Palaniappan Ramu

Robust Design architectures permit identifying designs in the input space that minimize the mean as well as the spread of the response in the performance space, when the input variables are uncertain. Often, information about uncertainties is not readily available and are usually characterized by scarce samples that might contain extremes. Since extremes are part of the data, they cannot be excluded but including extremes alter the measures of spread such as standard deviation. Hence, it is imperative to develop a robust design architecture where the measure of spread estimations are less sensitive or insensitive to extremes. We propose using L-moments to estimate the measure of spread, the second L-moment (l2) and use it in the robust design formulation. We consider the cases of design variables which can be deterministic or random, and random variables. Hence, we use a dual surrogate framework where a design surrogate is built first. At each point in the DoE, scarce samples that might include extremes of the random variables are propagated through the design surrogate. Mean and measure of spread are computed by the L-moments approach at each point in the DoE, from the responses computed upon propagation, and used to build analysis surrogate which is used for identifying the robust design. The proposed approach is demonstrated on 2D Aspenberg function, 5D truss and 17D rotor disk design examples. The results reveal the superiority of the proposed approach over the conventional formulation.

Uncertainties in the input variables are inevitable in any design process. As a consequence, the output responses are also uncertain. Robust design is one of the sought after approach to treat such uncertainties for controlling the variation in the output responses, while maximizing the mean performance. Variation is modeled by a measure of data spread. Often, the details of the uncertainties in the input space are not available readily and they are usually characterized from scarce sample realizations. In addition, there could also be outliers in the realizations. These will increase the error in the measure of spread of the output response. Hence, it is desirable that an approach that is insensitive to outliers but can characterize the spread of data is developed for robust design. In this work we propose using L moments to model the spread of data. The classical robust design formulation is reformulated using the second L moment (l2). The proposed approach is demonstrated on a turbine disk design with 17 design and random variables. The details of the uncertainties are not known. A DoE of 200 samples is used and at each DoE point, we propagate the uncertainties using scarce samples, which include outliers. Robust design is performed and it is shown that the proposed approach works better than the classical robust design formulation.

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.