Application of Sensitivity Methods to Analysis and Synthesis of Vehicle Dynamic Systems

SUMMARY

The development and application of sensitivity methods for determining the effects of parameter changes on the response of vehicle dynamic systems is presented. The procedures shown can be used to enhance the analysis and synthesis processes of virtually any road or rail vehicle system regardless of its complexity. The parametric sensitivity of vehicle models in time domain, steady state models and vehicle models in frequency domain can be investigated using different types of sensitivity functions, both dimensional and dimensionless including first order standard, percentage, logarithmic, second order standard, and logarithmic and percentage sensitivity measures. These sensitivity functions and measures are determined as functions of partial derivatives of system variables taken with respect to system parameters. In the case of sensitivity functions in the frequency domain the variable values are computed as either the magnitude or phase angle of a complex element of the transfer function matrix. The methods presented enable to determine the influence of all system primary (constant) and secondary (non-constant) parameters on system primary and secondary variables. The primary variables are state variables or elements of the transfer function matrix and the secondary variables may be any functions of primary variables and system parameters. Typical secondary system parameters which can be examined include initial conditions, time variant coefficients, natural frequencies, loads, and typical secondary variables are forces, weight transfers, stability factors and energy components. The analysis of sensitivity results obtained for three vehicle handling models in both linear and nonlinear regimes of vehicle performance and utilizing various types of sensitivity functions is also presented.