Robust Parameter Design and Tolerance Design with Computer Experiments


Student thesis: Doctoral Thesis

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Awarding Institution
Award date24 Jul 2018


This thesis consists of four chapters. Chapter 1 gives an introduction to the problems solved in the thesis, which includes various formulations of integrated parameter and tolerance design (IPTD) problems based on time-consuming computer models.

In Chapter 2, we propose a general methodology for IPTD of engineering systems with time-consuming computer models. Robust parameter design (RPD) and tolerance design (TD) are effective methods to improve process quality. It is reported in the literature that the traditional two-stage design (TSD) approach that performs RD followed by TD to reduce the sensitivity to variations of input characteristics is suboptimal. To mitigate the problem, an IPTD methodology that is suitable for linear models is suggested. In this chapter, a computer-aided IPTD approach for computer experiments is proposed, in which the means and tolerances of input characteristics are simultaneously optimized to minimize the total cost. A Gaussian Process (GP) metamodel is used to emulate the response function to reduce the number of simulations. A closed-form expression for the posterior expected quality loss is derived to facilitate optimization in computer-aided IPTD. As there is often uncertainty about the true quality and tolerance costs, multiobjective optimization with quality loss and tolerance cost as objective functions is proposed to find robust optimal solutions.

In Chapter 3, we propose an optimal tolerance region for IPTD with mixture proportion inputs. Computer experiments often have inputs that are proportions/fractions of components in a mixture. In these mixture computer experiments, it can be of interest to perform RPD and TD on the mixture proportions since the proportions are subjected to noise variations. Traditionally, manufacturing of mixture products is controlled via interval tolerances for mixture amounts. In this chapter, an optimal tolerance region for proportions, which gives optimal quality cost among all possible tolerance regions for mixture proportions with the same acceptance probability, is proposed for IPTD in mixture computer experiments. Real examples are given to demonstrate the improvements that can be achieved with the optimal tolerance region.

In Chapter 4, a real IPTD problem in aeronautical engineering that involves an extremely time-consuming computer simulation is solved. The design of robust centrifugal compressors, which are important components of aeronautical gas turbines, has attracted a lot of attention. Small geometric variations in the compressor often cause noticeable variations in compressor performance. This chapter reports the challenging problem of determining optimal nominal values and tolerances of ten geometric design variables of a centrifugal compressor simulated by a time-consuming computational fluid dynamics (CFD) computer code based on an IPTD approach. The expected compressor quality is evaluated based on the probability of conformance of three performance measures (PMs). Optimizing the CFD computer code directly is unaffordable due to the huge computational resources needed. Moreover, our attempt to use a two-level fractional factorial design and linear model analysis failed because of the complex functional relationships between inputs and PMs. To mitigate the problem, we utilize GP emulators, which accurately approximate the nonlinear relationships with a small number of CFD simulation runs. IPTD with objective function estimated using the GP emulator is performed. A conservative estimator of the probability of conformance that accounts for emulator prediction uncertainty is derived and employed in the objective function. Our analysis yields new insights and a better geometric design.