CN-115730465-B - Method for predicting service life of avionic product based on Weibull parameter

CN115730465BCN 115730465 BCN115730465 BCN 115730465BCN-115730465-B

Abstract

The invention relates to a method for predicting service life of an avionics product based on Weibull parameters, which comprises the following steps of 1, obtaining initial sample data of service life of the avionics product, processing and obtaining a failure data set, 2, calculating failure sample grade and cumulative failure probability of the initial sample data of the avionics product, 3, fitting Weibull distribution parameters of service life of the avionics product by using a least square method, and 4, drawing a service life curve of the avionics product according to the Weibull distribution parameters to realize life prediction of the avionics product. The invention is based on a grouping test method, and uses the failure data when the first time of failure occurs, thereby greatly shortening the test time. By grading the failure samples, the failure sample data and the failure sample data are comprehensively applied, so that the accumulated failure probability of the samples is more accurate, and the service life of the avionics products is further accurately predicted.

Inventors

JIANG SUWEN
BAI CHUNLEI
XU WENZHENG
SUN SHENG
XU YINGDONG

Assignees

中国航空综合技术研究所

Dates

Publication Date: 20260505
Application Date: 20221130

Claims (6)

1. The method for predicting the service life of the avionics product based on the Weibull parameter is characterized by comprising the following steps of: step 1, acquiring initial sample data of life of an avionic product, and processing and acquiring a failure data set, wherein the initial sample data comprise the following specific steps: Dividing the total number of N initial samples into N batches, ensuring the number m n of samples in each batch to be not less than 3, sequentially testing each batch of samples, stopping the batch of samples when one sample in the batch fails, recording the first sample failure occurrence time T n in the batch, then repeating the test for the next batch of samples until all batches of samples are tested, sorting and storing test data, arranging the failure sample occurrence times T n of each batch in time sequence, marking the time sequence of the failure time of each batch as T k , marking the minimum sample number which does not fail as S k , and forming a failure data set; Step 2, calculating failure sample grade and accumulated failure probability of initial sample data of the avionic product, wherein the steps comprise the following steps: step 21, the failure sample grade calculation method of the initial sample data of the avionic product is as follows: Wherein rank k represents the kth failure sample level, rank k-1 represents the kth-1 failure sample level, N represents the total sample data amount, rank k-2 represents the kth-2 failure sample level, S k represents the minimum sample number at the moment T k where no failure occurs, and k represents the time sequence of sample failure; Step 22, calculating the cumulative failure probability of the avionics initial sample data failure samples, wherein the calculation method is as follows: F (T k ) represents the cumulative failure probability of the avionics failure sample at the moment T k ; Fitting a Weibull distribution parameter of the life of the avionic product by using a least square method, wherein the method comprises the following substeps: step 31, the probability distribution function of the life of the avionic product is as follows: Wherein G (t) represents a probability distribution function value of the service life of the avionic product, t represents the service time of the avionic product, beta represents a shape parameter of the Weibull distribution, eta represents a scale parameter of the Weibull distribution, and e represents natural logarithm; taking the logarithm twice to obtain the logarithm calculation relation of the probability distribution function of the life of the avionic product, wherein the logarithm calculation relation is as follows: in the formula, ln represents logarithmic operation; step 32, carrying out variable replacement on parameters in the logarithmic calculation relation of the life probability distribution function of the avionic product, and completing linearization of complex parameters, so that the logarithmic calculation relation of the simplified probability distribution function can be obtained, wherein the logarithmic calculation relation is as follows: y=a+bx; wherein y represents the dependent variable of the simplified probability distribution function, a represents the intercept of the simplified probability distribution function, b represents the slope of the simplified probability distribution function, x represents the independent variable of the simplified probability distribution function; step 33, obtaining the intercept a of the simplified probability distribution function and the slope b of the probability distribution function by a least square method, wherein the steps are as follows: wherein: representing a first regression coefficient; Representing a second regression coefficient; x i represents the ith argument; Y i represents the ith dependent variable; N represents the initial sample batch number; Step 34, carrying the cumulative failure probability of the failure sample obtained by calculation in the step 2 into the calculation process in the step 3, and finally obtaining the parameter values of the Weibull distribution, wherein the parameter values are as follows: wherein: A shape parameter representing a weibull distribution; a scale parameter representing a weibull distribution; and 4, drawing a life curve of the avionic product according to the parameters of the Weibull distribution, and realizing life prediction of the avionic product, wherein the life curve comprises the following specific steps: shape parameters of the Weibull distribution obtained in step 34 And scale parameters of weibull distribution And (3) carrying out step 31, drawing a Weibull distribution curve of the life of the avionic product, and obtaining a prediction result of the life of the avionic product.
2. The method for predicting the service life of an avionics product based on weibull parameters according to claim 1, wherein the first rank 1 of the failed sample class in step 21 has a value of 1, and the failed sample class is obtained according to the failed sample class calculation method in step 21.
3. The method for predicting life of avionics based on Weibull parameters according to claim 1, wherein the step 21 of obtaining the minimum number of samples for which no failure occurs at time T k is performed by S k is performed by assigning M k to the nth batch of samples when the failure time T n is recorded as T k , wherein M 0 = 0, and the maximum number of samples for which failure occurs at time T k is The method for calculating the minimum number of samples S k without failure is as follows: Where S k represents the minimum number of samples at which no failure occurs at time T k , and M i represents the number of samples in the ith lot.
4. The method for predicting the service life of an avionics product based on weibull parameters according to claim 1, wherein the step 32 is to replace the logarithm processed parameters with variables to complete linearization of complex parameters, specifically:
5. The method for predicting the service life of an avionics product based on weibull parameters according to claim 1, wherein the method for obtaining the average value of the independent variables in the step 33 is as follows: wherein: Represents the mean value of the independent variables.
6. The method for predicting the service life of an avionics product based on weibull parameters according to claim 1, wherein the method for obtaining the mean value of the dependent variables in the step 33 is as follows: wherein: Mean value of dependent variable is shown.

Description

Method for predicting service life of avionic product based on Weibull parameter Technical Field The invention relates to the field of small sample test design and Weibull parameter estimation based on batch initial failure, in particular to a method for predicting the service life of an avionics product based on Weibull parameters. Background The weibull distribution is one of probability distributions widely used for failure data analysis and life data analysis. The weibull analysis involves a probabilistic analysis in the form of a graph intended to find a distribution that best represents a batch of sample life data for a given failure mode. In general, in order to fit an accurate Weibull distribution curve, a large amount of experimental statistical data is often collected to provide a sufficient basis for Weibull parameter fitting, but in many cases, the deviation of the estimation result of parameters with insufficient statistical data is larger due to insufficient sample size or overlong experimental period. In addition, more than half of samples in the test have too long waiting time for failure, thus greatly increasing the test cost. Therefore, based on the analysis of the small sample fault data, the acquisition of the characteristic life value and the life distribution function of the avionic product has important significance. At present, aiming at data statistics of small samples, a semi-empirical semi-evaluation method, a Bootstrap method, a virtual augmentation sample evaluation method and a Bayesian method are commonly used. The semi-empirical semi-evaluation method is a method which depends on a large amount of historical tests or similar avionic product information, fully combines field test data with mastered information, and performs data analysis and reliability evaluation within a certain error allowable range. This is difficult to apply for scenes lacking historical information and similar avionics. Both the Bootstrap method and the virtual augmentation sample evaluation method essentially extend a small amount of test data. In the Bootstrap method, the original sample data is resampled, so that the data processing method of the original complex statistic is approximated in a simulation mode. The virtual augmentation sample evaluation method is essentially a sample generation method based on data expansion and data mining, and replaces a real test with a result of a simulation test, so that a small sample condition is evolved into a proper number of samples, and then data processing is performed. In addition, two conditions must be satisfied when new sample data is amplified, namely, the sample expectation is not changed, and the standard deviation of similar avionic products is not changed, so that the application of the method has a certain limitation. The two methods have great advantages in expanding the sample size information, but large deviation can occur when parameter estimation is performed under the condition that the sample size is too small due to insufficient test time. The Bayesian method is characterized in that the prior information is used for representing the preliminary estimation of the parameter to be estimated, and the prior information is further updated through the test information, so that posterior distribution of the parameter to be estimated is obtained. Bayesian methods are essentially an information extension that increases the amount of information by introducing a priori information. However, the prior information has no quantization standard in practice and also has no judgment standard, so that the prior distribution is important for the Bayesian method parameter evaluation. The method for processing the small samples mainly carries out data expansion according to experience information, prior information or virtual augmentation information so as to meet the sample size required by parameter estimation. However, when similar avionics and historical information are absent and the sample size is too small, it is difficult to expand valid sample data. In the actual test, the increase of the sample size and the reduction of the test time are contrary, and the above method is difficult to balance the requirement of reducing the test time under the condition of ensuring high reliability of sample data. There is therefore a need to develop a new method that overcomes the above-mentioned drawbacks. Disclosure of Invention Aiming at the application limitation of the method in small sample Weibull distribution parameter estimation, the invention provides a small sample test design and Weibull parameter estimation method based on batch initial failure, which combines the test design to greatly reduce the test time and effectively utilizes sample data at the same time so that the Weibull distribution fitting process is more accurate. The invention provides a method for predicting the service life of an avionic product based on Weibull parameters under the condi