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Multivariable stochastic degradation system (MSDS) is quite common in industries such as blast furnace ironmaking, vehicle transportation, and aerospace manufacturing. Large‐scale complex equipments may be affected by multiple factors, resulting in not just a single deteriorating performance characteristic. It is difficult to handle unknown failure structures of practical systems by using traditional univariate degradation modeling methods. A novel health index (HI) is constructed to quantitatively analyze the health state for the overall system. Considering the interaction between internal reactions and external environments, the fractional Brownian motion (FBM), a typical non‐Markovian diffusion process, is added for the purpose of reflecting stochastic uncertainties and memory effects. Based on the wavelet estimators and the maximum likelihood estimation (MLE) algorithm, multi‐sensor observations of degradation variables are analyzed simultaneously to identify model parameters. A closed‐form distribution of system‐level remaining useful life (RUL) is obtained with a mild two‐layer approximation. Relevant case studies are then handled that adequately demonstrate the effectiveness and the practical utility of the proposed method. [ABSTRACT FROM AUTHOR]

Degradation processes of practical chemical engineering systems are difficult to model accurately because of complicated nonlinearities, non‐stationarities, and non‐Markovian properties. Traditional prognostics techniques tend to neglect the multi‐mode switching issue, and therefore cannot be used for predicting the remaining useful life (RUL) of a piece of long‐life equipment, especially when it is continuously operated under varying modes. Specifically, the stationarity of differential data also plays an important role in depicting the evolutionary trend, and further affects the extrapolation procedure for RUL prediction. In this paper, we construct a multi‐mode degradation model with regard to fractional diffusion processes by considering both stationary and non‐stationary increments. The drift term is represented as a time‐related nonlinear function, while the diffusion term is driven by fractional Brownian motion (FBM) or sub‐fractional Brownian motion (sub‐FBM), according to the results of the stationary test. Based on the monitored data, the model is identified by combining change‐point detection and parameter estimation. The closed‐form distribution of RUL is then derived through a weak convergence transformation. A numerical example and a case study of a large blast furnace are provided to evaluate the performance of the proposed prognostics framework. [ABSTRACT FROM AUTHOR]

Accurate remaining useful life (RUL) prediction is of great importance for predictive maintenance. With the recent advancements in sensor technology and artificial intelligence, the data-driven approaches to RUL prediction of industrial equipment have gained a lot of attention. However, past researches have not adequately considered the variety of degradation rates and the accumulated information in degradation processes. To deal with this problem, a novel two-stage machine learning approach of RUL prediction is proposed in this paper. A set of nonlinear health indicator functions are constructed to guide the training process of a long short-term memory learner of degradation processes, then a time delay neural network is utilized for RUL prediction. The superiority of the proposed approach in terms of prediction accuracy and conservativeness is demonstrated by a case study of rolling element bearing dataset. • Health indicator functions are constructed by considering various degradation rates. • The health indicator is utilized to guide the prediction modeling. • Long short-term memory learners are established to achieve the time scale alignment. • The time delay mechanism is introduced to fuse past feature information. • The approach has an advantage in accuracy and conservativeness. [ABSTRACT FROM AUTHOR]

It is widely noted in the literature that the degradation should be simplified into a memoryless Markovian process for the purpose of predicting the remaining useful life (RUL). However, there actually exists the long-term dependency in the degradation processes of some industrial systems, including electromechanical equipments, oil tankers, and large blast furnaces. This implies the new degradation state depends not only on the current state, but also on the historical states. Such dynamic systems cannot be accurately described by traditional Markovian models. Here we present an improved non-Markovian degradation model with both the long-term dependency and the item-to-item uncertainty. As a typical non-stationary process with dependent increments, fractional Brownian motion (FBM) is utilized to simulate the fractal diffusion of practical degradations. The uncertainty among multiple items can be represented by a random variable of the drift. Based on this model, the unknown parameters are estimated through the maximum likelihood (ML) algorithm, while a closed-form solution to the RUL distribution is further derived using a weak convergence theorem. The practicability of the proposed model is fully verified by two real-world examples. The results demonstrate that the proposed method can effectively reduce the prediction error. [ABSTRACT FROM AUTHOR]

For data-driven remaining useful life (RUL) prediction, an appropriate degradation model is critically important to achieve accurate prediction. The degradation processes in some practical systems are not only related to the age but also related to the current degradation state, and the degradation processes may be non-Markovian processes. However, most existing stochastic process-based degradation models only depend on the age, and simply assume that the increments are independent. In this paper, an age- and state-dependent degradation model with long-range dependence is developed, which is more general than most of the existing models based on either Brownian motions (BMs) or fractional Brownian motions (FBMs). The Radon-Nikodym derivative is utilized to obtain a likelihood ratio function of unknown parameters, and the estimates are obtained by maximizing the likelihood ratio function. A weak convergence theorem is introduced to approximate the FBM by a BM with a time-varying coefficient. A time-space transformation is further utilized to obtain an approximate explicit solution of the RUL. At last, numerical simulations and two real case studies of blast furnace walls and ball bearings are adopted to verify the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]