A Polynomial Chaos- Based Likelihood Approach for Parameter Estimation of Load Sensing Proportional Valve

As there are a variety of uncertainty contained in dynamic systems, this paper presents a method to identify the uncertain parameters of Load Sensing Proportional Valve in a heavy truck brake system. This method is derived from polynomial chaos theory and uses the maximum likelihood approach to estimate the most likely value of uncertain parameters, such as equivalent bearing area diameter of the diaphragm, preload of return spring and so on. The maximum likelihood estimates are obtained through minimizing the cost function derived from the prior probability for the measurement noise. Direct stochastic collocation has been shown to be more efficient than Galerkin approach in the simulation of systems with large number of uncertain parameters. The simulation model of Load Sensing Proportional Valve is built in software AMESim based on logic structure of the valve. The uncertain parameters are estimated through the simulation results which are treated as measurements. To work with a realistic set of measurements several levels of measurement noise are exerted to the results of simulation. The estimation accuracy is sensitive to the number of terms used in the polynomial expressions and to the number of sampling points. When the number of polynomial terms and sampling points are chosen suitably, the polynomial chaos estimation shows promising results by its ability to converge and maintain a stable estimate of the unknown parameter.