## 1 Introduction  
Rare earth elements are strategic resources in China, finding widespread application in fields such as electronics, optoelectronics, and metallurgy. In rare earth separation enterprises, the primary objective of automating production process is to obtain single rare earth elements with high-purity. A crucial step in this process involves real-time monitoring of the changes in the content of rare earth element components during the extraction process [1]. Traditional detection methods, such as Inductively Coupled Plasma Atomic Emission Spectroscopy (ICP-AES), Inductively Coupled Plasma Mass Spectrometry (ICP-MS), EDX-ray Fluorescence (XRF), and Ultraviolet-Visible (UV-VIS) spectrophotometry [2; 3; 4; 5] are commonly used both domestically and internationally for detecting the content of rare earth element detection. While these methods offer high accuracy and reliability, they often require extensive preparation and testing time, which does not meet the requirements of real-time online detection. Soft sensing methods, being data-driven modeling technologies, enable model training and prediction based on real-time data; thus, these methods can achieve real-time content prediction, facilitating online detection and quick response to anomalies. Consequently, soft sensing methods are increasingly becoming the preferred rapid detection approach. Owing to the unique physical and chemical properties of certain rare earth elements, rare earth solutions of different concentrations exhibit distinct colors under visible light. Researchers have attempted to leverage these color characteristics for rapid detection of their component content using soft sensing methods. In [6], an association was formulated between the H component and the composition of Pr/Nd elements in a solution, leveraging the least squares technique within the HSI color model. In subsequent research [7; 8], the H/S components of the HSI color model were employed as input variables for modeling. Least-square support vector machine (LSSVM) and multi-RBF models were subsequently developed for predicting component concentrations. Further, in the literature [9; 10], the first moments of the H, S, and I components were extracted. These features were used as the input variables of the model, and weighted least-square support vector machine (WLSSVM) and genetic algorithm-improved extreme learning machine (GA-ELM) models were employed to establish a soft sensor model of component content. In another study [11], ten color features, including RGB, HIS, RR, RG, RB, and CVA of Pr/Nd extracted from solution images were used as inputs, then an improved GRA-real-time learning algorithm was utilized to predict component content. However, these methods only consider the HSI features of the image color space, neglecting other representative features. This single feature extraction method often struggles to fully encapsulate all the information of the image; when there are too many single features, feature redundancy can easily occur. Additionally, different elements with varied concentrations in the solution can lead to changes in the color and brightness of the solution images. These alterations often appear as visual features, including variations in texture and the presence of spots. The Gray Level Co-occurrence Matrix (GLCM) [12] is a predominant tool in the realm of image texture feature extraction due to its simplicity of implementation, extensive applicability, and robust representational capability. For instance, in the literature [13], the GLCM has been employed to extract the building area of high-resolution SAR images. When combined with Bhattacharyya feature selection, it can achieve excellent results in detecting the boundaries of the building area. In another study [14], spectral features and spatial texture features extracted by the GLCM were combined to construct a random forest classifier, enabling the extraction of wolfberry planting information.