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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]

Bacteria in rural sewage collection systems have the important influences on operation and maintenance risks, such as sedimentation blockage and harmful gas accumulation, and pollutant pre-treatment ability. It is necessary to analyze and interpret the influence on bacterial communities caused by the location (sewage, biofilms, and deposits), season (winter and spring, summer and autumn), and system type (sewers and ditches) to better understand the bacterial characteristics in rural sewage collection systems. To achieve the above purpose, 96 samples obtained from practical rural sewage collection systems in eight villages were analyzed by 16S rRNA whole region sequencing methods. The results indicate that locations and seasons caused significant influences on the overall bacterial communities, which were mainly affected by temperature, sewage quality and bacterial survival preference, and 13 genera of sulfate-reducing bacteria (SRB), 2 genera of ammonia-oxidizing bacteria (AOB), 2 genera of nitrite-oxidizing bacteria (NOB), and 9 genera of water-related pathogenic bacteria (WPB) were detected in rural sewage collection systems. SRB, AOB, NOB, and WPB tended to inhabit in biofilms or deposits rather than in sewage. The total relative abundance of SRB in summer and autumn (∼2.19%) was higher than in winter and spring (∼0.41%), and the WPB distribution in different seasons showed significant distinction. Additionally, some of SRB, AOB, NOB, and WPB also showed significant differences in sewers and ditches. Overall, this study provided a deeper understanding of bacteria in rural sewage collection systems and could further provide the basic parameter for the operation and maintenance risk control. • Locations and seasons caused significant influences on bacterial communities. • SRB, AOB, NOB, and WPB tended to inhabit in biofilms or deposits. • Total abundance of SRB in summer and autumn was higher than in winter and spring. • Some of SRB, AOB, NOB, and WPB showed significant differences in sewers and ditches. [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]