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In this paper, a density-based topology optimization method using neural networks is used to design domains composed of multi-materials under combined thermo–mechanical loading. The neural network produces the topology density field by minimizing a loss function defined for the problem. Length scale control is conducted using a Fourier space projection. JAX, a high-performance automatic differentiation (AD) Python library is used to build an end-to-end differentiable neural network. The model can handle the sensitivity analysis automatically using the backpropagation process (automatic differentiation of loss function) and the need for solving adjoint equations manual sensitivity analysis is removed. The optimization problem is solved by minimizing the loss function of the network and other optimization algorithms such as the Method of Moving Asymptotes (MMA) are not required. The performance of the method is demonstrated through several examples and compared with those obtained from the popular Solid Isotropic Material with Penalization (SIMP) method. The network is able to handle high-resolution re-sampling, resulting in a more refined and smooth variation of optimal topologies. • A neural network-based topology optimization (TO) method is proposed. • The method is intended for multi-material domains under combined loading. • The NN utilizes JAX for automatic sensitivity analysis. • The loss function of the NN is minimized to solve the TO problem. • The method's effectiveness is demonstrated through examples. [ABSTRACT FROM AUTHOR]

Abstract Online sequential extreme learning machine (OS-ELM) learns data one-by-one or chunk-by-chunk, and the recursive least square (RLS) algorithm is commonly employed to train the topological parameters of OS-ELM. Since it is hard to guarantee the smallest estimation error of the state variable by the RLS, the regression performance of the OS-ELM easily fluctuates in practical applications. To address this gap, a new training approach of the OS-ELM using Kalman filter called KFOS-ELM is proposed, and state propagation is combined into extreme learning process to obtain the OS-ELM's topological parameters. Besides, an adaptive-weighted ensemble mechanism is developed and used to dynamically tune the weight coefficients of each KFOS-ELM in the learning network. The regression performance of the proposed methodology is evaluated using benchmark datasets. The simulation results show that proposed methods are superior to the OS-ELM and EOS-ELM in terms of the regression accuracy and stability without additional computational efforts. Furthermore, an enhanced multi-sensor prognostic model based on KFOS-ELM and logistic regression (LR) model is designed for remaining useful life (RUL) prediction of aircraft engine. The experimental results confirm our viewpoints. [ABSTRACT FROM AUTHOR]

Fail-safe robustness is an important design philosophy for critical structural systems such as airframes. The basic idea of fail-safe design is that a structure should be designed to survive normal loading conditions when local damage occurs. In the context of topology optimization, fail-safe consideration innovates the morphogenesis for structural design in addition to the parametric safety margin. Existing fail-safe topology optimization methods usually enumerate all/predefined possible damages among the design domain and optimize the worst-damage scenario. However, virtually all damages can occur and cause the structural system to stop functioning. This work proposes the Stochastic Fail-Safe Topology Optimization (S-FSTO) for computationally viable fail-safe topology optimization which considers all possible damages according to the associated severity, including the worst-damage scenario. Critical damages for density value updates are sampled through the proposed two-level sampling strategy, which allows arbitrary size and location of damages. A design domain segmentation strategy is proposed to improve the sampling efficiency. The required number of FEA runs could be reduced by multiple orders of magnitudes. The proposed S-FSTO could be conveniently equivalent to a variety of existing schemes by customizing the proposal distributions of the two-level sampling strategy. The dependence on subjective decisions for selecting local damages could be minimized. The proposed framework has been evaluated for the design of cantilever beams and airplane bearing brackets. The generated conceptual designs are significantly more robust than the deterministic ones when local damage occurs. For the design of cantilever beams, S-FSTO produced designs with similar performance as that from the original FSTO and saved 99.4% FEA runs. • A unifying and computationally viable framework for Fail-Safe design. • A two-level sampling technique considering both location and severity of damage. • An integrated parallelization scheme of U-FSTO through design domain clustering. • Innovative fail-safe designs for beams, airplane bearing brackets and bridges. [ABSTRACT FROM AUTHOR]