Hidden Semi-Markov Models for Predictive Maintenance

Realistic predictive maintenance approaches are essential for condition monitoring and predictive maintenance of industrial machines. In this work, we propose Hidden Semi-Markov Models (HSMMs) with (i) no constraints on the state duration density function and (ii) being applied to continuous or discrete observation. To deal with such a type of HSMM, we also propose modifications to the learning, inference, and prediction algorithms. Finally, automatic model selection has been made possible using the Akaike Information Criterion. This paper describes the theoretical formalization of the model as well as several experiments performed on simulated and real data with the aim of methodology validation. In all performed experiments, the model is able to correctly estimate the current state and to effectively predict the time to a predefined event with a low overall average absolute error. As a consequence, its applicability to real world settings can be beneficial, especially where in real time the Remaining Useful Lifetime (RUL) of the machine is calculated

Constrained models for optical absorption tomography

We consider the inverse problem of concentration imaging in optical absorption tomography with limited data sets. The measurement setup involves simultaneous acquisition of near infrared wavelength modulated spectroscopic measurements from a small number of pencil beams equally distributed among six projection angles surrounding the plume. We develop an approach for image reconstruction that involves constraining the value of the image to the conventional concentration bounds and a projection into low-dimensional subspaces to reduce the degrees of freedom in the inverse problem. Effectively, by reparameterising the forward model we impose simultaneously spatial smoothness and a choice between three types of inequality constraints, namely positivity, boundedness and logarithmic boundedness in a simple way that yields an unconstrained optimisation problem in a new set of surrogate parameters. Testing this numerical scheme with simulated and experimental phantom data indicates that the combination of affine inequality constraints and subspace projection leads to images that are qualitatively and quantitatively superior to unconstrained regularised reconstructions. This improvement is more profound in targeting concentration profiles of small spatial variation. We present images and convergence graphs from solving these inverse problems using Gauss-Newton's algorithm to demonstrate the performance and convergence of our method