Inverse Gaussian–based model with measurement errors for degradation analysis

2019 ◽  
Vol 233 (6) ◽  
pp. 1086-1098 ◽  
Author(s):  
Xudan Chen ◽  
Guoxun Ji ◽  
Xinli Sun ◽  
Zhen Li
Keyword(s):  
Measurement Errors ◽  
Random Effect ◽  
State Space Model ◽  
Expectation Maximization Algorithm ◽  
Particle Methods ◽  
Inverse Gaussian ◽  
Estimation Algorithms ◽  
Degradation Analysis ◽  
Degradation Models ◽  
Non Gaussian

To build more credible degradation models, it is necessary to consider measurement errors in degradation analysis. This article proposes an inverse Gaussian-based state space model with measurement errors that can capture the unit-to-unit variability of the degradation rate by incorporating a random effect. Then, the lifetime distribution and alarm probabilities are derived. Under the non-Gaussian assumptions, conventional parameter estimation algorithms cannot be applied directly. Therefore, an improved expectation–maximization algorithm that is combined with particle methods is developed to estimate parameters. Finally, this article concludes with a simulation study and two case applications to demonstrate the applicability and advantages of the proposed model.

Fault prognosis of complex mechanical systems based on multi-sensor mixtured hidden semi-Markov models

2012 ◽  
Vol 227 (8) ◽  
pp. 1853-1863 ◽  
Author(s):  
Zhongsheng Chen ◽  
Yongmin Yang ◽  
Zheng Hu ◽  
Qinghu Zeng
Keyword(s):  
Markov Models ◽  
Expectation Maximization Algorithm ◽  
Mechanical Systems ◽  
Stationary Time Series ◽  
Estimation Algorithms ◽  
Multiple Sensors ◽  
Observation Process ◽  
Fault Prognosis ◽  
Non Gaussian ◽  
Complex Mechanical Systems

Accurate fault prognosis is of vital importance for condition-based maintenance. As to complex mechanical systems, multiple sensors are often used to collect condition signals and the observation process may rather be non-Gaussian and non-stationary. Traditional hidden semi-Markov models cannot provide adequate representation for multivariate non-Gaussian and non-stationary time series. The innovation of this article is to extend classical hidden semi-Markov models by modeling the observation as a linear mixture of non-Gaussian multi-sensor signals. The proposed model is called as a multi-sensor mixtured hidden semi-Markov model. Under this new framework, modified parameter re-estimation algorithms are derived in detail based on the complete-data expectation maximization algorithm. In the end the proposed prognostic methodology is validated on a practical bearing application. The experimental results show that the proposed method is indeed promising to obtain better prognostic performance than classical hidden semi-Markov models.

scholarly journals Variational Bayesian-Based Improved Maximum Mixture Correntropy Kalman Filter for Non-Gaussian Noise

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 117
Author(s):  
Xuyou Li ◽  
Yanda Guo ◽  
Qingwen Meng
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
State Space Model ◽  
Performance Evaluations ◽  
Gaussian State ◽  
Variational Bayesian ◽  
Space Model ◽  
Bandwidth Parameter ◽  
Non Gaussian ◽  
Filtering Problem

The maximum correntropy Kalman filter (MCKF) is an effective algorithm that was proposed to solve the non-Gaussian filtering problem for linear systems. Compared with the original Kalman filter (KF), the MCKF is a sub-optimal filter with Gaussian correntropy objective function, which has been demonstrated to have excellent robustness to non-Gaussian noise. However, the performance of MCKF is affected by its kernel bandwidth parameter, and a constant kernel bandwidth may lead to severe accuracy degradation in non-stationary noises. In order to solve this problem, the mixture correntropy method is further explored in this work, and an improved maximum mixture correntropy KF (IMMCKF) is proposed. By derivation, the random variables that obey Beta-Bernoulli distribution are taken as intermediate parameters, and a new hierarchical Gaussian state-space model was established. Finally, the unknown mixing probability and state estimation vector at each moment are inferred via a variational Bayesian approach, which provides an effective solution to improve the applicability of MCKFs in non-stationary noises. Performance evaluations demonstrate that the proposed filter significantly improves the existing MCKFs in non-stationary noises.

Inverse Gaussian process models for degradation analysis: A Bayesian perspective

2014 ◽  
Vol 130 ◽  
pp. 175-189 ◽  
Author(s):  
Weiwen Peng ◽  
Yan-Feng Li ◽  
Yuan-Jian Yang ◽  
Hong-Zhong Huang ◽  
Ming J. Zuo
Keyword(s):  
Gaussian Process ◽  
Process Models ◽  
Inverse Gaussian ◽  
Inverse Gaussian Process ◽  
Degradation Analysis ◽  
Gaussian Process Models

scholarly journals Gauss process state-space model optimization algorithm with expectation maximization

2019 ◽  
Vol 15 (7) ◽  
pp. 155014771986221
Author(s):  
Hongqiang Liu ◽  
Haiyan Yang ◽  
Tao Zhang ◽  
Bo Pan
Keyword(s):  
State Space ◽  
Optimization Algorithm ◽  
Expectation Maximization ◽  
Conditional Expectation ◽  
State Space Model ◽  
Expectation Maximization Algorithm ◽  
Model Optimization ◽  
Laboratory Environment ◽  
Space Model ◽  
Gauss Process

A Gauss process state-space model trained in a laboratory cannot accurately simulate a nonlinear system in a non-laboratory environment. To solve this problem, a novel Gauss process state-space model optimization algorithm is proposed by combining the expectation–maximization algorithm with the Gauss process Rauch–Tung–Striebel smoother algorithm, that is, the EM-GP-RTSS algorithm. First, a theoretical formulation of the Gauss process state-space model is proposed, which is not found in previous references. Second, a Gauss process state-space model optimization framework with the expectation–maximization algorithm is proposed. In the expectation–maximization algorithm, the unknown system state is considered as the lost data, and the maximization of measurement likelihood function is transformed into that of a conditional expectation function. Then, the Gauss process–assumed density filter algorithm and the Gauss process Rauch–Tung–Striebel smoother algorithm are proposed with the Gauss process state-space model defined in this article, in order to calculate the smoothed distribution in the conditional expectation function. Finally, the Monte Carlo numerical integral method is used to obtain the approximate expression of the conditional expectation function. The simulation results demonstrate that the Gauss process state-space model optimized by the EM-GP-RTSS can simulate the system in the non-laboratory environment better than the Gauss process state-space model trained in the laboratory, and can reach or exceed the estimation accuracy of the traditional state-space model.

scholarly journals Estimating Nonlinear Selection on Behavioral Reaction Norms

2021 ◽  
Author(s):  
Jordan Scott Martin
Keyword(s):  
Individual Variation ◽  
Fixed Effects ◽  
Random Effect ◽  
Generalized Solution ◽  
Reaction Norm ◽  
Reaction Norms ◽  
Unbiased Estimation ◽  
Behavioral Strategies ◽  
Non Gaussian ◽  
Parameter Values

Individuals' behavioral strategies are often well described by reaction norms, which are functions predicting repeatable patterns of personality, plasticity, and predictability across an environmental gradient. Reaction norms can be readily estimated using mixed-effects models and play a key role in current theories of adaptive individual variation. Unfortunately, however, it remains challenging to assess the effects of reaction norms on fitness-relevant outcomes, due to the high degree of uncertainty in random effect estimates of reaction norm parameters, also known as best linear unbiased predictors (BLUPs). Current approaches to this problem do not provide a generalized solution for modelling reaction norm effects with nonlinear structure, such as stabilizing, disruptive, balancing, and/or correlational selection, which are necessary for testing adaptive theory of individual variation. To address this issue, I present a novel solution for straightforward and unbiased estimation of linear and nonlinear reaction norm effects on fitness, applicable to both Gaussian and non-Gaussian measurements. This solution involves specifying BLUPs as random effects on behavior and fixed effects on fitness within a Bayesian multi-response model. By simultaneously accounting for uncertainty in reaction norm parameters and their causal effects on other measures, the risks accompanying classical approaches to BLUPs can be effectively avoided. I also introduce a new method for visualizing the consequences of multivariate selection on reaction norms. Simulations are then used to validate that the proposed models provide unbiased estimates across realistic parameter values, and an extensive coding tutorial is provided to aid researchers in applying this method to their own datasets in R.

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