Reliability Modeling Method for Constant Stress Accelerated Degradation Based on the Generalized Wiener Process.

Although Wiener process models with the consideration of uncertainties, which are nonlinearity, random effects, and measurement errors, have been developed for lifetime prediction in the accelerated degradation test (ADT), they fail to describe the real degradation process because these models assume that the drift parameter correlates with the applied stress, while the diffusion parameter is constant. This paper put forward a nonlinear doubly Wiener constant-stress accelerated degradation model, where both diffusion and drift parameters were compatible with the applied stress according to the acceleration factor constant principle. When degradation data were available, we obtained the unknown parameters by applying a maximum likelihood estimation (MLE) algorithm in the constant-stress ADT (CSADT) model taking uncertainties into account. In addition, the proposed model’s effectiveness was validated through an illustrative example, and an application to the traveling wave tube (TWT) was carried out to demonstrate the superiority of our model in practical applications.

A multi-objective optimization method for constant stress accelerated degradation test is proposed in order to solve the problem of different or even conflicted test configuration under different optimization objectives. The inverse Gaussian process is used as a degradation model, and the unknown parameters are solved by maximum likelihood estimation. The two optimization criteria of the maximum determinant of the information matrix and the minimum asymptotic variance of P-quantile are considered. The improved multi-objective particle swarm optimization algorithm is proposed to search test optimal configuration, and the Pareto solution set for dual-objectives is obtained. Finally, the effectiveness of the method is illustrated by a group of examples of electrical connectors. Compared with the single-objective optimization design, the proposed method is more reasonable and convenient for test configuration. The performance index of the test function indicates that the optimal algorithm we proposed has some obvious advantages over the NSGA-II in diversity and convergence of the Pareto solutions and it is significant in guiding engineering practice.

This paper proposes a new life prediction method using time series and grey theory to predict product life based on Constant-Stress Accelerated Degradation Testing (CSADT) data. CSADT degradation data is modeled using time series method and predicted using grey theory. A four electric stress levels CSADT of miniature bulb is conducted to verify the proposed method. A comparison among life prediction by the proposed method, traditional methods, and real life of miniature bulb is processed. The result shows that life prediction by the proposed method is more accurate than traditional methods.

Degradation data analysis based on a generalized Wiener process subject to measurement error

Constant stress accelerated degradation tests (CSADT) are widely used in life perdition for highly reliable products to infer the lifetime distribution under operating conditions. Optimal design of an CSADT can improve life prediction accuracy and reduce test costs significantly. In the literature of CSADT design, most approaches focus on how to determine the sample allocation scheme, inspection frequency and test duration, but the issue of how to optimize the stress levels is seldom considered. In this work, we propose a novel method to optimize the CSADT considering both stress levels selection and samples allocation. First, an accelerated degradation model based on the Wiener process is used to model the degradation data. Next, under the constraint of sample size, a local-search based iterative algorithm is proposed to optimize parameters including stress levels and sample number under each level so as to obtain an accurate estimate of the distribution statistics. Finally, a case study of lithium-ion batteries is presented to validate the proposed method.

Most machine learning-based remaining useful life (RUL) prediction methods only yield point predictions, and their “black-box” nature results in low interpretability. Stochastic process-based modeling can predict RUL probability density function (PDF), yet it often suffers from inaccurate modeling and failure to fully utilize historical degradation data of the same equipment type. To overcome these limitations, this paper integrates the two approaches and proposes an Attention-Gaussian-LSTM-Wiener (AG-LSTM-Wiener)-based RUL prediction method, enabling dynamic weighted fusion of predicted PDFs. An AG-LSTM-Wiener model with a two-branch structure is constructed. Health indicator (HI) is fed into the corresponding branch models to generate two different PDF curves. Decision blocks are employed to estimate RUL, from which weights are derived to achieve dynamic weighted fusion of the PDFs. Experiments on the CMPASS turbofan engine degradation dataset validate the proposed method’s effectiveness. Results demonstrate that the proposed method not only prevents PDF curve distortion but also improves the prediction accuracy compared with other methods. With the root mean squared error (RMSE) and Score reduced by 32.8% and 46.1% on average, and the mean squared error of PDF ( $\mathrm{MSE}_{\mathrm{PDF}} $ MSE PDF ) improved by 99.3% compared to AG-LSTM, which exhibits the best performance among the contrast methods.

Conducting accurate reliability estimation plays an important role for solid lubricated bearings, because they are widely used in highly reliable space applications. This paper proposes a general Wiener process to describe the degradation process for solid lubricated bearings. The performance indicator for solid lubricated bearings is a fusion indicator from several time domain statistics of vibration signal during operation. Mahalanobis Distance (MD) is utilized to fuse these time-domain statistics indicators into one indicator representing the degradation process. Two different time scale functions in drift term and fluctuation term of Wiener process are used to capture the nonlinearity characteristics of degradation process. Bayesian MCMC method is used to estimate all the unknown parameters in the proposed degradation model. Degradation data from experiment is used to validate the model. Results show that general Wiener process degradation model is fit well for the degradation data.KeywordsSolid lubricated bearingsMahalanobis DistanceWiener processReliability estimation

Remaining useful life (RUL) prediction using deep learning networks primarily produces point estimates of RUL, but capturing the inherent uncertainty in RUL prediction is difficult. The use of the stochastic process approach can reflect the uncertainty in RUL predictions. However, the amount of data generated during equipment operation cannot be effectively utilized. This paper aims to propose an adaptive RUL prediction method tailored for extensive datasets and prediction uncertainty, effectively harnessing the strengths of deep learning methods in managing massive data and stochastic process techniques in quantifying uncertainties. RUL prediction method, based on stacked autoencoder (SAE) combined with Generalized Wiener Process, employs SAE to extract profound underlying features from the monitoring signals. Principal component analysis (PCA) is then used to select highly trending features as inputs. The output of PCA accurately reflects health status. A Generalized Wiener Process is used to construct a model for the evolution of the health indicators. The estimation values for the model parameters are determined using the Maximum Likelihood Estimation method. Furthermore, an adaptive update is performed based on Bayesian theory. Utilizing the sense of the first hitting time concept, the Probability Density Function for RUL prediction is derived accurately. Finally, the effectiveness and superiority of the proposed method is verified using numerical simulations and experimental studies of bearing degradation data. The method improves the life prediction accuracy while reducing the prediction uncertainty.

A wiener-based remaining useful life prediction method with multiple degradation patterns

Accelerated degradation test (ADT) has been widely used to assess highly reliable products’ lifetime. To conduct an ADT, an appropriate degradation model and test plan should be determined in advance. Although many historical studies have proposed quite a few models, there is still room for improvement. Hence we propose a Nonlinear Generalized Wiener Process (NGWP) model with consideration of the effects of stress level, product-to-product variability, and measurement errors for a higher estimation accuracy and a wider range of use. Then under the constraints of sample size, test duration, and test cost, the plans of constant-stress ADT (CSADT) with multiple stress levels based on the NGWP are designed by minimizing the asymptotic variance of the reliability estimation of the products under normal operation conditions. An optimization algorithm is developed to determine the optimal stress levels, the number of units allocated to each level, inspection frequency, and measurement times simultaneously. In addition, a comparison based on degradation data of LEDs is made to show better goodness-of-fit of the NGWP than that of other models. Finally, optimal two-level and three-level CSADT plans under various constraints and a detailed sensitivity analysis are demonstrated through examples in this paper.

Degradation dynamics modeling and health prognosis play extremely important roles in system prognostics and health management. Wiener process-based degradation models and remaining useful life (RUL) prediction methods have the advantage of high flexibility and efficiency, with features such as Brownian motion with drift and scale parameters. They can also quantify prediction uncertainty through inverse Gaussian distribution. However, prior studies use offline-identified model parameters, which can result in difficulties in both model adaptability and health prognosis. To improve the performance of Wiener process models, this article proposes a new data-driven Brownian motion model that utilizes the adaptive extended Kalman filter (AEKF) parameter identification method. The proposed model can update model parameters online and adapt to uncertain degradation operations. This data-driven method has the flexibility and efficiency of Brownian motion models but avoids their shortcomings in model adaptability and health prognosis. The model parameters and drift parameter are online estimated based on AEKF using limited historical system measurements. The effectiveness of the proposed data-driven framework in degradation modeling and RUL prediction is evaluated through simulations and experimental results on lithium-ion battery degradation data. The results show that the proposed approach has significant accuracy and robustness for both model adaptability and RUL prediction.

The lifetime information of highly reliable products is usually very difficult to be obtained within an affordable amount experimental time through using traditional life testing methods. Because the benefit of lower manufacturing cost for many highly reliable products, manufacturers can offer more highly reliable products for implementing an accelerated degradation test under constant-stress loading conditions. In this chapter, lumen degradation measurements of high power light emitting diodes based on their cumulative damage are studied. The measurements are collected by the constant-stress accelerated degradation testing method with the stress loadings of ambient temperature and drive current. Each cumulative damage process is model by a Wiener process, of which drift parameter depends on the two stress loadings. General statistical inference of the model parameters and percentiles of the lifetime distribution of light emitting diodes is addressed, and approximate lower confidence bounds of the lifetime percentiles are evaluated using the Fisher information of maximum likelihood estimators. Based on the obtained maximum likelihood estimates of the model parameters, an optimal strategy for implementing a constant-stress accelerated degradation test is established. The optimal strategy can reach a compromised decision between the experimental budget and estimation precision of reliability analysis. An algorithm is provided to search for the proposed optimal strategy. The proposed method is illustrated with an example of light emitting diodes.

Solid-state lasers have been widely used in machinery and electronics industry, and the input power is the main adjustable variable that affects the lifetime of solid-state lasers. This paper proposes a reliability-based usage strategy optimization for lifetime maximization of solid-state lasers. Firstly, considering the randomness and volatility of the quality characteristics, an accelerated degradation model based on the Wiener process is investigated, and the effect of input power is established by the Inverse Power Law model. Secondly, the unknown parameters in the accelerated model are estimated through maximum likelihood estimation (MLE). Thirdly, with the given number of stress levels n, a usage strategy optimization of n-stage stress levels application is proposed to maximize the lifetime of solid-state lasers. Finally, the implementation of the proposed method is illustrated by a real case study of constant stress accelerated degradation test (CSADT) of solid-state lasers.

In accelerated degradation testing (ADT), test data from higher than normal stress conditions are used to find stochastic models of degradation, e.g., Wiener process, Gamma process, and inverse Gaussian process models. In general, the selection of the degradation model is made with reference to one specific product and no consideration is given to model uncertainty. In this paper, we address this issue and apply the Bayesian model averaging (BMA) method to constant stress ADT. For illustration, stress relaxation ADT data are analyzed. We also make a simulation study to compare the $s\hbox{-}$ credibility intervals for single model and BMA. The results show that degradation model uncertainty has significant effects on the $p\hbox{-}$ quantile lifetime at the use conditions, especially for extreme quantiles. The BMA can well capture this uncertainty and compute compromise $s\hbox{-}$ credibility intervals with the highest coverage probability at each quantile.

There is a problem of poor predictive performance when predicting the remaining service life of products. Therefore, this paper proposes a finite data product remaining service life prediction method based on Gaussian stochastic processes. Analyze the types of product failure and degradation under limited data, and determine the factors affecting the degradation performance of product life through constant stress accelerated degradation tests, step stress accelerated degradation tests, and sequential stress accelerated aging tests; using the Wiener process to analyze the performance degradation characteristics of products, setting product failure thresholds, defining the remaining life of the product based on the degradation process, and using equal interval partitioning methods to determine the product health index, and clarifying the product failure process under limited data; by calculating the mathematical expected value, the numerical characteristics of the remaining life of the product are defined. Variance and moments are used to determine the predicted second-order central moment and origin moment. Based on the monotonic increasing characteristics of the inverse Gaussian process, the probability distribution of the random variable of product failure is determined after the Gaussian process. Under limited data, the actual working time of the product and the degradation amount at the time scale are clarified, and a preset threshold is set for the degradation amount. Build a residual life prediction model for product degradation and output the prediction results. The experimental results show that this method can accurately predict the remaining service life of the product and has good predictive performance.