Agus Sudjianto

Algorithmic construction of optimal symmetric Latin hypercube designs

Abstract We propose symmetric Latin hypercubes for designs of computer experiment. The goal is to offer a compromise between computing effort and design optimality. The proposed class of designs has some advantages over the regular Latin hypercube design with respect to criteria such as entropy and the minimum intersite distance. An exchange algorithm is proposed for constructing optimal symmetric Latin hypercube designs. This algorithm is compared with two existing algorithms by Park (1994. J. Statist. Plann. Inference 39, 95–111) and Morris and Mitchell (1995. J. Statist. Plann. Inference 43, 381–402). Some examples, including a real case study in the automotive industry, are used to illustrate the performance of the new designs and the algorithms.

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.

ON SEQUENTIAL SAMPLING FOR GLOBAL METAMODELING IN ENGINEERING DESIGN

Approximation models (also known as metamodels) have been widely used in engineering design to facilitate analysis and optimization of complex systems that involve computationally expensive simulation programs. The accuracy of metamodels is directly related to the sampling strategies used. Our goal in this paper is to investigate the general applicability of sequential sampling for creating global metamodels. Various sequential sampling approaches are reviewed and new approaches are proposed. The performances of these approaches are investigated against that of the one-stage approach using a set of test problems with a variety of features. The potential usages of sequential sampling strategies are also discussed.Copyright

Blind Kriging: A New Method for Developing Metamodels

Kriging is a useful method for developing metamodels for product design optimization. The most popular kriging method, known as ordinary kriging, uses a constant mean in the model. In this article, a modified kriging method is proposed, which has an unknown mean model. Therefore, it is called blind kriging. The unknown mean model is identified from experimental data using a Bayesian variable selection technique. Many examples are presented, which show remarkable improvement in prediction using blind kriging over ordinary kriging. Moreover, a blind kriging predictor is easier to interpret and seems to be more robust against mis-specification in the correlation parameters.

Enhancing Discrete Choice Demand Modeling for Decision-Based Design

Our research is motivated by the need for developing an approach to demand modeling that is critical for assessing the profit a product can bring under the decision-based design framework. Even though demand modeling techniques exist in market research, little work exists on demand modeling that addresses the specific needs of engineering design, in particular, that facilitates engineering decision making. In this work, we enhance the use of discrete choice analysis to demand modeling in the context of decision-based design. The consideration of a hierarchy of product attributes is introduced to map customer desires to engineering design attributes related to engineering analyses. To improve the predictive capability of demand models, the Kano method is employed to provide econometric justification when selecting the shape of the customer utility function. A (passenger) vehicle engine case study, developed in collaboration with the market research firm, J. D. Power & Associates, and the Ford Motor Company, is used to demonstrate the proposed approaches.

Relative Entropy Based Method for Probabilistic Sensitivity Analysis in Engineering Design

In this paper, a new Probabilistic Sensitivity Analysis (PSA) approach based on the concept of relative entropy is proposed for design under uncertainty. The relative entropy based method evaluates the impact of a random variable on a design performance by measuring the divergence between two probability density functions of the performance response, obtained before and after the variation reduction of the random variable. The method can be applied both over the whole distribution of a performance response [called global response probabilistic sensitivity analysis (GRPSA)] and in any interested partial range of a response distribution [called regional response probabilistic sensitivity analysis (RRPSA)]. Such flexibility of our approach facilitates its use under various scenarios of design under uncertainty, for instance in robust design, reliability-based design, and utility optimization. The proposed method is applicable to both the prior-design stage for variable screening when a design solution is yet identified and the post-design stage for uncertainty reduction after an optimal design has been determined. The saddlepoint approximation approach is introduced for improving the computational efficiency of applying our proposed method. The proposed method is illustrated and verified by numerical examples and industrial design cases.

Analytical Variance-Based Global Sensitivity Analysis in Simulation-Based Design Under Uncertainty

The importance of sensitivity analysis in engineering design cannot be over-emphasized. In design under uncertainty, sensitivity analysis is performed with respect to the probabilistic characteristics. Global sensitivity analysis (GSA), in particular, is used to study the impact of variations in input variables on the variation of a model output. One of the most challenging issues for GSA is the intensive computational demand for assessing the impact of probabilistic variations. Existing variance-based GSA methods are developed for general functional relationships but require a large number of samples. in this work, we develop an efficient and accurate approach to GSA that employs analytic formulations derived from metamodels. The approach is especially applicable to simulation-based design because metamodels are often created to replace expensive simulation programs, and therefore readily available to designers. In this work, we identify the needs of GSA in design under uncertainty, and then develop generalized analytical formulations that can provide GSA for a variety of metamodels commonly used in engineering applications. We show that even though the function forms of these metamodels vary significantly, they all follow the form of multivariate tensor-product basis functions for which the analytical results of univariate integrals can be constructed to calculate the multivariate integrals in GSA. The benefits of our proposed techniques are demonstrated and verified through both illustrative mathematical examples and the robust design for improving vehicle handling performance.

Analysis of Computer Experiments Using Penalized Likelihood in Gaussian Kriging Models

Kriging is a popular analysis approach for computer experiments for the purpose of creating a cheap-to-compute “meta-model” as a surrogate to a computationally expensive engineering simulation model. The maximum likelihood approach is used to estimate the parameters in the kriging model. However, the likelihood function near the optimum may be flat in some situations, which leads to maximum likelihood estimates for the parameters in the covariance matrix that have very large variance. To overcome this difficulty, a penalized likelihood approach is proposed for the kriging model. Both theoretical analysis and empirical experience using real world data suggest that the proposed method is particularly important in the context of a computationally intensive simulation model where the number of simulation runs must be kept small because collection of a large sample set is prohibitive. The proposed approach is applied to the reduction of piston slap, an unwanted engine noise due to piston secondary motion. Issues related to practical implementation of the proposed approach are discussed.

WireVis: Visualization of Categorical, Time-Varying Data From Financial Transactions

Large financial institutions such as Bank of America handle hundreds of thousands of wire transactions per day. Although most transactions are legitimate, these institutions have legal and financial obligations in discovering those that are suspicious. With the methods of fraudulent activities ever changing, searching on predefined patterns is often insufficient in detecting previously undiscovered methods. In this paper, we present a set of coordinated visualizations based on identifying specific keywords within the wire transactions. The different views used in our system depict relationships among keywords and accounts over time. Furthermore, we introduce a search-by-example technique which extracts accounts that show similar transaction patterns. In collaboration with the Anti-Money Laundering division at Bank of America, we demonstrate that using our tool, investigators are able to detect accounts and transactions that exhibit suspicious behaviors.

Selective Assembly in Manufacturing: Statistical Issues and Optimal Binning Strategies

Selective assembly is a cost-effective approach for reducing the overall variation and thus improving the quality of an assembled product. In this process, components of a mating pair are measured and grouped into several classes (bins) as they are manufactured. The final product is assembled by selecting the components of each pair from appropriate bins to meet the required specifications as closely as possible. This approach is often less costly than tolerance design using tighter specifications on individual components. It leads to high-quality assembly using relatively inexpensive components. In this article we describe the statistical formulation of the problem and develop optimal binning strategies under several loss functions and distributional assumptions. Optimal schemes under absolute and squared error loss are studied in detail. The results are compared with two commonly used heuristic schemes. We consider situations in which only one component of the mating pair is binned, as well as cases in which both components are binned.