Residual life prediction method based on nonlinear wear and random jump

Abstract

A residual life prediction method based on nonlinear wear and random jump comprises the following steps: firstly, constructing a health index of multi-source information fusion, and establishing a composite degradation model integrating a power law time scale function and a non-homogeneous Poisson process so as to simultaneously represent progressive accelerated wear and time-varying burst impact characteristics of equipment; then, designing an improved two-stage parameter estimation strategy, utilizing an expected condition maximization algorithm to process impact frequency hidden variables, identifying time-varying intensity parameters in combination with maximum likelihood estimation, and realizing robust identification of complex model parameters; deriving an approximate probability density function of the residual life based on a first passing time frame and a Gaussian approximation theory, and realizing probabilistic prediction through numerical integration; finally, a sliding window updating mechanism is established, and online self-adaptive adjustment and dynamic prediction of model parameters are achieved. The method is high in nonlinear fitting capability, sensitive in impact capture, high in prediction precision and accurate in uncertainty quantification under complex working conditions and limited observation data conditions.

Description

Technical Field

[0001] This invention belongs to the field of predictive health management (PHM) technology for mechanical equipment, specifically relating to a method for predicting remaining life based on nonlinear wear and random jumps. Background Technology

[0002] Predictive Health Management (PHM) technology assesses reliability and predicts Remaining Useful Life (RUL) by monitoring performance degradation throughout the entire lifecycle of equipment in real time, thereby optimizing equipment maintenance strategies and reducing operational risks. In modern industry, mechanical components, especially rotating parts such as bearings and turbines, inevitably degrade over time and are often affected by sudden load changes, environmental disturbances, and other shock events. Improper management can lead to unexpected failures, increased maintenance costs, and safety risks. Therefore, PHM technology is crucial, with RUL prediction, as a core function of predictive maintenance, possessing significant theoretical and engineering value. Current RUL prediction methods are mainly divided into three categories: physical model-based methods, artificial intelligence-based methods, and data-driven methods. Among these, the Wiener process model in data-driven methods has attracted much attention due to its sound mathematical foundation and practicality. This type of method achieves RUL prediction by establishing a stochastic process model between performance degradation and time. However, in practical applications, existing methods still have the following problems that urgently need to be addressed: (1) The traditional Wiener process model adopts the linear drift assumption, which cannot accurately describe the nonlinear degradation characteristics and is not sufficiently coupled with the random shock effect, resulting in the modeling deviation of the degradation process.

[0003] (2) Existing stochastic shock models are mostly based on homogeneous Poisson processes, ignoring the time-varying characteristics of shock occurrence rate, or assuming that shock and degradation are independent, thus failing to effectively capture their combined effect.

[0004] (3) The existence of latent variables under some observations makes the parameter estimation method prone to getting trapped in local optima, and it is not optimized for time-varying shock processes, resulting in insufficient estimation accuracy. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, such as insufficient nonlinear degradation modeling, limitations in describing stochastic impacts, and limited accuracy in parameter estimation under certain observation conditions, this invention proposes a residual life (RUL) prediction method based on nonlinear wear and stochastic jumps. This method integrates a nonlinear Wiener process and a nonhomogeneous Poisson jump process, establishing a composite degradation model capable of simultaneously describing progressive wear and sudden impacts. An improved two-stage parameter estimation strategy is employed to achieve accurate parameter estimation and reliable RUL prediction under partial observation data. This effectively overcomes the poor adaptability of single degradation models in complex industrial environments, providing strong theoretical support and technical assurance for condition-based maintenance of mechanical equipment.

[0006] The technical solution adopted by this invention to solve its technical problem is: A method for predicting remaining lifetime based on nonlinear wear and random jumps, the method comprising the following steps: Step 1: Vibration Signal Acquisition and Health Indicator Construction: Vibration signals are acquired using accelerometers installed on mechanical equipment. Since vibration signals generated during the operation of rotating machinery are often affected by various factors such as changes in operating conditions and sensor noise, the raw data suffers from low signal-to-noise ratio and difficulty in feature extraction. To overcome the reliance on prior knowledge in traditional feature construction methods and improve data distribution stability, this invention first employs the Z-score normalization method to preprocess the raw signal to eliminate sensor dimensional differences. The calculation formula is as follows: ,in The characteristic mean, The standard deviation is used; based on this, the maximum amplitude (MA), which has a high sensitivity to early bearing failure and impact, is extracted as a health indicator; finally, a degradation sequence is constructed. and its increment sequence This provides high-quality input data for subsequent modeling, ensuring that the input signal retains key fault characteristics while effectively suppressing environmental noise interference. Step 2: Construction of a Composite Degradation Model: Existing degradation models often employ linear assumptions or separately handle gradual wear and sudden damage, making it difficult to accurately describe the coupling effect of nonlinear degradation and random shocks in real-world systems. To address this limitation, this invention proposes a composite degradation model that integrates nonlinear time-scale wear and random jump effects. The model expression is as follows: ; The model consists of three core parts: first, a nonlinear drift term, which employs a power-law time scaling function. To characterize the nonlinear trend of degradation rate over time, where The drift coefficient, The term is a nonlinear exponent, which can effectively capture the characteristics of accelerated equipment degradation; the second is the diffusion term, which utilizes Brownian motion. Describes continuous random fluctuations during the degradation process. The diffusion coefficient is represented by the first term; the final term is the random jump term, which utilizes a non-homogeneous Poisson process. The number of simulated impacts, including impact intensity Dynamic changes over time can reflect the increased susceptibility to impacts as equipment ages. Indicates the first The damage amplitude caused by the secondary impact follows a normal distribution. This model captures the nonlinear characteristics of the degradation process by introducing a time scale function and combines a non-homogeneous Poisson process to describe the change of impact incidence over time, effectively solving the problem of insufficient modeling of the coupling effect of nonlinear degradation and dynamic impact in traditional models; Step 3: Two-stage parameter estimation: Since the model contains unobservable random jumps, i.e., latent variables, direct parameter estimation is extremely difficult. This invention designs an improved two-stage estimation strategy. The first stage uses the Expectation-Conditional Maximization (ECM) algorithm to handle latent variables. Specifically, the number of shocks is considered a latent variable; its posterior probability is calculated in the expectation step; and in the conditional maximization step, each conditional expectation is maximized to iteratively update the drift coefficients. diffusion parameters Nonlinear exponent And the impact amplitude parameters; this step, by decomposing the parameter space, effectively avoids the local optima problem caused by directly optimizing high-dimensional non-convex likelihood functions, significantly improving the convergence speed and numerical stability of parameter identification for complex hybrid models. The second stage employs the maximum likelihood estimation (MLE) method. Based on fixing the degradation and impact amplitude parameters obtained in the first stage, it specifically targets the intensity parameters of non-homogeneous Poisson processes. Maximum likelihood estimation is performed to accurately capture the time-varying patterns of shock occurrences by constructing and solving the log-likelihood function. Step 4, Derivation of Remaining Lifetime Distribution: Based on the First Pass Time (FHT) framework, the system failure threshold is defined as... The system failure time is the time when the degradation state first reaches the threshold. For composite degradation models containing random jump terms, this invention employs a combination of approximate analytical and numerical integration methods to solve the RUL distribution: First, the Gaussian approximation of the random jump terms in the model is applied using the central limit theorem, transforming the discrete composite Poisson process into a continuous stochastic process description; Second, the conditional probability density function of the remaining lifetime is derived based on the approximated model. The function is determined by model parameters such as drift coefficient, diffusion coefficient, nonlinear exponent, and impact intensity. Finally, the probability density function is solved by numerical integration to obtain the predicted distribution curve of remaining lifetime and the quantified uncertainty interval.

[0007] Furthermore, the method also includes the following steps: Step 5, Online Update and Performance Validation: Establish a sliding window update mechanism to achieve online adaptive adjustment of model parameters. Set an update cycle and collect new monitoring data. When new data is acquired, add it to the historical dataset and re-trigger the parameter estimation algorithm to update the model parameters in real time. Repeat Step 4 based on the updated parameters to achieve dynamic tracking and prediction. Simultaneously, a multi-index validation system is used to evaluate performance, including absolute error (AE) to measure instantaneous prediction deviation, root mean square error (RMSE) to assess overall accuracy, and cumulative relative accuracy (CRA) to examine trend-following capability. This ensures the model can adapt to dynamic changes during equipment degradation and improves long-term prediction reliability.

[0008] The beneficial effects of this invention are as follows: (1) Solving the problem of nonlinear degradation and impact coupling modeling: By integrating nonlinear time scale functions and non-homogeneous Poisson processes, the interaction between gradual wear and sudden damage is effectively captured, overcoming the prediction bias caused by the simplification assumptions of traditional models.

[0009] (2) Improve the accuracy of parameter estimation under partial observation data: The two-stage expectation condition maximization-maximum likelihood estimation (ECM-MLE) estimation strategy explicitly processes latent variables and achieves robust identification of model parameters under limited data conditions.

[0010] (3) Enhance engineering applicability: By using a sliding window update mechanism and numerical integration method, the computational complexity and prediction accuracy are balanced to meet the real-time monitoring requirements. Attached Figure Description

[0011] Figure 1 This is a flowchart of the overall process framework of the present invention. Detailed Implementation

[0012] The invention will now be further described with reference to the accompanying drawings.

[0013] Reference Figure 1 This invention proposes a method for predicting the remaining useful life (LUV) of mechanical equipment based on nonlinear wear and random jumps. To address the challenges in capturing nonlinear degradation characteristics, insufficient description of coupled random impact effects, and limited parameter estimation accuracy under certain observation conditions, this method addresses these issues. The core innovation lies in constructing a closed-loop mathematical framework encompassing nonlinear degradation modeling, latent variable parameter identification, and probabilistic LUV prediction. This framework effectively combines the power-law time-scale function's ability to characterize accelerated wear with the non-homogeneous Poisson process's ability to describe time-varying impacts, thereby achieving high-precision and high-reliability LUV prediction under complex operating conditions and limited observation data. Figure 1This is a flowchart of the overall process framework of the present invention. First, a degradation sequence reflecting the health status of the equipment is constructed by extracting the maximum amplitude and fusing the data. Second, a composite stochastic process model that integrates nonlinear drift and time-varying jumps is constructed to compensate for the shortcomings of traditional linear models. Subsequently, a two-stage expectation condition maximization-maximum likelihood estimation algorithm is designed to achieve robust identification of parameters in the presence of latent variables. Finally, the remaining lifetime probability distribution is derived based on the first through-time (FHT) to achieve a quantitative assessment of the equipment's operational risk.

[0014] This embodiment of a method for predicting remaining lifetime based on nonlinear wear and random jumps includes the following steps: Step 1: Vibration Signal Acquisition and Health Indicator Construction: Accelerometers installed on key parts of the mechanical equipment are used to collect time-domain vibration signals throughout the equipment's entire lifecycle. Given that raw signals collected in industrial settings often contain background noise and have varying dimensions, and that equipment degradation processes include both gradual wear and sudden impacts, directly using raw data for modeling is challenging. First, the raw vibration data is preprocessed using the Z-score normalization method. By calculating the mean and standard deviation of the raw signals, signals of different magnitudes are mapped to a unified distribution range to eliminate the influence of sensor sensitivity differences and operating condition fluctuations, and to improve the convergence speed of subsequent statistical model parameter estimation. Second, the maximum amplitude of the normalized signal is extracted as the key health indicator (HI). Compared to smoothing indicators such as the root mean square, the maximum amplitude is more sensitive to extreme value changes in the signal, effectively characterizing the energy changes in the equipment from a healthy state to failure, especially keenly capturing the early pulse characteristics caused by random impacts and the later accelerated wear trend. Finally, a degradation state sequence is constructed in chronological order. ,in, For the first The maximum amplitude value at each monitoring time point is used to calculate the first-order difference and obtain the incremental sequence. ,in This incremental sequence eliminates the influence of the cumulative trend and directly reflects the instantaneous rate of change and random fluctuations of the degradation process. It is the core input data for the subsequent construction of the nonlinear Wiener-Poisson composite model and the two-stage parameter estimation.

[0015] Step 2: Construct a composite degradation model that integrates nonlinear wear and time-varying impact. The process is as follows: 2.1 Nonlinear Wiener Process Modeling Based on Power-Law Transformation: To address the inability of traditional linear models to characterize the accelerated degradation characteristics of mechanical equipment (such as bearings and turbine blades) in the later stages of service, this approach introduces a time-scale transformation strategy. Unlike conventional models that assume the degradation path is merely a linear function of time, this embodiment employs a power-law form of the time-scale function. A nonlinear correction is applied to the drift term. The constructed continuous degradation part model is as follows: ; in, This is the initial degradation amount. The drift coefficient, Let be the diffusion coefficient. In this model, the nonlinear exponent... It plays a key role in regulating the curvature of the degradation trajectory: when When the degradation rate monotonically increases with time, it can accurately fit the accelerated performance degradation phenomenon caused by fatigue accumulation in equipment; when When the model degenerates into a linear form, it ensures the model's universality and flexibility for different degradation modes.

[0016] 2.2 Time-Varying Shock Modeling Based on Non-Homogeneous Poisson Process: Given the dynamic evolution of equipment's shock resistance throughout its lifecycle—that is, as equipment ages, the probability of experiencing a failure shock under the same operating conditions gradually increases—this scheme abandons the homogeneous Poisson process (constant shock rate) assumption. Instead, it adopts a non-homogeneous Poisson process. To describe the frequency of impact events, a time-varying intensity function is introduced. Within this framework, up to time... The cumulative expected number of impacts is determined by the cumulative intensity function. The determination is defined as the integral of the instantaneous intensity over the time domain: ; This cumulative intensity function can quantitatively describe... The average density of impacts occurring within the time interval. Simultaneously, the damage amplitude caused by each impact is defined. Follow the mean variance is The independent and identically distributed normal distributions are used to construct random jump terms that can reflect the "aging-vulnerability" mechanism.

[0017] 2.3 Gaussian approximation and continuous transformation of the composite model: Due to the original model constructed above... The inclusion of discrete composite Poisson jump terms results in a complex mixed distribution in its probability density function, making it difficult to directly use for analytical derivation of remaining lifetime. To address this computational challenge, this scheme proposes a two-step Gaussian approximation strategy. First, based on the central limit theorem, the cumulative jump damage is decomposed into a deterministic mean drift component and a random fluctuation component, i.e. ,in The variables are normally distributed with zero mean; furthermore, in order to achieve complete continuity of the model, the non-homogeneous Poisson process is... A further approximation is a continuous process driven by Brownian motion: ; in, Let be a standard normally distributed random variable. Finally, substituting the above approximation into the original model, we obtain an approximate analytical model for subsequent parameter estimation and lifetime prediction: ; This approximate model successfully transforms the discrete counting process into a continuous diffusion process controlled by statistical parameters, while preserving the time-varying characteristics of the impact, making it possible to derive the remaining lifetime probability density function for the first time using time theory.

[0018] Step 3: Parameter estimation based on a two-stage expectation condition maximization-maximum likelihood estimation strategy: Since the composite degradation model constructed in this invention contains a latent variable of "number of random shocks" that cannot be directly observed, and the coupling of nonlinear drift and time-varying jumps makes directly constructing a closed-form likelihood function extremely infeasible. To address this challenge, a two-stage parameter estimation strategy is adopted, decomposing the complex mixed parameter space into two sub-problems for solution.

[0019] Phase 1: Latent variable handling and distribution parameter estimation based on the expected conditional maximization algorithm The primary objective at this stage is to identify the drift coefficients of the degradation process. Diffusion-related parameters, nonlinear exponent and the statistical parameters of the impact amplitude (mean) ,variance Considering that the monitoring data is discretely sampled, this scheme first uses first-order difference to obtain the degradation increment sequence. Due to the presence of random shocks, the degradation increment within any time interval actually follows a Gaussian mixture model, whose mixture components correspond to the events occurring within that interval. Different scenarios of the impact.

[0020] Based on this characteristic, the expected condition maximization algorithm is used for iterative solution: Expectation step: Calculate the posterior probability of the latent variables. Based on the current parameter estimates, calculate the probability at the time of observation. Incremental data Under these conditions, it occurred during this time period. The posterior probability of the second impact .

[0021] Conditional maximization step: Construct the expected log-likelihood function (Q-function) of the complete data using the posterior probabilities obtained in the first step, and decompose it into four sub-optimization problems for alternating updates: (3.1) With fixed variance and nonlinear exponent, the drift coefficient is updated by maximizing the expectation function of the number likelihood function. and the average impact amplitude ; (3.2) Fix the mean class parameters and update the variance of the impact amplitude ; (3.3) Update the scale factor related to the diffusion coefficient This is to adjust the model's adaptability to background noise; (3.4) Update the nonlinear exponent using a one-dimensional search algorithm To accurately match the curvature characteristics of the degenerate trajectory.

[0022] The above process is repeated until the change in the estimated parameter value is less than the preset threshold.

[0023] Phase 2: Optimization of nonhomogeneous intensity parameters based on maximum likelihood estimation algorithm In the first stage, convergent degradation and magnitude parameters are obtained. Afterwards, the only remaining unknowns in the model are the intensity parameters of the non-homogeneous Poisson process. At this point, construct the marginal likelihood function for the mild parameter: ; In this likelihood function, The cutoff threshold indicating the number of impacts; This indicates that it occurred within the assumed current time period. Secondary impact, and the parameters of the first stage are known. Under these conditions, observation data The conditional probability density; This represents the probability of impact occurrence determined by the integral intensity function of a non-homogeneous Poisson process; its value is directly influenced by the intensity parameter. Control. Because this function eliminates hidden variables. To eliminate interference from other parameters, the quasi-Newton method can be used to quickly find the value that maximizes the likelihood function. This enables accurate identification of time-varying impact intensity.

[0024] Step 4, Derivation of Remaining Lifetime Probability Distribution: The remaining lifetime of the system is defined based on the first pass time, i.e., the system's first degradation state reaching the preset failure threshold. The time frame is considered. Given that the model contains skip terms, making analytical solutions difficult to obtain, this invention employs a combination of approximate analytical and numerical integration methods. First, the skip terms are approximated using Gaussian approximation, and the central limit theorem is used to approximate the composite Poisson process as a continuous process including drift and diffusion. Second, the conditional probability density function of the remaining lifetime is derived based on the approximated model. This function describes the remaining lifetime under known current monitoring conditions. and current degradation status In the event that the device experiences a certain duration in the future The probability density of post-failure can be approximated as follows: ; in, Represents a standard normal random variable The expected value. The intermediate parameters in the above formula are expressed as follows: intermediate variables and It mainly reflects the statistical characteristics and rate of change of random jump terms: ; Drift and diffusion related terms It integrates the effects of nonlinear wear trends, current degradation state, and random impacts: ; ; ; Approximate term of jump process moment and , represent the approximate cumulative impact intensity and its derivative within the prediction interval, respectively: ; ; in, This is the cumulative impact intensity function. is the instantaneous intensity function of a non-homogeneous Poisson process.

[0025] Finally, numerical integration methods are used to apply the above method to the expected term. The probability density function is used to calculate the predicted distribution curve, expected value, and confidence interval of the remaining lifetime. This method comprehensively considers the current degradation state, future nonlinear wear trends, and the cumulative effect of random shocks, quantifying the uncertainty of the prediction.

[0026] Step 5, Online Update and Performance Verification: To ensure the model remains adaptable to time-varying operating conditions during long-term equipment operation and to verify the reliability of prediction results, an online update and index verification mechanism is established. First, an online parameter update framework based on a sliding window is constructed. After the equipment enters the online monitoring phase, whenever new vibration data is collected and health indicators are extracted, they are added to the historical dataset, triggering the two-stage algorithm in Step 3 to update the model parameters. The derivation process in Step 4 is repeated using the updated parameters to calibrate the remaining life prediction results. Second, at the prediction result output, the system generates a RUL probability density surface that evolves over time in real time. As monitoring data accumulates, this surface typically shows a gradually narrowing distribution and a peak value approaching the actual failure time, indicating a reduction in prediction uncertainty. Finally, a multi-dimensional quantitative index system is used to verify the prediction performance. Through the above closed-loop mechanism, the robustness and accuracy of the method in practical industrial applications are ensured.

[0027] The embodiments described in this specification are merely examples of implementations of the inventive concept and are for illustrative purposes only. The scope of protection of this invention should not be considered limited to the specific forms described in these embodiments; rather, it extends to equivalent technical means conceived by those skilled in the art based on the inventive concept.

Claims

1. A method for predicting remaining lifetime based on nonlinear wear and random jumps, characterized in that, The method includes the following steps: Step 1: Vibration signal acquisition and health index construction: Vibration signals are acquired using accelerometers installed on mechanical equipment. First, the raw signals are preprocessed using the Z-score normalization method, and the maximum amplitude MA is extracted as a health index. Degradation sequences and their incremental sequences are constructed to provide high-quality input data for subsequent modeling. Step 2, Construction of Composite Degradation Model: A composite degradation model integrating nonlinear time-scale wear and random jump effect is proposed. By introducing a time-scale function, the nonlinear characteristics of the degradation process are captured, and the non-homogeneous Poisson process is combined to describe the law of change of impact rate over time. Step 3, Two-stage parameter estimation: In the first stage, the expected conditional maximization algorithm is used to process latent variables, treating the number of shocks as latent variables. In the expected step, its posterior probability is calculated. In the conditional maximization step, each conditional expectation is maximized to iteratively update the drift coefficient. diffusion parameters Nonlinear exponent In addition to the impact amplitude parameters; the second stage employs the maximum likelihood estimation method, which, based on the degradation and impact amplitude parameters obtained in the first stage, targets the intensity parameters of the non-homogeneous Poisson process. Maximum likelihood estimation is performed to accurately capture the time-varying patterns of shock occurrences by constructing and solving the log-likelihood function. Step 4, Derivation of Remaining Lifetime Distribution: Based on the first pass time frame, the system failure threshold is defined as... The system failure time is the time when the degradation state first reaches the threshold. For the composite degradation model containing random jump terms, the RUL distribution is solved by a combination of approximate analysis and numerical integration to obtain the predicted distribution curve of the remaining lifetime and the quantified uncertainty interval.

2. The remaining lifetime prediction method based on nonlinear wear and random jumps as described in claim 1, characterized in that, The method further includes the following steps: Step 5, Online Update and Performance Verification: Establish a sliding window update mechanism to achieve online adaptive adjustment of model parameters. Set the update cycle and collect new monitoring data. When new data is acquired, add it to the historical dataset and re-trigger the parameter estimation algorithm to update the model parameters in real time. Repeat Step 4 based on the updated parameters to achieve dynamic tracking and prediction. At the same time, adopt a multi-index verification system to evaluate performance, including the absolute error that measures the instantaneous prediction deviation, the root mean square error that evaluates the overall accuracy, and the cumulative relative accuracy that examines the trend tracking ability, to ensure that the model can adapt to the dynamic changes in the equipment degradation process.

3. The remaining lifetime prediction method based on nonlinear wear and random jumps as described in claim 1 or 2, characterized in that, In step 1, the Z-score normalization method is used to preprocess the original signal to eliminate sensor dimension differences. The calculation formula is as follows: ,in The characteristic mean, The standard deviation is denoted as .

4. The remaining lifetime prediction method based on nonlinear wear and random jumps as described in claim 3, characterized in that, In step 1, a degenerate state sequence is constructed in chronological order. ,in, For the first The maximum amplitude value at each monitoring time point is used to calculate the first-order difference and obtain the incremental sequence. ,in This incremental sequence eliminates the influence of cumulative trends and directly reflects the instantaneous rate of change and random fluctuations of the degradation process.

5. The remaining lifetime prediction method based on nonlinear wear and random jumps as described in claim 1 or 2, characterized in that, The process of step 2 is as follows: 2.1 Modeling of Nonlinear Wiener Processes Based on Power-Law Transformation: A time-scale transformation strategy is introduced, employing a power-law form of the time-scale function. After applying nonlinear corrections to the drift term, the continuously degenerate partial model is constructed as follows: ； in, This is the initial degradation amount. The drift coefficient, Let be the diffusion coefficient, and in this model, the nonlinear exponent is... It plays a key role in regulating the curvature of the degradation trajectory: when When the degradation rate monotonically increases with time, it can accurately fit the accelerated performance degradation phenomenon caused by fatigue accumulation in equipment; when When the model degenerates into a linear form, the model's universality and flexibility for different degradation modes are guaranteed. 2.2 Time-varying impact modeling based on non-homogeneous Poisson processes: A non-homogeneous Poisson process is used. To describe the frequency of impact events, a time-varying intensity function is introduced. up to the time The cumulative expected number of impacts is determined by the cumulative intensity function. The determination is defined as the integral of the instantaneous intensity over the time domain: ； Set the damage amplitude for each impact. Follow the mean variance is The independent and identically distributed normal distributions are used to construct random jump terms that can reflect the "aging-vulnerability" mechanism; 2.3 Gaussian Approximation and Continuity Processing of the Composite Model: A two-step Gaussian approximation strategy is proposed. First, based on the central limit theorem, the cumulative jump damage is decomposed into a deterministic mean drift component and a random fluctuation component, i.e. ,in For a zero-mean normal variable; furthermore, for a non-homogeneous Poisson process It can be approximated as a continuous process driven by Brownian motion: ； in, Assuming the variables are standard normal random variables, the above approximation is ultimately substituted into the original model to obtain an approximate analytical model for subsequent parameter estimation and lifetime prediction: 。 6. The remaining lifetime prediction method based on nonlinear wear and random jumps as described in claim 1 or 2, characterized in that, In step 3, in the first stage, based on the latent variable processing and distribution parameter estimation of the expected conditional maximization algorithm, the degradation increment sequence is first obtained using the first-order difference. The expected condition maximization algorithm is used for iterative solution: Expectation step: Calculate the posterior probability of the latent variables. Based on the current parameter estimates, calculate the probability at the time of observation. Incremental data Under these conditions, it occurred during this time period. The posterior probability of the second impact ; Conditional maximization step: Construct the expected log-likelihood function of the complete data using the posterior probabilities obtained in the first step, and decompose it into four sub-optimization problems for alternating updates: (3.1) With fixed variance and nonlinear exponent, the drift coefficient is updated by maximizing the expectation function of the number likelihood function. and the average impact amplitude ; (3.2) Fix the mean class parameters and update the variance of the impact amplitude ; (3.3) Update the scale factor related to the diffusion coefficient This is to adjust the model's adaptability to background noise; (3.4) Update the nonlinear exponent using a one-dimensional search algorithm To accurately match the curvature features of the degenerate trajectory; The above process is repeated until the change in the estimated parameter value is less than the preset threshold.

7. The remaining lifetime prediction method based on nonlinear wear and random jumps as described in claim 6, characterized in that, In step 3, during the second stage, the non-homogeneous intensity parameter optimization is performed based on the maximum likelihood estimation algorithm, and the convergent degradation and magnitude parameters are obtained in the first stage. Afterwards, the only remaining unknowns in the model are the intensity parameters of the non-homogeneous Poisson process. Construct the marginal likelihood function with respect to the light parameters: ； In this likelihood function, The cutoff threshold indicating the number of impacts; This indicates that it occurred within the assumed current time period. Secondary impact, and the parameters of the first stage are known. Under these conditions, observation data The conditional probability density; This represents the probability of impact occurrence determined by the integral intensity function of a non-homogeneous Poisson process; its value is directly influenced by the intensity parameter. Control, because this function eliminates hidden variables To eliminate interference from other parameters, the quasi-Newton method can be used to quickly find the value that maximizes the likelihood function. This enables accurate identification of time-varying impact intensity.

8. The remaining lifetime prediction method based on nonlinear wear and random jumps as described in claim 1 or 2, characterized in that, In step 4, the remaining lifetime of the system is defined based on the first time the system's degradation state first reaches the preset failure threshold. The time frame is determined using a combination of approximate analytical and numerical integration methods. First, the skip terms are approximated using Gaussian approximation, and the central limit theorem is used to approximate the composite Poisson process as a continuous process including drift and diffusion. Second, based on the approximated model, the conditional probability density function of the remaining lifetime is derived. This function describes the remaining lifetime under known current monitoring conditions. and current degradation status In the event that the device experiences a certain duration in the future The probability density of post-failure can be approximated as follows: ； in, Represents a standard normal random variable The expected value, and the intermediate parameters in the above formula are expressed as follows: intermediate variables and This reflects the statistical characteristics and rate of change of random jump terms: ； Drift and diffusion related terms It integrates the effects of nonlinear wear trends, current degradation state, and random impacts: ； ； ； Approximate term of jump process moment and , represent the approximate cumulative impact intensity and its derivative within the prediction interval, respectively: ； ； in, This is the cumulative impact intensity function. For a non-homogeneous Poisson process, the instantaneous intensity function is given. Finally, numerical integration methods are used to investigate the inclusion of the expectation term. The probability density function is used to calculate the predicted distribution curve, expected value, and confidence interval of the remaining lifespan.

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