Design of Complex Systems in the presence of Large Uncertainties: a statistical approach
The design or optimization of engineering systems is generally based on several assumptions related to the loading conditions, physical or mechanical properties, environmental effects, initial or boundary conditions etc. The effect of those assumptions to the optimum design or the design finally adopted is generally unknown particularly in large, complex systems. A rational recourse would be to cast the problem in a probabilistic framework which accounts for the various uncertainties but also allows to quantify their effect in the response/behavior/performance of the system. In such a framework the performance function(s) of interest are also random and optimization of the system with respect to the design variables has to be reformulated with respect to statistical properties of these objectives functions (e.g. probability of exceeding certain thresholds). Analysis tools are usually restricted to elaborate legacy codes which have been developed over a long period of time and are generally well-tested (e.g. Finite Elements). These do not however include any stochastic components and their alteration is impossible or ill-advised. Furthermore as the number of uncertainties and design variables grows, the problem quickly becomes computationally intractable. The present paper advocates the use of statistical learning in order to perform these tasks for any system of arbitrary complexity as long as a deterministic solver is available. The proposed computational framework consists of two components. Firstly advanced sampling techniques are employed in order to efficiently explore the dependence of the performance with respect to the uncertain and design variables. The proposed algorithm is directly parallelizable and attempts to maximize the amount of information extracted with the least possible number of calls to the deterministic solver. The output of this process is utilized by statistical classification procedures in order to derive the dependence of the performance statistics with respect to the design variables. For that purpose we explore parametric and non-parametric (kernel) probit regression schemes and propose an a priori boosting scheme that can improve the accuracy of the estimators. In all cases a Bayesian framework is adopted that produces robust estimates and can also be utilized to obtain confidence intervals. For that purpose the present paper advocates a framework that allows for calculating the values of response statistics with respect to design variables (the latter are deterministic variables) and provide global information about the sensitivity of those statistics to the design variables of interest.
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|Subject:||materials science | engineering | energy planning, policy and economy | general and miscellaneous//mathematics, computing, and information science | ACCURACY | ALGORITHMS | BOUNDARY CONDITIONS | CLASSIFICATION | DESIGN | ENVIRONMENTAL EFFECTS | LEARNING | MECHANICAL PROPERTIES | OPTIMIZATION | PERFORMANCE | PROBABILITY | SAMPLING | SENSITIVITY | STATISTICS|
|Type of publication:||Other|
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