Lee J. Wells

Bayesian reliability based design optimization using eigenvector dimension reduction (EDR) method

In practical engineering design, most data sets for system uncertainties are insufficiently sampled from un- known statistical distributions, known as epistemic uncer- tainty. Existing methods in uncertainty-based design optimization have difficulty in handling both aleatory and epistemic uncertainties. To tackle design problems engaging both epistemic and aleatory uncertainties, reliability-based design optimization (RBDO) is integrated with Bayes theorem. It is referred to as Bayesian RBDO. However, Bayesian RBDO becomes extremely expensive when employing the first- or second-order reliability method (FORM/SORM) for reliability predictions. Thus, this paper proposes development of Bayesian RBDO methodology and its integration to a numerical solver, the eigenvector dimension reduction (EDR) method, for Bayesian reliabil- ity analysis. The EDR method takes a sensitivity-free approach for reliability analysis so that it is very efficient and accurate compared with other reliability methods such as FORM/SORM. Efficiency and accuracy of the Bayesian RBDO process are substantially improved after this integration.

Variation propagation analysis on compliant assemblies considering contact interaction

Dimensional variation is inherent to any manufacturing process. In order to minimize its impact on assembly products it is important to understand how the variation propagates through the assembly process. Unfortunately, manufacturing processes are complex and in many cases highly nonlinear Traditionally, assembly process modeling has been approached as a linear process. However, many assemblies undergo highly complex nonlinear physical processes, such as compliant deformation, contact interaction, and welding thermal deformation. This paper presents a new variation propagation methodology considering the compliant contact effect, which will be analyzed through nonlinear frictional contact analysis. Its variation prediction will be accurately and efficiently conducted using an enhanced dimension reduction method. A case study is presented to show the applicability of the proposed methodology.

Methods for Monitoring Multiple Proportions When Inspecting Continuously

As technology advances, the need for methods to monitor processes that produce readily-available inspection data becomes essential. In this paper, a multinomial cumulative sum (CUSUM) chart is proposed to monitor in situations where items can be classified into more than two categories, the items are not put into subgroups, and the direction of the out-of-control shift in the parameter vector can be specified. It is shown through examples that the multinomial CUSUM chart can detect shifts in category probabilities at least as quickly and, in most cases, faster than using multiple Bernoulli CUSUM charts. The properties of the multinomial CUSUM chart are determined through a Markov chain representation. If the direction of the out-of-control shift in the parameter vector cannot be specified, we recommend the use of multiple Bernoulli CUSUM charts.

Enhanced Dimension-Reduction (eDR) Method for Sensitivity-Free Uncertainty Quantification

In this paper, the enhanced Dimension Reduction (eDR) method is proposed for uncertainty quantification that is an improved version of the DR method. It has been acknowledged that the DR method is accurate and efficient for assessing statistical moments of mildly nonlinear system responses. However, the recent investigation on the DR method has found difficulties of instability and inaccuracy for large-scale nonlinear systems, while maintaining reasonable efficiency. The eDR method is composed of four new technical elements: one-dimensional response approximation, Axial-Design of Experiment (A-DOE), numerical integration scheme, and a modified Pearson system. First, the Stepwise Moving Least Squares method is employed to accurately approximate the responses. Second, 2N+1 and 4N+1 A-DOEs are proposed to maintain high accuracy of the eDR method for UQ analysis. Third, in aid of approximated responses, any numerical integration scheme can be used with accurate but free response values at any set of integration points. Fourth, a modified Pearson system will be proposed to avoid its singular behavior while precisely predicting reliability and quality of engineering systems. Results for some engineering examples indicate that the eDR method is better than any other probability analysis methods in estimating statistical moments, reliability, and quality of the systems.

Stochastic Response Surface Using the Enhanced Dimension-Reduction (eDR) Method for Reliability-Based Robust Design Optimization

As the reliability analysis and design methodology has been advanced, its implementation becomes more complicated to improve computational efficiency and stability. Furthermore, most reliability analysis methods in RBDO require gradient (or sensitivity) information [1]. Therefore, this paper attempts to develop a stochastic response surface method. The method makes it possible to perform sensitivity-free RBDO using any deterministic optimizer. Recently, the dimension reduction (DR) method has been proposed [2]. Although the DR method is known to be an accurate and efficient method for the uncertainty quantification (UQ) of system responses, it may produce a relatively large error for the second-order or higher moments of nonlinear responses. Thus, this paper first proposes the enhanced dimension-reduction (eDR) method [3] by incorporating two alternative integration schemes and one-dimensional response approximations. Both moment based quadrature rule and an adaptive Simpson integration rule are alternatively used for numerical integration. The stepwise moving least squares (SMLS) method is proposed for response approximation. The SMLS is based on a moving least squares (MLS) method. Secondly, the paper proposes a stochastic response surface method. The stochastic response surface is built using the SMLS method with the results of the eDR method at sampled designs. In aid of the stochastic response surface method, RBDO or robust design optimization can be performed with commercial (deterministic) optimization softwares (e.g., Microsoft Excel, Matlab, etc.). In this paper, some examples are used to demonstrate the eDR method and further the stochastic response surface method for RBDO.

Sensitivity-Free Approach for Reliability-Based Robust Design Optimization

This paper attempts to integrate a derivative-free probability analysis method to Reliability-Based Robust Design Optimization (RBRDO). The Eigenvector Dimension Reduction (EDR) method is used for the probability analysis method. It has been demonstrated that the EDR method is more accurate and efficient than the Second-Order Reliability Method (SORM) for reliability and quality assessment. Moreover, it can simultaneously evaluate both reliability and quality without any extra expense. Three practical engineering problems (vehicle side impact, layered bonding plates, and lower control arm) are used to demonstrate the effectiveness of the EDR method.Copyright

Automated Part Inspection Using 3D Point Clouds

Ever advancing sensor and measurement technologies continually provide new opportunities for knowledge discovery and quality control (QC) strategies for complex manufacturing systems. One such state-of-the-art measurement technology currently being implemented in industry is the 3D laser scanner, which can rapidly provide millions of data points to represent an entire manufactured part’s surface. This gives 3D laser scanners a significant advantage over competing technologies that typically provide tens or hundreds of data points. Consequently, data collected from 3D laser scanners have a great potential to be used for inspecting parts for surface and feature abnormalities. The current use of 3D point clouds for part inspection falls into two main categories; 1) Extracting feature parameters, which does not complement the nature of 3D point clouds as it wastes valuable data and 2) An ad-hoc manual process where a visual representation of a point cloud (usually as deviations from nominal) is analyzed, which tends to suffer from slow, inefficient, and inconsistent inspection results. Therefore our paper proposes an approach to automate the latter approach to 3D point cloud inspection. The proposed approach uses a newly developed adaptive generalized likelihood ratio (AGLR) technique to identify the most likely size, shape, and magnitude of a potential fault within the point cloud, which transforms the ad-hoc visual inspection approach to a statistically viable automated inspection solution. In order to aid practitioners in designing and implementing an AGLR-based inspection process, our paper also reports the performance of the AGLR with respect to the probability of detecting specific size and magnitude faults in addition to the probability of a false alarms.Copyright

A Bio-Inspired Framework for a Self-Healing Assembly System

Statistical process monitoring and control has been popularized throughout the manufacturing industry as well as various other industries interested in improving product quality and reducing costs. Advances in this field have focused primarily on more efficient ways for diagnosing faults, reducing variation, developing robust design techniques, and increasing sensor capabilities. System level advances are largely dependent on the introduction of new techniques in the listed areas. A unique system level quality control approach is introduced in this paper as a means to integrate rapidly advancing computing technology and analysis methods in manufacturing systems. Inspired by biological systems, the developed framework utilizes immunological principles as a means of developing self-healing algorithms and techniques for manufacturing assembly systems. The principles and techniques attained through this bio-mimicking approach will be used for autonomous monitoring, detection, diagnosis, prognosis, and control of station and system level faults, contrary to traditional systems that largely rely on final product measurements and expert analysis to eliminate process faults.Copyright

Geometric optimization of a piezoelectric power harvesting plate for increased bandwidth

The continual advances in wireless technology and low power electronics have allowed the deployment of small remote sensor networks. However, current portable and wireless devices must be designed to include electrochemical batteries as the power source. The use of batteries can be troublesome due to their limited lifespan, thus necessitating their periodic replacement. Furthermore, the growth of battery technology has remained relatively stagnant over the past decade while the performance of computing systems has grown steadily, which leads to increased power usage from the electronics. In the case of wireless sensors that are to be placed in remote locations, the sensor must be easily accessible or of disposable nature to allow the device to function over extended periods of time. For this reason the primary question becomes how to provide power to each node. This issue has spawned the rapid growth of the energy harvesting field. Energy scavenging devices are designed to capture the ambient energy surrounding the electronics and convert it into usable electrical energy. The concept of power harvesting works towards developing self-powered devices that do not require replaceable power supplies. However, when designing a vibration based energy harvesting system the maximum energy generation occurs when the resonant frequency of the system is tuned to the input. This poses certain issues for their practical application because structural systems rarely vibrate at a signal frequency. Therefore, this effort will investigate the optimal geometric design of two dimensional energy harvesting systems for maximized bandwidth. Topology and shape optimization will be used to identify the optimal geometry and experiments will be performed to characterize the energy harvesting improvement when subjected to random vibrations.Copyright

Innovative Six Sigma Design Using the Eigenvector Dimension-Reduction (EDR) Method

This paper presents an innovative approach for quality engineering using the Eigenvector Dimension Reduction (EDR) Method. Currently industry relies heavily upon the use of the Taguchi method and Signal to Noise (S/N) ratios as quality indices. However, some disadvantages of the Taguchi method exist such as, its reliance upon samples occurring at specified levels, results to be valid at only the current design point, and its expensiveness to maintain a certain level of confidence. Recently, it has been shown that the EDR method can accurately provide an analysis of variance, similar to that of the Taguchi method, but is not hindered by the aforementioned drawbacks of the Taguchi method. This is evident because the EDR method is based upon fundamental statistics, where the statistical information for each design parameter is used to estimate the uncertainty propagation through engineering systems. Therefore, the EDR method provides much more extensive capabilities than the Taguchi method, such as the ability to estimate not only mean and standard deviation of the response, but also the skewness and kurtosis. The uniqueness of the EDR method is its ability to generate the probability density function (PDF) of system performances. This capability, known as the probabilistic “what-if” study, provides a visual representation of the effects of the design parameters (e.g., its mean and variance) upon the response. In addition, the probabilistic “what-if” study can be applied across multiple design parameters, allowing the analysis of interactions among control factors. Furthermore, the implementation of the probabilistic “what-if” study provides a basis for performing robust design optimization. Because of these advantages, it is apparent that the EDR method provides an alternative platform of quality engineering to the Taguchi method. For easy execution by field engineers, the proposed platform for quality engineering using the EDR method, known as Quick Quality Quantification (Q3 ), will be developed as a Microsoft EXCEL add-in.Copyright