A Data-Driven Modeling Method for Stochastic Nonlinear Degradation Process With Application to RUL Estimation
Abstract : This article proposes a novel modeling method for the stochastic nonlinear degradation process by using the relevance vector machine (RVM), which can describe the nonlinearity of degradation process more flexibly and accurately. Compared with the existing methods, where degradation processes are modeled as the Wiener process with a nonlinear drift function formulized as the power law or exponential law, this kind of modeling method can characterize degradation processes with more nonlinear behavior. Instead of modeling the drift coefficient of the Wiener process directly, the weighted combination of basis functions is utilized to express the increment of the Wiener process and the parameters are calculated by a sparse Bayesian learning algorithm. Based on the proposed model, a numerical approximation formula for the probability density function (PDF) of the remaining useful life (RUL) is derived. Finally, comparison studies, including a numerical simulation and a practical case, are provided to demonstrate the effectiveness and the accuracy of the proposed methods for RUL estimation.
? In most cases, the failure data from machines are not available, or only a few failure cases exist due to regular maintenance and the infrequent incidents.
? Most existing DL works will face substantial performance losses if the data distributions of training and test sets are not equal.
? Most existing machine learning algorithms result in a substantial performance loss because of the violation of the i.i.d. condition even with the same operating condition.
? We compare the performance of the proposed scheme to existing Bayesian approaches for predicting the RUL value of the experimental data of the PHM data challenge problem.
? This type of degradation naturally brings two interesting problems, that is, how to model the degradations and how to predict their RULs.
? Some important and interesting problems to be further studied, along with future directions for FBM-based prediction.
? To solve this problem, the authors used a measure transformation to transform the original degradation process into an independent increment process.
? In general, this problem can be addressed by filtering methods based on the state-space equations of the degradations.
? In addition, for complex systems, how to integrate information collected from multiple sensors, identify the hidden degradation state, and predict the RUL are also challenging problems.
• In the offline phase, the proposed method builds different health indicators representing degradation as a function of time using unsupervised variable selection, PCA, and trend extraction.
• The proposed CNN consists of multiple convolution and pooling layers to extract features and a logistic regression to convert the output features into a health indicator.
• The proposed prognostics integrate machine learning and mathematical degradation model of the time series data of the health indicator.
• The proposed feature importance ranking and PCA computes the health indicator based on the time series data in the online phase.
• However, our proposed scheme significantly reduces the computation complexity while guaranteeing the robustness against the possible uncertainty.
? Assuming that the concerned product has p-dimensional performance characteristics and the degradation of each performance characteristic is governed by model, the RUL is defined as the FPT when at least one performance characteristic reaches its threshold.
? In fact, as stated in the current BM-based studies, the online update parameters can improve the accuracy of the model as the number of observations increases, thereby improving the predictive performance of the RUL.
? The model usually includes a drift term and a standard BM with a diffusion coefficient and is also a Markov process with independent increments.
? The basic linear model has a constant drift coefficient and a BM with a constant diffusion coefficient.
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