Uncertainties in power computations in a turbocharger test bench

Abstract

A specific study of the uncertainties of turbine power output measured in turbocharger test benches is presented using the law of uncertainty propagation and the influence of the different terms that contribute to it is shown. Then, non-linear mixed integer mathematical programming algorithms used with the turbine power uncertainty expression become an essential tool to overcome the problem of selection new sensors to improve an existing test rig or to contribute to a new one. A method of optimisation is presented for two different scenarios: first, where the maximum cost is a constraint; second where the maximum uncertainty is a constraint and the total cost is minimised. When using a large transducers database, computational efforts may be reduced by solving the relaxed non-integer problem by means of sequential quadratic programming and then probing the ceilings and floors of the parameters to get an optimum approximation with low costs. A comparison between the linear uncertainty propagation model and Monte Carlo simulations is also presented, only showing benefits of the later method when computing high order statistical moments of the turbine power output probability distribution.