Probabilistic Analysis of Bimodal State Distributions in SCR Aftertreatment Systems

Rhys Comissiong; Thomas Steffen; Leo Shead

doi:10.4271/2020-01-0355

Sensor selection for the control of modern powertrains is a recognised technical challenge. The key question is which set of sensors is best suited for an effective control strategy? This paper addresses the question through probabilistic modelling and Bayesian analysis. By quantifying uncertainties in the model, the propagation of sensor information throughout the model can be observed.

The specific example is an abstract model of the slip behaviour of Selective Catalytic Reduction (SCR) DeNOx aftertreatment systems. Due to the ambiguity of the sensor reading, linearization-based approaches including the Extended Kalman Filter, or the Unscented Kalman Filter are not successful in resolving this problem.

The stochastic literature suggests approximating these nonlinear distributions using methods such as Markov Chain Monte Carlo (MCMC), which is able in principle to resolve bimodal or multimodal results. However, the most effective methods are Hamiltonian solvers, which again struggle with the strongly nonlinear system behaviour, often getting stuck in just one of the possible solutions.

This paper compares how the different samplers of the MCMC methods perform in resolving the multi-modal distribution. Metropolis Hastings demonstrated the best ability to resolve problems of this nature.

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Probabilistic Analysis of Bimodal State Distributions in SCR Aftertreatment Systems 2020-01-0355

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