**1. Introduction**

As the main type of mechanical equipment used for ore grinding, ball mills are widely used in the beneficiation process in mining operations [1]. It is imperative but challenging to develop effective modeling, monitoring, and control techniques for complex industrial systems [2–4]. Due to their complexity, it is difficult to investigate the internal charge dynamics of ball mills. Energy consumption is obviously related to rotational speed and mill load, and scholars have examined the influence of rotational speed on the energy consumption of mills and achieved good results [5]. For the mill load, it is important to be able to quickly and accurately identify the internal load of a ball mill to ensure that the mill is operating under the best possible working conditions, not only to reduce energy consumption during mineral processing, but also to ensure high grinding efficiency and output [6,7]. Therefore, a method of increasing the load recognition rate for ball mills would have great application value for improving the stability and economic benefits of the grinding process, and efforts to develop such methods have attracted the attention of many scholars at home and abroad [8,9]. To this end,

studies have shown that the vibration signal generated by a ball mill during the grinding process is correlated with the load [10].

The vibration signal of a ball mill is nonlinear and nonstationary. Currently, the most widely used methods for processing such signals include the wavelet packet algorithm, empirical mode decomposition (EMD), variable mode decomposition (VMD), local mean decomposition (LMD), and the complete integrated empirical decomposition algorithm (CEEMDAN) [11–14]. Liu et al. [15] combined the EMD algorithm with principal component analysis (PCA) to extract the vibration signal from the cylinder of a wet ball mill. The results showed that this method can distinguish among different load states, but that the recognition rate requires improvement. Tang et al. [16,17] reported a method of extracting the vibration signal characteristics of a ball mill based on ensemble empirical mode decomposition (EEMD) and interval partial least squares (iPLS) modeling and extended this method to the study of ball mill sound signals. Although the signal features were successfully extracted, there was residual noise in the intrinsic mode functions (IMFs) after decomposition, and white noise with a different amplitude was added each time. Although the above methods can be used to successfully extract signal features, they face problems related to noise residuals and computational burden. Therefore, the key to mill load identification is to find an effective method of extracting the characteristic information of the vibration signal of the ball mill cylinder. The proposed empirical wavelet transform (EWT) algorithm effectively compensates for the above shortcomings. This algorithm not only suppresses the modal aliasing problem and reduces residual noise, but also improves the completeness of decomposition. In reference [18], the EMD, EEMD, and EWT algorithms were compared and analyzed. The EWT algorithm was found to have the best processing effect. Specifically, the EWT algorithm had a better processing speed and better ability to extract modal component signals than the other algorithms. However, in practical engineering, especially under the harsh working conditions of a ball mill, the Fourier spectrum of the EWT segmentation signal easily encounters interference from background noise and must be further improved. In this paper, the adaptive frequency window is used to improve EWT. Compared with traditional EWT and other signal processing algorithms, the denoising effect is more significant.

In recent years, many nonlinear dynamic methods, such as multiscale entropy (MSE), singular value entropy (SVE), permutation entropy (PE), and fuzzy entropy (FE), have been widely used for fault diagnosis, classification, and recognition because of their good performance in terms of feature extraction [19–21]. Miao Y et al. [22] applied SVE to the identification of the optimal frequency band. Zhao L et al. [23] completed the fault diagnosis of a gearbox using PE optimization and modified the modal decomposition algorithm. Chang J L et al. [24] applied MSE for load recognition in machine tools. Liu H et al. [25] reported an example of MSE applied for the fault diagnosis of rolling bearings, but the recognition accuracy required further improvement. To diagnose the problem of rolling bearing faults, Zheng H D et al. [26] adopted the method of multiscale fuzzy entropy (MFE), which effectively overcame the defect in the MSE mutation, and the diagnosis result was improved. Compared with the above methods, MFE has some advantages for feature extraction because of its unique performance and ability to accurately reflect the feature information of the original signal.

As a tool for recognition and classification, an artificial neural network is a model abstracted based on neural network theory that originates from the field of physiology. Such models can be used for arbitrary data clustering and pattern classification and are widely used for tasks such as pattern recognition [27–29]. Specifically, a probabilistic neural network (PNN) is an artificial neural network with the advantages of a fast training speed, simple parameter adjustment, and good classification performance [30]. However, the classification effect of a probabilistic neural network is greatly influenced by the smoothing parameter σ, and if the selection of σ is not appropriate, then inaccurate results may be obtained. To solve this problem, an adaptive evolutionary particle swarm optimization (AEPSO) algorithm is proposed in this paper to optimize the smoothing parameters in a probabilistic neural network (PNN) so that the optimized network can identify the load state of a ball mill. In this paper, the AEPSO algorithm is used to improve the PNN clustering method; compared with the

traditional PNN clustering method and other clustering methods, it has the advantages of high speed and high accuracy.

Considering the nonstationary and nonlinear characteristics of the vibration signal from the cylinder of a ball mill, a load identification method for ball mills is proposed in this study based on improved EWT, MFE, and AEPSO\_PNN classification. First, the vibration signals are decomposed using improved EWT, and the mode components of the reconstructed signals are selected using a correlation coefficient threshold. Then, the load state of the ball mill is determined based on the magnitude of the calculated MFE. Finally, AEPSO\_PNN is used for learning and classification to enable the recognition of a different load state.

#### **2. Principles of the Load State Identification Method**
