Ying Sun

Since its introduction, the Transformer has demonstrated robust performance. However, its capacity to predict nonlinear dynamical systems remains constrained. In this study, we enhance the structure and propose a novel network model, S-Transformer (Simplified Transformer), which exhibits high efficiency and accuracy in forecasting the chaos time series. A convolutional attention mechanism is introduced in place of the attention mechanism inherent to the Transformer architecture, which replaces the traditional multihead attention mechanism. To evaluate the model's universality, experiments were conducted on both the deployable antenna beam-ring structure and the classic Lorenz-63 chaotic benchmark. The mean squared error (MSE) is employed as the evaluation metric. Numerical simulations on the beam-ring structure demonstrate that the prediction accuracy of the S-Transformer is 75% higher than the long short-term memory encoder-decoder (LSTM ED). Furthermore, the Conv-AT (Conv-Attention Transformer) model achieves a 96% improvement over the S-Transformer in this application. On the Lorenz-63 benchmark, the S-Transformer exhibits superior long-term stability and significantly extends the valid prediction horizon compared to the LSTM ED. It can be concluded that the enhanced networks exhibit a pronounced capability for forecasting complex nonlinear systems. Some of the research highlights are as follows: (1) A high-precision simplified Transformer model is constructed. (2) Convolutional attention replaces traditional attention for better results. (3) The simplified Transformer shows a 75% accuracy improvement over earlier models. (4) The new attention model further improves accuracy by 96%.

Traditional loss functions such as mean squared error (MSE) are widely employed, but they often struggle to capture the dynamic characteristics of high-dimensional nonlinear systems. To address this issue, we propose an improved loss function that integrates linear multistep methods, system-consistency constraints, and prediction-phase error control. This construction simultaneously improves training accuracy and long-term stability. Furthermore, the introduction of recursive loss and interpolation strategies brings the model closer to practical prediction scenarios, broadening its applicability. Numerical simulations demonstrate that this construction significantly outperforms both mean square error and existing custom loss functions in terms of performance.

This paper proposed a single-stage AC-DC converter based on boost circuit and CLCL-T resonant converter for improving the performance of the LED driver. In practice, the two-stage LED driver is not suitable for low-power lighting applications. To overcome the problems, by integrating the boost power factor correction (PFC) circuit and CLCL-T resonant DC–DC converter, the proposed LED driver exhibits high efficiency and high reliability. The CLCL-T resonant converter can achieve soft-switching on the power switch and rectifier diode and reduce the switch losses at high frequencies. Operation principle, performance analysis and design considerations for the proposed LED driver are analyzed and discussed. The results indicate that the proposed single-stage LED driver is superior in terms of efficiency, volume and number of components. Finally, a 100-W experimental prototype is implemented, and the experimental results verify the effectiveness and feasibility of the proposed LED driver.

In the complex dynamic problems of practical engineering, the method of establishing dynamic equations and numerical analysis based on theories of mechanics is difficult to meet the needs of high dimension, multi-scale and high precision. In this paper, data-driven models of nonlinear dynamic systems are built through neural network. The numerical solution of state equations is used to simulate the experimental data as well as training data of neural network. The loss function with two coefficients is constructed according to the relationship between the data. Forward Euler method and the trained neural network are combined to predict the response data of different excitation frequencies. Then, whole data-driven modeling and substructure data-driven modeling are presented to model and analyse a five-degree-of-freedom duffing oscillator. By comparison, the prediction accuracy of substructure data-driven modeling is higher. Furthermore, the influence of loss function, hidden layer, training data and noise on the accuracy of the model is studied. The results show that the selection of training data and the number of hidden layers have a great impact on the prediction ability, and verify accuracy, generalization and robustness of the model. In order to improve the prediction accuracy of substructure data-driven modeling, adjustable learning rate is adopted in the optimizer. The effects of adding control parameters to the network input (APNI) and not adding control parameters to the network input (NAPNI) on the dynamic characteristics are considered respectively. The prediction accuracy of the model can be effectively improved by adding control parameters to the network input.

The nonlinear bending of the sandwich plates with graphene nanoplatelets (GPLs) reinforced porous composite (GNRPC) core and two metal skins subjected to different boundary conditions and various loads, such as the concentrated load at the center, linear loads with different slopes passing through the center, linear eccentric loads, uniform loads, and trapezoidal loads, has been presented. The popular four-unknown refined theory accounting for the thickness stretching effects has been employed to model the mechanics of the sandwich plates. The governing equations have been derived from the nonlinear Von Karman strain–displacement relationship and principle of virtual work with subsequent solution by employing the classical finite element method in combination with the Newton downhill method. The convergence of the numerical results has been checked. The accuracy and efficiency of the theory have been confirmed by comparing the obtained results with those available in the literature. Furthermore, a parametric study has been carried out to analyze the effects of load type, boundary conditions, porosity coefficient, GPLs weight fraction, GPLs geometry, and concentrated load radius on the nonlinear central bending deflections of the sandwich plates. In addition, the numerical results reveal that the adopted higher order theory can significantly improve the simulation of the transverse deflection in the thickness direction.