Abstract
Given the multivariable coupling, strong nonlinearity and time-varying features in the wastewater treatment processes, adaptive strategies, including just-in-time learning (JITL), time difference (TD), and moving window (MW) methods have been chosen in this paper to enhance multi-output soft-sensor models to ensure online prediction for a variety of hard-to-measure variables simultaneously. In the proposed adaptive multi-output soft-sensors, multi-output partial least squares (MPLS), multi-output relevant vector machine (MRVM) and multi-output Gaussian process regression (MGPR) served as the multi-output models. The integration of adaptive strategies and multi-output models not only provides a solution for multi-output prediction, but also offers a potential to alleviate the degradation of multi-output soft-sensors. To further improve the adaptive ability, four adaptive soft-sensors, termed TD-MW, TD-JIT, JIT-MW, and TD-JIT-MW, have been proposed by mixing the three aforementioned adaptive strategies to upgrade multi-output soft-sensors. All the adaptive multi-output soft-sensors are analyzed and compared in terms of simulation data and practical industrial data, which exhibit stationary and nonstationary behaviors, respectively.
Highlights
Soft-sensors are generally applied in the predictions of difficult-to-measure but quality-related variables, such as the chemical oxygen demand (COD) and biological oxygen demand for five days (BOD5) in wastewater treatment plants (WWTPs), mainly due to expensive analyzer costs, hostile working surroundings and large time delays of hardware sensors measurement [1]
JIT-based models always produce the worst performance, after time difference (TD) processing, the TD-JIT models provide very high-quality performance in dealing with data drifting and abrupt changes. Both the TD-moving window (MW) and TD-JIT mixed methods can adapt to data drifting and abrupt changes effectively
We can choose appropriate adaptive strategies and multi-output models according to different application scenarios through the following guidelines: 1) In the process with data drifting slowly, it is better to choose the linear model multi-output partial least squares (MPLS) based on TD-MW method
Summary
Soft-sensors are generally applied in the predictions of difficult-to-measure but quality-related variables, such as the chemical oxygen demand (COD) and biological oxygen demand for five days (BOD5) in wastewater treatment plants (WWTPs), mainly due to expensive analyzer costs, hostile working surroundings and large time delays of hardware sensors measurement [1]. Xiao et al [9] developed multi-output soft-sensors using Multivariate Linear Regression model (MLR), MRVM and MGPR models aiming to predict multiple hard-to-measure variables simultaneously and to capture the joint distribution of the response variables. Yuan et al [3] proposed a spatio-temporal adaptive soft-sensor modeling framework, which called TD-MW-JITLWPLS in sulfur recovery unit and blast furnace ironmaking process These literatures [3], [7], [18]–[20] had demonstrated that the combination of these adaptive methods can effectively improve the prediction ability of the model in the face of model degradation.
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