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Journal ArticleDOI: 10.1109/TIM.2021.3063749

Generalized Cauchy Degradation Model With Long-Range Dependence and Maximum Lyapunov Exponent for Remaining Useful Life

04 Mar 2021-IEEE Transactions on Instrumentation and Measurement (IEEE)-Vol. 70, pp 1-12
Abstract: A new long-range-dependent (LRD) degradation model is described based on the generalized Cauchy (GC) process. The GC process is a two-parameter model, which describes local irregularities and global correlation characteristics of the data time sequence by the Hurst parameter $H$ and fractal dimension $D$ . Compared with the fractional Brownian motion (fBm) with linear relationship $H=2-D$ , two parameters of the GC process are independent of each other. The GC process is taken as the diffusion term to describe the LRD characteristics and uncertainty of the degradation process, and the degradation model is established in the form of power law and exponential drift. The Gaussian assumption of the GC process allows us to use linear system theory and statistics to derive its incremental distribution for obtaining the difference iteration form of the GC degradation model. Besides, the dimensionless factors, the principal component analysis (PCA), and the iterative method are used to eliminate the interference of noise on the degradation data. Then, the maximum prediction range of the GC degradation model in the degradation sequence is obtained by the reciprocal of the maximum Lyapunov exponent. Finally, the GC degradation model was applied for prediction of the remaining useful life (RUL) of rolling bearing. The validity of the GC degradation model is verified.

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Topics: Fractional Brownian motion (54%), Hurst exponent (53%), Lyapunov exponent (52%) ... read more
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9 results found


Journal ArticleDOI: 10.1016/J.YMSSP.2021.107974
Shouwu Duan1, Wanqing Song1, Enrico Zio2, Enrico Zio3  +2 moreInstitutions (4)
Abstract: Some equipment degradation processes have long-range dependence (LRD) and multi-modes characteristics. The multi-modes are caused by changes of the external environment, the operating conditions and the loads throughout the lifetime of the equipment. In the present paper, a multi-modal Fractional Levy Stable Motion (FLSM) degradation model is developed to predict the product technical life or remaining useful life (RUL) of equipment. The advantage of FLSM lies in its LRD characteristics and its ability to describe multiple stochastic distributions as the tail parameter α changes. Multi-modes, switching points and modal categories are identified by change point detection and clustering algorithms, and a Markov state transition matrix describes the modes switching law. The probability density function (PDF) of RUL is established by Monte Carlo Simulation. The effectiveness of the prediction model is verified by a practical example of a blast furnace.

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Topics: Markov chain (53%), Monte Carlo method (50%)

5 Citations


Journal ArticleDOI: 10.1016/J.ISATRA.2021.05.002
He Liu1, Wanqing Song1, Enrico Zio2, Enrico Zio3  +1 moreInstitutions (4)
10 May 2021-Isa Transactions
Abstract: The reliability prediction of gearbox is a complex and challenging topic. The purpose of this research is to propose a hybrid difference iterative forecasting model to forecast reliability of the gearbox. On this score, a hybrid model based on the fractional Levy stable motion (fLsm), the Grey Model (GM) and the metabolism method is proposed. To solve the problem of insensitivity to weak faults inside the gearbox, we use feature extraction method to reveal the gearbox degradation. Then, the least square theory is used to separate the degradation sequence in the gearbox into a deterministic term with monotonicity and a stochastic term with Long-Range Dependence (LRD). Next, the fLsm with LRD and non-Gaussian is used to forecast the stochastic term, the deterministic term is simulated by the GM, and the hybrid forecasting model is used to modify the prediction results. The metabolism method is used to update the degradation sequence and to forecast longer-term trend. Finally, a case demonstrated that superiority and generality of the hybrid forecasting model.

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3 Citations


Journal ArticleDOI: 10.1016/J.JVCIR.2021.103199
Fangzheng Tian1, Yongbin Gao1, Zhijun Fang1, Gu Jia1  +1 moreInstitutions (1)
Abstract: Dense 3D reconstruction is required for robots to safely navigate or perform advanced tasks. The accurate depth information of the image and its pose are the basis of 3D reconstruction. The resolution of depth maps obtained by LIDAR and RGB-D cameras is limited, and traditional pose calculation methods are not accurate enough. In addition, if each image is used for dense 3D reconstruction, the dense point clouds will increase the amount of calculation. To address these issues, we propose a 3D reconstruction system. Specifically, we propose a depth network of contour and gradient attention, which is used to complete and correct depth maps to obtain high-resolution and high-quality depth maps. Then, we propose a method of fusion of traditional algorithms and deep learning for pose estimation to obtain accurate localization results. Finally, we adopt the method of autonomous selection of keyframes to reduce the number of keyframes, the surfel-based geometric reconstruction is performed to reconstruct the dense 3D environment. On the TUM RGB-D, ICL-NIUM, and KITTI datasets, our method significantly improves the quality of the depth maps, the localization results, and the effect of 3D reconstruction. At the same time, we have also accelerated the speed of 3D reconstruction.

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Topics: Pose (57%), 3D reconstruction (56%), Surfel (53%) ... read more

2 Citations


Journal ArticleDOI: 10.1016/J.MEASUREMENT.2021.110269
Guangxu Hong1, Wanqing Song1, Yan Gao1, Enrico Zio2  +2 moreInstitutions (3)
27 Oct 2021-Measurement
Abstract: The degradation process of lithium-ion batteries has memory, i.e. it has long-range dependence (LRD). In this paper, an iterative model of the generalized Cauchy (GC) process with LRD characteristics is proposed for the remaining useful life (RUL) prediction of lithium-ion batteries. The GC process uses two independent parameters, fractal dimension and Hurst exponent, to measure the LRD of the degradation process. The diffusion term of the GC iterative model is replaced by the increment of the GC time sequences, constructed via the autocorrelation function (ACF) to describe uncertainty and the LRD characteristics of the lithium-ion batteries capacity degradation. Linear and nonlinear drift terms are used to explain the degradation trend of the lithium-ion batteries capacity. A comparison is made with fractional Brownian motion (FBM) and long-short-term memory (LSTM) network models to show how the GC iterative model has the best performance in RUL prediction of lithium-ion batteries.

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Open accessJournal ArticleDOI: 10.1109/ACCESS.2021.3095054
06 Jul 2021-IEEE Access
Abstract: It is very important to accurately extract the instantaneous frequency (IF) of complex non-stationary signals, so the signal processing methods based on IF are widely used in engineering. However, in non-stationary complex vibration signals, it is difficult to extract the instantaneous frequency under strong noise because the frequency changes rapidly. This paper proposes an improved multi-ridge extraction method based on differential synchro-squeezing wavelet transform (DSWT). First, an improved method DSWT is proposed to reduce the computation time and image noise of synchro-squeezing wavelet transform (SWT). The running time of the algorithm can be further reduced by segmenting the signal and compressing the time-frequency matrix. The image noise can be significantly reduced by differentiating SWT time-frequency matrix. It lays a good foundation for the extraction of the time-frequency ridge line. Secondly, an improved multi-ridge extraction method is proposed. The ridge jump due to end effect can be eliminated adaptively in segmented extraction. It further improves the time-frequency aggregation and extraction effect of the wavelet ridgeline image. Finally, the improved multi-ridge extraction method based on DSWT (DSWT-IMRE) is verified by the simulation data and experimental data under different conditions. Compared with the method proposed in previous study, the results show that DSWT-IMRE has higher extraction accuracy.

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Topics: Wavelet (60%), Wavelet transform (59%), Continuous wavelet transform (55%) ... read more

References
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49 results found


Journal ArticleDOI: 10.1162/NECO.1997.9.8.1735
Sepp Hochreiter1, Jürgen Schmidhuber2Institutions (2)
01 Nov 1997-Neural Computation
Abstract: Learning to store information over extended time intervals by recurrent backpropagation takes a very long time, mostly because of insufficient, decaying error backflow. We briefly review Hochreiter's (1991) analysis of this problem, then address it by introducing a novel, efficient, gradient based method called long short-term memory (LSTM). Truncating the gradient where this does not do harm, LSTM can learn to bridge minimal time lags in excess of 1000 discrete-time steps by enforcing constant error flow through constant error carousels within special units. Multiplicative gate units learn to open and close access to the constant error flow. LSTM is local in space and time; its computational complexity per time step and weight is O. 1. Our experiments with artificial data involve local, distributed, real-valued, and noisy pattern representations. In comparisons with real-time recurrent learning, back propagation through time, recurrent cascade correlation, Elman nets, and neural sequence chunking, LSTM leads to many more successful runs, and learns much faster. LSTM also solves complex, artificial long-time-lag tasks that have never been solved by previous recurrent network algorithms.

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49,735 Citations



Journal ArticleDOI: 10.1137/S1052623496303470
Abstract: The Nelder--Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder--Mead algorithm. This paper presents convergence properties of the Nelder--Mead algorithm applied to strictly convex functions in dimensions 1 and 2. We prove convergence to a minimizer for dimension 1, and various limited convergence results for dimension 2. A counterexample of McKinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the Nelder--Mead algorithm converges to a nonminimizer. It is not yet known whether the Nelder--Mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions.

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Topics: Simplex algorithm (58%), Convex function (56%), Nelder–Mead method (54%) ... read more

6,497 Citations


Journal ArticleDOI: 10.1016/J.YMSSP.2017.11.016
Yaguo Lei1, Naipeng Li1, Liang Guo1, Ningbo Li1  +2 moreInstitutions (1)
Abstract: Machinery prognostics is one of the major tasks in condition based maintenance (CBM), which aims to predict the remaining useful life (RUL) of machinery based on condition information. A machinery prognostic program generally consists of four technical processes, i.e., data acquisition, health indicator (HI) construction, health stage (HS) division, and RUL prediction. Over recent years, a significant amount of research work has been undertaken in each of the four processes. And much literature has made an excellent overview on the last process, i.e., RUL prediction. However, there has not been a systematic review that covers the four technical processes comprehensively. To fill this gap, this paper provides a review on machinery prognostics following its whole program, i.e., from data acquisition to RUL prediction. First, in data acquisition, several prognostic datasets widely used in academic literature are introduced systematically. Then, commonly used HI construction approaches and metrics are discussed. After that, the HS division process is summarized by introducing its major tasks and existing approaches. Afterwards, the advancements of RUL prediction are reviewed including the popular approaches and metrics. Finally, the paper provides discussions on current situation, upcoming challenges as well as possible future trends for researchers in this field.

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Topics: Prognostics (61%)

697 Citations


Journal ArticleDOI: 10.1016/J.PATCOG.2009.03.001
Jian Li1, Qian Du2, Caixin Sun1Institutions (2)
Abstract: Fractal dimension (FD) is a useful feature for texture segmentation, shape classification, and graphic analysis in many fields. The box-counting approach is one of the frequently used techniques to estimate the FD of an image. This paper presents an efficient box-counting-based method for the improvement of FD estimation accuracy. A new model is proposed to assign the smallest number of boxes to cover the entire image surface at each selected scale as required, thereby yielding more accurate estimates. The experiments using synthesized fractional Brownian motion images, real texture images, and remote sensing images demonstrate this new method can outperform the well-known differential boxing-counting (DBC) method.

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Topics: Image texture (62%), Box counting (59%), Fractal dimension (53%) ... read more

376 Citations