The Complex Probability Paradigm and Analytic Linear Prognostic for Vehicle Suspension Systems | Science Publications

American Journal of Engineering and Applied Sciences

Abdo Abou Jaoude¹ 

关键词: Extended Kolmogorov’    s Axioms;    Complex Set;    Probability Norm;    Degree of Our Knowledge;    Chaotic Factor;    Linear Damage;    Degradation;    Remaining Useful Lifetime;    Prognostic;   

DOI  :  10.3844/ajeassp.2015.147.175

学科分类：工程和技术（综合）

来源: Science Publications

【 摘 要 】

The Andrey N. Kolmogorov’s system of axioms can be extendedto encompass the imaginary set of numbers and this by adding to his originalfive axioms an additional three axioms. Hence, any experiment can thus beexecuted in what is now the complex set Cwhich is the sum of the real set Rwith its corresponding real probability and the imaginary set M with its corresponding imaginaryprobability. The objective here is to evaluate the complex probabilities byconsidering supplementary new imaginary dimensions to the event occurring inthe “real” laboratory. Whatever the probability distribution of the inputrandom variable in R is, thecorresponding probability in the whole set Cis always one, so the outcome of the random experiment in C can be predicted totally. The result indicates that chance andluck in R is replaced now by totaldeterminism in C. This is theconsequence of the fact that the probability in C is got by subtracting the chaotic factor from the degree of ourknowledge of the system. This novel complex probability paradigm will beapplied to the concepts of degradation and the remaining useful lifetime of avehicle suspension system, thus to the field of prognostic.

【 授权许可】

Unknown