Palaniappan Ramu

In the design evolution of a product, designers often require solving similar functions repeatedly across different designs. These functions are usually related to each other and typically share topology, common features and physics. Thus, solving one function referred to as a source that characterizes a problem can yield knowledge that can be reused to solve other related function referred to as target. Re-purposing such shared knowledge, especially in cases of complex optimization, aids in faster convergence, more accurate solutions, and reduced computational costs, among others. The concept of transfer learning (TL) is built on this notion of passing the gained knowledge between related problems to lessen the algorithmic and/or modeling complexities. Transfer of knowledge between source and target that are not related leads to negative transfer circumstances, where the algorithm's performance degrades on transferring. Hence, identifying a similar source to share the knowledge is of fundamental importance in transfer learning approaches. Literature has often skipped this step of identifying related or similar functions by artificially constructing functions or assuming apriori that the considered functions are similar to each other. Current work proposes to use interpretable self-organizing map and an image comparison technique to quantify the topological similarity between the source and the target. Metrics such as mean squares, structural similarity index, and Cosine similarity are used to quantify the level of similarity mathematically. The proposed approach is implemented on a suite of benchmark analytical functions with varying order, complexity, and dimensions, engineering examples, and real-world application functions. It is demonstrated that the proposed approach is able to identify appropriate source function for a given target, even when they are of varying dimensions. Results of engineering examples show that functions representing problems with similar physics are identified correctly. Hence, the proposed approach can be used to identify appropriate source functions for a given target, permitting transfer learning and thus accelerating convergence, and reducing computational cost.

Treatment of uncertainties in structural design involves identifying the boundaries of the failure domain to estimate reliability. When the structural responses are discontinuous or highly nonlinear, the failure regions tend to be an island in the design space. The boundaries of these islands are to be approximated to estimate reliability and perform optimization. This work proposes Alpha (α) shapes, a computational geometry technique to approximate such boundaries. The α shapes are simple to construct and only require Delaunay Tessellation. Once the boundaries are approximated based on responses sampled in a design space, a computationally efficient ray shooting algorithm is used to estimate the reliability without any additional simulations. The proposed approach is successfully used to decompose the design space and perform Reliability based Design Optimization of a tube impacting a rigid wall and a tuned mass damper.

Machine Learning (ML) techniques have been used in an extensive range of applications in the field of structural and multidisciplinary optimization over the last few years. This paper presents a survey of this wide but disjointed literature on ML techniques in the structural and multidisciplinary optimization field. First, we discuss the challenges associated with conventional optimization and how Machine learning can address them. Then, we review the literature in the context of how ML can accelerate design synthesis and optimization. Some real-life engineering applications in structural design, material design, fluid mechanics, aerodynamics, heat transfer, and multidisciplinary design are summarized, and a brief list of widely used open-source codes as well as commercial packages are provided. Finally, the survey culminates with some concluding remarks and future research suggestions. For the sake of completeness, categories of ML problems, algorithms, and paradigms are presented in the Appendix.

Design optimization of structural and multidisciplinary systems under uncertainty has been an active area of research due to its evident advantages over deterministic design optimization. In deterministic design optimization, the uncertainties of a structural or multidisciplinary system are taken into account by using safety factors specified in the regulations or design codes. This uncertainty treatment is a subjective and indirect way of dealing with uncertainty. On the other hand, design under uncertainty approaches provide an objective and direct way of dealing with uncertainty. This paper provides a review of the uncertainty treatment practices in design optimization of structural and multidisciplinary systems under uncertainties. To this end, the activities in uncertainty modeling are first reviewed, where theories and methods on uncertainty categorization (or classification), uncertainty handling (or management), and uncertainty characterization are discussed. Second, the tools and techniques developed and used for uncertainty modeling and propagation are discussed under the broad two classes of probabilistic and non-probabilistic approaches. Third, various design optimization methods under uncertainty which incorporate all the techniques covered in uncertainty modeling and analysis are reviewed. In addition to these in-depth reviews on uncertainty modeling, uncertainty analysis, and design optimization under uncertainty, some real-life engineering applications and benchmark test examples are provided in this paper so that readers can develop an appreciation on where and how the discussed techniques can be applied and how to compare them. Finally, concluding remarks are provided, and areas for future research are suggested.