A literature review on RSM-based robust parameter design (RPD): Experimental design, estimation modeling, and optimization methods

This book on experimental design is somewhat similar in flavor to the classic book by G.E

ABSTRACT: Robust parameter design (RPD) involves the effects size, component restrictions, and fixed effects of mixture-process-noise variables (MPNV) in product and process design. The traditional methodology does not necessarily ensure a minimum variance and a reasonable model adjustment. Contrary to process and noise variables, mixture factor levels are not independent, negative proportions are not allowed, and their summary must be equal to unity. A transformation function enables the incorporation of noise factors into the response surface model, thus estimating the mixture-process optimum variables that minimize the variance expression without a cross array. In addition, it allows the determination of a confidence region over a point to achieve another component combination with similar or higher quality products. The third-generation process capability index, Cpkm as an alternative signal to noise ratio (SNR) estimator, improve process capability and product quality for fixed factor problems for full factorial and fractional experiment designs with or without repeated measures. Keywords: Robust Parameter Design, Dual Response, Process Capability, Mixture Experiments, Signal-To-Noise Ratio, Response Surface Methodology.

The purpose of this article is to provide a survey of the various stages in the development of response surface methodology (RSM). The coverage of these stages is organized in three parts that describe the evolution of RSM since its introduction in the early 1950s. Part I covers the period, 1951–1975, during which the so‐called classical RSM was developed. This includes a review of basic experimental designs for fitting linear response surface models, in addition to a description of methods for the determination of optimum operating conditions. Part II, which covers the period, 1976–1999, discusses more recent modeling techniques in RSM, in addition to a coverage of Taguchi's robust parameter design and its response surface alternative approach. Part III provides a coverage of further extensions and research directions in modern RSM. This includes discussions concerning response surface models with random effects, generalized linear models, and graphical techniques for comparing response surface designs. Copyright © 2010 John Wiley & Sons, Inc.This article is categorized under:Statistical Models > Linear ModelsStatistical Models > Nonlinear Models

Dual response surface methodology (DRSM) and nonparametric methodology (NPM) are main approaches used to achieve robust parameter design (RPD) of industrial processes and products. When the relationship between influential input factors and output quality characteristic of a process is very complex, both approaches have their limitations. For DRSM, it fails to fit the real response surfaces of process mean and variance by using the second order polynomial models. For NPM, it is hard to optimize parameters of fitting equation, and it needs more experiments as well. From a machine learning perspective, this paper generalizes RPD as a restricted active learning problem and proposes a new approach to achieve it. It fits process mean and variance responses by support vector machines (SVM), and then optimizes levels of design parameters by genetic algorithm. In order to reduce experiment times, the influence of priori knowledge on generalized error of fitting model is studied. Then a prior knowledge based experiment design is developed. Moreover, the approach selects the form of kernel function and optimizes parameters in SVM by comparing the upper bounds of generalized error of different SVM models without extra samples. The example given in the paper shows that, the generalized error and the experiment times of the approach decrease by no less than 45% and 39% respectively, compared with traditional approaches. All these results demonstrate the adaptability and superiority of the approach proposed in the paper.

Mixture experiments in a robust parameter design (RPD) setting are commonly encountered in industry. The objective of a mixture-process RPD problem is to find levels for the controllable variables that result in a product that has a desirable mean response and that has small variability in the response transmitted from the noise variables. We consider statistical designs for experiments involving mixture variables, continuous noise variables, and categorical noise variables. We show how to construct designs for the RPD problem in the case of a mixture-process experiment with both continuous and categorical noise variables that simultaneously optimize the scaled prediction variances for the mean model and the slope model.

Design of systems based on computer simulations is prevalent. An important idea to improve design quality, called robust parameter design (RPD), is to optimize control factors based on the expectation of a loss function so that the design is robust to noise factor variations. When computer simulations are time consuming, optimizing the simulator based on a Gaussian process (GP) emulator for the response is a computationally efficient approach. For this purpose, acquisition functions (AFs) are used to sequentially determine the next design point so that the GP emulator can more accurately locate the optimal setting. Despite this, few articles consider AFs for positive definite quadratic forms such as the expected quadratic loss (EQL) function, which is the standard expected loss function for RPD with nominally-the-best responses. This paper proposes new AFs for optimizing the EQL, analyzes their convergence, and develops quick and accurate methods based on the characteristic function of the EQL to compute them. We apply the AFs to RPD problems with internal noise factors based on a GP model and an initial design tailored for such problems. Numerical results indicate that all four AFs considered have similar performance, and they outperform an optimization approach based on modeling the quadratic loss as a GP and maximin Latin hypercube designs. MATLAB codes for reproducing reported results are given in the online supplement.

On the use of three level orthogonal arrays in robust parameter design

Multiple parameter optimization methodology by integrating a game theory principle into priority-based decision making

SummaryRobust parameter design is an effective methodology for reducing variance and improving the quality of a product and a process. Recent work has mainly concentrated on two‐level robust parameter designs. We consider general robust parameter designs with factors having two or more or mixed levels these levels being either qualitative or quantitative. We propose a methodology and develop a generalised minimum aberration optimality criterion for selecting optimal robust parameter designs. A catalogue of 18‐run optimal designs is constructed and tabulated.

This study focuses on the modeling and optimization of geothermal binary Organic Rankine Cycle (ORC) systems to enhance power generation from geothermal systems using water as geofluid. Aspen HYSYS, utilizing the Peng-Robinson property package, was used to simulate the process, generating critical process data for subsequent modeling and optimization. Response Surface Methodology (RSM) and an Artificial Neural Network (ANN) were employed to model the relationships between input factors and output response, utilizing a Box-Behnken Design (BBD) for three key input variables: working fluid flow rate, working fluid outlet pressure, and turbine outlet pressure. Both RSM and ANN demonstrated strong predictive capabilities, with RSM achieving an R2 value of 0.9966 and an RMSE of 12.254, while ANN achieved an R2 value of 0.9886 and an RMSE of 23.722, indicating that RSM marginally outperformed ANN in terms of modelling accuracy. Optimization of the ORC system was conducted using RSM and ANN coupled with a Genetic Algorithm (ANN-GA), aimed at determining the optimal values for input and output parameters. The ANN-GA optimization results were validated using Aspen HYSYS and showed superior performance over RSM. ANN-GA predicted optimal values of working fluid flow rate, working fluid outlet pressure, and turbine outlet pressure as 12 kg/s, 19 bar, and 1.2 bar, respectively, which perfectly matched the Aspen HYSYS validation results. This optimization yielded a power output of 958.48 kW, which closely aligned with the Aspen HYSYS validation output of 952.9 kW, reflecting a minimal percentage error of 0.59%. Conversely, RSM predicted slightly deviated optimal values of 11.8 kg/s, 18.47 bar, and 1.2 bar, with a corresponding power output of 940.78 kW. When validated with HYSYS, the RSM-predicted output was 927.2 kW, resulting in a higher percentage error of 1.46%, thereby underperforming relative to ANN-GA. The study highlights the comparative strengths of RSM and ANN-GA, demonstrating that while RSM excels in accurately modeling the relationship and interactions between input factors and output responses, the ANN-GA framework exhibits a significantly higher capability in navigating complex nonlinear optimization landscapes. This highlights the effectiveness of integrating machine learning models with meta-heuristic algorithms for enhanced optimization performance. The findings contribute to advancing the methodology for optimizing geothermal ORC systems and offer a robust framework for improving power generation efficiency in geothermal energy applications.

A new method for welded joint fatigue reliability analysis on bogie frame of high-speed electric multiple unit (EMU) is proposed according to the International Union of Railways (UIC) standard, the Britain Standard Institute (BSI) standard and the Miner rule. Firstly, the fatigue calculation condition is loaded according to the UIC standard. The welded joint damage ratio is calculated by the BSI standard. Fatigue reliability analysis is conducted for a typical welded joint based on probabilistic design system (PDS) module in software ANSYS 14.0. In the system, the automatic program is prepared by ANSYS parametric design language (APDL) to calculate the welded joint fatigue damage ratio. Meantime, the relationship between the input variables and the output response is fitted by the response surface (RS) method. Then, the RS method is improved by the orthogonal design. Specifically, the selecting process optimization for the RS method based on the orthogonal design is conducted to improve the fitting efficiency of the RS method. Finally, a program of the automatic analysis documents is generated by Microsoft foundation class (MFC) technique. Through the self-defined interface, the researchers can easily import the automatic generation of the orthogonal table into the PDS module and analyze the fatigue reliability. Results show that the improved RS method can better fit the RS which covers the sample area, and the distribution law agrees well with the actual situation. At the same time, the improved RS method reduces the calculation time.

In recent years, the demand for plastic products has increased, and along with the deepening of academics, mass production, weight reduction, and high precision are progressing. In the fields of design development and production technology, there are many issues related to quality assurance such as molding defects and product strength. In particular, in the resin molding process, there is a high degree of freedom in product shape and mold structure, and it is an important issue to create quality functions that apply analysis of complex multidimensional information. In this study, the important factors of the resin molding process related to the optimization of resin strength are extracted by applying the multivariate analysis method and robust parameter design. As a result of verification of the proposed method, it is clarified that uniformization of the resin filling density in the mold is extremely important for stabilizing the resin strength.

ABSTRACTThe response surface-based robust parameter design, with its extensive use of optimization techniques and statistical tools, is known as an effective engineering design methodology for improving production processes, when input variables are quantitative on a continuous scale. In many engineering settings, however, there are situations where both qualitative and quantitative variables are considered. In such situations, traditional response surface designs may not be effective. To rectify this problem, this article lays out a foundation by embedding those input variables into a factorial design with pseudo-centre points. A 0–1 mixed-integer nonlinear programming model is then developed and the solutions found using three optimization tools, namely the outer approximation method, the branch-and-bound technique and the hybrid branch-and-cut algorithm, are compared with traditional counterparts. The numerical example shows that the proposed models result in better robust parameter design solutions than the traditional models.

Nowadays, several optimal parameter design tools have been developed for the nonlinear structures. These traditional approaches manage only the expectation values of the design variables, the loading conditions, and the assembly processes, although it is sure that there is variation due to the manufacturing or the assembling errors. The neglect sometimes causes the failure of the structures. There is no doubt that it is a better way to carry out optimal design of structure with consideration of the variation of design parameters and assembly processes. In this study, a technique of reliability design with considering the variation of the design variables was introduced into the optimization method of the SDSS (Statistical Design Support System) to achieve the robust and optimal parameter design for the nonlinear structures, where the second moment method was applied to evaluate the structure reliability. The SDSS was proposed by Yokohama National University, and it is an integrated design system based upon the response surface methodology and the design of experiments. The parameter optimization can be carried out with this system basing upon a small number of case studies. As an application of the proposed approach, the design optimization of a hydraulic servo valve was carried out, and the variation of assembly factors was considered.

This study examined the modelling and optimisation of the electrocoagulation-flocculation (ECF) recovery of aquaculture effluent (AQE) using aluminium electrodes. The response surface methodology (RSM), artificial neural network (ANN), and adaptive neuro-fuzzy inference system (ANFIS) were used for the modelling, while the optimisation tools were the numerical RSM and genetic algorithm (GA). Furthermore, the kinetics of the ECF process was studied to provide insight into the mechanism governing the ECF of AQE. The experimental design was performed using the central composite design (CCD) of the RSM. The ANFIS modelling was accomplished via the Grid Partition (GP) of the data set, while the ANN used the multi-layer perceptron (MLP) based feed-forward system. Statistically, the prediction accuracy of the models followed the order: ANFIS (R2: 0.9990), ANN (R2: 0.9807), and RSM (R2: 0.9790). The process optimisation gave optimal turbidity (TD) removal efficiencies of 98.98, 97.81, and 96.01% for ANFIS-GA, ANN-GA, and RSM optimisation techniques, respectively. The ANFIS-GA gave the best optimization result at optimum conditions of pH 4, current intensity (3 A), electrolysis time (7.2min), settling time (23min), and temperature (43.8°C). In the kinetics study, the experimental data was analysed using pseudo-first-order (0.8787), pseudo-second-order (0.9395), and Elovich (R2: 0.9979) kinetic models; the Elovich model gave the best correlation with the experimental data showing that the process is governed by electrostatic interaction mechanism. This study effectively demonstrated that ECF recovery of AQE can effectively be modelled using RSM, ANN, and ANFIS and be optimised using RSM, ANN-GA, and ANFIS-GA techniques, and the order of performance is ANFIS > ANN > RSM and ANFIS-GA > ANN-GA > RSM, respectively.