In order to design an active deformation mirror for projection objective aberration imaging quality control, a topology optimization design method of active deformation mirrors based on discrete orthogonal Zernike polynomials is proposed in this paper. Firstly, in order to solve the problem that continuous Zernike polynomials do not have orthogonality on the discrete coordinates inside the unit circle, which causes the instability of topology optimization results, discrete orthogonal Zernike polynomials are used to characterize the active deformation mirror wave aberrations. Then, the optical and structural deformations are combined to establish an optical-mechanical coupling topology optimization model with the help of the variable density method to derive the sensitivity of the mathematical model. Finally, a wave aberration corrected deformation mirror in an optical machine system is used as an arithmetic example for topology optimization, and the results show that the absolute value of the Zernike coefficient Z₄ after optimization is improved by nearly one order of magnitude compared with the value before optimization, and the vibration characteristics of the optimized structure meet the design requirements. The optimization effect is significant, which improves the optical performance of the deformed mirror and provides a new scheme for the design of the deformed mirror structure which has a certain practical value for engineering.

Bearing is an important part of rotating machinery, and its early fault diagnosis and accurate classification have always been difficult in engineering application. At present, the models based on the fusion of various optimization algorithms and neural networks have become one of the emerging techniques for accurate fault identification. Firstly, an improved antlion optimizer (ALO) algorithm based on estimation of distribution algorithm (EDA) and variable-step Lévy flight strategy, abbreviated as ELALO, is proposed as a new bionic intelligence. During the initialization of population, the individuals with poor fitness are redistributed by the Gaussian probability model. In view of the stagnation of iteration, Lévy flight strategy is introduced and the adaptive change of disturbance step length is controlled. Experimental results on 4 benchmark functions show that the novel ELALO can effectively improve the solution accuracy and convergence speed, compared with the original ALO. Secondly, in order to solve the disadvantage that extreme learning machine (ELM) network is easy to fall into local optimization, this ELALO algorithm is used to initialize the weights and thresholds of its network and to form the new pattern recognition model, ELALO-ELM. Finally, the bearing data of 8 patterns from Western Reserve University are decomposed by local mean decomposition (LMD), and then the symbolic entropy (SE) of the first three product function (PF) components signals is extracted and used as the input eigenvectors. Compared with the standard ELM and ALO-ELM models, the ELALO-ELM model has better generalization and stronger robustness and it can effectively improve the efficiency of network training and the accuracy of early fault pattern classification in bearing fault diagnosis. The new ELALO-ELM model can also be used for other difficult classification problems.

According to BESO’s principle of binarizing continuous design variables and the excellent performance of the standard HPO algorithm in terms of solving continuous optimization problems, a discrete binary Hunter-prey optimization algorithm is introduced to construct an efficient topology optimization model. It was used to solve the problems that the BESO method of topology optimization has, such as easily falling into the local optimal value and being unable to obtain the optimal topology configuration; the metaheuristic algorithm was able to solve the topology optimization model’s low computational efficiency and could easily produce intermediate elements and unclear boundaries. Firstly, the BHPO algorithm was constructed by discrete binary processing using the s-shape transformation function. Secondly, BHPO-BESO topology optimization theory was established by combining the BHPO algorithm with BESO topology optimization. Using the sensitivity information of the objective function and the updated principle of the meta-heuristic of the BHPO algorithm, a semi-random search for the optimal topology configuration was carried out. Finally, numerical simulation experiments were conducted by using the three typical examples of the cantilever beam, simply supported beam, and clamping beam as optimization objects and the results were compared with the solution results of BESO topology optimization. The experimental results showed that compared with BESO, BHPO-BESO could find the optimal topology configuration with lower compliance and maximum stiffness, and it has higher computational efficiency, which can solve the above problems.