Page - 63 - in Maximum Tire-Road Friction Coefficient Estimation

4. Sensitivity Analysis Nopublished recordwas foundonanunprejudicedmathematical analysis that indicated which vehicle state variables are most affected by the friction potential for different driving states, see first research question in Section 1.4. Unlike published approaches, which are heuristic to some degree, the present concept aims at a more mathematical solution to the problem of identifying relevant variables for friction estimation in the first place. In order to find the optimum variables affected by the friction potential for each driving state, a sensitivity analysis was performed based on the vehicle and tire model derived in Section 3. The vehicle’s state variables describe the time-varying vehicle reaction and are assumed to contain information on the tire-road contact which canbeexploitedbyanobserver. This chapter includesa short introductionto sensitivity analysis, a detailed explanation of the chosen approach and a presentation of the results. 4.1. Sensitivity analysis of ordinary differential equation systems Sensitivity analyses are often used when the parameters and initial conditions of models are not accurately known and the influence of variations of these parameters is of in- terest. A parameter is considered sensitive when small changes in the parameter cause large changes in the solution. In the present work, sensitivity analysis is used for an- other purpose, namely to identify the variables that change with respect to the friction potential depending on the current driving states, see first research question in Section 1.4. According to Campolongo et al., sensitivity analyses can be categorized as factor screening, global methods and local methods, [CSST00]. Factor screening is useful for finding influential factors in a system with many factors and is thus often used as a preliminary step to reduce factors prior to a local or global method. Global methods ap- portion the influence of the uncertainty of the input factors on the output factors. This method is helpful when investigating the parameterisation of a model, but distributions