An intelligent PSO-LBFNN algorithm for reliability enhancement of nonlinear piezoelectric vibration energy harvesters under time-delayed control

The PSO-LBFNN algorithm integrates Particle Swarm Optimization (PSO) with a Logistic Basis Function Neural Network (LBFNN), which uniquely employs a Logistic probability density function as its basis function. A key innovation lies in that only one hidden layer with 600 neurons is sufficient to achieve the desired accuracy. Furthermore, unlike conventional approaches that rely on search-based optimization methods such as Adam, the proposed PSO-LBFNN algorithm employs an iterative formula as the training mechanism to directly minimize the loss function. It can simultaneously solve the reliability equation and optimize implicit objectives, providing a theoretical foundation for reliability estimation and optimal control in engineering applications. To evaluate performance, the proposed algorithm is compared with classical methods such as Genetic Algorithm+ANN (GA-ANN) and Differential Evolution+ANN (DE-ANN). Results demonstrate that our Algorithm has a better performance than both GA-ANN and DE-ANN in convergence speed and solution accuracy. As for the optimal control, compared to the uncontrolled case, PSO-LBFNN enhances the reliability function by 63.8%. In addition, the mean first-passage time (MFPT) under PSO-LBFNN prolongs significantly from 24.4183 (uncontrolled) to 38.6786 (controlled), far exceeding GA-ANN and DE-ANN. At last, a Mann-Whitney U test confirms the statistical superiority of PSO-LBFNN with high confidence (p<0.01).