Hu Wang

Jichao Yin, Ziming Wen, Shuhao Li et al.

Integration of machine learning (ML) into the topology optimization (TO) framework is attracting increasing attention, but data acquisition in data-driven models is prohibitive. Compared with popular ML methods, the physics-informed neural network (PINN) can avoid generating enormous amounts of data when solving forward problems and additionally provide better inference. To this end, a dynamically configured PINN-based topology optimization (DCPINN-TO) method is proposed. The DCPINN is composed of two subnetworks, namely the backbone neural network (NN) and the coefficient NN, where the coefficient NN has fewer trainable parameters. The designed architecture aims to dynamically configure trainable parameters; that is, an inexpensive NN is used to replace an expensive one at certain optimization cycles. Furthermore, an active sampling strategy is proposed to selectively sample collocations depending on the pseudo-densities at each optimization cycle. In this manner, the number of collocations will decrease with the optimization process but will hardly affect it. The Gaussian integral is used to calculate the strain energy of elements, which yields a byproduct of decoupling the mapping of the material at the collocations. Several examples with different resolutions validate the feasibility of the DCPINN-TO method, and multiload and multiconstraint problems are employed to illustrate its generalization. In addition, compared to finite element analysis-based TO (FEA-TO), the accuracy of the displacement prediction and optimization results indicate that the DCPINN-TO method is effective and efficient.

Yu Li, Hu Wang, Wenquan Shuai et al.

With the improvement of the pattern recognition and feature extraction of Deep Neural Networks (DPNNs), image-based design and optimization have been widely used in multidisciplinary researches. Recently, a Reconstructive Neural Network (ReConNN) has been proposed to obtain an image-based model from an analysis-based model [1, 2], and a steady-state heat transfer of a heat sink has been successfully reconstructed. Commonly, this method is suitable to handle stable-state problems. However, it has difficulties handling nonlinear transient impact problems, due to the bottlenecks of the Deep Neural Network (DPNN). For example, nonlinear transient problems make it difficult for the Generative Adversarial Network (GAN) to generate various reasonable images. Therefore, in this study, an improved ReConNN method is proposed to address the mentioned weaknesses. Time-dependent ordered images can be generated. Furthermore, the improved method is successfully applied in impact simulation case and engineering experiment. Through the experiments, comparisons and analyses, the improved method is demonstrated to outperform the former one in terms of its accuracy, efficiency and costs.

Yu Li, Hu Wang, Xinjian Deng

The heat transfer performance of Plate Fin Heat Sink (PFHS) has been investigated experimentally and extensively. Commonly, the objective function of the PFHS design is based on the responses of simulations. Compared with existing studies, the purpose of this study is to transfer from analysis-based model to image-based one for heat sink designs. Compared with the popular objective function based on maximum, mean, variance values etc., more information should be involved in image-based and thus a more objective model should be constructed. It means that the sequential optimization should be based on images instead of responses and more reasonable solutions should be obtained. Therefore, an image-based reconstruction model of a heat transfer process for a 3D-PFHS is established. Unlike image recognition, such procedure cannot be implemented by existing recognition algorithms (e.g. Convolutional Neural Network) directly. Therefore, a Reconstructive Neural Network (ReConNN), integrated supervised learning and unsupervised learning techniques, is suggested and improved to achieve higher accuracy. According to the experimental results, the heat transfer process can be observed more detailed and clearly, and the reconstructed results are meaningful for the further optimizations.

Kangjia Mo, Hu Wang, Zhenxing Cheng et al.

An Iterative Reanalysis Approximation (IRA) is integrated with the Moving Morphable Components (MMCs) based topology optimization (IRA-MMC) in this study. Compared with other classical topology optimization methods, the Finite Element (FE) based solver is replaced with the suggested IRA method. In this way, the expensive computational cost can be significantly saved by several nested iterations. The optimization of linearly elastic planar structures is constructed by the MMC, the specifically geometric parameters of which are taken as design variables to acquire explicitly geometric boundary. In the suggested algorithm, a hybrid optimizer based on the Method of Moving Asymptotes (MMA) approach and the Globally Convergent version of the Method of Moving Asymptotes (GCMMA) is suggested to improve convergence ratio and avoid local optimum. The proposed approach is evaluated by some classical benchmark problems in topology optimization, where the results show significant time saving without compromising accuracy.

Yu Li, Hu Wang, Kangjia Mo et al.

A variety of modeling techniques have been developed in the past decade to reduce the computational expense and improve the accuracy of modeling. In this study, a new framework of modeling is suggested. Compared with other popular methods, a distinctive characteristic is "from image based model to analysis based model (e.g. stress, strain, and deformation)". In such a framework, a reconstruction neural network (ReConNN) model designed for simulation-based physical field's reconstruction is proposed. The ReConNN contains two submodels that are convolutional neural network (CNN) and generative adversarial net-work (GAN). The CNN is employed to construct the mapping between contour images of physical field and objective function. Subsequently, the GAN is utilized to generate more images which are similar to the existing contour images. Finally, Lagrange polynomial is applied to complete the reconstruction. However, the existing CNN models are commonly applied to the classification tasks, which seem to be difficult to handle with regression tasks of images. Meanwhile, the existing GAN architectures are insufficient to generate high-accuracy "pseudo contour images". Therefore, a ReConNN model based on a Convolution in Convolution (CIC) and a Convolutional AutoEncoder based on Wasserstein Generative Adversarial Network (WGAN-CAE) is suggested. To evaluate the performance of the proposed model representatively, a classical topology optimization procedure is considered. Then the ReConNN is utilized to the reconstruction of heat transfer process of a pin fin heat sink. It demonstrates that the proposed ReConNN model is proved to be a potential capability to reconstruct physical field for multidisciplinary, such as structural optimization.

Hu Wang

The artificial neural network shows powerful ability of inference, but it is still criticized for lack of interpretability and prerequisite needs of big dataset. This paper proposes the Rule-embedded Neural Network (ReNN) to overcome the shortages. ReNN first makes local-based inferences to detect local patterns, and then uses rules based on domain knowledge about the local patterns to generate rule-modulated map. After that, ReNN makes global-based inferences that synthesizes the local patterns and the rule-modulated map. To solve the optimization problem caused by rules, we use a two-stage optimization strategy to train the ReNN model. By introducing rules into ReNN, we can strengthen traditional neural networks with long-term dependencies which are difficult to learn with limited empirical dataset, thus improving inference accuracy. The complexity of neural networks can be reduced since long-term dependencies are not modeled with neural connections, and thus the amount of data needed to optimize the neural networks can be reduced. Besides, inferences from ReNN can be analyzed with both local patterns and rules, and thus have better interpretability. In this paper, ReNN has been validated with a time-series detection problem.

Zhenxing Cheng, Hu Wang

A controllable crack propagation (CCP) strategy is suggested. It is well known that crack always leads the failure by crossing the critical domain in engineering structure. Therefore, the CCP method is proposed to control the crack to propagate along the specified path, which is away from the critical domain. To complete this strategy, two optimization methods are engaged. Firstly, a back propagation neural network (BPNN) assisted particle swarm optimization (PSO) is suggested. In this method, to improve the efficiency of CCP, the BPNN is used to build the metamodel instead of the forward evaluation. Secondly, the popular PSO is used. Considering the optimization iteration is a time consuming process, an efficient reanalysis based extended finite element methods (X-FEM) is used to substitute the complete X-FEM solver to calculate the crack propagation path. Moreover, an adaptive subdomain partition strategy is suggested to improve the fitting accuracy between real crack and specified paths. Several typical numerical examples demonstrate that both optimization methods can carry out the CCP. The selection of them should be determined by the tradeoff between efficiency and accuracy.