Using the total probability theorem, we propose a method to calculate the failure rate of a linear vibratory system with random parameters excited by stationary Gaussian processes. The response of such a system is non-stationary because of the randomness of the input parameters. A space-filling design, such as optimal symmetric Latin hypercube sampling or maximin, is first used to sample the input parameter space. For each design point, the output process is stationary and Gaussian. We present two approaches to calculate the corresponding conditional probability of failure. A Kriging metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure and the failure rate of the dynamic system. The proposed method is demonstrated using a vibratory system. Our approach can be easily extended to non-stationary Gaussian input processes.


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    Title :

    An Efficient Method to Calculate the Failure Rate of Dynamic Systems with Random Parameters Using the Total Probability Theorem


    Additional title:

    Sae Int. J. Mater. Manf
    Sae International Journal of Materials and Manufacturing



    Conference:

    SAE 2015 World Congress & Exhibition ; 2015



    Publication date :

    2015-04-14


    Size :

    9 pages




    Type of media :

    Conference paper


    Type of material :

    Print


    Language :

    English






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