Ying Hung

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.

Optimizing Latin hypercube designs by particle swarm

Latin hypercube designs (LHDs) are widely used in many applications. As the number of design points or factors becomes large, the total number of LHDs grows exponentially. The large number of feasible designs makes the search for optimal LHDs a difficult discrete optimization problem. To tackle this problem, we propose a new population-based algorithm named LaPSO that is adapted from the standard particle swarm optimization (PSO) and customized for LHD. Moreover, we accelerate LaPSO via a graphic processing unit (GPU). According to extensive comparisons, the proposed LaPSO is more stable than existing approaches and is capable of improving known results.

Analysis of Computer Experiments With Functional Response

This article is motivated by a computer experiment conducted for optimizing residual stresses in the machining of metals. Although kriging is widely used in the analysis of computer experiments, it cannot be easily applied to model the residual stresses because they are obtained as a profile. The high dimensionality caused by this functional response introduces severe computational challenges in kriging. It is well known that if the functional data are observed on a regular grid, the computations can be simplified using an application of Kronecker products. However, the case of irregular grid is quite complex. In this article, we develop a Gibbs sampling-based expectation maximization algorithm, which converts the irregularly spaced data into a regular grid so that the Kronecker product-based approach can be employed for efficiently fitting a kriging model to the functional data. Supplementary materials are available online.

Design and Analysis of Computer Experiments With Branching and Nested Factors

In many experiments, some of the factors exist only within the level of another factor. Such factors are often called nested factors. A factor within which other factors are nested is called a branching factor. Suppose, for example, that we want to experiment with two processing methods. The factors involved in these two methods can be different. Thus in this experiment, the processing method is a branching factor, and the other factors are nested within the branching factor. The design and analysis of experiments with branching and nested factors are challenging and have not received much attention in the literature. Motivated by a computer experiment in a machining process, we have developed optimal Latin hypercube designs and kriging methods that can accommodate branching and nested factors. Through the application of the proposed methods, optimal machining conditions and tool edge geometry are attained, which resulted in a remarkable improvement in the machining process.

Discrete particle swarm optimization for constructing uniform design on irregular regions

Central composite discrepancy (CCD) has been proposed to measure the uniformity of a design over irregular experimental region. However, how CCD-based optimal uniform designs can be efficiently computed remains a challenge. Focusing on this issues, we proposed a particle swarm optimization-based algorithm to efficiently find optimal uniform designs with respect to the CCD criterion. Parallel computation techniques based on state-of-the-art graphic processing unit (GPU) are employed to accelerate the computations. Several two- to five-dimensional benchmark problems are used to illustrate the advantages of the proposed algorithms. By solving a real application in data center thermal management, we further demonstrate that the proposed algorithm can be extended to incorporate desirable space-filling properties, such as the non-collapsing property.

Adaptive Probability-Based Latin Hypercube Designs

Adaptive sampling is an effective method developed mainly for regular regions. However, experimental regions in irregular shapes are commonly observed in practice. Motivated by a data center thermal management study, a new class of adaptive designs is proposed to accommodate a specific type of irregular region. Because the adaptive procedure introduces biases into conventional estimators, several design-unbiased estimators are given for estimating the population mean. Efficient and easy-to-compute unbiased estimators are also introduced. The proposed method is applied to obtain an adaptive sensor placement plan to monitor and study the thermal distribution in a data center. All of the supplemental materials used in this work are available online.

Effects of Warpage on Fatigue Reliability of Solder Bumps: Experimental and Analytical Studies

Out-of-plane displacement (warpage) has been a major thermomechanical reliability concern for board-level electronic packages. Printed wiring board (PWB) and component warpage results principally from CTE mismatch among the materials that make up the PWB assembly (PWBA). Warpage occurring during surface-mount assembly reflow processes and normal operations may lead to severe solder bump reliability problems. In this research, the effect of initial PWB warpage on the low cycle thermal fatigue reliability of the solder bumps in plastic ball grid array (PBGA) packages was studied using experimental and analytical methods. A real-time projection moire warpage measurement system was used to measure the surface topology of PWBA samples at different temperatures. The thermal fatigue reliability of solder bumps was evaluated from experimental thermal cycling tests and finite element simulation results. Three-dimensional (3-D) models of PWBAs with varying board warpage were used to estimate the solder bump fatigue life for different types of PBGAs mounted on PWBs. In order to improve the accuracy of FE results, the projection moire method was used to measure the initial warpage of PWBs, and this warpage was used as a geometric input to the FEM. The simulation results were validated and correlated with the experimental results obtained using the projection moire technique and accelerated thermal cycling tests. An advanced prediction model was generated to predict board level solder bump fatigue life based on the initial PWB warpage, package dimensions and locations, and solder bump materials.

Effects of warpage on fatigue reliability of solder bumps: Experimental and analytical studies

Out-of-plane displacement (warpage) has been a major thermomechanical reliability concern for board-level electronic packages. Printed wiring board (PWB) and component warpage results principally from coefficient of thermal expansion mismatch among the materials that make up the PWB assembly (PWBA). Warpage occurring during surface-mount assembly reflow processes and normal operations may lead to severe solder bump reliability problems. In this research, the effect of initial PWB warpage on the low cycle thermal fatigue reliability of the solder bumps in plastic ball grid array (PBGA) packages was studied using experimental and analytical methods. A real-time projection moire¿ warpage measurement system was used to measure the surface topology of PWBA samples at different temperatures. The thermal fatigue reliability of solder bumps was evaluated from experimental thermal cycling tests and finite element simulation results. Three-dimensional (3-D) models of PWBAs with varying board warpage were used to estimate the solder bump fatigue life for different types of PBGAs mounted on PWBs. In order to improve the accuracy of FE results, the projection moire¿ method was used to measure the initial warpage of PWBs, and this warpage was used as a geometric input to the finite element method. The simulation results were validated and correlated with the experimental results obtained using the projection moire¿ technique and accelerated thermal cycling tests. An advanced prediction model was generated to predict board level solder bump fatigue life based on the initial PWB warpage, package dimensions and locations, and solder bump materials.

Binary Time Series Modeling With Application to Adhesion Frequency Experiments

Repeated adhesion frequency assay is the only published method for measuring the kinetic rates of cell adhesion. Cell adhesion plays an important role in many physiological and pathological processes. Traditional analysis of adhesion frequency experiments assumes that the adhesion test cycles are independent Bernoulli trials. This assumption often can be violated in practice. Motivated by the analysis of repeated adhesion tests, a binary time series model incorporating random effects is developed. A goodness-of-fit statistic is introduced to assess the adequacy of distribution assumptions on the dependent binary data with random effects. The asymptotic distribution of the goodness-of-fit statistic is derived, and its finite-sample performance is examined through a simulation study. Application of the proposed methodology to real data from a T-cell experiment reveals some interesting information, including the dependency between repeated adhesion tests.

Robust Kriging Models in Computer Experiments

In the Gaussian Kriging model, errors are assumed to follow a Gaussian process. This is reasonable in many cases, but such an assumption is not appropriate for the situations when outliers are present. Large prediction errors may occur in those cases and more robust estimation is critical. In this article, we propose a robust estimation of Kriging parameters by utilizing other loss functions rather than classical L2. In the Gaussian Kriging model, regression parameters are estimated by generalized least squares, which are also referred to as L2 criterion. To make these estimators more robust to outliers, the L1 and the ɛ-insensitive loss functions are introduced in place of L2 in this article. Mathematical programming formulations are developed upon the idea of support vector machine. A machining experiment data are analysed to verify usefulness of the proposed method.