Probability, Reliability and Statistical Methods in Engineering Design

Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles

Optimization for structural crashworthiness and energy absorption has become an important topic of research attributable to its proven benefits to public safety and social economy. This paper provides a comprehensive review of the important studies on design optimization for structural crashworthiness and energy absorption. First, the design criteria used in crashworthiness and energy absorption are reviewed and the surrogate modeling to evaluate these criteria is discussed. Second, multiobjective optimization, optimization under uncertainties and topology optimization are reviewed from concepts, algorithms to applications in relation to crashworthiness. Third, the crashworthy structures are summarized, from generically novel structural configurations to industrial applications. Finally, some conclusions and recommendations are provided to enable academia and industry to become more aware of the available capabilities and recent developments in design optimization for structural crashworthiness and energy absorption.

On design optimization for structural crashworthiness and its state of the art

Recent advances in engineering design optimisation: Challenges and future trends

Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data

A probabilistic approach for representation of interval uncertainty

This paper proposesmethods to estimate the discretization error in the system output of coupledmultidisciplinary simulations. In such systems, the governing equations for each discipline are numerically solved by a different computational code, and each discipline has different mesh size parameters. A classic example of multidisciplinary analysis involves fluid–structure interaction, where the element sizes in fluid and structure meshes are typically different. The general case of three-dimensional steady-state problems is considered in the current paper, where mesh refinement is possible in all three spatial directions for each discipline. Two aspects of discretization error, which are of interest in multidisciplinary analysis, are considered: disciplinary mesh sizes and the mismatch of disciplinary meshes at the interface at which boundary conditions are exchanged. Two alternate representations for the discretization error for the previously specified generic case are presented: 1) ignoring mesh mismatch at the interface and 2) considering mesh mismatch at the interface. Polynomial, rational function, and Gaussian process error models are used to represent the discretization error. The proposed error models are illustrated using a threedimensional fluid–structure interaction problem of an aircraft wing.

Discretization Error Estimation in Multidisciplinary Simulations

In this paper, we propose a new approach to include robustness considerations in problems with multiple performance functions under uncertainty. Robustness of performance under uncertainty is typically ensured by minimizing the variation of the performance function, usually modeled by its variance or standard deviation. Such moment-based methods generally become cumbersome to solve as the number of performance functions increases, because of a large number of objective functions. The current paper proposes a new approach that tackles both robustness and optimality using the joint probability density function of all the performance functions. For a set of designer-specified thresholds, which can be viewed as upper bounds on the performance functions (for minimization), joint optimality is ensured by maximizing a single quantity irrespective of the number of performance functions: the joint probability that the design's performance is bounded by the thresholds. To ensure joint robustness, we minimize a single scalar quantity irrespective of the number of performance functions: the determinant of the covariance matrix of the performance functions. Two examples are presented: an automobile side impact problem with two performance functions and a two-stage-to-orbit launch vehicle conceptual design problem with three performance functions.

Design optimization for robustness in multiple performance functions

This paper presents a new approach to solve multiobjective optimization problems under uncertainty. Unlike the existing state-of-the-art, where means/variances of the objectives are used to ensure optimality, we employ a distributional formulation. The proposed formulations are based on joint probability, i.e., probability that all objectives are simultaneously bound by certain design thresholds under uncertainty. For minimization problems, these thresholds can be viewed as the desired upper bounds on the individual objectives. The tradeoffs are illustrated using the so-called decision surface, which is the surface of maximized joint probabilities for a set of design thresholds. Two optimization formulations to generate the decision surface are proposed, which provide the designer with the distinguishing capability that is not available in the existing literature, namely, decision making under uncertainty, while ensuring joint objective performance: (1) Maximum probability design: Given a set of thresholds (preferences within each objective), find a design that maximizes the joint probability while using a probabilistic aggregation as against an ambiguous weight-based method. (2) Optimum threshold design: Given a designer-specified joint probability, find a set of thresholds that satisfy the joint probability specification while allowing for a specification of preferences among the objectives.

Sirisha Rangavajhala

Papers

A probabilistic approach for representation of interval uncertainty

Discretization Error Estimation in Multidisciplinary Simulations

Design optimization for robustness in multiple performance functions

Joint Probability Formulation for Multiobjective Optimization Under Uncertainty

Optimization-based feasibility study of an active thermal insulator