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Boosting Engineering Optimization With a Novel Recursive Transfer Bifidelity Surrogate Modeling

JOURNAL OF MECHANICAL design 2025年第3期147卷 031704页

作者： Song, Xueguan Zhang, Shuai Pang, Yong Li, Jianji Zhang, Jiankang Dalian Univ Technol Sch Mech Engn Dalian 116024 Peoples R China Dalian Univ Technol State Key Lab High Performance Precis Mfg Dalian 116024 Peoples R China

In the engineering optimization, there often exist the multiple sources of information with different fidelity levels. In general, low-fidelity (LF) information is usually more accessible than high-fidelity (HF) information, while the latter is usually more accurate than the former. Thus, to capitalize on the advantages of this information, this study proposes a novel recursive transfer bifidelity surrogate modeling to fuse information from HF and LF levels. First, the selection method of optimal scale factor is proposed for constructing bifidelity surrogate model. Then, a recursive method is developed to further improve its performance. The efficacy of the proposed model is comprehensively evaluated using numerical problems and an engineering example. Comparative analysis with some surrogate models (five multifidelity and a single-fidelity surrogate models) demonstrates the superior prediction accuracy and robustness of the proposed model. Additionally, the impact of varying cost ratios and combinations of HF and LF samples on the performance of the proposed model is also investigated, yielding consistent results. Overall, the proposed model has superior performance and holds potential for practical applications in engineering design optimization problems.

关键词： information fusion bi-fidelity surrogate model maximum mean discrepancy recursive method approximation-based optimal design metamodeling

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A Right-Hand Side Function Surrogate Model-based Method for the Black-Box Dynamic Optimization Problem

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JOURNAL OF MECHANICAL design 2023年第9期145卷 091701-091701页

作者： Zhang, Qi Wu, Yizhong Qiao, Ping Lu, Li Xia, Zhehao Huazhong Univ Sci & Technol Natl CAD Supported Software Engn Ctr Sch Mech Sci & Engn Wuhan 430074 Peoples R China Suzhou Univ Sci & Technol Sch Mech Engn Suzhou 215101 Peoples R China

When solving the black-box dynamic optimization problem (BDOP) in the sophisticated dynamic system, the finite difference technique requires significant computational efforts on numerous expensive system simulations to provide approximate numerical Jacobian information for the gradient-based optimizer. To save computational budget, this work introduces a BDOP solving framework based on the right-hand side (RHS) function surrogate model (RHSFSM), in which the RHS derivative functions of the state equation are approximated by the surrogate models, and the Jacobian information is provided by inexpensive estimations of RHSFSM rather than the original time-consuming system evaluations. Meanwhile, the sampling strategies applicable to the construction of RHSFSM are classified into three categories: direct, indirect, and hybrid sampling strategy, and the properties of these strategies are analyzed and compared. Furthermore, to assist the RHSFSM-based BDOP solving framework search for the optimum efficiently, a novel dynamic hybrid sampling strategy is proposed to update RHSFSM sequentially. Finally, two dynamic optimization examples and a co-design example of a horizontal axis wind turbine illustrate that the RHSFSM-based BDOP solving framework integrated with the proposed dynamic hybrid sampling strategy not only solves the BDOP efficiently but also achieves the optimal solution robustly and reliably compared to other sampling strategies.

关键词： black-box dynamic system black-box dynamic optimization right-hand side function surrogate model dynamic hybrid sampling hypercube shrinking approximation-based optimal design metamodeling

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Toward Reusable Surrogate Models: Graph-based Transfer Learning on Trusses

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JOURNAL OF MECHANICAL design 2022年第2期144卷 021704-021704页

作者： Whalen, Eamon Mueller, Caitlin MIT Computat Sci & Engn Cambridge MA 02139 USA MIT Civil & Environm Engn Cambridge MA 02139 USA

Surrogate models have several uses in engineering design, including speeding up design optimization, noise reduction, test measurement interpolation, gradient estimation, portability, and protection of intellectual property. Traditionally, surrogate models require that all training data conform to the same parametrization (e.g., design variables), limiting design freedom and prohibiting the reuse of historical data. In response, this article proposes graph-based surrogate models (GSMs) for trusses. The GSM can accurately predict displacement fields from static loads given the structure's geometry as input, enabling training across multiple parametrizations. GSMs build upon recent advancements in geometric deep learning, which have led to the ability to learn on undirected graphs: a natural representation for trusses. To further promote flexible surrogate models, this article explores transfer learning within the context of engineering design and demonstrates positive knowledge transfer across data sets of different topologies, complexities, loads, and applications, resulting in more flexible and data-efficient surrogate models for trusses.

关键词： graph neural network geometric deep learning transfer learning surrogate model metamodel structural design approximation-based optimal design conceptual design design methodology design of experiments design representation expert systems machine learning metamodeling simulation-based design structural optimization

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Scalable Gaussian Processes for Data-Driven design Using Big Data With Categorical Factors

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JOURNAL OF MECHANICAL design 2022年第2期144卷 021703-021703页

作者： Wang, Liwei Yerramilli, Suraj Iyer, Akshay Apley, Daniel Zhu, Ping Chen, Wei State Key Lab Mech Syst & Vibrat 800 Dongchuan Rd Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ Sch Mech Engn Shanghai Key Lab Digital Manufacture Thin Walled 800 Dongchuan Rd Shanghai 200240 Peoples R China Northwestern Univ Dept Mech Engn 2145 Sheridan Rd Evanston IL 60208 USA Northwestern Univ Dept Ind Engn & Management Sci 2145 Sheridan Rd Evanston IL 60208 USA

Scientific and engineering problems often require the use of artificial intelligence to aid understanding and the search for promising designs. While Gaussian processes (GP) stand out as easy-to-use and interpretable learners, they have difficulties in accommodating big data sets, categorical inputs, and multiple responses, which has become a common challenge for a growing number of data-driven design applications. In this paper, we propose a GP model that utilizes latent variables and functions obtained through variational inference to address the aforementioned challenges simultaneously. The method is built upon the latent-variable Gaussian process (LVGP) model where categorical factors are mapped into a continuous latent space to enable GP modeling of mixed-variable data sets. By extending variational inference to LVGP models, the large training data set is replaced by a small set of inducing points to address the scalability issue. Output response vectors are represented by a linear combination of independent latent functions, forming a flexible kernel structure to handle multiple responses that might have distinct behaviors. Comparative studies demonstrate that the proposed method scales well for large data sets with over 10(4) data points, while outperforming state-of-the-art machine learning methods without requiring much hyperparameter tuning. In addition, an interpretable latent space is obtained to draw insights into the effect of categorical factors, such as those associated with "building blocks" of architectures and element choices in metamaterial and materials design. Our approach is demonstrated for machine learning of ternary oxide materials and topology optimization of a multiscale compliant mechanism with aperiodic microstructures and multiple materials.

关键词： Gaussian process machine learning big data categorical factor multi-response latent variable topology optimization approximation-based optimal design artificial intelligence data-driven design design of engineered materials system

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design and Analysis of Multifidelity Finite Element Simulations

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JOURNAL OF MECHANICAL design 2023年第6期145卷 061703-061703页

作者： Yuchi, Henry Shaowu Joseph, V. Roshan Wu, C. F. Jeff H Milton Stewart Sch Ind & Syst Engn Georgia Inst Technol Atlanta GA 30332 USA A Russell Chandler Chair III & Prof H Milton Stewa Georgia Inst Technol Atlanta GA 30332 USA Georgia Inst Technol Coca Cola Chair Engn Stat Atlanta GA 30332 USA

The numerical accuracy of finite element analysis (FEA) depends on the number of finite elements used in the discretization of the space, which can be varied using the mesh size. The larger the number of elements, the more accurate the results are. However, the computational cost increases with the number of elements. In current practice, the experimenter chooses a mesh size that is expected to produce a reasonably accurate result, and for which the computer simulation can be completed in a reasonable amount of time. Improvements to this approach have been proposed using multifidelity modeling by choosing two or three mesh sizes. However, mesh size is a continuous parameter, and therefore, multifidelity simulations can be performed easily by choosing a different value for the mesh size for each of the simulations. In this article, we develop a method to optimally find the mesh sizes for each simulation and satisfy the same time constraints as a single or a double mesh size experiment. A range of different mesh sizes used in the proposed method allows one to fit multifidelity models more reliably and predict the outcome when meshes approach infinitesimally small, which is impossible to achieve in actual simulations. We illustrate our approach using an analytical function and a cantilever beam finite element analysis experiment.

关键词： approximation-based optimal design design of experiments metamodeling space-filling design

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design of Trustworthy Cyber-Physical-Social Systems With Discrete Bayesian Optimization

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JOURNAL OF MECHANICAL design 2021年第7期143卷 071702页

作者： Wang, Yan Georgia Inst Technol Woodruff Sch Mech Engn Atlanta GA 30332 USA

Cyber-physical-social systems (CPSS) with highly integrated functions of sensing, actuation, computation, and communication are becoming the mainstream consumer and commercial products. The performance of CPSS heavily relies on the information sharing between devices. Given the extensive data collection and sharing, security and privacy are of major concerns. Thus, one major challenge of designing those CPSS is how to incorporate the perception of trust in product and systems design. Recently, a trust quantification method was proposed to measure the trustworthiness of CPSS by quantitative metrics of ability, benevolence, and integrity. The CPSS network architecture can be optimized by choosing a subnet such that the trust metrics are maximized. The combinatorial network optimization problem, however, is computationally challenging. Most of the available global optimization algorithms for solving such problems are heuristic methods. In this paper, a surrogate-based discrete Bayesian optimization method is developed to perform network design, where the most trustworthy CPSS network with respect to a reference node is formed to collaborate and share information with. The applications of ability and benevolence metrics in design optimization of CPSS architecture are demonstrated.

关键词： cyber-physical-social systems probabilistic graph model trust ability benevolence Bayesian optimization approximation-based optimal design design for X systems design

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Solving Three-Dimensional Path Planning Problem Using a Visibility-based Graphical Representation of the design Space

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JOURNAL OF MECHANICAL design 2022年第8期144卷 081704-081704页

作者： Masoudi, Nafiseh Fadel, Georges Clemson Univ Dept Mech Engn Clemson SC 29634 USA

Planning the shortest collision-free path among scattered obstacles is an NP-complete problem. As reviewed in this paper, a variety of deterministic as well as heuristic methods have been developed to address different instances of the problem. The focus of the deterministic methods is primarily on the optimality of the final solution and has been applied exclusively to regular shapes such as spheres or cubes. Nevertheless, due to the problem's intrinsic complexities (especially in 3D), researchers mainly resort to heuristics that offer acceptable (yet possibly suboptimal) solutions with reasonable resources. Therefore, less attention has been given to further the state-of-the-art in deterministic methods, which for 3D problems primarily focuses on approximating the solution. However, with the advancements in high-performance computing, we believe it is time to focus on solution quality. As such, this study aims to further the efforts in deterministic optimization methods for 3D path planning by overcoming some challenges of the existing methods and improving the optimality of the solution. The proposed approach is rooted in visibility-based planning methods where the obstacle-free space is modeled as a connectivity graph to be searched for the shortest path. The advantage of the proposed method in constructing the representative graph is that it does not make approximations to identify the graph nodes, unlike the existing methods. Nor does it limit the objects' geometries to specific shapes such as blocks or spheres. The capability of the method in finding the shortest collision-free paths in environments cluttered with convex polyhedra is demonstrated using sample test problems.

关键词： approximation-based optimal design computational geometry design for assembly design optimization design representation

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Multi-Model Bayesian Optimization for Simulation-based design

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JOURNAL OF MECHANICAL design 2021年第11期143卷 111701-111701页

作者： Tao, Siyu van Beek, Anton Apley, Daniel W. Chen, Wei Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA

We enhance the Bayesian optimization (BO) approach for simulation-based design of engineering systems consisting of multiple interconnected expensive simulation models. The goal is to find the global optimum design with minimal model evaluation costs. A commonly used approach is to treat the whole system as a single expensive model and apply an existing BO algorithm. This approach is inefficient due to the need to evaluate all the component models in each iteration. We propose a multi-model BO approach that dynamically and selectively evaluates one component model per iteration based on the uncertainty quantification of linked emulators (metamodels) and the knowledge gradient of system response as the acquisition function. Building on our basic formulation, we further solve problems with constraints and feedback couplings that often occur in real complex engineering design by penalizing the objective emulator and reformulating the original problem into a decoupled one. The superior efficiency of our approach is demonstrated through solving two analytical problems and the design optimization of a multidisciplinary electronic packaging system.

关键词： approximation-based optimal design multidisciplinary design and optimization simulation-based design uncertainty modeling

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Hierarchical Control Co-design Using a Model Fidelity-based Decomposition Framework

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JOURNAL OF MECHANICAL design 2021年第1期143卷 011708页

作者： Nash, Austin L. Jain, Neera Purdue Univ Sch Mech Engn W Lafayette IN 47907 USA

Increasing performance demands and constraints are necessitating the design of highly complex, integrated systems across multiple sectors, including transportation and energy. However, conventional design approaches for such systems are largely siloed and focused on steady-state operation. To accommodate tightening operating envelopes, new design paradigms are needed that explicitly consider system-component interactions and their implications on transient performance at the system design stage. In this work, we present a model fidelity-based decomposition (MFBD) hierarchical control co-design (HCCD) algorithm designed to optimize system performance characteristics, with an emphasis on robustness to transient disturbances during real-time operation. Our framework integrates system level control co-design (CCD) with high-fidelity component design optimization in a computationally efficient manner for classes of highly coupled systems in which the coupling between subproblems cannot be fully captured using existing analytical relationships. Our algorithm permits scalable decomposition of computationally intensive component models and addresses coupling issues between subproblems in part by introducing an intermediate optimization procedure to solve for reduced-order model parameters that maximize the accuracy of the lumped-parameter control model required in the CCD algorithm. We demonstrate the merits of the MFBD HCCD algorithm, in comparison to an all-at-once (AAO) CCD approach, through a case study on aircraft dynamic thermal management. Our results show that our decomposition-based solution matches the AAO optimal cost to within 2.5% with a 54% reduction in computation time.

关键词： approximation-based optimal design design methodology design optimization energy systems design hierarchical modeling multiobjective optimization simulation-based design systems design

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An Image-Driven Uncertainty Inverse Method for Sheet Metal Forming Problems

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JOURNAL OF MECHANICAL design 2022年第2期144卷 022001-022001页

作者： Li, Yu Wang, Hu Li, Biyu Wang, Jiaquan Li, Enying Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Zhuzhou CRRC Times Elect Co Ltd Technol Ctr Zhuzhou 412001 Hunan Peoples R China Cent South Univ Forestry & Technol Coll Mech & Elect Engn Changsha 41004 Peoples R China

The purpose of this study is to obtain a margin of safety for material and process parameters in sheet metal forming. Commonly applied forming criteria are difficult to comprehensively evaluate the forming quality directly. Therefore, an image-driven criterion is suggested for uncertainty parameter identification of sheet metal forming. In this way, more useful characteristics, material flow, and distributions of safe and crack regions, can be considered. Moreover, to improve the efficiency for obtaining sufficient statistics of Approximate Bayesian Computation (ABC), a manifold learning-assisted ABC uncertainty inverse framework is proposed. based on the framework, the design parameters of two sheet metal forming problems, an air conditioning cover and an engine inner hood, are identified.

关键词： approximation-based optimal design data-driven design machine learning surrogate model

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