Optimization problems in real-world applications often involve dynamic environmental changes, requiring algorithms to adapt quickly, track optimal solutions, and maintain efficiency. Existing dynamic multiobjective optimization evolutionary algorithms (DMOEAs) typically rely on fixed or limited dynamic response mechanisms, which are often insufficient to handle complex and varied dynamic environments. To overcome these limitations, this article proposes an adaptive dynamic response-based DMOEA (ADR-DMOEA), which employs a subpopulation-level adaptive mechanism to coordinate diversity-driven, prediction-driven, and memory-driven strategies. The strategy weights are dynamically adjusted according to the static optimization distance of each subpopulation, ensuring that appropriate strategies are adaptively deployed in different environments. This design overcomes the inefficiency of fixed assignments and the instability of individual-level perturbations, enabling coordinated and stable evolution. Extensive experiments on DF benchmark functions and a blast furnace (BF) ironmaking case study demonstrate that ADR-DMOEA achieves superior convergence, diversity, and robustness compared to state-of-the-art algorithms, effectively supporting real-world decision-making under dynamic conditions.

In this paper, a P-type adaptive predictive control (PAPC) method is presented for a category of unknown multi-input multi-output (MIMO) discrete-time systems with nonaffine nonlinear dynamics. First, the unknown nonlinear model is altered to a linear form containing an unknown pseudo-partial derivative (PPD) matrix utilizing the partial-form dynamic linearization (PFDL). A predictive model is then established by employing the modified projection algorithm, an auto-regressive model, and an output estimation technique. Based on the predictive model, an adaptive learning law that incorporates estimated tracking error information is used to generate the virtual error. Then, a data-driven PFDL-PAPC algorithm is constructed by replacing the actual tracking error in the P-type controller with the virtual one. The bounded convergence properties of the output estimation and tracking error dynamics are theoretically analyzed using the contraction mapping principle. The effectiveness of the PFDL-PAPC method is demonstrated through coupled tanks and actual data-based blast furnace ironmaking experiments. Note to Practitioners—Model-based control strategies are highly dependent on the model of the controlled plant, which makes it challenging to apply them in complicated industrial processes. In this paper, a P-type adaptive predictive control algorithm is presented. It is directly driven by the virtual error generated through the multi-layer prediction mechanism without requiring any modeling procedure. The operators can flexibly adjust the linearization length according to the system’s dynamic complexity. Furthermore, the proposed algorithm can effectively resist the negative influence of input disturbances. The coupled tanks and actual blast furnace ironmaking data-based experiments are provided to verify the effectiveness of the proposed algorithm.

For the output probability density function (PDF) control problem of singularly perturbed systems, a new neural networks-based output PDF shape identification and control is proposed to address the impact of fast and slow time scales. First, an identification scheme for the output probability density function of singularly perturbed systems based on multi-time scale neural networks is proposed, by designing a new weight adaptive update algorithm through the optimal bounded ellipsoid constraint. Second, two control methods are proposed under different uncertainty conditions. By uncertainty approximation assumption, a direct optimization method based on derivation is proposed. Then, to enhance the applicability, a control strategy based on convergence domain and the gradient descent optimization method is proposed to update the control parameters. The closed-loop stability is analyzed by constraining the convergence domain under Lyapunov stability, ensuring the tracking effect of the system state. Simulation results and grinding process confirm the effectiveness of the proposed method.

Conformal prediction (CP) is known to theoretically guarantee prediction interval coverage under the exchangeability assumption. However, industrial time series collected from real-world industrial processes often violates this assumption due to temporal dependencies and distribution drift. Therefore, an uncertainty quantification framework is proposed for industrial time series, with the prediction interval composed of two one-sided intervals. Specifically, it adopts CP as the basic framework and integrates entire and local nonconformity score information to adjust the confidence levels of two one-tailed intervals over time. This enables the proposed method can adapt quickly to distribution shifts and provides effective prediction intervals. Two experiments show that the proposed method improves the efficiency of prediction intervals while guaranteeing coverage. Specifically, under a nominal confidence level 95%, the proposed method achieves an average empirical coverage of 95.0% with a 6.29% reduction in prediction interval width in the wastewater dataset. While in the actual sintering production dataset, it achieves a similar improvement, with a 95.6% coverage and a 15.70% reduction in width, compared to the best-performing benchmark model.

Industrial streaming data exhibits the concept drift characteristic due to the time-variant operating conditions, which degrades the performance of models established by traditional offline batch learning. Moreover, the widespread outliers and the correlations between data variables in industrial data streams can have a devastating impact on modeling. Therefore, this paper presents a novel online sequential sparse robust neural networks with random weights (OSSR-NNRW) for imperfect industrial streaming data to achieve highly reliable online modeling of time-variant dynamic systems. First, sparse partial least squares regression is used to replace least squares estimation for network output weights calculation, which not only can effectively solve the multicollinearity problem caused by correlations, but also enable variable selection to improve the performance and interpretability. Second, we introduce the online sequential learning strategy with forgetting factor to realize adaptive updating of model parameters, thus enhancing the online learning ability and overcoming the time-variant dynamics of industrial systems. More importantly, in order to strengthen the robustness of the model, Schweppe generalized M-estimation is adopted to determine the modeling weights by the model residual size and the distance information of input vectors in the high-dimensional space to resolve the prevalent existence of outliers in the input and output samples. Finally, data experiments on two industrial systems have validated the effectiveness, advancement, and practicality of the proposed method. Note to Practitioners—In the process industry, the product quality relies on the timely and accurate measurement of key production indicators. However, owing to the time-varying characteristics of industrial processes and the limitations of measurement devices, conventional batch learning-based data-driven models are difficult to apply to imperfect industrial data stream scenarios. To this end, the OSSR-NNRW is proposed for online robust modeling of complex time-variant dynamic systems by combining sparse robust modeling and online learning strategy in a unified framework of neural networks with random weights. The OSSR-NNRW enables online learning based on industrial data streams while resolving correlations between data variables and mitigating the negative effects of outliers from both input and output samples on the modeling process. Experimental results using two typical process industry datasets show that the proposed OSSR-NNRW has high estimation accuracy and can be easy to implement in industrial processes.

With the rapid development of advanced sensing, communication, and the industrial Internet of Things, it has become much easier to obtain, transmit, and, store a massive amount of real-world data. However, imperfect data is inevitable in real-world systems, such as the existence of outliers, contaminated, incomplete, inaccurate, and even missing information in the data. This phenomenon is called data imperfection, which usually makes traditional datadriven modeling and automation methods either unfeasible or ending at undesired inaccuracies. This has been a wellknown challenge to data-driven methods when applied to real-world systems, such as process industry, manufacturing, energy networks, and transportation systems.

Aiming at the operation optimization of the wastewater treatment process (WWTP) with nonstationary time-varying dynamics and complex multiconstraint, this article proposes a novel adaptive constraint penalty decomposed multiobjective evolutionary algorithm with synthetical distance (SD)-based cross-generation crossover. First, the concept of spatial SD is presented to comprehensively evaluate the similarity of individual solutions from two aspects of distance and angle, and the individual information between two adjacent generations is used to enhance the diversity of individuals and accelerate the convergence of the algorithm. Second, aiming at the complex multiconstraint during the operation optimization of WWTP, an adaptive penalty algorithm is further adopted to punish the individual solutions that violate the constraints, so as to improve the handling efficiency and success rate of constraints. Furthermore, in view of the time-varying dynamics of actual WWTP, a recursive bilinear subspace identification method based on sliding window is adopted to establish the optimization models as well as the constraint models with self-learning parameter, which provides accurate model guarantee for high-performance multiobjective operation optimization. Finally, the effectiveness, superiority, and practicability of the proposed method are verified through test function experiments as well as operation optimization control experiments of WWTP.

In this article, we aim to offer an interpretable learning paradigm for incremental random weight neural networks (IRWNNs). IRWNNs have become a hot research direction of neural network algorithms due to their ease of deployment and fast learning speed. However, existing IRWNNs have difficulty explaining how hidden nodes (parameters) affect the convergence of network residuals. To address this gap, this article proposes an interpretable construction algorithm (ICA). Specifically, we first conduct a spatial geometric analysis of the network construction process and establish the spatial geometric relationship between the network residuals and hidden parameters to visualize the influence of hidden parameters on the convergence of the network residuals. Second, based on the spatial geometric relationship and node pool strategy, an interpretable control strategy with spatial geometry information is established to obtain hidden parameters conducive to the convergence of network residuals. In addition, to facilitate ICA to handle complex tasks of big data, this article proposes a lightweight ICA with low complexity, namely ICA+. Finally, it is proved theoretically that the ICA and ICA+ proposed in this article have universal approximation properties. The experimental results on two real-world datasets and seven benchmark datasets demonstrate the advantages of the proposed ICA and ICA+ in terms of fast learning, good generalization, and compactness of network structure.

This article proposes a multiobjective operation optimization method based on reinforcement self-learning and knowledge guidance for quality assurance and consumption reduction of wastewater treatment process (WWTP) with nonstationary time-varying dynamics. First, operation optimization models are developed by online sequential random vector functional-link (OS-RVFL) neural network, which can realize online sequential learning of model parameters. Then, a knowledge base is established to store typical optimization cases for knowledge guiding the subsequent optimizations. Based on it, a reinforcement self-learning-based multiobjective particle swarm optimization (RSL-MOPSO) algorithm is proposed to perform optimization calculation. In this algorithm, reinforcement self-learning is used for interaction learning between environment and action in optimization, and the particle motion trend of algorithm is adjusted according to the feedback information of the optimization process. The effects of wastewater state parameters on particles are recorded and reused to improve the solution quality and calculation efficiency of optimization. Moreover, to make good use of the information of the previous optimizations and balance the coordination between global search in the early stage and local search in the later stage, a selective information feedback mechanism is further proposed to ensure the diversity and convergence of the algorithm. Finally, prediction-based intelligent decision making is performed to select the final optimization solution as the final setpoints for the lower-level controllers from the Pareto frontier with considering specific technical requirements. Data experiments show that the proposed method can effectively reduce energy consumption and ensure effluent quality.

The inverse calculation of burden distribution matrix (BDM) is one of the most important challenges in the blast furnace iron-making processes. Focusing on this practical challenge, this paper proposes a new burden distribution spatial model in burden charging process, and develops a B-spline approximation-based probability density function (PDF) control algorithm to assign the expected thickness distribution of burden layer and perform the required inverse calculation of BDM. First, a novel method for the thickness distribution of burden layer is given using B-spline model. Then, according to the coexistence of continuous and bounded discrete variables in BDM, a novel hybrid optimization control method by combining integer programming and PDF tracking is further established. Finally, the proposed PDF-based iterative inverse calculation of BDM using B-spline models are tested using industrial data. The simulation results show that the proposed method is well-suited to solve the BDM inverse calculation problem in practice.

Aiming at the nonstationary characteristics of many practical industrial systems as well as the long memory and seasonality of some process data, this article proposes a novel nonstationary process anomaly detection method based on fractional cointegration vector autoregression (FCVAR). First, the augmented Dickey–Fuller (ADF) test is used to divide the variables into stationary and nonstationary categories. For the nonstationary variables, the trend extraction algorithm is used to extract the nonstationary trend of the variables to avoid the trend information from being overwhelmed due to the strong seasonality of the process data. Meanwhile, considering that the extracted trend time series have a long-memory characteristic and the fractional cointegration describes the intrinsic long-term equilibrium relationship of the trend series better than the integer cointegration, a novel anomaly detection algorithm based on the FCVAR model is proposed. For the stationary variables, including the original stationary variables and the detrended series of nonstationary variables after trend extraction, the proposed method merges the two components into a new matrix and establishes an anomaly detection model based on the kernel principal component analysis (kpca) algorithm. Finally, simulations using wastewater treatment process (WWTP) data have indicated that the proposed method achieves the desired results and exhibits high detection performance, particularly in the detection of tiny gradual-type anomalies.

The automatic control of blast furnace (BF) ironmaking process has always been an important yet arduous task in metallurgic engineering and automation. In this article, a novel Kalman filter-based robust model-free adaptive predictive control (MFAPC) method is proposed for the direct data-driven control of molten iron quality in BF ironmaking. First, a compact-form dynamic linearization-based extended MFAPC method for multivariable molten iron quality control is proposed by generalizing the existing single-variable MFAPC method to multivariable systems. Based on it, a Kalman filter-based robust MFAPC is further proposed considering the problems of data loss and measurement noise in quality detection. Specifically, the robust mechanism in the robust MFAPC combines a novel dynamic linearization method with a concept termed Pseudo-Jacobian matrix to predict the missing data during data loss. After that, a Kalman filter is constructed based on a prediction model to filter the measurement noise. The stability of the proposed control method is analyzed, and various data experiments using actual industrial data are performed to verify the effectiveness of the proposed methods.Note to Practitioners—The extremely complicated dynamics of blast furnace ironmaking process make the model-based controllers difficult to realize in practice. In this article, a novel robust model-free adaptive predictive control method is proposed for direct data-driven control of multivariate molten iron quality in the ironmaking process. This method directly uses the process input and output data to design the multivariable quality controller online by the compact-form dynamic linearization technology and the internal multilayer prediction mechanism, thus avoids the drawback of model-based controllers in troublesome process modeling. Moreover, the proposed method can effectively avoid the influence of data loss and measurement noise on the controller performance with the designed Kalman filter-based robust mechanism. The superiority and practicability of the proposed method are verified using various experiments against actual industrial data.

Optimal operation of an actual mine main fan switchover process relies heavily on a good measurement of underground airflow quantity (UAQ). However, real-time measuring the UAQ is difficult using conventional measurement techniques. In this article, a novel randomized learning model, named compact incremental random weight network (CIRWN), is proposed to estimate the UAQ. Since the hidden parameters of the original IRWN are generated in a fixed scope with a random manner, which is prone to create redundant hidden nodes, a CIRWN with new inequality constraints is proposed. The inequality constraints have several attractive properties, including dynamically guiding the generation of hidden parameters, effectively enhancing the convergence rate, and successfully establishing a universal approximator. Experiments using four benchmark datasets and an industrial dataset show that the established model possesses a more compact network structure and better modeling accuracy as well as faster convergence rate compared with other methods.

This article proposes an improved incremental random vector functional-link network (RVFL) with a compact structure and presents its application to quality prediction of blast furnace (BF) ironmaking processes. Different from the original RVFL, the improved incremental RVFL has no input-output direct links and no output bias (NLNB) and approaches the desired network output by sequentially updating the output weights of fixed hidden neurons. Moreover, it is proved that this improved incremental RVFL with NLNB (I-I-RVFL-NLNB) is able to approximate a given continuous function with arbitrary small errors with fewer hidden neurons. As a result, the developed network has more compact requiring less execution time, while retaining the conventional incremental RVFL's advantage of monotonically decreasing errors and avoiding the overfitting issue of the basic RVFL-NLNB. Since the zero approximation error is not needed in practical applications, the terminal condition of the existing incremental RVFL is improved by using the difference of root mean squared error (RMSE) between two consecutive iterations as one of the indices to characterize the imperceptible descending trend of RMSE. A series of comparisons are made by both benchmark simulations and a real quality modeling problem for a large BF ironmaking plant in South China, which show that the proposed algorithm has better performance in terms of modeling accuracy and efficiency.

The fiber length and the Canadian standard freeness (CSF) are two key indices in measuring pulp quality of the refining process with non-Gaussian stochastic distribution dynamics. Among them, it is defective to use the conventional 1-D average fiber length (AFL) as a pulp quality index because the AFL is insufficient to describe the 2-D probability density function (pdf) shaping of fiber length distribution (FLD) with non-Gaussian types. In this article, a data-driven multiobjective predictive optimal control method is proposed to control the 2-D pdf shaping of FLD and the 1-D CSF, simultaneously. First, a radial basis function neural network (RBF-NN) based stochastic distribution model is developed to approximate the 2-D pdf shaping of FLD, and the parameters of RBF basis functions are updated by an iterative learning rule. Then, taking the developed pulp quality models, including the 2-D pdf model of FLD and the model of 1-D CSF as two predictors, a multiobjective predictive controller is designed by solving the nonlinear programming problems with constraints. Then, the stability of the resulted closed-loop system is also analyzed. Ultimately, the industrial experiments demonstrate the effectiveness of the proposed method.

In railway operation, train delays may occur due to various reasons (e.g. severe weather, infrastructure failure, human factors, etc.) and may change and spread rapidly to subsequent trains. Prediction of train delay changes and propagation is important to provide decision-making support for railway dispatchers to reschedule. In this paper, a multi-stage intelligent method is proposed for predicting the dynamic changes and propagation of train delays using random vector functional-link networks (RVFLNs) with improved transfer learning and ensemble learning. First, to improve the prediction performance of the single RVFLNs model, a novel improved Stacking ensemble learning RVFLNs (SRN) regression algorithm is proposed for prediction modeling of the delay changes. Then, to ensure the classification accuracy of unlabeled and class-imbalanced train data, an improved transfer learning RVFLNs (ITRN) classifier is proposed to decide whether the initial delay will lead to associated delays, with the aid of the improved SMOTE algorithm for processing imbalanced data. If associated delays are identified by the ITRN classifier, the proposed SRN algorithm will be further to predict the subsequent associated delays. By iterating the classification and prediction procedures, the propagation range and chain of train delays can be obtained. The effectiveness and practicability of the proposed method are verified by using two experiments against actual train graph data from different railway lines.

Pulp is the most important raw material in paper industries, whose fiber length stochastic distribution (FLSD) shaping directly determines the energy consumption and paper quality of the subsequent papermaking processes. However, the mean and variance are insufficient to describe the FLSD shaping, which displays non-Gaussian distributional properties. Therefore, the traditional control method based on the mean and variance of the fiber length is difficult to control the FLSD shaping effectively. In this article, a novel data-driven predictive probability density function (PDF) control method is proposed for the FLSD shaping in the refining process. First, the PDF of FLSD shaping is approximated by a radial basis function neural network (RBF-NN) and the parameters of each RBF basis function are tuned by using an iterative learning law. Second, the random vector functional link network (RVFLN)-based data-driven modeling method is employed to construct the prediction model of the weight vector. Consequently, the predictive controller is designed based on the constructed PDF model of the FLSD shaping in the refining process and the stability issue of the resulted closed-loop system is discussed. The experiments using industrial data are given to illustrate the effectiveness of the proposed method. Note to Practitioners-Pulp quality control in the refining process plays a critical role in the optimization of product quality and energy saving in the pulping and papermaking processes. Different from the conventional control method based on the mean and variance of the fiber length, a novel data-driven predictive PDF control method is proposed for the non-Gaussian stochastic distribution dynamic characteristics of the fiber length, which is used to achieve the desired PDF shaping of fiber length distribution. This kind of novel control method includes the control of the traditional mean and variance of the fiber length in some sense and has applications that are more extensive.

By dealing with robust modeling and online learning together in a unified random vector functional-link networks (RVFLNs) framework, this paper presents a novel robust online sequential RVFLNs for data modeling of dynamic time-varying systems together with its application for a blast furnace (BF) ironmaking process. First, to overcome the difficulties caused by the nonlinear time-varying dynamics of process and to enable the RVFLNs to learn online and to avoid data saturation, an improved online sequential version of RVFLNs (OS-RVFLNs) is presented by sequential learning with forgetting factor. It has been shown that the improved OS-RVFLNs with forgetting factor is not only suitable for the large-scale and real-time data transfer situation but also can adjust the sensitivity of the algorithm to different samples. Second, in order to solve the issue of modeling robustness when the dataset is contaminated with various outliers, a Cauchy distribution function weighted M-estimator is introduced to strengthen the robustness of the improved OS-RVFLNs. The non-Gaussian Cauchy distribution function is used to estimate the weights of different data and thus the corresponding contribution on modeling can be properly distinguished. Experiments using actual industrial data of a large BF ironmaking process have demonstrated that the proposed algorithm produces a much stronger robustness and better estimation accuracy than other algorithms.

As one of the most important unit in the papermaking industry, the high consistency (HC) refining system is confronted with challenges such as improving pulp quality, energy saving, and emissions reduction in its operation processes. In this correspondence, an optimal operation of HC refining system is presented using nonlinear multiobjective model predictive control strategies that aim at set-point tracking objective of pulp quality, economic objective, and specific energy (SE) consumption objective, respectively. First, a set of input and output data at different times are employed to construct the subprocess model of the state process model for the HC refining system, and then the Wiener-type model can be obtained through combining the mechanism model of Canadian Standard Freeness and the state process model that determines their structures based on Akaike information criterion. Second, the multiobjective optimization strategy that optimizes both the set-point tracking objective of pulp quality and SE consumption is proposed simultaneously, which uses NSGA-II approach to obtain the Pareto optimal set. Furthermore, targeting at the set-point tracking objective of pulp quality, economic objective, and SE consumption objective, the sequential quadratic programming method is utilized to produce the optimal predictive controllers. Finally, the simulation results demonstrate that the proposed methods can make the HC refining system provide a better performance of setpoint tracking of pulp quality when these predictive controllers are employed. In addition, while the optimal predictive controllers orienting with comprehensive economic objective and SE consumption objective, it has been shown that they have significantly reduced the energy consumption.

Optimal operation of an industrial blast furnace (BF) ironmaking process largely depends on a reliable measurement of molten iron quality (MIQ) indices, which are not feasible using the conventional sensors. This paper proposes a novel data-driven robust modeling method for the online estimation and control of MIQ indices. First, a nonlinear autoregressive exogenous (NARX) model is constructed for the MIQ indices to completely capture the nonlinear dynamics of the BF process. Then, considering that the standard least-squares support vector regression (LS-SVR) cannot directly cope with the multioutput problem, a multitask transfer learning is proposed to design a novel multioutput LS-SVR (M-LS-SVR) for the learning of the NARX model. Furthermore, a novel M-estimator is proposed to reduce the interference of outliers and improve the robustness of the M-LS-SVR model. Since the weights of different outlier data are properly given by the weight function, their corresponding contributions on modeling can properly be distinguished, thus a robust modeling result can be achieved. Finally, a novel multiobjective evaluation index on the modeling performance is developed by comprehensively considering the root-mean-square error of modeling and the correlation coefficient on trend fitting, based on which the nondominated sorting genetic algorithm II is used to globally optimize the model parameters. Both experiments using industrial data and industrial applications illustrate that the proposed method can eliminate the adverse effect caused by the fluctuation of data in BF process efficiently. This indicates its stronger robustness and higher accuracy. Moreover, control testing shows that the developed model can be well applied to realize data-driven control of the BF process.

This paper introduces the development and implementation of a ball mill grinding circuit simulator, NEUSimMill. Compared to the existing simulators in this field which focus on process flowsheeting, NEUSimMill is designed to be used for the test and verification of grinding process control system including advanced control system such as integrated control. The simulator implements the dynamic ball mill grinding model which formulates the dynamic responses of the process variables and the product particle size distribution to disturbances and control behaviors as well. First principles models have been used in conjunction with heuristic inference tools such as fuzzy logic and artificial neural networks: giving rise to a hybrid intelligent model which is valid across a large operating range. The model building in the simulator adopts a novel modular-based approach which is made possible by the dynamic sequential solving approach. The simulator can be initiated with connection to a real controller to track the plant state and display in real-time the effect of various changes on the simulated plant. The simulation model and its implementation is verified and validated through a case of application to the design, development, and deployment of optimal setting control system.

Efficient operation of the integrated optimization or automation system in an industrial plant depends mainly on good measurement of product quality. However, measuring or estimating the product quality online in many industrial plants is usually not feasible using the available techniques. In this paper, a data-driven soft-sensor using case-based reasoning (CBR) and fuzzy-similarity rough sets is proposed for product quality estimation. Owning to the sustained learning ability, the modeling of a CBR soft-sensor does not need any additional model correction which is otherwise required by the neural network based methods to overcome the slow time-varying nature of industrial processes. Because the conventional k-nearest neighbor ( k-NN) algorithm is strongly influenced by the value of k, an improved k-NN algorithm with dynamic adjustment of case similarity threshold is proposed to retrieve sufficient matching cases for making a correct estimation. Moreover, considering that the estimation accuracy of the CBR soft-sensor system is closely related to the weights of case feature, a feature weighting algorithm using fuzzy-similarity rough sets is proposed in this paper. This feature weighting method does not require any transcendental knowledge, and its computation complexity is only linear with respect to the number of cases and attributes. The developed soft-sensor system has been successfully applied in a large grinding plant in China. And the application results show that the system has achieved satisfactory estimation accuracy and adaptation ability.

During the operation of a grinding circuit (GC) in mineral processing plant the main purpose of control and optimal operation is to control the product quality index, namely the product particle size, into its technically desired ranges. Moreover, the grinding production rate needs to be maximized. However, due to the complex dynamic characteristics between the above two indices and the control loops, such control objectives are difficult to achieve using existing control methods. The complexity is reflected by the existence of process heavy nonlinearities, strong coupling and large time variations. As a result, the lower level loop control with human supervision is still widely used in practice. However, since the setpoints to the involved control loops cannot be accurately adjusted under the variations of the boundary conditions, the manual setpoints control cannot ensure that the actual production indices meet with technical requirements all the time. In this paper, an intelligent optimal-setting control (IOSC) approach is developed for a typical two-stage GC so as to optimize the production indices by auto-adjusting on line the setpoints of the control loops in response to the changes in boundary conditions. This IOSC approach integrates case-based reasoning (CBR) pre-setting controlling, neural network (NN)-based soft-sensor and fuzzy adjusting into one efficient control model. Although each control element is well known, their innovative combination can generate better and more reliable performance. Both industrial experiments and applications show the validity and effectiveness of the proposed IOSC approach and its bright application foreground in industrial processes with similar features.