation between the average gas temperature and the power of the gas turbine according to the embodiment of the present invention;
FIG. 3 is a graph of a non-linear fit of gas turbine power to gas average temperature for an embodiment of the present invention;
FIG. 4 is a graph of data fitted to the average gas turbine temperature for an embodiment of the invention;
FIG. 5 is a graph of actual gas turbine gas average temperature data for an embodiment of the present invention;
FIG. 6 is a graph of gas turbine engine gas average temperature residual error data for an embodiment of the present invention;
FIG. 7 is a diagram illustrating a statistical result of residual frequency distribution according to an embodiment of the present invention;
FIG. 8 is a graph of a residual probability density function according to an embodiment of the present invention;
FIG. 9 is a diagram showing the relationship between the dispersion point of actual data of the average temperature and the power of the fuel gas and the upper and lower limits of the threshold in the embodiment of the present invention;
FIG. 10 is a diagram of a normal data set T in an embodiment of the present invention 1 A test result chart of (2);
FIG. 11 is a diagram of an abnormal data set T according to an embodiment of the present invention 2 The test result chart of (1).
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be further noted that, for the convenience of description, only some of the structures related to the present invention are shown in the drawings, not all of the structures.
As shown in fig. 1, the self-adaptive warning method for state parameters of a gas turbine under time-varying operating conditions according to the technical solution of the present invention includes the following steps:
step 1: data acquisition and preprocessing: the method comprises the steps of acquiring gas turbine state parameter data acquired from a ship state monitoring system, and uniformly removing data of a stop moment and abnormal points or null values generated due to sensor abnormality or other faults in order to reduce calculation amount and improve data analysis accuracy.
Step 2: and (3) correlation analysis: calculating a correlation coefficient of the state parameter of each measuring point and the power of the gas turbine by adopting a pearson correlation coefficient method; then judging whether the correlation coefficient is larger than 0.5, if so, regarding the state parameter as being related to the working condition, otherwise, regarding the state parameter as being not related to the working condition; and finally obtaining a state parameter list relevant to the working condition of the gas turbine and a corresponding correlation coefficient value.
And 3, step 3: nonlinear fitting: firstly, taking the power of the gas turbine as an independent variable and the average value of the state parameters of the gas turbine as a dependent variable to carry out 2 times of nonlinear fitting, wherein the fitting formula is as shown in formula (1):
wherein p is a gas turbine state parameter, x is the gas turbine power, k is the polynomial order, n is the total number of polynomials, a k Is the polynomial coefficient of the k-th term,
is a k-th term polynomial.
Calculating the difference value between the actual data and the numerical value of the corresponding fitting curve to obtain all residual errors r of the 2 fitting curves; finally, the root mean square error R of the residual error is calculated RMSE And the mean absolute error R MAE And R is judged RMSE And R MAE If the mean value is the minimum value, the final nonlinear fitting model is confirmed, and if not, the final nonlinear fitting model is confirmedThe polynomial order is increased and the fitting analysis continues, in the course of which the polynomial order is increased no more than 5 times.
The non-linear fit model can be expressed as:
y’＝ax 5 +bx 4 +cx 3 +dx 2 +ex+f (2)
wherein y' is the state parameter data of the gas turbine, a, b, c, d and e are coefficients of a polynomial, and f is a constant term.
The root mean square error R RMSE And the mean absolute error R MAE The calculation formulas of (a) and (b) are respectively shown as formula (3) and formula (4):
in the formula (I), the compound is shown in the specification,
as fitting value, x i N is the actual value and the number of data points.
Step 4, residual error analysis: and obtaining the residual data of the state parameters by calculating the difference value between the state parameter fitting data obtained in the step 3 and the state parameter actual data obtained in the step 1. Counting frequency distribution of residual data, and performing parameter estimation of a Gaussian mixture model based on an EM algorithm according to a distribution rule, wherein the frequency distribution is as shown in a formula (5):
Θ＝(θ 1 ,θ 2 ,…,θ k ) T (5)
wherein theta is a parameter estimation result of the Gaussian mixture model, and theta 1 As weight estimates, θ 2 Is a mean estimate, θ k And determining the residual error r to be subjected to normal distribution, two-dimensional Gaussian distribution or three-dimensional Gaussian distribution according to the parameter estimation result of the Gaussian mixture model.
Step 5, threshold setting: according to the 3 sigma principle of two-dimensional Gaussian distribution, the confidence interval when the confidence rate is 99.7% is [ R ] 1 ，R 2 ]And (4) combining the nonlinear fitting model of the residual error r obtained in the step (3) to obtain the final upper and lower threshold limits L of the state parameter down And L up The calculation formula is shown in formula (6) and formula (7):
L down ＝y’-R 1 (6)
L up ＝y’+R 2 (7)
equations (6) and (7) are input into the condition monitoring system and compared to the monitored condition parameters.
Step 6, monitoring and early warning: and respectively adopting normal state data T1 and abnormal data T2 of other navigation stages as test sets to verify the early warning method. And triggering an alarm when the state parameter of the gas turbine monitored by the monitoring system continuously exceeds the threshold range for 5 times.
In the present invention, the state parameters of the gas turbine include temperature and pressure.
In some embodiments of the present invention, the monitoring, early warning and analyzing of the average gas temperature of the gas turbine are performed by the following steps:
Step 3, nonlinear fitting:
the power of the gas turbine is used as an independent variable, the average temperature of the gas is used as a dependent variable, and nonlinear fitting analysis based on least squares is carried out. The fitting orders are respectively set to be 1 order, 2 orders, 3 orders, 4 orders and 5 orders, polynomial fitting analysis is carried out, the root mean square error value and the average absolute error value of the fitted residual errors are calculated, meanwhile, the error mean value is calculated, when the curve fitting is a polynomial model of 5 orders, the root mean square error, the average absolute error and the mean value of the residual errors are minimum, therefore, the polynomial fitting order is set to be 5 orders, and the fitting curve is shown in figure 3. In the figure, the scatter points represent the actual data, the line with scatter points is the fitting result, and the nonlinear model is:
y'＝8.70×10 -19 x 5 -4.94×10 -14 x 4 +1.07×10 -9 x 3
-1.13×10 -5 x 2 +0.07x+279.09
step 4, residual error analysis:
residual analysis: and (4) obtaining the gas average temperature residual data by calculating the difference value between the gas average temperature fitting data obtained in the step (3) and the gas average temperature actual data. The results of the fitting data of the average gas temperature, the actual data of the average gas temperature and the residual data of the average gas temperature are shown in fig. 4 to 6, and it can be known from the figures that the fitting data has basically consistent numerical value change and smaller residual compared with the actual data, and the maximum absolute value of the residual is 66.37 as found by calculating the absolute value comparison of the residual in fig. 6, which proves that the nonlinear model obtained in the step 3 has high accuracy.
The frequency distribution statistics is performed on the residual errors, and the result shown in fig. 7 is obtained. According to statistical results, residual errors do not obey a simple normal distribution model, threshold setting can not be directly carried out according to the 3 sigma principle, mixed Gaussian distribution needs to be adopted to approximate the real distribution of the residual errors, and the purpose of threshold setting is further achieved.
The analyzed data does not completely cover all working conditions, and the difference between the data quantity of the high working conditions and the data quantity of the low working conditions is large, so that the data is incomplete, a residual statistical distribution model obtained after data fitting is unknown, but the residual statistical distribution model can be intuitively regarded as linear superposition of several normal distribution models and meets the requirement of mixed Gaussian distribution. Therefore, the parameters of the mixture gaussian distribution are estimated by using the EM algorithm, and since the lateral error and the longitudinal error corresponding to the two-dimensional gaussian distribution are both minimum, the estimated parameters of the two-dimensional gaussian distribution model are selected, the residual probability density function is calculated, and the curve of the function is drawn, as shown in fig. 8. In this embodiment, the estimation parameters of the two-dimensional gaussian distribution model estimated by the EM algorithm are: alpha is alpha 1 ＝0.36、μ 1 ＝-19.54、σ 1 ＝0.18，α 2 ＝0.64、μ 2 ＝18.37、μ 2 ＝0.23。
Step 5 threshold setting
According to the two-dimensional Gaussian distribution estimation parameters obtained in the step 4 and the 3 sigma principle, when the confidence rate is 99.7%, the confidence interval is calculated to be [ -20.08, 19.06 ]]. Therefore, combining the non-linear fitting curve y' obtained in step 3, the lower threshold value L can be calculated down = y' -20.08, upper threshold limit L up ＝y’+19.06；
And inputting a calculation formula of the upper and lower limits of the threshold value into the state monitoring system. And respectively drawing a relation graph of actual data scatter points and threshold upper and lower limits of the average gas temperature and the power, as shown in fig. 9.
Step 6, self-adaptive monitoring and early warning
And selecting a data set of the gas turbine under the conditions of normal and abnormal conditions for verification and analysis. The normal data set is T 1 Most working conditions under the two-engine two-propeller and four-engine two-propeller modes are covered, and 10733 data points are total. The abnormal data set is T 2 6419 data points were shared, and an abnormal condition was exhibited in which the gas temperature suddenly increased at lower operating conditions. When setting the alarm mechanism, to avoid false alarm caused by accidental errorAnd defining that the average gas temperature exceeds the threshold value for 5 times continuously as an abnormal condition of the equipment, thereby giving fault early warning.
Normal data set T 1 The test results of (2) are shown in fig. 10, where a total of 3 data points exceed the lower threshold, but are not consecutive in time; and no data point exceeds the upper threshold, the set alarm mechanism is not met, and the gas turbine is considered to be in a normal state in the operating time of the period, which is consistent with the fact.
Abnormal data set T 2 The test results of (2) are shown in fig. 11, and the data points where abnormality occurs are 5108 th to 5124 th points. Under the condition that the power of the gas turbine is hardly changed, the average temperature of the gas is suddenly increased, and continuously increased data points exceed 5, which indicates that the temperature increase of the gas is not caused by the change of working conditions, and then the state monitoring system triggers an abnormal alarm in time.
The foregoing is a preferred embodiment of the present invention, and it should be noted that modifications and embellishments can be made by those skilled in the art without departing from the principle of the present invention, and should be considered as the scope of the present invention.
Claims (3)
1. A self-adaptive early warning method for state parameters of a gas turbine under time-varying working conditions is characterized by comprising the following steps: the early warning method comprises the following steps:
step 1: data acquisition and preprocessing: acquiring the state parameter data of the gas turbine from a ship state detection system, and uniformly removing the data at the stop moment and abnormal points or null values generated by sensor abnormality or other faults;
and 2, step: and (3) correlation analysis: calculating the correlation coefficient of the state parameter of each measuring point and the power of the gas turbine by adopting a pearson correlation coefficient method; then judging whether the correlation coefficient is larger than 0.5, if so, regarding the state parameter as being related to the working condition, otherwise, regarding the state parameter as being not related to the working condition; finally, the state parameter list relevant to the working condition of the gas turbine and the corresponding correlation coefficient value are obtained;
and step 3: nonlinear fitting: and carrying out 2 times of nonlinear fitting by taking the power of the gas turbine as an independent variable and the average value of the state parameters of the gas turbine as a dependent variable, wherein the fitting formula is as shown in formula (1):
wherein p is a gas turbine state parameter, x is the gas turbine power, k is the polynomial order, n is the total number of polynomials, a k Is the polynomial coefficient of the k-th term,
is a kth polynomial;
then calculating the difference value between the actual data and the numerical value of the corresponding fitting curve to obtain all residual errors r of the fitting curve for 2 times; finally, the root mean square error R of the residual error is obtained RMSE And the mean absolute error R MAE And determining R RMSE And R MAE If so, determining a final nonlinear fitting model, otherwise, adding a polynomial order and continuing to perform fitting analysis, wherein the polynomial order is added for no more than 5 times in the process;
the non-linear fit model may be expressed as:
y’＝ax 5 +bx 4 +cx 3 +dx 2 +ex+f (2)
wherein y' is gas turbine state parameter data, a, b, c, d and e are coefficients of a polynomial, and f is a constant term;
the root mean square error R RMSE And the mean absolute error R MAE The calculation formulas of (a) and (b) are respectively shown as formula (3) and formula (4):
in the formula (I), the compound is shown in the specification,
as fitting value, x i N is the number of data points;
and 4, step 4: residual analysis: obtaining residual data of the state parameters by calculating a difference value between the state parameter fitting data obtained in the step 3 and the state parameter actual data obtained in the step 1;
counting frequency distribution of residual data, and performing parameter estimation of a Gaussian mixture model based on an EM algorithm according to a distribution rule, wherein the formula (5) is as follows:
Θ＝(θ 1 ,θ 2 ,…,θ k ) T (5)
in the formula, theta is a parameter estimation result of the Gaussian mixture model, and theta 1 As weight estimate, θ 2 As mean estimate, θ k Determining the residual error r to obey normal distribution, two-dimensional Gaussian distribution or three-dimensional Gaussian distribution according to the parameter estimation result of the mixed Gaussian model as a standard deviation estimation value;
and 5: setting a threshold value: according to the 3 sigma principle of two-dimensional Gaussian distribution, the confidence interval when the confidence rate is 99.7% is [ R ] 1 ，R 2 ]Combining the nonlinear fitting model of the residual error r obtained in the step 3 to obtain the final upper and lower threshold limits L of the state parameter down And L up The calculation formula is shown in formula (6) and formula (7):
L down ＝y’-R 1 (6)
L up ＝y’+R 2 (7)
inputting the formula (6) and the formula (7) into the state monitoring system, and comparing with the monitored state parameters;
step 6, monitoring and early warning: respectively adopting normal state data T1 and abnormal data T2 of other navigation stages as test sets to verify the early warning method;
and when the state parameter of the gas turbine monitored by the state monitoring system continuously exceeds the threshold range for 5 times, triggering an alarm.
2. The adaptive state parameter early warning method for the time-varying working condition of the gas turbine as claimed in claim 1, characterized in that: the state parameters of the gas turbine include pressure and temperature parameters.
3. The adaptive state parameter early warning method for the time-varying working condition of the gas turbine as claimed in claim 1, characterized in that: in the step 4, when the parameter estimation of the gaussian mixture model based on the EM algorithm is performed, the number k of parameter estimation may be increased according to the requirement and the complexity of the gaussian mixture model.
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