Abstract
System uncertainties play a vital role in the robustness (or sensitivity) analysis of system designs. In an iterative procedure such as design optimisation, the robustness analysis that is simultaneously accurate and computationally efficient is essential. Accordingly, the current state-of-the-art techniques such as univariate dimension reduction method (DRM) and performance moment integration (PMI) approach have been developed. They are commonly used to express the sensitivity while utilising the statistical moments of a performance function in an advanced design optimisation paradigm known as the reliability-based robust design optimisation (RBRDO). However, the accuracy and computational efficiency scalability for increasing the problem dimension (i.e. the number of input variables) have not been tested. This study examines the scalability of the above-mentioned pioneering techniques. Additionally, it also introduces a novel analytical method that symbolically calculates the sensitivity of the performance function prior to the iterative optimisation procedure. As a result, it shows a better computational cost scalability when tested on performance functions with increased dimensionality. Most importantly, when applied to real-world RBRDO problems such as the vehicle side impact crashworthiness, the proposed technique is three times faster than the mainstream method while yielding a high quality and safe vehicle design.
Highlights
In the increasingly complex and competitive modern technological environment, engineers from a wide variety of fields constantly strive toward finding the most economical designs by using the least amount of resources
The equivalent function evaluation (EFE) counts for the dimension reduction method (DRM) and performance moment integration (PMI) methods increase with the number of quadrature points nq showing that the higher computational cost is associated with more quadrature points
Increasing the number of quadrature points did not guarantee an increase in the variance estimation accuracy for the PMI method as it does for the DRM
Summary
In the increasingly complex and competitive modern technological environment, engineers from a wide variety of fields constantly strive toward finding the most economical designs by using the least amount of resources. RBRDO is a unified framework that combines two approaches: (a) the reliability-based design optimisation [9] which optimises design objectives for a given set of probabilistic (or reliability) constraints and (b) the RDO [10] which increases the robustness of a designed system by minimising the sensitivity of the design objectives to process variabilities. This paper investigates the scalability of some of the representative techniques in the moment-based approach for problems with an increased dimensionality It introduces a novel analytical moment-based evaluation method that shows a better scalability of the computational cost when tested with the increasing number of random variables (up to 20). The section discusses the implication of such a technique for design engineers facing real-world RBRDO problems
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