House of Quality

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Citizen Science: A Study of People, Expertise and Sustainable Development

International Joint Conference on Neural Networks

Computational methods in optimization considering uncertainties – An overview

Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles

A novel data-driven visualization of n-dimensional feasible region using interpretable self-organizing maps (iSOM)

Transfer learning in optimization: Interpretable self-organizing maps driven similarity indices to identify candidate source functions

Bayesian inference is a powerful technique for damage/flaw detection in critical structures. This paper explores the application of Bayesian inference to identify the flaws (voids/inclusions) and its parameters, assuming no information about the flaws is known a priori. Multiple flaws are represented by a parameter vector that contains the locations and the geometric information. In the inverse problem framework, the Scaled Boundary Finite Element Method (SBFEM) with quadtree decomposition is used to solve the forward problem. The flaw parameters are statistically quantified using the Bayesian inference. The likelihood function and prior information update the joint distribution of the number of flaws and their corresponding flaw parameters. The sampling to estimate the posterior distribution of the flaw parameters is based on the trans-dimensional Reversible Jump Markov Chain Monte Carlo (RJMCMC). Also, the impact of additive Gaussian noise on the observed data is investigated. Numerical examples include identifying multiple voids of different shapes such as circle and ellipse and identifying voids and inclusions, using the proposed approach with input sensor data at different noise levels. 

SBFEM and Bayesian inference for efficient multiple flaw detection in structures


 Design preferences or targets are typically available at system level. A designer is usually interested in understanding patches of design space at component levels, across different stages and process that corresponds to such system targets or preferences. This demands a thorough design space exploration permitting both forward and inverse designs. Such exploration becomes cumbersome with large variables and complex systems with conflicting goals. Current work proposes using interpretable self organising map (iSOM) as a visual enabler of decision support system for exploring designs to understand the trade off in system targets/goals. The novelty lies in being able to use a visual form to compare greater than three conflicting goals simultaneously while accounting for design variables. The proposed approach is demonstrated using two test problems: i) hot rolling and cooling process chain design for the production of steel rods and ii) head and neck-injury risk evaluations for vehicular crashworthiness. Using the first problem, we demonstrate the capability of iSOM for the solution space exploration of a many-objective steel manufacturing process chain problem to realize the design of a steel product, in the context of a compromise Decision Support Problem formulation. In the second problem, we demonstrate the capability of iSOM for early-stage design space exploration to identify critical injury-risk regions of interest for different car crash scenarios. These two case studies illustrate the capability to carry out a forward and inverse design, by the proposed approach.

Data Driven Integrated Design Space Exploration Using iSOM

Importance sampling is a variance reduction technique that is used to improve the efficiency of Monte Carlo estimation. Importance sampling uses the trick of sampling from a distribution, which is located around the zone of interest of the primary distribution thereby reducing the number of realizations required for an estimate. In the context of reliability-based structural design, the limit state is usually separable and is of the form Capacity (C)–Response (R). The zone of interest for importance sampling is observed to be the region where these distributions overlap each other. However, often the distribution information of C and R themselves are not known, and one has only scarce realizations of them. In this work, we propose approximating the probability density function and the cumulative distribution function using kernel functions and employ these approximations to find the parameters of the importance sampling density (ISD) to eventually estimate the reliability. In the proposed approach, in addition to ISD parameters, the approximations also played a critical role in affecting the accuracy of the probability estimates. We assume an ISD which follows a normal distribution whose mean is defined by the most probable point (MPP) of failure, and the standard deviation is empirically chosen such that most of the importance sample realizations lie within the means of R and C. Since the probability estimate depends on the approximation, which in turn depends on the underlying samples, we use bootstrap to quantify the variation associated with the low failure probability estimate. The method is investigated with different tailed distributions of R and C. Based on the observations, a modified Hill estimator is utilized to address scenarios with heavy-tailed distributions where the distribution approximations perform poorly. The proposed approach is tested on benchmark reliability examples and along with surrogate modeling techniques is implemented on four reliability-based design optimization examples of which one is a multi-objective optimization problem.

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Palaniappan Ramu

Papers

A novel data-driven visualization of n-dimensional feasible region using interpretable self-organizing maps (iSOM)

Transfer learning in optimization: Interpretable self-organizing maps driven similarity indices to identify candidate source functions

SBFEM and Bayesian inference for efficient multiple flaw detection in structures

Data Driven Integrated Design Space Exploration Using iSOM

Scarce Sample-Based Reliability Estimation and Optimization Using Importance Sampling