## 1 Introduction
In many cases, the VMD method provides a solid solution to the mode mixing problem in empirical mode decomposition (EMD) methods. As a result, this method has been used in many research areas such as mechanical diagnostics [8]. VMD methods have also provided good performance in planetary gearbox research, as was executed by [PERSON] et al. using joint VMD-based amplitude and frequency demodulation analysis and by [PERSON] et al. using VMD power spectral entropy and deep neural networks (DNNs) [9]. To detect faults in a two-stage planetary gearbox, [PERSON] et al. demonstrated a new method based on Renyi entropy, two-dimensional VMD, full-vector spectral techniques, and compressive sensing [10]. To verify correctness, an experimental study of fault test signals from a gearbox was carried out [11]. [PERSON] et al. proposed a VMD based on the Locust Optimization algorithm for the selection of mode numbers and balance parameters [12]. These proposals provide a good solution for selecting the mode number [13]. Quantification of the fault information contained in a time series of vibration signals that have undergone variational mode decomposition can be calculated using time series complexity metrics, such as approximate entropy, arrangement entropy, and other methods. Among them, the permutation entropy (PE) method is based on the spatial characteristics of a time series. Based on the spatial characteristics of the time series, it amplifies the small changes in the signal, which is more effective than other indicators in the diagnosis of abnormal states of mechanical equipment. Therefore, this paper chooses to apply permutation entropy in the process of gear transmission feature extraction to reflect the dynamic changes in the time series in different states of transmission. With the rapid development of computer technology in recent years, LSTM models based on deep learning theory [14] have been heavily researched in recent years. Compared with other data-driven models, the LSTM neural network shows better prediction results, but the model performance is still vulnerable to the influence of data series and initial values of model parameters. Its convergence performance is greatly reduced when the number of classifications increases due to the increase in sample size. For this reason, optimization algorithms can be introduced to optimize its parameters. Commonly used examples are grid search methods, genetic algorithm, etc., but these methods have large computational complexity and easily fall into local optimum and present other problems. For this reason, a new algorithm named intelligent optimization is introduced to perform parameter optimization and fault classification on LSTM models. There have been many studies on the analysis of runoff sequences and the optimization of model parameters' initial values [15]. For example, [PERSON] constructed the idea of \"decomposition-prediction-reconstruction\" and used a variational mode decomposition LSTM neural network model for runoff prediction of the Three Gorges reservoir, and the results showed that the model could effectively improve the accuracy of runoff prediction [15]. [PERSON] et al. developed a simulated annealing long short-term memory network (SA-LSTM) model, which can more accurately describe the dynamic lag time relationship between hydropower stations [15]. However, most of these studies focus on single data series decomposition or initial value optimization of LSTM model parameters, while there are few research results combining both. In this paper, we propose a coupled model, including variational mode decomposition (VMD), chameleon search algorithm (CSA), and long short-term memory (LSTM) neural networks, which is used in the mechanical field for fault diagnosis of a gearbox.