Novel L1 Regularized Extreme Learning Machine for Soft-sensing of an Industrial Process
Abstract : Extreme learning machine (ELM) is suitable for nonlinear soft sensor development. Yet it faces an over-fitting problem. To overcome it, this work integrates bound optimization theory with Variational Bayesian (VB) inference to derive novel L1 norm-based ELMs. An L1 term is attached to the squared sum cost of prediction errors to formulate an objective function. Considering the non-convexity and non-smoothness of the objective function, this work uses bound optimization theory, and constructs a proper surrogate function to equivalently convert a challenging L1 norm-based optimization problem into easy one. Then, VB inference is adopted for optimizing the converted problem. Thus an L1 norm-based ELM can be efficiently optimized by an alternating optimization algorithm with a proved convergence. Finally, a soft sensor is developed based on the proposed algorithm. An industrial case study is carried out to demonstrate that the proposed soft sensor is competitive against recent ones.
? There are two options available to meet the government's requirements: either building new high-performance facilities or enhancing the efficiency of existing plants by incorporating advanced monitoring and control techniques.
? The first option is likely impossible due to the high capital investment needed for the construction of new WWTPs. Moreover, the required land for the construction of new wastewater treatment sites may not be readily available because of environmental restrictions.
? In contrast, the GP model is transparent and can generate explicit equations that are very convenient for direct online implementation in the existing process information and control systems.
? To overcome the shortage of judgment made experienced operators and workers, a new soft sensor method based on kernel semi-supervised ELM is proposed to identify ST in this paper.
? We also propose a novel activation function to replace the Gaussian function to avoid the outlier weight imbalance problem.
? The main framework of the IG-SSELM is presented as follows. First, Select the appropriate characteristics based on expert experience.
? Priori information plays an important role in a determined classification problem. Generally speaking, the Gaussian kernel has a satisfactory result when the data are sampled from a Gaussian Mixture distribution.
• To compare the proposed approaches with the traditional FD method, a principal component analysis (PCA) model was also developed.
• By applying soft-sensors, the residual signal, i.e., the difference between estimated and measured VFA values, can be generated.
• The soft-sensors update can be performed automatically or by its developer. To automatically update the softsensors variety of approaches have been proposed.
• The proposed methodology provides a recursive minimization strategy to deal with missing values; it also offers kernel density estimation (KDE) to calculate the confidence interval.
? The main framework of the IG-SSELM is presented as follows. First, Select the appropriate characteristics based on expert experience. Then, utilize all the collected data (labelled and unlabeled data) to train our model with the proposed kernel activation function.
? Finally, for evaluating the performance of IG-SSELM, which further applied ST identification to industrial aluminum reduction cell. The main advantage of IG-SSELM is described:
? A novel kernel activation function is proposed in the ST identification model.
? All the dataset (labelled and unlabeled data) was used in the training process which improves the accuracy.
? Laplacian regularization is introduced to ELM for obtaining better robustness and generation ability.
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