CN110750848A - Method for estimating remaining life of software-hardware degradation system by considering software operation - Google Patents
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Abstract
The invention discloses a method for estimating the residual life of a software-hardware degradation system by considering software operation, which comprises the following steps: constructing and screening the performance degradation indexes of the software-hardware system; constructing a system degradation model; providing a residual life estimation algorithm; analyzing a performance degradation model based on the hidden Markov model; and optimizing the system segmental degradation model by adjusting the state transition parameters of the software, further respectively constructing the system degradation model by the performance indexes, and extrapolating the residual life estimation of the whole software-hardware system according to the system structure of the system. The invention has the advantages that: aiming at the traditional problem of estimating the residual life of a software and hardware system by independently considering the software reliability or the hardware reliability, a discrete hidden Markov process is adopted to describe the transfer between software modules, the relation between a hidden state and actual degradation is established, different degradation models are established according to the number of inflection points in a system performance degradation index sample under different software running conditions, and the residual life is estimated according to a system structure.
Description
Technical Field
The invention relates to an analysis method for efficiently estimating system-level residual life, and particularly provides a simple and easy-to-use mathematical analysis method aiming at the problems of complicated simulation experiment process and huge manpower and material consumption of a large software-hardware integrated complex system.
Background
With the continuous improvement of the informatization level, the functions of various control systems are gradually realized by software, and the characteristics of high density of the software and continuous improvement of the complexity are presented. Integration of hardware and software has become an inherent form of large systems of all kinds. The system reliability of the system depends on software and hardware respectively, and further depends on the mutual influence in the process of combining the software and the hardware. Therefore, the reliability analysis of software and hardware interaction for software and hardware systems is more and more widely regarded. The traditional residual life estimation theory needs a large amount of life data, and with the technical progress, the life of modern large-scale systems is longer and longer, so that the failure is rarely generated in a limited development period, enough life data is difficult to obtain, and the existing reliability assessment is difficult to implement. In fact, failure mechanism analysis is the basis for reliability assessment and life prediction. For most systems, the failure mechanism is related to the performance degradation process, which therefore contains a large amount of reliability information. The traditional reliability theory only focuses on the information such as the service life data and the failure times at the failure moment, neglects the relation between the system failure and the performance degradation process, and has the defects in the reliability and residual life evaluation of a high-reliability long-service-life system. In fact, whether the system is failed or not, a cluster of performance degradation data which changes along with time can be measured, the performance degradation data provides a rich and key information source for product life prediction and reliability evaluation, and life characteristics and reliability of the system can be extrapolated, so that a new feasible way is provided for reliability evaluation.
The demand of modern military industry and the development of scientific technology determine that a mechanical system is continuously developed towards high speed, high precision and high reliability; on the other hand, many military system devices are bulky in structure and complex in function. Even if the device is excellent, its performance and state gradually deteriorate with continuous operation and cause occurrence of a failure. Failure of the system not only reduces production efficiency and system reliability, but also may cause serious safety problems and even cause personal injury and death. If the faults occurring in the system operation process can be accurately predicted and corresponding maintenance strategies can be formulated, the method is very meaningful for improving the system performance and avoiding the occurrence of major accidents and casualties. In addition, along with the aggravation of market competition, the design and manufacturing technology of the system is continuously improved, the performance of hardware materials is continuously improved, the reliability of the system is higher and higher, and the service life is longer and longer. In order to ensure the availability of system functions, the reliability index of the system needs to be determined, predicted and evaluated, otherwise, the functional design loses significance. Therefore, how to quickly and accurately estimate the reliability of a high-reliability long-life system within a limited research and development period and test expenses is a problem to be solved in the current reliability engineering field. The existing comprehensive test method for the reliability of the software and hardware hybrid system simply avoids the difference of the failure mechanisms of the software and hardware and does not solve the influence caused by the difference of the failure mechanisms of the software and hardware.
Reliability assessment modeling performance indicators of degraded systems is more advantageous and has been extensively studied by many scholars. The model building method of the degradation quantity generally adopts a random process method, namely a certain random process function is selected to describe the degradation process, and then the relevant parameters of the random process characteristic are solved and determined according to the degradation data. Through distribution fitting inspection, if the distribution rule of the degradation amount is not obvious, the relative increment of the degradation data meets a certain distribution rule, or a random accumulated change rule exists in the performance index, a random process with an independent increment characteristic is used, but modeling on the degradation data is a more appropriate choice.
However, problems associated with large system evaluations still exist, particularly the dynamic modeling of the operational process over time and its complexity. Based on the method, a new viewpoint is provided from a modeling object, the problem of estimation of the residual service life of a software-hardware system influenced by the operation of software modules is considered, the software operation is considered as one kind of impact or influence of hardware performance degradation, the transition between different software modules is described by adopting a discrete hidden Markov process, the relation between the actual degradation and the hidden state is constructed, and the degradation process of the hardware performance is analyzed on the basis.
Disclosure of Invention
The invention aims to invent a method for more accurately estimating the residual life of a system in limited budget and time, namely a degradation quantity segmented modeling method based on a hidden Markov model. And the traditional method for estimating the residual life based on failure data is improved, and the used degradation data samples are easier to obtain and have more key information.
The specific technical scheme of the invention comprises the following steps:
the method comprises the following steps: and (3) defining a software-hardware degradation system, constructing a degradation performance index, and extracting and screening the index.
Step two: and constructing a system degradation model by using a hidden Markov model according to the degradation performance index.
Step three: and designing a system-level residual life estimation algorithm according to the system architecture.
Step four: and (4) experimental design, wherein feature extraction and screening are carried out on the sample data set, the model is constructed, the residual life is predicted, a performance evaluation index is given, and the precision of the estimated value of the residual life is obtained.
The technical scheme provided by the invention has the following beneficial effects:
the hidden Markov model-based degradation quantity segmented modeling method provided by the invention aims at the problems of complicated simulation experiment process and huge manpower and material consumption of a large software-hardware integrated complex system, provides a simple and easy-to-use mathematical analysis method, combines the hidden Markov model to perform segmented modeling of degradation indexes, efficiently improves the accuracy of residual life estimation, improves the traditional failure data-based residual life estimation method, and uses degradation data samples which are easier to obtain and have more key information.
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FIG. 1 is a general flow diagram of the process of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and related algorithms.
The invention is based on the degradation data of the system to analyze, and obtains the performance degradation index as a data sample by a signal decomposition and dimension reduction method. And selecting a hidden Markov model to describe the influence of the operation of the software module on the hardware performance, predicting a hidden software state sequence, and solving a path of software operation state transition. Therefore, the degradation data of the hardware performance is modeled in a segmented mode, and the estimation of the residual service life at different stages is closer to a true value. The specific implementation steps are as follows:
1. index extraction and dimensionality reduction
The estimation of the remaining life of the software-hardware system first needs to determine key characteristic indexes representing the operation state of the system. The characteristic indexes not only comprise functional performance parameters of the system, but also comprise indirect characteristic parameters extracted from sensor monitoring signals of vibration, noise, temperature and the like. These features are greatly affected by software shock. During the operation of the software-hardware system, various detection signals of the system are information carriers reflecting whether the system is normally operated or not. Because the sensor monitoring information can not be directly used for degradation modeling, in order to improve the degradation evaluation precision, a signal processing method is required to be utilized to deeply research a life characteristic extraction method, so that the adopted method and the extracted characteristics can fully reflect the running state of the system. At present, the characteristic domains for representing the performance degradation indexes of the vibration signals are 3 types of time domains, frequency domains and time-frequency domains. The time domain features include an average value, a root mean square, an RMS, a kurtosis index, and the like. The frequency domain characteristics may represent the dispersion or concentration of the spectrum, the variation of the main band, etc. The frequency domain and time-frequency domain features are processed by methods such as wavelet transformation, empirical mode decomposition and the like. The specific process is shown as algorithm 1 and algorithm 2. In addition, after feature extraction is performed on the system monitoring signal data, some feature vectors may be very correlated, resulting in overlapping information. Therefore, in order to reduce data redundancy, the experiment adopts a Principal Component Analysis (PCA) method to reduce the dimension. The PCA protocol is shown in algorithm 3.
Algorithm 1: extraction of features by wavelet decomposition
In wavelet decomposition, a Hilbert space is decomposed into orthogonal sums of a plurality of subspaces according to different scale factors j, and further decomposed into a closed-packet subspace, and a wavelet packet base sequence is constructed to meet the following conditions:
wherein h and g are high-pass filter and low-pass filter coefficients respectively; k is 1, 2, …, j is a time position parameter and n is a frequency parameter.
After decomposition, reconstructing the decomposition coefficients of each frequency band to the 0 th layer by layer, and extracting signals in each frequency band, wherein if the data length of the original signal x (k) is N, the signal energy of each frequency band after decomposition is represented as:
wherein the content of the first and second substances,
representing the magnitude of a discrete signal located in a subspace in a wavelet decomposition at a resolution j. The feature vector corresponding to the energy sequence can be determined therefrom.
And 2, algorithm: EMD decomposition method for extracting features
The EMD decomposition involves the concept of eigenmode functions, which must satisfy the following two conditions:
1) the number of local extreme points and zero crossings must be equal or differ by at most one over the entire data range.
2) At any time, the average value of the upper envelope formed by the local maximum point and the lower envelope formed by the local minimum point is zero, that is, the upper envelope and the lower envelope are locally symmetrical with respect to the time axis.
EMD decomposition process:
1) all local maximum points of the signal data x (t) are found, all the local maximum points are connected by a cubic spline curve to form an upper envelope line, and all the local minimum points are connected to form a lower envelope line.
2) Mean value m of upper and lower envelope lines1Subtracting the mean value from the original signal data to obtain a new data sequence h1：
x(t)-m1＝h1
If h is1Two conditions for the eigenmode function are satisfied, then h1Is the first IMF component c decomposed1. Otherwise h1Instead, h is required to be1Repeating step 1) as the original signal, and continuing the screening until a first IMF component c is generated1。
3) And (3) calculating:
r1＝x(t)-c1
will r is1Repeating the steps 1) to 3) as the original signal, and so on to obtain n components of the original signal and a residual component r which can not be decomposed any morenNamely:
algorithm 3: principal component analysis method for reducing dimension
(1) Raw data indices were normalized:
(2) calculating a correlation coefficient matrix R ═ (R)ij)：
(3) Calculating a characteristic value and a characteristic vector:
solving a characteristic equation | λ I-R | ═ 0, solving characteristic values by a common Jacobian method, and arranging the characteristic values in the order of magnitude: lambda [ alpha ]1≥λ2≥...≥λp≥0。
Respectively determining corresponding characteristic values lambdaiCharacteristic vector e ofi(i ═ 1, 2,. p.) such that | | | ei||＝1；
(4) Calculating the principal component contribution rate and the accumulated contribution rate:
contribution toRate of change(i＝1，2，...，p)
Cumulative contribution rate
(i＝1，2，...，p)。
2. Hidden Markov model
The method comprises the steps of constructing a system degradation and failure domain model by using a hidden Markov model, estimating parameters of the hidden Markov model by using a Baum-Welch algorithm, predicting a hidden state sequence by using a Viterbi algorithm, and solving a path of software running state transition. And (3) assuming that K inflection points exist in the hidden sequence, determining an optimal value of K by adopting a Bayesian Information Criterion (BIC), segmenting the degraded data according to the value of K, and respectively constructing a hardware performance degradation model for each segment.
The hidden Markov model is specifically processed as described in algorithm 4.
And algorithm 4: based on hidden Markov model
Inputting: observing the sequence of states, the parameter K, and the termination condition
Initialization: initial state probability vector pi, state transition probability matrix A
And (3) outputting: software running state transition path
# set initial hidden State
z＜-runif(121，min＝1，max＝3)
# Bayesian Information Criterion (BIC) determination of k
k＜-3
Probability of transfer
p＜-matrix(c(.4，.3，.3，.4，.5，.1，0，0，1)，3，3)
Initial probability initial value of # hidden state
pi＝c(1，0，0，0)
# known hidden State sequence, time series of varying points T
3. Model of degenerate domain
Y (n) is at time tnThe predicted sensor index value d (n), Y (n) -Y (n-1) is set to a period [ (n-1) h, nh]The performance degradation model of the software-hardware system can be described as:
the performance degradation models given by the above equations may further be combined, assuming that under a given software operating state Z (n-1) ═ i, Z (n) ═ j, the system performance degradation increment d (n) has a probability density function G (d | i, j, Θ)ij) I.e. by
D(n)～G(d|i，j，Θij)，i，j∈I
Wherein, thetaijIs a parameter vector determined by Z (n-1) ═ i, Z (n) ═ j. Thus, of all possible I, j e I, the probability density set G ═ G (d | I, j, Θ) of the system performance degradation increments d (n) in each stateij)，i，j∈I}。
Under the condition of determining the distribution of the degradation increment in different software running states, the future performance degradation amount of the system in different software running states can be easily analyzed, and the future performance degradation amount can be specifically determined by the following formula:
wherein n iscIs the current number of cycles, Y (n'c) To be at the moment of timeThe amount of degradation in the performance index observed.
At a given significance level of α of 0.05, T-tests were chosen for goodness of fit tests, all with P values greater than 0.05, so the original hypothesis was accepted.According to the set hardware performance failure threshold D, the performance degradation data obeys normal distribution
The probability distribution function of (a) is:
and estimating parameters of the performance degradation model by using a nonlinear least square method to obtain normal distribution model parameters of each section of data. Given different time nodes, the remaining life of each piece of hardware can be estimated, assuming a failure threshold.
The evaluation index is measured by Root Mean Square Error (RMSE), mean error (AE) and Mean Square Percentage Error (MSPE) between the estimated residual life and the real residual life, and the smaller the value, the better the prediction result.
Root Mean Square Error (RMSE)
Mean error (AE)
Mean Square Percent Error (MSPE)
Wherein, yiDenotes true value, y'iIndicating the predicted value.
And algorithm 5: construction of degenerate domain model
Inputting: degradation index data, parameter K
And (3) outputting: k degradation model functions
% plotted initial data histogram
histfit(data)；
% normal distribution test
normplot(data)；
% parameter estimation
[mu，sigma，muci，sigmaci]＝normfit(data)；
% T test
[h，sig，ci]＝ttest(data，mu)；
4. Remaining life estimation algorithm
Assuming that the software-hardware system failure is defined as the time when the system performance index value enters the failure area for the first time under the operation state of different software modules, and the failure time is the time when the system performance index value enters the failure area for the first time. According to the hidden Markov process of software operation, the time t is generated by simulationNNh software execution state sequence { z (n): n iscN is less than or equal to N. Each software execution state sequence generated by simulation can be regarded as a determined software running path, and the residual life of the system can be used as the residual life estimation of the whole software-hardware system by solving the average residual life of all paths by utilizing a law of large numbers. The specific estimation process is as follows:
(1) the maximum possible life (cycle) of the software-hardware system is set to N, and the number of simulation generated path samples is set to M (for example, M is 1000). Where the maximum lifetime N may be determined from historical data observed by the actual software-hardware system, such as 557 maximum system lifetime in the observed system performance data set for a certain equipment system, and thus N may be set to 600.
(2) According to the observed system performance index data set, index data with obvious performance index change in different software running states are selected, and failure domain models of different performance indexes in different software running states are constructed.
(3) Generating M software execution transfer paths by simulation, and generating corresponding system performance index degradation amount in each software execution transfer, thereby forming corresponding degradation path data pair { (i, v)i)，i＝nc，nc+1，...，N}。
(4) Degenerate path data pair { (i, v) generated using simulationi)，i＝nc，nc+ 1.. ang.N }, at each occurrenceA point in time tnCalculate the expected degradation value of performance E [ Y (n) for each state]Then, the remaining life of z (n) k, k e I in different software execution states is determined. Here, the remaining life is determined by the time when the system performance index first enters the failure region:
from the M paths, an estimate of the remaining life of the system in M +1 states can thus be obtained.
(5) In order to reduce the data pollution of the collected performance degradation indexes, the simulation is repeatedly carried out by adopting b different simulation starting points, namely, the simulation is carried out by adopting
Taking the time point as a new current time point, repeatedly carrying out the simulation of (3) and (4), and estimating
The estimates are then weighted averaged
Wherein the weight ω isiAnd assigning according to the reliability of each sample data.
(6) For a sufficiently large integer M, the remaining life of the different subsystems can be estimated:
(7) the remaining life of the different subsystems is estimated separately.
(8) And estimating the system-level residual life of the software-hardware system by using the system structure.
5. Residual life estimation accuracy improvement
The method comprises the steps of extracting and screening indexes by using a signal decomposition algorithm and a principal component analysis method to obtain performance degradation indexes, describing the influence of the operation of a software module on the hardware performance by using a hidden Markov model, predicting a hidden software state sequence and solving the path of software operation state transition. Therefore, the degradation data of the hardware performance is subjected to segmented modeling, so that the estimation of the residual service life at different stages is closer to a true value, and the prediction precision is improved. And the traditional method for estimating the residual life based on failure data is improved, and the used degradation data samples are easier to obtain and have more key information.
Claims (5)
1. The method for improving the residual life estimation precision of the software and hardware degradation system under the software running condition is characterized by comprising the following steps of:
(1) and (3) defining a software-hardware degradation system, constructing a degradation performance index, and extracting and screening the index.
(2) And constructing a system hardware performance degradation model by using the hidden Markov model according to the degradation performance index.
(3) And designing a system-level residual life estimation algorithm according to the system architecture.
(4) And (4) experimental design, wherein feature extraction and screening are carried out on the sample data set, the model is constructed, the residual life is predicted, a performance evaluation index is given, and the precision of the estimated value of the residual life is obtained.
2. The method of claim 1, wherein the step (1) of establishing and screening the degradation performance index comprises the following steps:
by using the signal processing method, the adopted method and the extracted characteristics can fully reflect the running state of the system. At present, the characteristic domains for representing the performance degradation indexes of the vibration signals are 3 types of time domains, frequency domains and time-frequency domains. The time domain features include an average value, a root mean square, an RMS, a kurtosis index, and the like. The frequency domain and time-frequency domain features are processed by methods such as wavelet transformation, empirical mode decomposition and the like. In addition, after feature extraction is performed on the system monitoring signal data, some feature vectors may be very correlated, resulting in overlapping information. Therefore, in order to reduce data redundancy, the experiment adopts a Principal Component Analysis (PCA) method to reduce the dimension.
Wavelet decomposition process:
in wavelet decomposition, a Hilbert space is decomposed into orthogonal sums of a plurality of subspaces according to different scale factors j, and further decomposed into a closed-packet subspace, and a wavelet packet base sequence is constructed to meet the following conditions:
wherein h and g are high-pass filter and low-pass filter coefficients respectively; k is 1, 2, …, j is a time position parameter and n is a frequency parameter.
After decomposition, reconstructing the decomposition coefficients of each frequency band to the 0 th layer by layer, and extracting signals in each frequency band, wherein if the data length of the original signal x (k) is N, the signal energy of each frequency band after decomposition is represented as:
wherein the content of the first and second substances,representing the magnitude of a discrete signal located in a subspace in a wavelet decomposition at a resolution j. The feature vector corresponding to the energy sequence can be determined therefrom.
The EMD decomposition involves the concept of eigenmode functions, which must satisfy the following two conditions:
1) the number of local extreme points and zero crossings must be equal or differ by at most one over the entire data range.
2) At any time, the average value of the upper envelope formed by the local maximum point and the lower envelope formed by the local minimum point is zero, that is, the upper envelope and the lower envelope are locally symmetrical with respect to the time axis.
EMD decomposition process:
1) all local maximum points of the signal data x (t) are found, all the local maximum points are connected by a cubic spline curve to form an upper envelope line, and all the local minimum points are connected to form a lower envelope line.
2) Mean value m of upper and lower envelope lines1Subtracting the mean value from the original signal data to obtain a new data sequence h1：
x(t)-m1＝h1
If h is1Two conditions for the eigenmode function are satisfied, then h1Is the first IMF component c decomposed1. Otherwise h1Instead, h is required to be1Repeating step 1) as the original signal, and continuing the screening until a first IMF component c is generated1。
3) And (3) calculating:
r1＝x(t)-c1
will r is1Repeating the steps 1) to 3) as the original signal, and so on to obtain n components of the original signal and a residual component r which can not be decomposed any morenNamely:
the PCA algorithm is summarized as follows:
raw data were normalized:
calculating a correlation coefficient matrix R ═ (R)ij)：
Calculating a characteristic value and a characteristic vector:
solving a characteristic equation | λ I-R | ═ 0, solving characteristic values by a common Jacobian method, and arranging the characteristic values in the order of magnitude:
λ1≥λ2≥...≥λp≥0。
respectively finding corresponding characteristic valuesλiCharacteristic vector e ofi(i ═ 1, 2,. p.) such that | | | ei||＝1。
Calculating the principal component contribution rate and the accumulated contribution rate:
rate of contribution
Cumulative contribution rate
。
3. The method according to claim 1, wherein the hidden Markov model is used to construct the system degradation model in step (2), and the method is divided into two steps, namely, the hidden Markov model is estimated by using Baum-Welch algorithm, and the hidden state sequence is predicted by using Viterbi algorithm to obtain the path of the software running state transition. Assuming that K inflection points exist in the hidden sequence, determining an optimal value of K by adopting a Bayesian Information Criterion (BIC), segmenting the degraded data according to the value of K, and respectively constructing a hardware performance degradation model for each segment; and secondly, a distribution function of the degradation amount can be obtained by fitting nonparametric distribution of degradation index data when the hardware is degraded under different software running states. Assuming that, given a software operating state Z (n-1) ═ i, Z (n) ═ j, the system performance degradation increment d (n) has a probability density function G (d | i, j, Θ)ij) I.e. by
D(n)～G(d|i，j，Θij)，i，j∈I
Wherein, thetaijIs a parameter vector determined by Z (n-1) ═ i, Z (n) ═ j. Thus, of all possible I, j e I, the probability density set G ═ G (d | I, j, Θ) of the system performance degradation increments d (n) in each stateij)，i，j∈I}。
Under the condition of determining the distribution of the degradation increment in different software running states, the future performance degradation amount of the system in different software running states can be easily analyzed, and the future performance degradation amount can be specifically determined by the following formula:
wherein n iscFor the current number of cycles, Y (n)c) To be at the moment of time
The amount of degradation in the performance index observed.
4. The method of claim 1, wherein step (3) designs a system level remaining life estimation algorithm. According to the observed system performance index data set, index data with obvious performance index change in different software running states are selected, and degradation models of different performance indexes in different software running states are constructed. At each time point tnCalculate the expected degradation value of performance E [ Y (n) for each state]Then, the remaining life of z (n) k, k e I in different software execution states is determined. Here, the remaining life is determined by the time when the system performance index first enters the failure region:
for a sufficiently large integer M, the remaining life of the different subsystems can be estimated:
the remaining life of the different subsystems is estimated separately. And estimating the system-level residual life of the software-hardware system by using the system structure.
5. The method according to claim 1, wherein the step (4) predicts the remaining life based on the constructed model, and derives the accuracy of the estimated value of the remaining life based on the evaluation index.
Obtaining a state sequence of hidden software operation according to the state transition probability by applying a hidden Markov model, and obtaining a hidden software operation state sequence according to a transition nodeObtaining the degradation amount of a hardware system in different states, obtaining that each section of data belongs to a normal distribution model by Matlab fitting, selecting T test to carry out goodness-of-fit test under the condition that the given significance level α is 0.05, and obtaining that the P values of the test are all larger than 0.05, so that the original hypothesis is accepted
The probability distribution function of (a) is:
and estimating parameters of the performance degradation model by using a nonlinear least square method to obtain normal distribution model parameters of each section of data. Given different time nodes, the remaining life of each piece of hardware can be estimated, assuming a failure threshold.
The evaluation index is measured by Root Mean Square Error (RMSE), mean error (AE) and Mean Square Percentage Error (MSPE) between the predicted residual life and the real residual life, and the smaller the value, the better the prediction result.
Root Mean Square Error (RMSE)
Mean error (AE)
Mean Square Percent Error (MSPE)
Wherein, yiDenotes true value, y'iIndicating the predicted value.
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