The paradigm of complex probability and analytic nonlinear prognostic for vehicle suspension systems.

Adding three novel axioms to Kolmogorov's five established probability axioms which were laid in 1933 extends classical probability theory to encompass the imaginary set of numbers. Therefore, all random experiments will be executed in the complex setwhich is the sum of the real setwith its real probability component, and the corresponding imaginary setwith its imaginary probability component. The purpose of extending Kolmogorov's axioms is to add supplementary imaginary dimensions to any random event that occurs in the ‘real’ laboratory and hence to be able to evaluate the associated complex probability in the complex planewhich is always equal to one. My purpose in this work is to link the complex probability paradigm to the vehicle suspension system analytic prognostic in the nonlinear damage accumulation case. Hence, by calculating the parameters of the new prognostic model, we will be able to determine the magnitude of the chaotic factor, the degree of our knowledge, the complex probability, the system failure and survival probabilities, and the remaining useful lifetime probability, after thatNload cycles have been applied to the suspension, and which are all functions of the system degradation subject to random effects. [ABSTRACT FROM AUTHOR]