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Topology optimization by optimally distributing materials in a given domain requires non-gradient optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would require millions of Finite Element Method (FEM) calculations whose computational cost is huge and impractical. Here we report Self-directed Online Learning Optimization (SOLO) which integrates Deep Neural Network (DNN) with FEM calculations. A DNN learns and substitutes the objective as a function of design variables. A small number of training data is generated dynamically based on the DNN’s prediction of the optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. The optimum predicted by the DNN is proved to converge to the true global optimum through iterations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 ~ 5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. This approach enables solving large multi-dimensional optimization problems.

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The purpose of this study is to present a new method for estimating the fatigue life of the screw blade in the screw sand washing machine. To ensure the accuracy of numerical simulation, the loading area and the value of load are determined by means of the theoretical analysis. To ascertain the location of the stress peak and stress range, the static analysis of the screw blade is executed via the finite element method. To reduce the research cost and ensure the feasibility of the research method, Markov chain Monte Carlo (MCMC) is employed to simulate the random load with the Gauss distribution on the screw blade. In addition, the Nondominated Sorting Genetic Algorithm (NSGA-II) is utilized to find out an optimum variation coefficient of the stress, aiming at guaranteeing the precision of the random load. The rainflow cycle extrapolation is adopted to generate the fatigue load spectrum closer to the real condition, taking account of the possibility of the extreme loads caused by overload occurrence. Subsequently, the rainflow matrix after extrapolation, the estimated P-S-N curve, Goodman stress correction method and Miner's rules are made use of assessing the service life of the screw blade. In particular, the effects of the surface roughness, residual stresses and fatigue notch factors on the fatigue life are taken into consideration. Ultimately, the non-linear surface fitting technique is used to obtain the equation concerning the fatigue life of the screw blade versus residual stresses and fatigue notch factors. The numerical results show that the stress peak is in the root of the screw blade and the service life of the screw blade declines exponentially with growing residual stresses and fatigue notch factors.

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