arXiv subjects

Weixin Wang

Publications and source records attributed to Weixin Wang.

22 records · Page 2Linked to original sources

arXiv2021

Joint Prediction of Remaining Useful Life and Failure Type of Train Wheelsets: A Multi-task Learning Approach

The failures of train wheels account for disruptions of train operations and even a large portion of train derailments. Remaining useful life (RUL) of a wheelset measures the how soon the next failure will arrive, and the failure type reveals how severe the failure will be. RUL prediction is a regression task, whereas failure type is a classification task. In this paper, we propose a multi-task learning approach to jointly accomplish these two tasks by using a common input space to achieve more desirable results. We develop a convex optimization formulation to integrate both least square loss and the negative maximum likelihood of logistic regression, and model the joint sparsity as the L2/L1 norm of the model parameters to couple feature selection across tasks. The experiment results show that our method outperforms the single task learning method by 3% in prediction accuracy.

cs.LG↗

arXiv2020

An overview of optimal control optimization problems driven by non-convexity measures

Recently, literature on dynamic coherent risk measures has broadened the choices for risk-sensitive performance evaluation. A running example includes Cumulative prospect theory and Conditional variance at risk. Most of them can be can be interpreted in general as a non-linear transformation of a given random variable. Non-convexity property has implied a lot of mathematical intricacies and challenges. The paper gives overview on the recent development of dynamic programming optimal control optimization problems driven by non-convex measures.

math.OC↗

arXiv2020

Matrix Fisher-Gaussian Distribution on $\mathrm{SO}(3)\times\mathbb{R}^n$ for Attitude Estimation with a Gyro Bias

In this paper, a new probability distribution, referred to as the matrix Fisher-Gaussian (MFG) distribution, is proposed on the nonlinear manifold $\mathrm{SO}(3)\times\mathbb{R}^n$. It is constructed by conditioning a (9+n)-variate Gaussian distribution from the ambient Euclidean space into $\mathrm{SO}(3)\times\mathbb{R}^n$, while imposing a certain geometric interpretation of the correlation terms to avoid over-parameterization. The unique feature is that it may represent large uncertainties in attitudes, linear variables of an arbitrary dimension, and angular-linear correlations between them in a global fashion without singularities associated with local parameterizations. Various stochastic properties and an approximate maximum likelihood estimator of MFG are developed. Furthermore, two methods are developed to propagate uncertainties though a stochastic differential equation representing attitude kinematics. Based on these, a Bayesian estimator is proposed to estimate the attitude and time-varying gyro bias concurrently. Numerical studies indicate that the proposed estimator exhibits a better accuracy against the well-established multiplicative extended Kalman filter for two challenging cases.

math.OC↗

arXiv2020

Spectral Bayesian Estimation for General Stochastic Hybrid Systems

General Stochastic Hybrid Systems (GSHS) have been formulated to represent various types of uncertainties in hybrid dynamical systems. In this paper, we propose computational techniques for Bayesian estimation of GSHS. In particular, the Fokker-Planck equation that describes the evolution of uncertainty distributions along GSHS is solved by spectral techniques, where an arbitrary form of probability density of the hybrid state is represented by a mixture of Fourier series. The method is based on splitting the Fokker-Planck equation represented by an integro-partial differential equation into the partial differentiation part for continuous diffusion and the integral part for discrete transition, and integrating the solution of each part. The propagated density function is used with a likelihood function in the Bayes' formula to estimate the hybrid state for given sensor measurements. The unique feature of the proposed technique is that the probability density describing complete stochastic properties of the hybrid state is constructed without relying on the common Gaussian assumption, in contrast to other methods that compute certain expected values such as mean or variance. We apply the proposed method to the estimation of two examples: the bouncing ball model and the Dubins vehicle model. We show that the proposed technique yields propagated densities consistent with Monte Carlo simulations, more accurate estimates over the Gaussian based approach and some computational benefits over a particle filter.

math.OC↗