In view of the characteristics of the collected time series, such as being high noise, non-stationary and nonlinear, most of the current methods are designed to smooth or denoise the whole time series at one time and then divide the training set and testing set, which will lead to using the information of the testing set in the training process, resulting in data leakage and other problems. In order to reduce the impact of noise on time series prediction and prevent data leakage, a prediction method with data leakage suppression for time series (DLS) is proposed. This prediction method carries out multiple variational mode decomposition on the time series by overlapping slicing and improves the noise reduction threshold function to perform noise reduction processing on the decomposed time series. Furthermore, the idea of deep learning is introduced to establish a neural network multi-step prediction model, so as to improve the performance of time series prediction. The different datasets are selected as experimental data, and the results show that the proposed method has a better prediction effect and lower prediction error, compared with the common multi-step prediction methods, which verifies the superiority of the prediction method.

We present a parallel numerical method of simulating the interaction of atoms with a strong laser field by solving the time-depending Schrödinger equation (TDSE) in spherical coordinates. This method is realized by combining constructing block diagonal matrices through using the real space product formula (RSPF) with splitting out diagonal sub-matrices for short iterative Lanczos (SIL) propagator. The numerical implementation of the solver guarantees efficient parallel computing for the simulation of real physical problems such as high harmonic generation (HHG) in these interaction systems.

With the broadband, noise-like, and non-periodic characteristics of chaotic signals, chaotic digital modulation schemes have received extensive attention. A new short reference orthogonal double bit rate differential chaotic shift keying (SR-ODBR-DCSK) communication scheme is proposed in the paper. The modulation technology generates two orthogonal chaotic signals by using the orthogonality of the chaotic signals acting on the Walsh function and modulates the continuous two-bit data information respectively to achieve the simultaneous transmission of two signals at the same time slot. Odd information bits and even information bits are modulated to two orthogonal signals so as to reach a double transmission rate on the basis of the original channel. In this paper, the performance of SR-ODBR-DCSK in the additive white Gaussian noise (AWGN) channel is analyzed, and a Monte Carlo simulation test is carried out. The bit error rate of this modulation method is compared with that of SR-DCSK. The results show that the SR-ODBR-DCSK system is excellent and promising.

Chaotic time series have been involved in many fields of production and life, so their prediction has a very important practical value. However, due to the characteristics of chaotic time series, such as internal randomness, nonlinearity, and long-term unpredictability, most prediction methods cannot achieve high-precision intermediate or long-term predictions. Thus, an intermediate and long-term prediction (ILTP) method for n-dimensional chaotic time series is proposed to solve this problem. Initially, the order of the model is determined by optimizing the preprocessing and constructing the joint calculation strategy, so that the observation sequence can be decomposed and reorganized accurately. Furthermore, the RBF neural network is introduced to construct a multi-step prediction model of future sequences, with a feedback recursion mechanism. Compared with the existing prediction methods, the error of the ILTP method can be reduced by 1–6 orders of magnitude, and the prediction step can be increased by 10–20 steps. The ILTP method can provide reference technology for the application of time series prediction with chaotic characteristics.

A short reference differential chaotic shift keying communication system based on reference signal scrambling transformation (RSST-SR-DCSK) is proposed in this paper. The system introduces information-bit-driven scramblers at the transmission end to effectively eliminate the correlation between the reference signal and information signal. At the receiving end, a descrambler is used to restore the correlation, thereby enhancing information transmission security. Additionally, the system employs a short reference transmission mechanism to further increase the information transmission rate. The transmitter and receiver structures of the system are designed through signal structure analysis. Theoretical analyses and simulations conducted in an additive white Gaussian noise (AWGN) channel demonstrate promising performance, including a low bit error rate (BER) and a favorable data-energy-to-bit-energy ratio (DBR). Simulation verification is performed to examine the impact of parameters on the bit error rate performance. A comparative analysis with traditional DCSK and SR-DCSK systems highlights the superior performance of the RSST-SR-DCSK system.

In the process of big data processing, especially in fields like industrial fault diagnosis, there is often the issue of small sample sizes. The data generation method based on Generative Adversarial Networks(GANs) is an effective way to solve this problem. Most of the existing data generation methods do not consider temporal characteristics in order to reduce complexity. This can lead to insufficient feature extraction capability. At the same time, there is a high degree of overlap between the generated data due to the low category differentiation of the real data. This leads to a lower level of category differentiation and reliability of the generated data. To address these issues, a time series data generation method with High Reliability based on the ACGAN (HR-ACGAN) is proposed, applied to the field of industrial fault diagnosis. First, a Bi-directional Long Short-Term Memory (Bi-LSTM) network layer is introduced into the discriminator.It can fully learn the temporal characteristics of the time series data and avoid the insufficient feature extraction capability. Further, an improved training objective function is designed in the generator to avoid high overlap of generated data and enhance the reliability of generated data. Finally, two representative datasets from the industrial fault domain were selected to conduct a simulation analysis of the proposed method. The experimental results show that the proposed method can generate data with high similarity. The dataset expanded with the generated data achieves high classification accuracy, effectively mitigating the issue of dataset imbalance. The proposed HR-ACGAN method can provide effective technical support for practical applications such as fault diagnosis.