A method for predicting the remaining life of a multi-state complex system with digital-analog linkage

Abstract

The present invention discloses a method for predicting the remaining life of a multi-state complex system with digital-analog linkage, which specifically comprises the following steps: step 1: using a three-state hidden semi-Markov model to describe the degradation process of the system, wherein the three states include a healthy state A, an unhealthy state B, and a failure state; step 2: analyzing the residence time distribution of the multi-state complex system in the hidden state and the state transition probability from macroscopic and microscopic scales; step 3: converting the continuous-time three-state semi-Markov chain into a multi-state Markov chain through hyper-Erlang distribution and transition probability; step 4: constructing a random degradation model; step 5: estimating unknown state parameters and observation parameters in the random degradation model; and step 6: predicting the remaining life of the multi-state complex system in real time based on the estimated state parameters and observation parameters.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical engineering, and in particular relates to a method for predicting the remaining life of a multi-state complex system with digital-analog linkage. Background Art

[0002] As modern equipment becomes increasingly large-scale, complex, and sophisticated, systems and their components often exhibit multi-state characteristics during the failure process, posing new challenges to predictive maintenance, which relies heavily on health status. Traditional two-state reliability theory assumes that a system and its components exist in only two states: normal operation and complete failure. However, in actual engineering applications, a system or its components often undergoes several intermediate states during its evolution from normal operation to complete failure. These intermediate states can be continuous, such as the system continuously degrading as damage accumulates, or discrete, such as the system transitioning from a high-performance state to a low-performance state. Degradation assessment of multi-state systems has always been a primary and challenging issue in maintenance decision-making. Given the random and nonlinear characteristics of degradation processes, current research has mostly used stochastic processes to describe them, believing that stochastic processes can better describe changes in the dynamic operating environment and the mechanisms that cause failures.

[0003] Reliability modeling, analysis, and assessment methods for multi-state systems are generally categorized into four categories: Boolean expansion models, Markov models, universal generating functions, and Monte Carlo simulation. Compared to other models, the Markov model is the most widely used for degradation modeling of complex multi-state systems. It consists of two stochastic processes: an unobservable Markov chain that reflects the system's true degradation state, and observable observational information that is randomly correlated with the system's true state. Current research on hidden Markov models assumes that the system's dwell time in hidden states follows an exponential distribution, which is limited. As an extension of the hidden Markov model, the hidden semi-Markov model (HSM) does not impose exponential distribution constraints on the dwell time in each operating state, and its degradation process is more realistic. However, existing studies assume that the system's dwell time in each state follows a normal distribution, an Erlang(2,λ) distribution, or a Weibull distribution. However, these probability distribution assumptions for hidden state dwell time are not universally applicable. Therefore, the remaining life prediction methods for multi-state complex systems based on these models are still somewhat elusive to engineering practice. Summary of the Invention

[0004] Purpose of the invention: In order to solve the problems existing in the above-mentioned prior art, the present invention provides a method for predicting the remaining life of a multi-state complex system with digital-analog linkage.

[0005] Technical solution: The present invention provides a method for predicting the remaining life of a multi-state complex system with digital-analog linkage, comprising the following steps:

[0006] Step 1: Use a three-state hidden semi-Markov model to describe the degradation process of the system, where the three states include healthy state A, unhealthy state B, and failure state; classify the hidden states to obtain k1 substates of healthy state A and k2 substates of unhealthy state B, and establish a new state space Θ, Θ = {K1, K2, K3}, K1 represents the substate set of healthy state, K1 = {1, ..., k1}, K2 represents the substate set of unhealthy state, K2 = {k1+1, ..., k1+k2}, K3 represents the failure substate; the hidden state is healthy state A or unhealthy state B;

[0007] Step 2: Analyze the residence time distribution of multi-state complex systems in hidden states from macroscopic and microscopic scales And the state transition probability γ represents the transfer rate. When the multi-state complex system is in the healthy state A, k = k1 and γ = λ. When the multi-state complex system is in the unhealthy state, k = k2 and γ = μ. τ represents the residence time of the multi-state complex system in the hidden state, and X represents the hidden state.

[0008] Step 3: Convert the continuous-time three-state semi-Markov chain into a multi-state Markov chain through hyper-Erlang distribution and transition probability;

[0009] Step 4: Construct a random degradation model;

[0010] Step 5: Estimate the unknown state parameters and observation parameters in the stochastic degradation model;

[0011] Step 6: Real-time prediction of the remaining service life of the multi-state complex system based on the estimated state parameters and observed parameters.

[0012] Furthermore, in step 1, the hyper-Erlang distribution is used to describe the residence time distribution of the multi-state complex system in the hidden state:

[0013]

[0014] in, represents the cumulative distribution function of the Erlang distribution with substate i and transition rate γ, and F(.) represents the cumulative distribution function of the hyper-Erlang distribution;

[0015] The transition probability expression of a multi-state complex system in the hidden state is as follows:

[0016]

[0017] Where Pr(.) represents the probability distribution function.

[0018] Furthermore, each sub-state is randomly associated with the observation data through a mapping function.

[0019] Furthermore, the random degradation model in step 4 is: when the multi-state complex system is in a healthy state, the jth sub-state ends at the current moment, and the system degrades with probability Transfer out of healthy state, or by probability Transfer to the j+1th sub-state; if the multi-state complex system ends in the jth sub-state and the next moment the system has the probability When the multi-state complex system is in an unhealthy state, the jth sub-state ends at the current moment, and the system transitions to an unhealthy state with probability p or a failure state with probability q at the next moment. Transition out of unhealthy state, or by probability Transfer to the j+1th exponential phase; if the multi-state complex system ends at the jth substate and the next moment the system is If the system switches from an unhealthy state to a healthy state at the next moment with probability p, or switches to a failed state with probability q.

[0020] Furthermore, the step 5 is specifically as follows:

[0021] Step 5.1: Construct the likelihood function L = (Λ,Ψ|O), where Λ is the state parameter set, Ψ is the observation parameter set, o is the set of N groups of condition monitoring failure history data and M groups of truncated history data, Λ = (p, q, k1, λ, k2, μ), Ψ = (μ0, μ1, Σ0, Σ1), O = {F1, ..., F N ,S1,...,S M}, where μ0 represents the mean of the observation parameters of each dimension when the multi-state complex system is in a healthy state, μ1 represents the mean of the observation parameters of each dimension when the multi-state complex system is in an unhealthy state, Σ0 represents the covariance of the observation parameters of each dimension when the multi-state complex system is in a healthy state, and Σ1 represents the covariance of the observation parameters of each dimension when the multi-state complex system is in an unhealthy state;

[0022] Step 5.2: Use the expectation maximization algorithm and the maximum pseudo-likelihood function to iteratively solve the state parameter and observation parameter set. The specific steps are as follows:

[0023] Step 5.2.1: Calculate the pseudo-log-likelihood function

[0024]

[0025] in, represents the likelihood function of the vth group of failure history data, represents the likelihood function of the v1th group of censored historical data; is the estimated value of Λ, is the estimated value of Ψ;

[0026] Step 5.2.2: Select Λ * ,Ψ * , making

[0027] Among them, Λ * is the optimal solution of Λ, Ψ * is the optimal solution of Ψ, is the augmented set of o, judge Λ * and Ψ * Whether the convergence condition is met, if so, stop the calculation, otherwise, the Λ obtained by the current iteration is * and Ψ * Substitute the initial value into step 5.2.1 and perform the next iterative calculation until Λ * and Ψ * The convergence condition is satisfied, and the convergence condition is: ε is the preset threshold.

[0028] Furthermore, step 6 is specifically as follows:

[0029] According to the fact that the residence time of a multi-state complex system in a healthy state obeys the phase distribution PH(α1,T1) with the k1-order state space {1,2,...,k1}, the residence time of a multi-state complex system in an unhealthy state obeys the phase distribution PH(α2,T2) with the k2-order state space {1,2,...,k2}, and the failure time ξ of a multi-state complex system obeys the phase distribution PH(α * ,T * ); the conditional reliability function of the remaining life of the multi-state complex system at the nth sampling moment and the expression of the average remaining life of the multi-state complex system are as follows:

[0030] Conditional reliability function of remaining life:

[0031] Average remaining lifespan:

[0032] Among them, nΔ represents the time of the nth sampling, t1 represents the time after nΔ, represents the posterior probability vector at the nth sampling time, π n (i1) represents the posterior probability that the multi-state complex system is in sub-state i1 at the nth sampling time, i1=1,2,...,k1+k2; T * , α *, the expressions of T1, α1, T2 and α2 are as follows,

[0033]

[0034]

[0035] Among them, ' represents the matrix transpose, e=(1,...,1).

[0036] Furthermore, the method further includes performing dimensionality reduction processing on the multi-source observation data collected by the sensor to obtain parameters after dimensionality reduction. The objective function of the dimensionality reduction processing is:

[0037]

[0038] Among them, w represents the dimension reduction parameter vector, N1 represents the total number of samples, α is the adjustment coefficient, is the predicted value of the remaining life of the randomly degraded system at the n1th sampling moment, is the true value of the remaining life at the n1th sampling moment, is the standard deviation of the remaining life prediction value at the n1th sampling moment, is the standard deviation of the true value of the remaining life at the n1th sampling moment;

[0039] By minimizing J(w), we can get the optimal solution w of the dimension-reduced parameter vector. * .

[0040] Beneficial effects:

[0041] The present invention adopts the hyper-Erlang distribution with a universal distribution form to describe the residence time of complex multi-state systems in the hidden state, which makes up for the limitations of traditional methods in that the residence time of the hidden state obeys the distribution of exponential, Weibull, normal and Gaussian mixture. On this basis, the state space is expanded, and the three macro states of the system (healthy, unhealthy and failed) are divided into several sub-states at the micro level, so as to realize the degradation assessment of the system at different health status levels in line with the actual process. The present invention uses Bayes' theorem to update the posterior probability of the system being in an unhealthy state in real time, and updates the conditional reliability function of the system's remaining life distribution in real time. Based on real-time state monitoring data and a hidden semi-Markov model considering the hyper-Erlang residence time distribution, the remaining life prediction of multi-state complex systems is made more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0043] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0044] This embodiment provides a method for predicting the remaining life of a multi-state complex system with digital-analog linkage. Figure 1 As shown, the specific steps include:

[0045] Step 1: Analyze the residence time distribution and state transition probability of the system's hidden state from the macro and micro scales. A three-state (state 0, 1, 2) hidden semi-Markov model is used to describe the degradation process of the system. Among them, states 0 and 1 are unobservable, representing the healthy state A and the unhealthy state B respectively. Only state 2 is observable, representing the failure state. These three states represent different degradation processes of the system. The residence time in the two unobservable states obeys a certain distribution. The states of different degradation processes are transferred through the state transition probability matrix. To describe the observed data characteristics of the system, it is assumed that under periodic sampling, the observed data Y of the system is (Y k :k∈N + ) are independent under the given system state and obey N in each state d (μ X ,Σ X ),X=0,1, where μ X Represents the mean of the observation data in state x in each dimension, Σ X represents the covariance of the observation data in state x in each dimension,

[0046] In this embodiment, the probability distribution of the system's dwell time in each hidden state is described by the hyper-Erlang distribution, whose cumulative distribution function is:

[0047]

[0048] in, is the cumulative distribution function of the Erlang distribution with phase i and transfer rate γ, k is a positive integer order; that is, in the healthy state A, it obeys the hyper-Erlang distribution with order k1 and transfer rate λ, and in the unhealthy state B, it obeys the hyper-Erlang distribution with order k2 and transfer rate μ. F(.) represents the cumulative distribution function of the hyper-Erlang distribution; t represents the residence time of the multi-state complex system in the hidden state. Considering the non-decreasing characteristic of the failure rate, the transition probability of the system in each hidden state exponential phase is Described by the following model:

[0049]

[0050] Where τ is the residence time of a multi-state complex system in each state, j represents the phase, X represents the state, X(·) is the failure rate function, and Pr is the probability distribution function.

[0051] A new state space Θ is established, Θ = {K1, K2, K3}, K1 represents the sub-state set of the healthy state, K1 = {1, ..., k1}, K2 represents the sub-state set of the unhealthy state, K2 = {k1+1, ..., k1+k2}, and K3 represents the failure sub-state; the hidden state is the healthy state A or the unhealthy state B.

[0052] Through the hyper-Erlang distribution and transition probability, the continuous-time three-state semi-Markov chain can be transformed into a multi-state Markov chain. Specifically, each sub-state is randomly associated with the observation data through a mapping function.

[0053] Based on the above description, a random degradation model is constructed from the micro scale: when the multi-state complex system is in a healthy state, the jth sub-state ends at the current moment, and the system is in a state of Transfer out of healthy state, or by probability Transfer to the j+1th sub-state; if the multi-state complex system ends in the jth sub-state and the next moment the system has the probability When the multi-state complex system is in an unhealthy state, the jth sub-state ends at the current moment, and the system transitions to an unhealthy state with probability p or a failure state with probability q at the next moment. Transition out of unhealthy state, or with probability Transfer to the j+1th exponential phase; if the multi-state complex system ends at the jth substate and the next moment the system is If a system transitions out of an unhealthy state, the multi-state complex system will transition to a healthy state with probability p or to a failed state with probability q at the next moment. At each moment, the system randomly generates an observation vector that is randomly correlated with the system's true state. During this process, the probability of failure increases as the system's operating time increases.

[0054] Step 2: Estimate the unknown state parameters and observation parameters in the random degradation model. Each state of the system degradation process can be transferred through the transition probability. Therefore, the unknown state parameters Λ=(p,q,k1,λ,k2,μ) and observation parameters Ψ=(μ0,μ1,Σ0,Σ1) in the degradation model can be estimated based on the sample of observation data. Use O={F1,...,F N ,S1,...,S M} represents a set of N sets of condition monitoring failure history data and M sets of truncated history data, and L = (Λ,Ψ|O) is the corresponding likelihood function. Since the sample path of the system's true degradation process is unobservable, it is difficult to find an analytical expression for maximizing the likelihood function. The present invention uses the expectation maximization algorithm to solve the parameters, which iteratively solves by maximizing the pseudo-likelihood function to approximate the optimal estimate of the parameters. Let and is the initial value of the parameter to be estimated. The specific steps of the EM algorithm are as follows:

[0055] E-step: Calculate the pseudo-log likelihood function:

[0056]

[0057] M-step: Select Λ * ,Ψ * , making

[0058]

[0059] The parameter Λ is updated at each step * ,Ψ * Then substitute it into E-step as the initial value, and make E-step and M-step iterative operations until the Euclidean norm converges The optimal estimated values ​​of the state parameters and observation parameters can be obtained. ε is an arbitrarily small positive number, generally 10 -6 . is the expectation of the log-likelihood function, is the augmented set of o.

[0060] For fixed state parameters and observation parameters, the pseudo-log likelihood function of the collected N groups of failure history data and M groups of censored history data is:

[0061]

[0062] represents the likelihood function of the vth group of failure history data, represents the likelihood function of the v1th group of censored historical data.

[0063] For the state parameters p and q, the unique stationary point can be solved by the maximization formula:

[0064]

[0065] The updated k1, k2, λ, μ at each step can be obtained by maximizing the following formula:

[0066]

[0067] Among them, a2, a3, b2,b3, are the parameters related to the pseudo-likelihood function, represents the failure time ξ of the given system and the residence time t in the healthy state f The probability density function of the observed data under the condition that the total sampling time is greater than the failure time of the assumed system.

[0068] For the observation parameter Ψ, the stationary point can be obtained by the formula and the formula to update the parameter:

[0069]

[0070] Step 3: Real-time prediction of the remaining service life of multi-state complex systems.

[0071] After using the Hyper-Erlang distribution to approximate the distribution of residence time, the residence time of the multi-state system in the healthy state obeys the phase-type distribution PH(α1,T1) with a k1-order state space of {1,2,...,k1}:

[0072]

[0073] Among them, ' represents the matrix transpose.

[0074] Then, the approximate distribution of the healthy state residence time is f1(x)=α1exp(T1x)T1 0 ,x represents the residence time of the healthy state, T1 0 =-T1e, e=(1,…,1).

[0075] Similarly, the residence time in the unhealthy state follows the phase distribution PH(α2,T2) with the k2-order state space {1,2,...,k2}, where:

[0076]

[0077] The approximate distribution of unhealthy state residence time is Here, x represents the dwell time of the unhealthy state.

[0078] The failure time ξ of the system follows the phase distribution PH(α * ,T * ):

[0079]

[0080] In the above formula,

[0081] Use π n (i1) represents the posterior probability that the system is in the i1th sub-state at the nth sampling moment, is the posterior probability vector, i1=1,2,…,k1+k2. According to Bayes’ theorem, at each sampling moment, the posterior probability π of the state monitoring data n (i) can be updated iteratively using the following formula:

[0082]

[0083] It means that in sub-state i1, the system has not failed at the current nΔ sampling time, and the observed data is y (n-1)Δ , the posterior probability is π n-1 Multivariate normal distribution under conditions; It means that at the current nΔ sampling time, the system has not failed and the observed data is y (n-1)Δ , the posterior probability is π n-1 The probability that the system is in substate i1 under the condition

[0084] The conditional reliability function of the remaining life of the system at the nth sampling moment is:

[0085]

[0086] R(·) is the conditional reliability function of the remaining life, Pr(·) is the probability distribution function; Z nΔ+t Is greater than the current nΔ The substate at time t1.

[0087] The average remaining life is:

[0088]

[0089] Definition of the underlined parameters, E(·) refers to the expected function of the average remaining life.

[0090] Step 4: Construct an optimization objective function for the interaction between multi-source monitoring data and random processes. Use deep learning, kernel principal component analysis, or weighted methods to reduce the dimensionality of multi-source monitoring data. The degradation characteristics after integrating multi-sensor monitoring data are expressed as:

[0091]

[0092] Among them, f(.) represents the dimensionality reduction function, w represents the parameter to be reduced, x i,j (t) is the monitoring data collected by the cth (c=1,2,...,C)th sensor of the n2th (n1=1,2,...,N2)th random degradation system at time t (t≥0).

[0093] To describe the uncertainty of the remaining life prediction, the mean and standard deviation of the life prediction are integrated to construct an optimization objective function that characterizes the prediction effect:

[0094]

[0095] Among them, w is the dimension reduction parameter vector; N1 represents the total number of samples, α is the adjustment coefficient, is the predicted value of the remaining life of the randomly degraded system at the n1th sampling moment, is the true value of the remaining life at the n1th sampling moment, is the standard deviation of the remaining life prediction value at the n1th sampling moment, is the standard deviation of the true value of the remaining life at the n1th sampling moment;

[0096] Step 5: Optimize and solve the objective function of minimizing prediction uncertainty. Based on the remaining life prediction results obtained in the above process, reversely optimize and adjust the multi-source data dimensionality reduction parameters to achieve the purpose of automatically matching the degradation feature construction with the random degradation process model. Based on the constructed prediction uncertainty quantification objective function, the optimal solution W of the dimensionality reduction parameter can be obtained by minimizing J(W) * :

[0097]

[0098] The above process can make full use of the historical monitoring data and online monitoring data of multi-state complex systems to establish a performance degradation model, and optimize the model parameters by quantifying the uncertainty of remaining life prediction, thereby more accurately evaluating the remaining life of multi-state complex systems in real time.

[0099] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for predicting the remaining life of a multi-state complex system with digital-analog linkage, characterized in that: The steps include: Step 1: Use a three-state hidden semi-Markov model to describe the degradation process of the system, where the three states include healthy state A, unhealthy state B, and failure state; classify the hidden states to obtain k1 substates of healthy state A and k2 substates of unhealthy state B, and establish a new state space Θ, Θ = {K1, K2, K3}, K1 represents the substate set of healthy state, K1 = {1, ..., k1}, K2 represents the substate set of unhealthy state, K2 = {k1+1, ..., k1+k2}, K3 represents the failure substate; the hidden state is healthy state A or unhealthy state B; Step 2: Analyze the residence time distribution of multi-state complex systems in hidden states from macroscopic and microscopic scales And the state transition probability j = 1, 2, …, k; γ represents the transfer rate. When the multi-state complex system is in the healthy state A, k = k1 and γ = λ. When the multi-state complex system is in the unhealthy state, k = k2 and γ = μ. τ represents the residence time of the multi-state complex system in the hidden state, and X represents the hidden state. Step 3: Convert the continuous-time three-state semi-Markov chain into a multi-state Markov chain through hyper-Erlang distribution and transition probability; Step 4: Construct a random degradation model; Step 5: Estimate the unknown state parameters and observation parameters in the stochastic degradation model; Step 6: Real-time prediction of the remaining service life of the multi-state complex system based on the estimated state parameters and observed parameters; In step 2, the hyper-Erlang distribution is used to describe the residence time distribution of the multi-state complex system in the hidden state: in, represents the cumulative distribution function of the Erlang distribution with substate i and transition rate γ, and F(.) represents the cumulative distribution function of the hyper-Erlang distribution; The transition probability expression of a multi-state complex system in the hidden state is as follows: Where Pr represents the probability distribution function; Step 6 is as follows: According to the fact that the residence time of a multi-state complex system in a healthy state obeys the phase distribution PH(α1,T1) with the k1-order state space {1,2,...,k1}, the residence time of a multi-state complex system in an unhealthy state obeys the phase distribution PH(α2,T2) with the k2-order state space {1,2,...,k2}, and the failure time ξ of a multi-state complex system obeys the phase distribution PH(α * ,T * ); the conditional reliability function of the remaining life of the multi-state complex system at the nth sampling moment and the expression of the average remaining life of the multi-state complex system are as follows: Conditional reliability function of remaining life: Average remaining lifespan: Among them, nΔ represents the time of the nth sampling, t1 represents the time after nΔ, represents the posterior probability vector at the nth sampling time, π n (i1) represents the posterior probability that the multi-state complex system is in sub-state i1 at the nth sampling time, i1=1,2,...,k1+k2; T * , α * , the expressions of T1, α1, T2 and α2 are as follows, Among them, ' represents the matrix transpose, It means that when the multi-state complex system is in a healthy state, the first sub-state ends at the current moment, and the system is in a healthy state with probability Out of health state, It means that when the multi-state complex system is in an unhealthy state, the first sub-state ends at the current moment, and the system is in an unhealthy state with probability Transition out of unhealthy state; The method also includes performing dimensionality reduction processing on multi-source observation data collected by the sensor to obtain parameters after dimensionality reduction.

2. According to the method for predicting the remaining life of a multi-state complex system with digital-analog linkage according to claim 1, step 3 specifically comprises: randomly correlating each sub-state with the observation data through a mapping function.

3. The method for predicting the remaining life of a multi-state complex system with digital-analog linkage according to claim 1 is characterized in that: The random degradation model in step 4 is: when the multi-state complex system is in a healthy state, the jth sub-state ends at the current moment, and the system is in a healthy state with probability Transfer out of healthy state, or by probability Transfer to the j+1th sub-state; if the multi-state complex system ends in the jth sub-state and the next moment the system has the probability When the multi-state complex system is in an unhealthy state, the jth sub-state ends at the current moment, and the system transitions to an unhealthy state with probability p or a failure state with probability q at the next moment. Transition out of unhealthy state, or with probability Transfer to the j+1th exponential phase; if the multi-state complex system ends at the jth substate and the next moment the system is If the system switches from an unhealthy state to an unhealthy state, the multi-state complex system switches to a healthy state with probability p or switches to a failed state with probability q at the next moment.

4. The method for predicting the remaining life of a multi-state complex system with digital-analog linkage according to claim 3 is characterized in that , the step 5 is specifically as follows: Step 5.1: Construct the likelihood function L = (Λ,Ψ|O), where Λ is the state parameter set, Ψ is the observation parameter set, O is the set of N groups of condition monitoring failure history data and M groups of truncated history data, Λ = (p, q, k1, λ, k2, μ), Ψ = (μ0, μ1, Σ0, Σ1), O = {F1, ..., F N ,S1,...,S M }, where μ0 represents the mean of the observation parameters of each dimension when the multi-state complex system is in a healthy state, μ1 represents the mean of the observation parameters of each dimension when the multi-state complex system is in an unhealthy state, Σ0 represents the covariance of the observation parameters of each dimension when the multi-state complex system is in a healthy state, and Σ1 represents the covariance of the observation parameters of each dimension when the multi-state complex system is in an unhealthy state; Step 5.2: Use the expectation maximization algorithm and the maximum pseudo-likelihood function to iterate the state parameter and observation parameter set to solve. The specific steps are as follows: Step 5.2.1: Calculate the pseudo-log-likelihood function in, represents the likelihood function of the vth group of failure history data, represents the likelihood function of the v1th group of censored historical data; is the estimated value of Λ, is the estimated value of Ψ; Step 5.2.2: Select Λ * ,Ψ * , making Among them, Λ * is the optimal solution of Λ, Ψ * is the optimal solution of Ψ, is an augmented set of O, and we can judge whether Λ * and Ψ * Whether the convergence condition is met, if so, stop the calculation, otherwise, the Λ obtained by the current iteration is * and Ψ * Substitute the initial value into step 5.2.1 and perform the next iterative calculation until Λ * and Ψ * The convergence condition is satisfied, and the convergence condition is: ε is the preset threshold.

5. The method for predicting the remaining life of a multi-state complex system with digital-analog linkage according to claim 1 is characterized in that ,The objective function of dimensionality reduction processing is: Among them, w represents the dimension reduction parameter vector, N1 represents the total number of samples, α is the adjustment coefficient, is the predicted value of the remaining life of the randomly degraded system at the n1th sampling moment, is the true value of the remaining life at the n1th sampling moment, is the standard deviation of the remaining life prediction value at the n1th sampling moment, is the standard deviation of the true value of the remaining life at the n1th sampling moment; By minimizing J(w), we can get the optimal solution w of the dimension-reduced parameter vector. * .

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