## 1 Introduction  
There are many complex problems in the soft sensor modeling of industrial processes, such as process nonlinearity, process dynamics, quality variables lagging behind process variables, and quality variables not matching process variables [1, 2, 3]. When dealing with complex industrial processes and massive industrial data, shallow neural networks are not enough to deal with these high-dimensional data and dynamic process scenarios, which leads to problems such as insufficient prediction accuracy and poor generalization of soft sensor models [4, 5]. With the development of artificial intelligence, the feature representation ability of deep neural networks has become more and more prominent [6]. The deep neural network transforms the original input into higher dimensional and more complex features, which can better simulate the nonlinearity and dynamics of the industrial process so as to obtain a more accurate soft sensor model [7]. Deep neural networks can be divided into two categories: static networks represented by deep belief network (DBN) [8] and stacked auto-encoder (SAE) [9] and dynamic networks represented by recurrent neural network (RNN) [10]. In a variety of static networks, it is generally assumed that there is no time-dynamic dependence between samples in the industrial process. In order to establish a soft sensor model, the static model constructs an augmented matrix according to the input dimension of the data to overcome the process dynamics [11], but determining how to reasonably construct the augmented matrix can only rely on expert experience. The correlation of each sample in the process data hides the dynamic information of the industrial process, and capturing this information is the key to improving the accuracy of the soft sensor model. Sequential model RNN has been applied to industrial processes [12]. To solve the long-term dependence of RNN, soft sensor models using long short-term memory (LSTM) [13] or gated recurrent unit (GRU) [14; 15] have achieved good prediction results in some industrial scenarios. Based on LSTM, [PERSON] et al. constructed a supervised LSTM unit for learning the hidden dynamic information related to quality in the industrial process and verified the effectiveness of the proposed supervised LSTM soft sensor model on multiple datasets [16]. In the research of the sequential model, [PERSON] et al. proposed sample convolution and interaction networks (SCINet) [17] for time series forecasting. SCINet enhances the original sequence's predictability by capturing features' temporal dependence at different temporal resolutions [18]. It has a stronger feature extraction ability and superior long-term and short-term prediction ability in wind power prediction and stock trading [19]. All the above sequential models are designed as end-to-end models. Although these models have powerful dynamic feature extraction capabilities, their regressors are generally single- or multilayer, fully connected networks. When performing regression fitting on the extracted features, the performance of the models is limited. Ensemble models in machine learning have strong generalization ability by constructing multiple sub-regressors, but such ensemble models cannot be trained directly with deep networks. Therefore, to combine the advantages of both, some researchers have used deep neural networks for extracting complex dynamic features and used ensemble models as regressors to transfer dynamic features [20; 21]. [PERSON] et al. used DBN combined with a particle swarm optimization algorithm to extract features as the support vector regression (SVR) input to establish a soft sensor model, achieving good results [22]. [PERSON] et al. used DBN to extract the features of auxiliary variables and input them into the extreme learning machine for training to obtain the soft sensor model [23]. [PERSON] et al. proposed a hidden layer feature extractor based on continuous restricted Boltzmann machine (CRBM) and established the CRBM-SVR soft sensor model [24].