It is noteworthy that different kernel function types and kernel parameters have different characteristics in the LVMs [33; 34; 35]; thus, the same input variable structure will be mapped to different latent variable modeling subspaces (LVS). This character of LVMs can be added to the base model diversity enhancement mechanism [29; 36]. In ensemble learning, many could be better than all [37; 38]. Therefore, selectively choosing ensemble parts of base models that are based on certain standards and show better comprehensive performance and lower similarity from base models is another key step for high-performance ensemble learning soft sensor model construction. The selection process of base models is also called ensemble pruning [39; 40]. Whether the ensemble pruning effect is satisfactory depends on reasonable quantitative indexes of base model accuracy and diversity criteria on one hand and quick and easy selection methods on the other hand. For soft sensor models, the accuracy is often measured by quantitative indicators such as root-mean-square error (RMSE), mean square error (MSE), etc. [7; 18]. However, there is no unified standard for the quantitative parameters of diversity. Mutual information of variables or covariance and other correlation or complementarity indicators are usually chosen [41]. The based models in subensemble sets obtained by ensemble pruning are expected to be precise and different, but this work often is NP-complete hard and even intractable to approximate, so the selection method of base models has always been the focus of researchers. Based on the quantitative indicators of accuracy and diversity, a comprehensive performance evaluation function of the subensemble set was constructed by using weighting algorithms and other methods. Then the greedy search algorithm or optimization algorithm was used to solve the evaluation function for ensemble pruning. However, a multi-step analysis and a relatively large amount of overall computation are always required in these methods. In terms of detailed parameter design, not only does the weight value between the two indicators need to be constantly adjusted according to the changeable model condition and data characteristics, but the number of base models in the subensemble set also needs to be artificially set in advance [40; 42; 43]. Motivated by the above problems of ensemble soft sensor modeling, the mechanism of base model diversity generation and the method of base model integrated pruning are the focus of this study research. The main contributions of this study are as follows:  
(1) A diversified base model construction method based on adaptive multi-kernel supervised LVSs is proposed. The method takes advantage of the diversification and variation of different kernel function types and kernel function parameters, uses multiple kernel functions and an adaptive kernel parameter choosing algorithm to map each variable space obtained by variable selection to different and reasonable modeling LVSs, adds random perturbations to the construction of variable subspace, and generates base model parameters. (2) According to the predictions of each base model on the verification set, a diversity quantification parameter called the comprehensive Euclidean distance (CED) is designed, which is used to establish the diversity level of the subensemble model set during the ensemble pruning. (3) A subensemble set generation method based on formalizing ensemble pruning with simultaneous diversity and accuracy into a multi-objective optimization problem is proposed. The selection of each base model is defined as the decision objective, and the comprehensive quantitative parameter of accuracy and diversity is used as the objective function. The multi-objective gray wolf optimization algorithm is applied to solve the problem, which simplifies the integrated pruning process. (4) A detailed comparative experiment is designed to verify the effectiveness of this research method.