Metaheuristic algorithms are widely used in engineering problems due to their high efficiency and simplicity. However, engineering challenges often involve multiple control variables, which present significant obstacles for metaheuristic algorithms. The Crested Porcupine Optimizer (CPO) is a metaheuristic algorithm designed to address engineering problems, but it faces issues such as falling into a local optimum. To address these limitations, this article proposes three new strategies: composite Cauchy mutation strategy, adaptive dynamic adjustment strategy, and population mutation strategy. The three proposed strategies are then introduced into CPO to enhance its optimization capabilities. On three well-known test suites, the improved CPO (CAPCPO) outperforms 11 metaheuristic algorithms. Finally, comparative experiments on seven real-world engineering optimization problems demonstrate the advantages and potential of CAPCPO in solving complex problems. The multifaceted experimental results indicate that CAPCPO consistently achieves superior solutions in most cases.

Many studies indicated that ionospheric total electron content (TEC) prediction is vital for terrestrial and space-based radio-communication systems. In previous TEC prediction schemes based on RNN, they learn TEC representations from previous time steps, and each time-step made an equal contribution to a prediction. To overcome these drawbacks, we propose two improvements in our study: (1) To predict TEC with both past and future time-step, Bidirectional Gate Recurrent Unit (BiGRU) was presented to improve the capabilities. (2) To highlight critical time-step information, attention mechanism was used to provide weights to each time-step. The proposed attentional BiGRU TEC predicting method was evaluated on the publicly available data set from the Centre for Orbit Determination in Europe. We chose three geographical locations in low latitude, middle latitude, and high latitude to verify the performance of our proposed model. Comparative experiments were conducted using Deep Neural Network (DNN), Artificial Neural Network (ANN), Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM), Bidirectional Long Short-Term Term memory (BiLSTM), and Gated Recurrent Unit (GRU). Experimental results show that the proposed Attentional BiGRU model is superior to the other models in the selected nine regions. In addition, the paper discussed the effects of latitudes and solar activities on the performance of Attentional BiGRU model. Experimental results show that the higher the latitude, the higher the prediction accuracy of our proposed model. Experimental results also show that in the middle latitude, the prediction accuracy of the model is less affected by solar activity, and in other areas, the model is greatly affected by solar activity.

Total electron content (TEC) is a vital parameter for describing the state of the ionosphere, and precise prediction of TEC is of great significance for improving the accuracy of the Global Navigation Satellite System (GNSS). At present, most deep learning prediction models just consider TEC temporal variation, while ignoring the impact of spatial location. In this paper, we propose a TEC prediction model, ED-ConvLSTM, which combines convolutional neural networks with recurrent neural networks to simultaneously consider spatiotemporal features. Our ED-ConvLSTM model is built based on the encoder-decoder architecture, which includes two modules: encoder module and decoder module. Each module is composed of ConvLSTM cells. The encoder module is used to extract the spatiotemporal features from TEC maps, while the decoder module converts spatiotemporal features into predicted TEC maps. We compared the predictive performance of our model with two traditional time series models: LSTM, GRU, a spatiotemporal mode1 ConvGRU, and the TEC daily forecast product C1PG provided by CODE on a total of 135 grid points in East Asia (10°–45°N, 90°–130°E). The experimental results show that the prediction error indicators MAE, RMSE, MAPE, and prediction similarity index SSIM of our model are superior to those of the comparison models in high, normal, and low solar activity years. The paper also analyzed the predictive performance of each model monthly. The experimental results indicate that the predictive performance of each model is influenced by the monthly mean of TEC. The ED-ConvLSTM model proposed in this paper is the least affected and the most stable by the monthly mean of TEC. Additionally, the paper compared the predictive performance of each model during two magnetic storm periods when TEC changes sharply. The results indicate that our ED-ConvLSTM model is least affected during magnetic storms and its predictive performance is superior to those of the comparative models. This paper provides a more stable and high-performance TEC spatiotemporal prediction model.

In this paper, we propose a novel Total Electron Content (TEC) map prediction model, named ED‐AttConvLSTM, using a Convolutional Long Short‐Term Memory (ConvLSTM) network and attention mechanism based on encoder‐decoder structure. The inclusion of the attention mechanism enhances the efficient utilization of spatiotemporal features extracted by the ConvLSTM, emphasizing the significance of crucial spatiotemporal features in the prediction process and, as a result, leading to an enhancement in predictive performance. We conducted experiments in East Asia (10°N–45°N, 90°E−130°E). The ED‐AttConvLSTM was trained and evaluated using the International GNSS Service TEC maps over a period of six years from 2013 to 2015 (high solar activity years) and 2017 to 2019 (low solar activity years). We compared our ED‐AttConvLSTM with IRI‐2016, COPG, LSTM, GRU, ED‐ConvLSTM and ED‐ConvGRU. The results indicate that our model surpasses the comparison models in forecasting both high and low solar activity years, across most months and UT moments in a day. Moreover, our model exhibits notably superior prediction performance during the most severe phases of a magnetic storm when compared to the comparison models. Subsequently, we then also discuss how the prediction performance of our model is affected by latitude. Finally, we discuss the diminishing performance of our model in multi‐day predictions, demonstrating that its reliability for forecasts ranging from one to 4 days in advance. Beyond the fifth day, there is a pronounced decline in the model's performance.

The high‐precision prediction of total ionospheric electron content (TEC) is of great significance for improving the accuracy of global navigation satellite systems. There are two problems with the current prediction of TEC: (a) The existing TEC prediction models mainly based on stacked structure, which has insufficient predictive ability when the network has fewer layers, and loss of fine‐grained features when there are more layers, resulting in a decrease in predictive performance; (b) The existing research on ionospheric TEC prediction mainly focuses on building deep learning prediction models, while there is little research on optimizing the hyper‐parameters of TEC prediction models. Optimization can help find a better quasi‐optimal hyperparameter combination and improve the performance of the model. This paper proposed an automatic deep learning framework for global TEC map prediction, named MAOOA‐Residual‐Attitude‐BiConvLSTM. This framework includes a TEC prediction model, Residual‐Attention‐BiConvLSTM, which can simultaneously consider both coarse‐grained and fine‐grained spatiotemporal features. It also includes an optimization algorithm, MAOOA, for optimizing the hyper‐parameters of the model. We conducted comparative experiments between our framework and C1PG, ConvLSTM, ConvGRU, and ED‐ConvLSTM during high solar activity years, low solar activity years, and a magnetic storm event. The results indicate that in all cases, the framework proposed in this paper outperforms the comparative models.

In order to explore the abnormal disturbance of the space electric field caused by earthquakes using the electric field data of the ULF and VLF frequency bands of the electric field observed by the ZH-1 satellite, and taking the Mw7.7 earthquake in the Caribbean Sea in the southern sea area of Cuba on 29 January 2020 as an example, the signal-to-noise ratio of the NAA and NLK artificial source VLF transmitting stations in the Northern Hemisphere and the height of the lower ionosphere was calculated. The disturbance of the electric field in the ULF band was extracted using the S-G filtering method. The results indicate that: (1) The ionospheric anomaly caused by this earthquake appeared 20 days before the earthquake, and before the earthquake, there were significant anomalous changes in all parameters within the pregnant seismic zone. The signal-to-noise ratios of the NAA and NLK artificial source transmitter stations decreased by 30%, and the height of the low ionosphere decreased by 5–10 km, while there were anomalous perturbations in several orbits of the ULF electric field, and the magnitude of the perturbations exceeded three times the standard deviation. (2) The SNR of the artificial source transmitting stations before and after the earthquake was significantly reduced in the third period before the earthquake and recovered after the earthquake. (3) The low ionospheric height appears to be reduced before the earthquake and recovers after the earthquake. (4) The decrease in the S/N ratio occurred simultaneously with the decrease in ionospheric height 15 days–10 days before the earthquake. This provides a reference for extracting pre-earthquake ionospheric precursor anomalies.