As an amendment to the deep forest, deep forest regression (DFR) has been recently proposed for industrial process modeling. However, training DFR models is an arduous task in terms of computational cost, which incurs limitations for practical industrial applications, such as soft measurement models of difficult-to-measure key process indices. Therefore, we propose a lightweight and high-precision DFR (LHDFR) algorithm to (1) shrink model size, (2) reduce computation cost, and (3) improve modeling accuracy simultaneously without increasing calculation operations. This algorithm is implemented simply and effectively in a deep ensemble structure. In particular, we utilize an unbiased estimation to weaken the swamping effect of representation features among cascade layers. Furthermore, two different types of decision tree algorithms are applied to the forest algorithms in each layer. Then, we present a gradient enhancement strategy with a step factor among layers to enhance the accuracy of the model. The shrinking layer-by-layer method is employed to take advantage of the depth of the decision tree. The comparative results based on six benmark datasets and an actual dioxin soft sensing application case on municipal solid waste incineration process demonstrate the superior performance of our LHDFR model.

The furnace temperature is a critical operational indicator for ensuring the safe and stable operation of municipal solid waste incineration (MSWI) processes. However, temperature data often exhibit strong nonlinear, multidimensional, and coupling characteristics, which pose significant challenges for the qualitative analysis of state changes. To address these issues, this study proposes a novel qualitative temperature state analysis method based on multilevel feature fusion and nonparametric detection. First, feature analysis is integrated into tree-based models to distinguish strongly and weakly relevant features, after which statistical fusion and a variational autoencoder are used to characterize the two types. Next, the fusion feature space is further optimized by incorporating information contribution, resulting in a compact yet informative feature representation. Finally, a nonparametric two-sided detection method is applied to identify changepoints and construct qualitative state datasets. In practical deployments, the availability of ground-truth state labels would enable more rigorous quantitative comparison and validation; however, such labels are often unavailable in real-world MSWI systems. In such cases, the proposed method offers an auxiliary reference for evaluation in unlabeled scenarios. Experiments conducted on real MSWI datasets demonstrate the effectiveness of the proposed method in accurately capturing temperature state transitions and generating high-quality state data.

As one of the by-products of the municipal solid waste incineration (MSWI) process, dioxin (DXN) is not only difficult to detect but also potential harm to humans and the environment. The article proposes a method for detecting DXN emissions. It addresses the challenge of poor generalization performance in detection models due to the dynamic nature of the MSWI process. Firstly, the method constructs a historical soft sensor model and a drift detection model based on historical samples. Secondly, it assesses online samples for drift detection. When drift is detected, it calculates a distance threshold to prune the ensemble model. Subsequently, it reconstructs new ensemble sub-models and integrates them with the historical model to form a preliminary online ensemble model. Finally, it conducts local pruning and reconstruction on each sub-model, refining the final online ensemble model based on weighted posterior information. The efficacy of this approach is validated using synthetic, benchmark, and real DXN datasets from an MSWI plant in Beijing.

The furnace temperature (FT) control is the key for ensuring the stable operation and effective pollution reduction in municipal solid waste incineration (MSWI) processes. However, conventional control strategies encounter challenges in effectively managing FT due to uncertainties associated with material composition, feeding modes, and equipment maintenance. In response to these challenges, this article introduces a control approach utilizing a Bayesian optimization-based interval type-2 fuzzy neural network (BO-IT2FNN), which achieves offline optimization and online control through the FT controller constructed by IT2FNN. In offline optimization process, the BO algorithm is used to optimize the learning rate of multiple types parameter of IT2FNN controller. In the online control process, fine-tuned by gradient descent method with multiple LR for adaptability. In addition, the stability of control system is confirmed using theorem of Lyapunov, providing the theoretical foundation. Experiments with real MSWI data, tested on a hardware-in-loop platform, prove the effectiveness of the proposed method.

Dioxin (DXN) is a persistent organic pollutant produced from municipal solid waste incineration (MSWI) processes. It is a crucial environmental indicator to minimize emission concentration by using optimization control, but it is difficult to monitor in real time. Aiming at online soft-sensing of DXN emission, a novel fuzzy tree broad learning system (FTBLS) is proposed, which includes offline training and online measurement. In the offline training part, weightedk-means is presented to construct a typical sample pool for reduced learning costs of offline and online phases. Moreover, the novel FTBLS, which contains a feature mapping layer, enhance layer, and increment layer, by replacing the fuzzy decision tree with neurons applied to construct the offline model. In the online measurement part, recursive principal component analysis is used to monitor the time-varying characteristic of the MSWI process. To measure DXN emission, offline FTBLS is reused for normal samples; for drift samples, fast incremental learning is used for online updates. A DXN data from the actual MSWI process is employed to prove the usefulness of FTBLS, where the RMSE of training and testing data are 0.0099 and 0.0216, respectively. This result shows that FTBLS can effectively realize DXN online prediction.

Broad learning system based on neural network (BLS-NN) has poor efficiency for small data modeling with various dimensions. Tree-based BLS (TBLS) is designed for small data modeling by introducing nondifferentiable modules and an ensemble strategy to the traditional broad learning system (BLS). TBLS replaces the neurons of BLS with the tree modules to map the input data. Moreover, we present three new TBLS variant methods and their incremental learning implementations, which are motivated by deep, broad, and ensemble learning. Their major distinction is reflected in the incremental learning strategies based on: 1) mean square error (mse); 2) pseudo-inverse; and 3) pseudo-inverse theory and stack representation. Therefore, this study further explores the domain of BLS based on the nondifferentiable modules. The simulations are compared with some state-of-the-art (SOTA) BLS-NN and tree methods under high-, medium-, and low-dimensional benchmark datasets. Results show that the proposed method outperforms the BLS-NN, and the modeling accuracy is remarkably improved with the small training data of the proposed TBLS.

Fuzzy decision trees (FDTs) is one of the considerably excellent methods. Most of the existing FDTs’ methods are oriented to classification tasks. Applying FDTs to regression tasks may solve complex industrial modeling problems. In this article, we propose the Takagi–Sugeno (T–S) fuzzy regression tree (TSFRT), which uses the hypothesis of “feature screening followed by T–S fuzzy reasoning.” In the TSFRT, the growth process (crisp set theory) can be deemed as feature screening, and each leaf node (fuzzy set theory) is viewed as a T–S inference reasoning system. Thus, the TSFRT becomes a top-down structure. We develop multiple strategies to identify the parameters of the T–S system in the leaf node using sample-by-sample and batch samples. To improve the method's generalization performance, we also generalize an ensemble method with pseudoinverse and ridge regression. The proposed methods are evaluated by several high- and low-dimensional complex industrial processes. The experimental results show that the proposed method remarkably outperforms other popular regression methods.