Robust design using multiobjective optimisation and artificial neural networks with application to a heat pump radial compressor

Although robustness is an important consideration to guarantee the performance of designs under deviation, systems are often engineered by evaluating their performance exclusively at nominal conditions. Robustness is sometimes evaluated a posteriori through a sensitivity analysis, which does not guarantee optimality in terms of robustness. This article introduces an automated design framework based on multiobjective optimisation to evaluate robustness as an additional competing objective. Robustness is computed as a sampled hypervolume of imposed geometrical and operational deviations from the nominal point. In order to address the high number of additional evaluations needed to compute robustness, artificial neutral networks are used to generate fast and accurate surrogates of high-fidelity models. The identification of their hyperparameters is formulated as an optimisation problem. In the frame of a case study, the developed methodology was applied to the design of a small-scale turbocompressor. Robustness was included as an objective to be maximised alongside nominal efficiency and mass-flow range between surge and choke. An experimentally validated 1D radial turbocompressor meanline model was used to generate the training data. The optimisation results suggest a clear competition between efficiency, range and robustness, while the use of neural networks led to a speed-up by four orders of magnitude compared to the 1D code.

Reliability-Based Robust Design Optimization in Consideration of Manufacturing Tolerance by Multi-Objective Evolutionary Optimization with Repair Algorithm

There are inherently various uncertainties in practical engineering, and reliability-based design optimization (RBDO) and robust design optimization (RDO) are two well-established methodologies when considering the uncertainties. Naturally, reliability-based robust design optimization (RBRDO) is a methodology developed recently by combining RBDO and RDO, in which the tolerances of random design variables are always assumed as constants. However, the tolerance of random design variables is a key factor for the objective robustness and manufacturing cost, and the tolerance allocation is the core problem in mechanical manufacturing. Inspired by the cost–tolerance relationship in mechanical manufacturing, this paper presents an integrated framework to simultaneously find the optimal design variable and the corresponding tolerance in the multi-objective RBRDO, with the trade-off between objective robustness and manufacturing cost. The failure mechanism of the constraint handling strategy of the constrained reference vector-guided evolutionary algorithm (C-RVEA) is discussed to solve the multi-objective optimization formulation. Then the robust repair operator and reliability-based repair operator are proposed to transform unfeasible solutions to the feasible ones under reliability constraints. Numerical results reveal that the proposed repair algorithm is effective. By solving the integrated multi-objective optimization problem, the Pareto front with the compromised solutions between the objective robustness and manufacturing cost could be obtained, from which decision makers can select the satisfying solution conveniently according to the preferred requirements.

Reliability-Based Design Optimization Concerning Objective Variation Under Mixed Probabilistic and Interval Uncertainties

Uncertainties, inevitable in nature, can be classified as probability based and interval based uncertainties in terms of its representations. Corresponding optimization strategies have been proposed to deal with these two types of uncertainties. It is more likely that both types of uncertainty can occur in one single problem, and thus, it is trivial to treat all uncertainties the same. A novel formulation for reliability-based design optimization (RBDO) under mixed probability and interval uncertainties is proposed in this paper, in which the objective variation is concerned. Furthermore, it is proposed to efficiently solve the worst-case parameter resulted from the interval uncertainty by utilizing the Utopian solution presented in a single-looped robust optimization (RO) approach where the inner optimization can be solved by matrix operations. The remaining problem can be solved utilizing any existing RBDO method. This work applies the performance measure approach to search for the most probable failure point (MPFP) and sequential quadratic programing (SQP) to solve the entire problem. One engineering example is given to demonstrate the applicability of the proposed approach and to illustrate the necessity to consider the objective robustness under certain circumstances.

Reliability Based Design Optimization Concerning Objective Variation Under Mixed Probabilistic and Interval Uncertainties

Uncertainties, inevitable in nature, can be classified as probability based and interval based uncertainties, in terms of its representations. Corresponding optimization strategies have been proposed to deal with these two types of uncertainties individually. However, it is more likely that both types of uncertainty occur in one single problem and so it is trivial to treat all uncertainties the same. In this paper a novel formulation for reliability based design optimization (RBDO) under mixed probability and interval uncertainties is proposed, in which the objective variation or the objective robustness is also concerned. Furthermore, it is proposed to efficiently solve the worst case parameter resulted from the interval uncertainty by utilizing the Utopian solution presented in a single-looped robust optimization approach, in which the inner optimization problem can be solved by performing matrix operations. The remaining problem can be solved utilizing any existing RBDO method. This work applies the performance measure approach to search for the most probable failure point (MPFP) and sequential quadratic programming (SQP) to solve the entire problem. Two engineering examples are given to demonstrate the applicability of the proposed approach and to illustrate the necessity to consider the objective robustness under certain circumstances.

Sequential Quadratic Programming for Robust Optimization With Interval Uncertainty

Uncertainty plays a critical role in engineering design as even a small amount of uncertainty could make an optimal design solution infeasible. The goal of robust optimization is to find a solution that is both optimal and insensitive to uncertainty that may exist in parameters and design variables. In this paper, a novel approach, Sequential Quadratic Programing for Robust Optimization (SQP-RO), is proposed to solve single-objective continuous nonlinear optimization problems with interval uncertainty in parameters and design variables. This new SQP-RO is developed based on a classic SQP procedure with additional calculations for constraints on objective robustness, feasibility robustness, or both. The obtained solution is locally optimal and robust. Eight numerical and engineering examples with different levels of complexity are utilized to demonstrate the applicability and efficiency of the proposed SQP-RO with the comparison to its deterministic SQP counterpart and RO approaches using genetic algorithms. The objective and/or feasibility robustness are verified via Monte Carlo simulations.

An Integrated Framework for Optimization Under Uncertainty Using Inverse Reliability Strategy

In this work, we propose an integrated framework for optimization under uncertainty that can bring both the design objective robustness and the probabilistic design constraints into account. The fundamental development of this work is the employment of an inverse reliability strategy that uses percentile performance for assessing both the objective robustness and probabilistic constraints. The percentile formulation for objective robustness provides us an accurate evaluation of the variation of an objective performance and a probabilistic measurement of the robustness. We can obtain more reasonable compound noise combinations for a robust design objective compared to using the traditional approach proposed by Taguchi. The proposed formulation is very efficient to solve since it only needs to evaluate the constraint functions at the required reliability levels. The other major development of this work is a new search algorithm for the Most Probable Point of Inverse Reliability (MPPIR) that can be used to efficiently evaluate percentile performances for both robustness and reliability assessments. Multiple strategies are employed in the MPPIR search, including using the steepest ascent direction and an arc search. The algorithm is applicable to general non-concave and non-convex performance functions of random variables following any continuous distributions. The effectiveness of the MPPIR search algorithm is verified using example problems. Overall, an engineering example on integrated robust and reliability design of a vehicle combustion engine piston is used to illustrate the benefits of our proposed method.