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- Conditional diffusion models for the inverse design of lattice structures
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Abstract: Inverse design, a critical area of mechanical design, focuses on determining the optimal configuration of a structure or material to achieve desired properties or performance. However, the vast array of design possibilities for manufacturable unit cells presents a significant challenge in inverse design: efficiently identifying a complex lattice that meets specific target properties. To address these challenges and, moreover, to offer a solution, we propose a simple yet effective framework that leverages conditional diffusion models, a class of generative models known for their ability to produce high-quality samples conditioned on specific input parameters. Our model, named LatticeOptDiff, enables the efficient exploration of the vast design space, including surface-based, truss-based, and hybrid surface-truss-based lattice structures, by guiding the generation process toward configurations that meet predefined criteria such as Young’s modulus, Poisson’s ratio, and volume fraction. Results indicate that (1) our method can generate various unit cells that satisfy specified material properties with higher accuracy compared to a state-of-the-art conditional generative adversarial network (GAN) and (2) the lattice structures generated through our method exhibit superior mechanical performance when compared to those generated by the GAN. The engineering applications are verified through finite element (FE) simulations and tests on 3D-printed lattice structures. By introducing LatticeOptDiff into the design of lattice structures, we show that conditional diffusion models can outperform GANs in engineering design synthesis, thereby broadening the scope for research and practical applications across diverse engineering fields.
PubDate: 2025-03-29
- Analysis and multi-objective optimization of an interior permanent magnet
synchronous motor for a comprehensive performance enhancement-
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Abstract: The optimization of interior permanent magnet synchronous motors (IPMSMs) is inherently challenging because of the complex interplay between parameters and the difficulty of balancing multiple performance objectives. In this paper, a multi-objective of IPMSM optimization method is proposed to achieve a comprehensive performance improvement. Initially, the optimization objectives and parameters are theoretically analyzed. A sensitivity analysis is then performed to identify the highly correlated parameters. The impacts of these parameters on the objectives are further investigated via a response surface methodology. The functional relationships between the objectives and parameters are subsequently fitted via the least-squares method and their accuracy is subsequently assessed via evaluation indices. Furthermore, the relationships between multiple targets are revealed via the Pearson correlation coefficient and a comprehensive performance index function is established by introducing weight coefficients, enabling the normalization of the multi-objective optimization process. Finally, the simulated annealing algorithm (SAA) is employed to extract the optimal solution. The results indicate that the torque ripple is significantly reduced while ensuring a higher torque output. Additionally, working harmonic content and efficiency improvements are observed, confirming the effectiveness of the proposed optimization approach.
PubDate: 2025-03-29
- Enhancing aerodynamic and aeroelastic performance of axial compressor
through multi-degree-of-freedom parameterization and data-driven
multidisciplinary optimization-
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Abstract: Multidisciplinary design optimization (MDO) facilitates a comprehensive consideration of inter-disciplinary coupling, overcoming the lengthy processes of conventional serial design and charting a progressive trajectory for compressor optimization. However, the presence of multiple disciplines poses challenges concerning computational efforts and system organizational integration. This paper introduces a novel MDO system by integrating a directly manipulated free-form deformation (DFFD) method and a data-driven model with pre-screening strategy. The DFFD enables precise deformation of compressor surfaces with fewer control points to reduce variables, while data-driven models can significantly accelerate the convergence of complex multi-objective optimization problems. It is applied to an axial compressor to enhance its aerodynamic and aeroelastic performance. A fluid-domain mesh-based method is employed to construct the blade finite element model, addressing the fluid–structure interface interpolation. By progressively increasing the outlet pressure to search the compressor near surge point, the prediction accuracy of surge margin during the optimization process is effectively improved. Compared to the prototype, the isentropic efficiency of optimized compressor at the design point and peak increases by 1.22 and 0.8 percentage points, respectively, and the surge margin improves by 3.23%. Besides aerodynamic performance, the mechanical properties of the rotor blades also show substantial improvement, with the maximum equivalent stress at the blade root reduces by 35.7%, and the low-order resonance margin is also enhanced. The optimization results demonstrate that the developed MDO system can effectively handle the aerodynamic and aeroelastic collaborative optimization of compressor and improve its comprehensive performance.
PubDate: 2025-03-29
- A t-SNE-based embedding for transfer optimisation with non-overlapping
design variables-
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Abstract: The cold start problem is a chief concern in the context of surrogate-based optimisation, as it can slow down or prevent convergence towards a global minimum. Transfer optimisation (TO) has recently emerged as a promising solution, positing the reuse of historical data to improve the quality of the surrogate predictor. However, the requirement for constant design parameters across the source and target tasks severely limits the range of applicability of TO. Several strategies have been proposed to overcome this constraint. However, they typically require either linked samples or linked design variables, and thus only offer a slight extension of the aforementioned scope. This paper proposes a new transfer optimisation method that enables varying design parameters. It removes the link constraint by using simulation physics, rather than a mapping function, to represent the distribution of source and target samples. Then, it employs a t-SNE inspired optimisation routine to recreate this distribution in the target task’s design variable space. Multiple-output Gaussian processes are used to model the resulting distribution of target and source samples. Results indicate significant improvements of 30-60% in optimisation performance over traditional Kriging-based approaches.
PubDate: 2025-03-29
- Plastic layout optimization of hybrid truss and beam structures
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Abstract: Classical layout optimization is a well-established structural design tool, however it considers only truss structures composed solely of axially loaded bars, limiting its applicability to many structures. To address this limitation, this study introduces a novel approach that takes into account moment-resisting beams in the optimization framework. The interaction between moment, shear, and axial forces is simplified for inclusion in the optimization problem, solved effectively via a sequential conic programming scheme. Various numerical examples show that the proposed approach identifies structures with lower-volume than the classical layout optimization in problems involving multiple load cases or pre-existing members. Additionally, the method can also be used to solve problems that classical layout optimization cannot address, including constrained design spaces and point moment loads. The findings indicate that the proposed approach provides greater flexibility and efficiency in designing hybrid truss and beam structures, paving the way for versatile structural solutions.
PubDate: 2025-03-27
- Shape optimization of floating bridge pontoons with mooring constraints
under wave actions-
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Abstract: This study optimizes the shape of mooring pontoons for deep-water floating bridges to reduce their motion amplitude under wave action. To this end, a Fourier series expansion in spherical coordinates is proposed to represent arbitrary smooth spatial geometries, with Fourier coefficients serving as the design variables. The gradient of the objective function with respect to the design variables is then obtained via the discrete adjoint method. The optimization aims to reduce the surge motion and the coupled surge and pitch motion amplitudes of the pontoon. The results show that the optimized shape reduced the surge and pitch motion amplitudes by a maximum of 77.84% and 89.73%, respectively, under different wave numbers $$kR$$. Additionally, the optimization effectively suppresses the free surface wave height around the structure. The influence of the Fourier coefficient truncation order on the optimization results is also examined, and an equivalent cross-sectional shape of the pontoon is proposed, which significantly reduces surge and pitch motions under various wave conditions. This study provides valuable insights for optimizing and designing floating foundations.
PubDate: 2025-03-25
- An 88-48-88 line MATLAB code for asymptotic homogenisation of spatially
varying multiscale configurations-
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Abstract: Nowadays, partly thanks to the development of novel manufacturing techniques, more complex multiscale configurations whose microstructural building blocks can vary smoothly in space, have gained increasing research interest. Compared with periodic multiscale structures, the microstructural variance in spatially varying multiscale configuration (SVMSC) leads to innumerate cell problems to solve, if it is analysed with asymptotic homogenisation (AH). Algorithms and/or softwares for the compliance evaluation of SVMSCs are naturally needed. Zhu et al. proposed an improved asymptotic homogenisation method (AH plus) for evaluating the stiffness performance of SVMSC. Then to facilitate practical application, machine learning models are trained to summarise the macro-micro transition indicated by the cell problems. However, the implementation and application of this algorithm still present challenges due to these complex mathematical treatments behind the realisation of theory in computation. In order to offer a shortcut to readers doing spatially varying multiscale analysis on their owns, this article provides and explains a set of MATLAB codes based on the AH plus method for the performance evaluation of multiscale structures, especially when the structure exhibits spatial gradients. This code package is composed of three moduli: an 88-line script to compute the homogenised properties of a given irregular-shaped building block, a 48-line script to train a neural network expressing the homogenised properties, and an 88-line script to conduct online compliance computation. Several numerical examples are provided to demonstrate the effectiveness and accuracy of the code presented in this article. The complete Matlab codes are given in the Appendixes and can be downloaded from the web-site https://github.com/DLUTMARG/MLBAH88-48-88.
PubDate: 2025-03-24
- A comparative study of acquisition functions for active learning kriging
in reliability-based design optimization-
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Abstract: Many acquisition functions are available to improve active learning-based kriging models while conducting reliability-based design optimization (RBDO). A considerable challenge for computationally expensive models is deciding which acquisition function provides the greatest chance to complete the optimization with a minimum number of function evaluations. This paper presents a comprehensive comparative study of nine different acquisition functions in terms of the number of completed optimizations, total function evaluations, and repeatability. The comparative study was conducted. The comparative study was conducted on problems with varying levels of input uncertainty and surrogate uncertainty thresholds to evaluate the performance across a range of problem settings. Two well-known mathematical examples and one engineering example are employed to compare the performance of different acquisition functions. A unified metric is proposed to evaluate the overall performance of different acquisition functions for RBDO. The results of the comparative study show that: (1) The performance of the acquisition functions can be categorized into two distinct groups based on whether they include a term for the joint probability density function; the acquisition functions within a group have similar performance; and the acquisition functions that included a term for the joint probability density function had the best performance. (2) Local approximations have a higher success rate of finding the RBDO optimum than global approximations due to higher surrogate model fidelity in the optimum region. (3) This paper also explores a common typographical error in the expected feasibility function (EFF) that limits the ability of the function to explore the design space. This error decreases the effectiveness of EFF when compared to other acquisition functions.
PubDate: 2025-03-22
- A novel impact loads simplification method for the stiffest design of
impact-resistant structures employing topology optimization-
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Abstract: High nonlinearities and expensive computational costs in analysis have led to a lack of effective solutions for impact-resistant design using topology optimization. Equivalent Static Loads Method (ESLM) transforms dynamic loads to static loads based on displacement, effectively avoiding the above-mentioned issues. It is an effective method for some simple impact problems (i.e., the deformation trends barely change with the structural configuration). However, when dealing with complex impact problems, it is challenging to obtain a satisfactory design due to the significant difference between static loads and impact loads. A novel Impact Loads Simplification Method (ILSM) is proposed to improve the impact resistance by enhancing the stiffness of the structures, and a topology optimization framework is established. This method transforms dynamic loads to static loads based on actual impact forces. The variation of impact forces in both time domain and spatial domain is fully considered. Two representative examples including an impacted beam (a simple impact problem) and a wing subjected to bird strike (a complex impact problem) are used to validate the effectiveness of ILSM. The results show that designs with higher stiffness, measured by the maximum displacement during the impact, can be obtained compared to ESLM, especially in complex impact scenarios.
PubDate: 2025-03-20
- Concurrent topology optimization for double-skin stiffened structures
considering external shape and modal characteristics-
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Abstract: In addition to lightweight and high load-bearing capacity, certain scenarios in aerospace field place further requirements on thin-walled structures, particularly double-skin stiffened structures, such as low moment of inertia and high flutter resistance. A concurrent stiffener-skin topology optimization method is proposed to enhance stiffness and reduce weight, while suppressing flutter by considering constraints on external aerodynamic shape and modal characteristics. The stiffener layout is optimized using the adaptive growth method, inspired by natural branch systems, while skin thickness is optimized through geometry optimization with material interpolation. A dual nodal system model is developed to maintain external shape by offsetting skin elements inward and allowing adaptive changes in stiffener geometry. Additionally, partitioned mass center location constraint is introduced as an indirect scheme to control mode shapes, aiming to achieve modal decoupling. Applied the method to a rudder structure, a tree-like stiffeners and tree crown-like skins are obtained, and the optimized rudder structure shows enhanced static–dynamic performance and greatly reduced moment of inertia. Furthermore, the coupling degree of bending-torsion modes is lowered, leading to a notable increase of the forecast flutter frequency. This method innovatively introduces a dual nodal model to avoid component overlaps and integrates variable thickness skin to balance stiffness and mass distribution, combining multiple components for concurrent topology optimization. The approach highlights the importance of integrative stiffness-mass-mass center design in decoupling bending-torsion modes, which in turn suppresses flutter, and offers a flexible and universal solution for the design of high-performance thin-walled structures.
PubDate: 2025-03-19
- An easy-to-use univariate mapping-based method for multi-material topology
optimization with implementation in MATLAB-
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Abstract: This article presents a novel univariate mapping-based material interpolation method for density-based multi-material topology optimization. The proposed multi-material interpolation model maps the single-variable design field to the multi-variable physical field based on a smoothed Heaviside projection. Multi-material topology optimization problems can be efficiently addressed, and definitive binary results (0 or 1) can be obtained for each candidate material through a parameter continuation scheme. The proposed interpolation function and its first derivative demonstrate continuity, enabling their application in gradient-based optimization algorithms. The issues associated with false material coexistence and material envelope in single-variable interpolation schemes for multiple materials are examined, and a new filtering technique is developed to mitigate these problems. An educational MATLAB code is presented for 2D and 3D multi-material topology optimization problems utilizing the proposed univariate mapping-based interpolation scheme. This document presents a solution for the topology optimization of multiple materials aimed at minimum compliance while adhering to a total mass constraint. It includes details on the multi-material interpolation model, specialized filtering techniques, optimization iterations, and post-processing procedures. Benchmark numerical examples involving multiphase materials illustrate the effectiveness and efficiency of the code, highlighting the impact of parameters on the optimization results. The outcomes obtained by the proposed approach are compared with those of other state-of-the-art methods documented in the literature. The appendix section of this article includes the educational MATLAB code, which is also accessible on the website (https://github.com/TopJay/SVMMTO) for further learning.
PubDate: 2025-03-13
- An uncertainty-aware deep learning framework-based robust design
optimization of metamaterial units-
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Abstract: Mechanical metamaterials represent an innovative class of artificial structures, distinguished by their extraordinary mechanical characteristics, which are beyond the scope of traditional natural materials. The use of deep generative models has become increasingly popular in the design of metamaterial units. The effectiveness of using deep generative models lies in their capacity to compress complex input data into a simplified, lower-dimensional latent space, while also enabling the creation of novel optimal designs through sampling within this space. However, the design process does not take into account the effect of model uncertainty due to data sparsity or the effect of input data uncertainty due to inherent randomness in the data. This might lead to the generation of undesirable structures with high sensitivity to the uncertainties in the system. To address this issue, a novel uncertainty-aware deep learning framework-based robust design approach is proposed for the design of metamaterial units with optimal target properties. The proposed approach utilizes the probabilistic nature of the deep learning framework and quantifies both aleatoric and epistemic uncertainties associated with surrogate-based design optimization. We demonstrate that the proposed design approach is capable of designing high-performance metamaterial units with high reliability. To showcase the effectiveness of the proposed design approach, a single-objective design optimization problem and a multi-objective design optimization problem are presented. The optimal robust designs obtained are validated by comparing them to the designs obtained from the topology optimization method as well as the designs obtained from a deterministic deep learning framework-based design optimization where none of the uncertainties in the system are explicitly considered.
PubDate: 2025-03-11
- Constraint-free length scale control for topology optimization using the
velocity field level set method-
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Abstract: The length scale limitation is an important issue of the structural manufacturability. It is usually involved in the topology optimization by introducing geometrical constraints or projections on design variables. This paper proposes a novel topology optimization method with a constraint-free length scale control strategy utilizing the velocity field level set framework. The local length scale of structural members is represented by using the skeleton based on the signed distance property of the level set function. Then, a length scale control strategy is proposed by adjusting the velocity design variable bounds to drive the structural local sizes to the required values in the velocity field level set method, leading to no additional constraints or penalty functions involved. The topological derivative is also introduced to eliminate the dependency on the initial design. Utilizing the level set model achieves clear/smooth material boundaries and facilitates the length scale representation. Moreover, the proposed method provides an efficient way to perform optimization designs directly in the feasible domain meeting the length scale limitations. The constraint-free strategy greatly simplifies the sensitivity analysis, numerical implementation, and iteration convergence in the optimization process, especially when considering multiple length scale limitations.
PubDate: 2025-03-11
- Subspace enhanced active learning method for high-dimensional reliability
analysis-
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Abstract: Subspace-based surrogate modeling methods are extensively used for high-dimensional reliability analysis due to their ability to mitigate the “curse of dimensionality”. The accuracy of the subspace fundamentally determines the credibility of the reliability analysis. However, existing methods may construct the subspace with poor accuracy because they reduce the dimensionality only based on responses and gradients of limited samples, making the results of the failure probability inaccurate. To tackle this issue, this paper proposes a novel high-dimensional reliability analysis method by combining subspace enhancement and active learning. First, we calculate a projection matrix using slice inverse regression to obtain an initial subspace. To calibrate the projection direction, a nested optimization strategy is developed to refine the parameters of the projection matrix using the manifold optimization technique. In the early stages of active learning, a similarity-preserving global sampling strategy is proposed to select samples that are most beneficial for enhancing dimensionality reduction accuracy. Once the dimensionality reduction reaches sufficient precision, a local sampling strategy is implemented to identify samples near the limit state boundary, enhancing the accuracy of failure probability estimation. Finally, the learning process is terminated using a stopping criterion based on the upper bound estimate of relative error. The performance of the proposed method is validated through two numerical cases and two engineering cases.
PubDate: 2025-03-11
- StructureGraph: a universal performance evaluation method for engineering
structures via heterogeneous graph neural network-
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Abstract: In recent years, numerous studies have applied Graph Neural Network (GNN) to engineering structure analysis. However, a common drawback of these methods is that they can only be applied to structures corresponding to homogeneous graphs and fail immediately when applied to structures corresponding to heterogeneous graphs, which are more prevalent in real-world scenarios. To address this challenge, we propose a universal performance evaluation method (called StructureGraph) for engineering structures via Heterogeneous Graph Neural Network (HGNN). It effectively overcomes the limitations of previous GNN-based methods, significantly expanding their applicability. First, engineering structures are transformed into heterogeneous graph representations, which can be processed by HGNN to inference the target performance. Subsequently, an optimal network model for the current performance prediction task is established through the HGNN design space search. To further improve the prediction precision of the surrogate model, Finite Element Method (FEM) equations are employed to construct an additional physical loss, effectively guiding the training direction of the model. In numerical experiments of car frames with plates, StructureGraph achieved very high prediction precision (99.33%) on the validation dataset, demonstrating its effectiveness. In addition, comparisons with other surrogate modeling methods highlight the significant advantages of StructureGraph in terms of prediction precision and scalability.
PubDate: 2025-03-07
- Vehicle suspension recommendation system: multi-fidelity neural
network-based mechanism design optimization-
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Abstract: Mechanical mechanisms are designed to perform specific functions in a variety of fields. In most cases, there is not a unique mechanism that performs a well-defined function. For example, vehicle suspensions are designed to improve driving performance and ride comfort, but different types are available depending on the environment in which they are used. This variability in design due to different usage environments makes performance comparison difficult. In addition, the industry’s traditional design process is multi-step, gradually reducing the number of design candidates while performing costly analysis to achieve target performances. Recently, artificial intelligence models have been used to replace the computational cost of finite element analysis (FEA). However, there are limitations in data availability and different analysis environments, especially when moving from low-fidelity to high-fidelity analysis. In this paper, we propose a multi-fidelity design framework aimed at recommending optimal types and designs of mechanical mechanisms. As an application, vehicle suspension systems were selected, and several types were defined. For each type, mechanism parameters were generated and converted into 3D CAD models, followed by low-fidelity rigid body dynamic analysis under driving conditions. To effectively build a deep learning-based multi-fidelity surrogate model, the results of the low-fidelity analysis were analyzed using Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and sampled at 5% for the high-cost flexible body dynamic analysis. After training a multi-fidelity model, a multi-objective optimization problem was formulated for the performance metrics of each suspension type. Finally, we recommend the optimal type and design based on the input (sprung mass) to optimize the ride comfort-related performance metrics. Subsequently, to validate the proposed methodology, we extracted basic design rules for Pareto solutions using data mining techniques. We also verified the effectiveness and applicability by comparing the results with those obtained from a conventional deep learning-based design process.
PubDate: 2025-03-07
- A novel self-adaptive method based on oscillation judgment factor for
robust and efficient structural reliability analysis-
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Abstract: In structural reliability analysis, oscillation has a significant impact on the efficiency and robustness of the iterative process. The application of traditional reliability calculations, which fails to account for oscillations in the iterative process, may lead to the generation of unstable and inaccurate results. It first clarifies the mechanism of oscillation judgment based on the limit state function decline, then a new oscillation judgment factor for detecting iterative quality has been proposed by former iterative information, which can accurately and promptly determine the quality of the current iteration. Subsequently, the control conditions for step size intervention are proposed according to the oscillation judgment factor. After that, an adaptive control strategy of optimal step size is constructed to facilitate the adaptive step size adjustment of iterative computation. The exceptional performance in efficiency and robustness of the proposed method is confirmed by nine examples. The parameters involved are also discussed, the most suitable values are suggested.
PubDate: 2025-03-01
- Virtual Nash optimization algorithms inspired by the balance between
blocking the interference among design variables and motivating their
coordinated development-
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Abstract: Mutual interference among large-scale design variables can have a large impact on both optimization efficiency and the quality of the optimal solution. The authors of this paper have investigated the effects of design variables with different characteristics. It is found in this paper that even variables with the same characteristics can strongly interfere with each other in the optimization process. An approach to block the interference among variables is proposed by introducing the virtual Nash equilibrium to divide the variables into different groups in the optimization and to isolate the interference among optimization variables in different groups. Detailed virtual Nash optimization algorithms are also provided and the characteristics and essence of the virtual Nash equilibrium solution are discussed. Furthermore, by reasonably controlling two parameters in the algorithm, i.e., the number of subgroups and the frequency of elite information exchange, the mechanism by which the method of this paper improves the optimization efficiency is reasonably explained, i.e., reasonably adjusting the balance between blocking the interference among variables and enhancing the coordinated development of variables is the key point for improving the optimization efficiency. Once this balance is disrupted, the efficiency becomes poor instead. Finally, it was used to solve the inverse design of three-dimensional aerodynamic shapes to verify the efficiency of the algorithm and the effectiveness of theoretical analysis in this paper.
PubDate: 2025-03-01
- Compliant design of self-dilating vascular stent based on robustness
meta-heuristic evolution-
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Abstract: This paper presents a compliant design method of a self-dilating vascular stent based on robustness meta-heuristic evolution (RME). The initial conceptual design prototype of a biodegradable vascular stent is built, comprising a concave hexagonal base structure and a bionic honeycomb shape structure. Bending stiffness and flexibility simulation are carried out to construct the relationship between design variables and compliant performance. The test points used to obtain the initial scheme are generated by the Latin Hypercube Sampling (LHS) method, which can work well in small sample conditions. The Kriging agent is employed to simplify the optimization objective function. To implement non-convex optimization, the rime ice optimization algorithm, enhanced by chaotic mapping and Cauchy variants, is explored to find the global optimum. For the multidisciplinary design issue, the multi-objective optimization (MOO) can further evolve to the Pareto-optimal solutions (POS), using non-dominated sorting method rather than simply weighting method. From the perspective of comparatively verification, more coherent comparisons are examined, including blood flow velocity via hemodynamics simulation, vessel displacement and stress, as well as vascular stents radial displacement with variable narrowing rates. The physical experiment with a case of Peripheral Artery Disease (PAD) in lower limb is provided. The practice indicates that robustness optimization enhances the stent’s structural performance and reliability. RME thus has the advantage of efficient optimization convergence under hybrid uncertainty, especially involving multidisciplinary structure optimization.
PubDate: 2025-03-01
- Robust design optimization with limited data for char combustion
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Abstract: This work presents a robust design optimization approach for a char combustion process in a limited-data setting, where simulations of the fluid-solid coupled system are computationally expensive. We integrate a polynomial dimensional decomposition (PDD) surrogate model into the design optimization and induce computational efficiency in three key areas. First, we transform the input random variables to have fixed probability measures, which eliminates the need to recalculate the PDD’s basis functions associated with these probability quantities. Second, using the limited data available from a physics-based high-fidelity solver, we estimate the PDD coefficients via sparsity-promoting diffeomorphic modulation under observable response-preserving homotopy regression. Third, we propose a single-pass surrogate model training that avoids the need to generate new training data and update the PDD coefficients during the derivative-free optimization. The results provide insights for optimizing process parameters to ensure consistently high energy production from char combustion.
PubDate: 2025-03-01
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