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For efficiently estimating the dynamic failure probability of the structure with the multiple temporal and spatial parameters, a transferred limit state function technique is first proposed in this paper. By finding the effective first-crossing point which controls the failure of the structural system, the transferred technique is constructed to transform the dynamic reliability problem into a static one. For determining the effective first-crossing point, the parameter domain is first divided into different dominant domain corresponding to every parameter. Based on the parameter dominant domain, the first-crossing point about each parameter is obtained by comparing the difference value between the point on the failure boundary and the corresponding parameter upper bound. Finally, the effective first-crossing point is determined by finding the point which controls the structure failure. With the transferred technique, two strategies (including the sparse grid integration based on fourth-moment method and the maximum entropy based on dimensional reduction method) are proposed to efficiently estimate the dynamic failure probability. Several examples are employed to illustrate the significance and effectiveness of the transferred technique and the proposed methods for solving the multiple temporal and spatial parameters dynamic reliability. The results show that the proposed methods can estimate the multiple temporal and spatial parameters dynamic failure probability efficiently and accurately.

Short-term load forecasting (STLF) is crucial for intelligent energy and power scheduling. The time series of power load exhibits high volatility and complexity in its components (typically seasonality, trend, and residuals), which makes forecasting a challenge. To reduce the volatility of the power load sequence and fully explore the important information within it, a three-stage short-term power load forecasting model based on CEEMDAN-TGA is proposed in this paper. Firstly, the power load dataset is divided into the following three stages: historical data, prediction data, and the target stage. The CEEMDAN (complete ensemble empirical mode decomposition with adaptive noise) decomposition is applied to the first- and second-stage load sequences, and the reconstructed intrinsic mode functions (IMFs) are classified based on their permutation entropies to obtain the error for the second stage. After that, the TCN (temporal convolutional network), GRU (gated recurrent unit), and attention mechanism are combined in the TGA model to predict the errors for the third stage. The third-stage power load sequence is predicted by employing the TGA model in conjunction with the extracted trend features from the first and second stages, as well as the seasonal impact features. Finally, it is merged with the error term. The experimental results show that the forecast performance of the three-stage forecasting model based on CEEMDAN-TGA is superior to those of the TCN-GRU and TCN-GRU-Attention models, with a reduction of 42.77% in MAE, 46.37% in RMSE, and 45.0% in MAPE. In addition, the R2 could be increased to 0.98. It is evident that utilizing CEEMDAN for load sequence decomposition reduces volatility, and the combination of the TCN and the attention mechanism enhances the ability of GRU to capture important information features and assign them higher weights. The three-stage approach not only predicts the errors in the target load sequence, but also extracts trend features from historical load sequences, resulting in a better overall performance compared to the TCN-GRU and TCN-GRU-Attention models.