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Feedforward neural network (FNN) is the most popular network model, and the appropriate structure and learning algorithms are the key of its performance. This paper proposes an online self-organizing algorithm for feedforward neural network (OSNN) with a single hidden layer. The proposed OSNN optimizes the structure of FNN for time-varying system including structure design and parameter learning. In structure design, this paper measures the contribution ratios of hidden nodes by local sensitivity analysis based on differentiation method. OSNN merges hidden nodes with the others that have the highest correlation when their contribution ratios are almost zero and adds new hidden nodes by error reparation. For parameter learning, an improved online gradient method (OGM), called online gradient method with fixed memory (FMOGM), is proposed to improve the convergence speed and accuracy of OGM. In addition, this paper calculates the contribution ratios and the network error and estimates the local minima by using the fixed-sized training set of FMOGM instead of one sample at the current time, which can obtain more effective local information and a compact network structure. Finally, the proposed OSNN is verified using a number of benchmark problems and a practical problem for biochemical oxygen demand prediction in wastewater treatment. The experimental results show that OSNN has better convergence speed and accuracy than other algorithms. [ABSTRACT FROM AUTHOR]

In this study, a modular design methodology inherited from cognitive neuroscience and neurophysiology is proposed to develop artificial neural networks, aiming to realize the powerful capability of brain—divide and conquer—when tackling complex problems. First, a density-based brain-like partition method is developed to construct the modular architecture, with a highly connected center in each sub-network as the human brain. The whole task is also divided into different sub-tasks at this stage. Then, a compact radial basis function (RBF) network with fast learning speed and desirable generalization performance is applied as the sub-network to solve the corresponding task. On the one hand, the modular structure helps to improve the ability of neural networks on complex problems by implementing divide and conquer. On the other hand, sub-networks with considerable ability could guarantee the parsimonious and generalization of the entire neural network. Finally, the novel modular RBF (NM-RBF) network is evaluated through multiple benchmark numerical experiments, and results demonstrate that the NM-RBF network is capable of constructing a relative compact architecture during a short learning process with achievable satisfactory generalization performance, showing its effectiveness and outperformance. [ABSTRACT FROM AUTHOR]

In this paper, for the operations of wastewater treatment processes (WWTPs), an intelligent multi-objective optimization control (IMOOC), based on an adaptive multi-objective differential evolution (AMODE) algorithm, is proposed to search for the suitable set-points to balance the treatment performance and the operational costs. In this IMOOC, the combination of an AMODE algorithm and the multi-objective critical issues helps us to fulfill all the control objectives simultaneously. To improve the optimization efficiency and achieve fast convergence, the AMODE algorithm is designed to improve the local search and the global exploration abilities: The adaptive adjustment strategies are developed to select the suitable scaling factor and crossover rate in the process of searching. Meanwhile, the multi-objective critical issues, according to the state of the processes, are given as a nonlinear multi-objective optimization problem to evaluate the operational performance of WWTPs. Therefore, once the nonlinear multi-objective optimization problem is solved at each sampling time, the most appropriate set of Pareto is selected as suitable set-points to achieve the process performance. To demonstrate the merits of our proposed method, the proposed IMOOC is applied to the Benchmark Simulation Model No. 1 of WWTPs. The results show that the proposed IMOOC effectively provides process control. The performance comparison with other algorithms also indicates that the proposed optimal strategy yields better effluent qualities and lower average operation consumption. [ABSTRACT FROM AUTHOR]

This study investigates an adaptive fuzzy neural network control system for the multiobjective operation of wastewater treatment process (WWTP) with standard effluent quality (EQ) as well as low energy consumption (EC). The control system consists of an optimization module with the adaptive multiobjective differential evolution (AMODE) algorithm and a control module with the adaptive fuzzy neural network (AFNN). First, an AMODE algorithm, using the adaptive adjustment strategies for selecting the suitable scaling factor and crossover rate, is developed to optimize all objectives simultaneously. Then, the optimal set-points of the dissolved oxygen concentration in the fifth tank ( S O5 ) and the nitrogen nitrate concentration in the second anoxic tank ( S NO2 ) of WWTP can be obtained by the AMODE algorithm. Second, an AFNN controller, based on an adaptive second order algorithm, is employed to trace the set-points of S O5 and S NO2 for achieving the process performance. Finally, the proposed control system is applied on the Benchmark Simulation Model 1 (BSM1). The performance comparison with other algorithms indicates that the proposed control system yields better effluent qualities and lower average operation consumption. [ABSTRACT FROM AUTHOR]

Modular neural networks have shown distinct advantages in many regimes due to the "modular design". However, how to design an effective decomposition algorithm for improving the prediction accuracy is still a challenge for time series prediction. In this article, a novel modular neural network model based on empirical mode decomposition (EMD) technique and multi-view learning (MNN-EMDMVL) is introduced for time series prediction, which can simultaneously and effectively decompose time series and improve the prediction accuracy of time series. Most of modular neural networks divide time series based on sample space using clustering algorithm without considering its time characteristic, which has an undesirable effect on prediction accuracy. Therefore, the structure of the proposed model consists of two parts: (1) time series decomposition, which can decompose time series into several subseries. (2) network learning, which can further improve the prediction performance of model. Firstly, this paper employs EMD technique to decompose time series into several subseries based on the local characteristic time scale, which can help subnetworks to learn the decomposed subseries more easily. But some subseries with high frequency feature fluctuates greatly, and changes fleetly, which may restrict the performance of subnetworks. Therefore, a novel multi-view learning with winner-take-all strategy (MVWTAS) is proposed to further improve the prediction performance of subnetworks. In MVWTAS, one or more views (features) of subseries with high frequency are selected as the auxiliary tasks and simultaneously learned. Then, the "best model" can be obtained from the auxiliary and main tasks in each time period of the subseries using winner-take-all strategy, thereby improving the prediction accuracy of the subseries with high frequency. Finally, experimental investigations using two benchmark time series and two real-world time series show that compared with other modular neural networks and single modes, MNN-EMDMVL has the distinct advantage in the terms of prediction performance both by time series decomposition using EMD and the developed multi-view learning with winner-take-all strategy. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a constructing-and-pruning (CP) approach to optimise the structure of a feedforward neural network (FNN) with a single hidden layer. The number of hidden nodes or neurons is determined by their contribution ratios, which are calculated using a Fourier decomposition of the variance of the FNN''s output. Hidden nodes with sufficiently small contribution ratios will be eliminated, while new nodes will be added when the FNN cannot satisfy certain design objectives. This procedure is similar to the growing and pruning processes observed in biological neural networks. The performance of the proposed method is evaluated using a number of examples: real-life date classification, dynamic system identification, and the key variables modelling in a wastewater treatment system. Experimental results show that the proposed method effectively optimises the network structure and performs better than some existing algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, a novel self-organizing radial basis function (SORBF) neural network is proposed for nonlinear identification and modeling. The proposed SORBF consists of simultaneous network construction and parameter optimization. It offers two important advantages. First, the hidden neurons in the SORBF neural network can be added or removed, based on the neuron activity and mutual information (MI), to achieve the appropriate network complexity and maintain overall computational efficiency for identification and modeling. Second, the model performance can be significantly improved through the parameter optimization. The proposed parameter-adjustment-based optimization algorithm, utilizing the forward-only computation (FOC) algorithm instead of the traditionally forward-and-backward computation, simplifies neural network training, and thereby significantly reduces computational complexity. Additionally, the convergence of the SORBF is analyzed in both the structure organizing process phase and the phase following the modification. Lastly, the proposed approach is applied to model and identify the nonlinear dynamical systems. Simulation results demonstrate its effectiveness. [Copyright &y& Elsevier]

Abstract: Despite extensive research that has been done on sludge bulking, it remains a widespread problem in the operation of activated sludge processes, which brings severe economic and environmental consequences. In this study, a self-organizing radial basis function (SORBF) neural network method is utilized to predict the evolution of the sludge volume index (SVI). The hidden nodes in the SORBF neural network can be grown or pruned based on the node activity (NA) and mutual information (MI) to achieve the appropriate network complexity and maintain overall computational efficiency. The growing and pruning criteria of the SORBF can vary its structure dynamically with the objective to enhance its performance. Moreover, the input–output selection to calculate the SVI values is also discussed. The variables with key relations to the sludge bulking are used as the inputs for the SVI. Finally, the SORBF neural network is applied to the activated sludge wastewater treatment processes (WWTPs) for predicting the SVI, and then for predicting the sludge bulking. Experimental results show the excellent performance of the SORBF method. The performance comparison demonstrates the effectiveness of the proposed SORBF. [Copyright &y& Elsevier]

Abstract: The dissolved oxygen (DO) concentration in activated sludge wastewater treatment processes (WWTPs) is difficult to control because of the complex nonlinear behavior involved. In this paper, a self-organizing radial basis function (RBF) neural network model predictive control (SORBF-MPC) method is proposed for controlling the DO concentration in a WWTP. The proposed SORBF can vary its structure dynamically to maintain prediction accuracy. The hidden nodes in the RBF neural network can be added or removed on-line based on node activity and mutual information (MI) to achieve the appropriate network complexity and the necessary dynamism. Moreover, the convergence of the SORBF is analyzed in both the dynamic process phase and the phase following the modification of the structure. Finally, the SORBF-MPC is applied to the Benchmark Simulation Model 1 (BSM1) WWTP to maintain the DO concentration. The results show that SORBF-MPC effectively provides process control. The performance comparison also indicates that the proposed model''s predictive control strategy yields the most accurate for DO concentration, better effluent qualities, and lower average aeration energy (AE) consumption. [Copyright &y& Elsevier]

This paper presents a repair algorithm for the design of a Radial Basis Function (RBF) neural network. The proposed repair RBF (RRBF) algorithm starts from a single prototype randomly initialized in the feature space. The algorithm has two main phases: an architecture learning phase and a parameter adjustment phase. The architecture learning phase uses a repair strategy based on a sensitivity analysis (SA) of the network's output to judge when and where hidden nodes should be added to the network. New nodes are added to repair the architecture when the prototype does not meet the requirements. The parameter adjustment phase uses an adjustment strategy where the capabilities of the network are improved by modifying all the weights. The algorithm is applied to two application areas: approximating a non-linear function, and modeling the key parameter, chemical oxygen demand (COD) used in the waste water treatment process. The results of simulation show that the algorithm provides an efficient solution to both problems. [ABSTRACT FROM AUTHOR]

Abstract: A fast unit pruning algorithm for feedforward neural network is presented and the way used by the algorithm which based on optimal brain surgeon (OBS) is to remove the unneeded hidden units directly so that carry out the self-organization design on the architecture of neural networks. The algorithm is tested on several modeling problems, and is compared with OBS. It is found that the fast unit pruning algorithm is much more efficient than OBS which can not only reduce the complexity of the network but also accelerate the learning speed. [Copyright &y& Elsevier]

Gradient-based algorithms are commonly used for training radial basis function neural network (RBFNN). However, one of the challenges in the training process is determining how to avoid vanishing gradient. To solve this problem, an accelerated gradient algorithm (AGA) is designed to improve the learning performance of RBFNN in this paper. First, an indirect detection mechanism, based on the instantaneous gradient decay rate (IGDR) and instantaneous convergence rate (ICR), is developed to identify the vanishing gradient in learning process. Second, an amplification gradient strategy (AGS), which can increase the gradient value of learning parameters, is designed to accelerate the learning speed of RBFNN. Third, the analysis of AGA-based RBFNN (AGA-RBFNN) is given to guarantee the successful application. Finally, some benchmark and real problems are used to illustrate the effectiveness of AGA-RBFNN. The results demonstrate the effectiveness of AGA-RBFNN. [ABSTRACT FROM AUTHOR]

Sludge bulking is very common in wastewater treatment process (WWTP), which will degrade the operation performance or even destroy the process. In order to diagnose sludge bulking accurately, a data-knowledge-driven diagnosis (DKD) method is proposed to identify the occurrence and cause variable in this paper. This proposed DKD method contains the following advantages. First, a data-driven detection model, using a recursive kernel principal component analysis (RKPCA) algorithm, is designed to capture the intrinsic nonlinear and time-varying characteristic of sludge bulking. Then, the occurrence of sludge bulking can be detected with high accuracy. Second, a DKD model, based on the Bayesian network (BN), is developed to extract the causality among process variables to identify the root cause variables of sludge bulking. Then, the root cause variables of sludge bulking can be diagnosed to improve the operation performance of WWTP. Finally, the proposed DKD method was tested on the measured data from a real WWTP. Experimental results confirmed the effectiveness of the proposed DKD method. • Detect the occurrence of sludge bulking from the water qualities by using RKPCA detection model. • Diagnose the root cause variable of sludge bulking via the BN. • This DKD method has been successfully used in a real wastewater treatment plant. [ABSTRACT FROM AUTHOR]

Under boundary measurement (BM), this paper solves the synchronization problem via intermittent boundary proportional–derivative (PD) control of delayed reaction–diffusion neural networks (RDNNs), where the random time-varying delay (RTVD) belongs to two intervals and is considered by a probabilistic way to take the influence of uncertain factors. The intermittent boundary PD synchronization scheme, which considers the inevitable actuator limitations, is based on BM and only available at some specified boundary position. By using the inequality techniques and switching Lyapunov functional, the mean square exponential stability (MSES) of the synchronization error system (SES) containing the response and drive dynamics is ensured by some synchronization criteria, which are established via an intermittent boundary PD controller under BM and expressed as linear matrix inequalities. Lastly, the proposed intermittent boundary PD synchronization approach is verified by a numerical example. [ABSTRACT FROM AUTHOR]

This paper investigates the observer‐based sampled‐data control problem for networked systems with consecutive packet dropouts. A new consecutive packet dropout model is established to describe the phenomenon of packet dropout in both the sensor‐controller (S‐C) and controller‐actuator (C‐A) channels. First, the considered system with observer‐based control scheme is studied in the discrete‐time domain by using equivalent discretization transformation. In order to simplify subsequent analysis, matrix exponential computation is employed to transform the discrete‐time system into a more tractable form. Then, the proposed new consecutive packet dropout model is taken into consideration to establish the stochastic mean square exponential stability condition. Furthermore, a novel two‐step synthesis approach is used to design the observer‐based controller. Finally, the effectiveness of the proposed observer‐based sampled‐data control approach is verified using a numerical example. In addition, the advantages of the proposed approach are validated through comparisons. [ABSTRACT FROM AUTHOR]

In this paper, a self-organizing fuzzy neural network with adaptive gradient algorithm (SOFNN-AGA) is proposed for nonlinear systems modeling. First, a potentiality of fuzzy rules (PFR) method is introduced by using the output of normalized layer and the error reduction ratio (ERR) in the training process. And a structure learning approach is developed to determine the network size based on PFR. Second, a novel adaptive gradient algorithm (AGA) with adaptive learning rate is designed to adjust the parameters of SOFNN-AGA. Moreover, a theoretical analysis on the convergence of SOFNN-AGA is given to show the efficiency in both fixed structure and self-organizing structure cases. Finally, to demonstrate the merits of SOFNN-AGA, simulation and experimental results of several benchmark problems and a real world application are examined for nonlinear systems modeling with comparisons against other existing methods. Some promising results are reported in this study, indicating that the proposed SOFNN-AGA performs better favorably in terms of both convergence speed and modeling accuracy. [ABSTRACT FROM AUTHOR]

The training of recurrent neural networks (RNNs) concerns the selection of their structures and the connection weights. To efficiently enhance generalization capabilities of RNNs, a recurrent self-organizing neural networks (RSONN), using an adaptive growing and pruning algorithm (AGPA), is proposed for improving their performance in this paper. This AGPA can self-organize the structures of RNNs based on the information processing ability and competitiveness of hidden neurons in the learning process. Then, the hidden neurons of RSONN can be added or pruned to improve the generalization performance. Furthermore, an adaptive second-order algorithm with adaptive learning rate is employed to adjust the parameters of RSONN. And the convergence of RSONN is given to show the computational efficiency. To demonstrate the merits of RSONN for data modeling, several benchmark datasets and a real world application associated with nonlinear systems modeling problems are examined with comparisons against other existing methods. Experimental results show that the proposed RSONN effectively simplifies the network structure and performs better than some exiting methods. [ABSTRACT FROM AUTHOR]

This paper investigates how to construct a recurrent radial basis function neural network (RRBFNN) by an information-oriented algorithm (IOA) and how to adjust the parameters by a gradient algorithm simultaneously. In this IOA-based RRBFNN (IOA-RRBFNN), the proposed IOA is used to calculate the information processing strength (IPS) of hidden neurons, such that the independent component contributions between the hidden neurons and output neurons can be extracted. Then, a novel self-organizing strategy is proposed to optimize the structure of RRBFNN based on the input IPS and output IPS of hidden neurons. Meanwhile, a gradient algorithm is developed to update the parameters of IOA-RRBFNN. The proposed IOA-RRBFNN can be used to organize the network structure and adjust the parameters to improve its performance. Finally, several examples are presented to illustrate the effectiveness of IOA-RRBFNN. The results demonstrate that the proposed IOA-RRBFNN is more competitive in solving the nonlinear system modeling problems compared with some existing methods. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive second order algorithm (ASOA) has been developed to train the fuzzy neural network (FNN) to achieve fast and robust convergence for nonlinear system modeling. Different from recent studies, this ASOA-based FNN (ASOA-FNN) has the quasi Hessian matrix and gradient vector which are accumulated as the sum of related sub matrices and vectors, respectively. Meanwhile, the learning rate of ASOA-FNN is designed to accelerate the learning speed. In addition, the convergence of the proposed ASOA-FNN has been proved both in the fixed learning rate phase and the adaptive learning rate phase. Finally, several comparisons have been realized and they have shown that the proposed ASOA-FNN has faster convergence speed and more accurate results than that of some existing methods. [ABSTRACT FROM AUTHOR]

It is challenging to introduce an optimization strategy for enhancing the operational performance of wastewater treatment process (WWTP) on account of its multi-task characteristics. To cope with this problem, an adaptive multi-task optimization (AMTO) strategy is proposed to realize the optimal operation of WWTP. First, a multi-task optimization (MTO) framework is developed to depict the multi-task characteristics of WWTP. Then, it is conducive to achieve the optimization of nitrogen removal and phosphorus removal processes simultaneously. Second, a data-driven MTO model, based on the relevant process data, is established to describe the characteristics of nitrogen removal task and phosphorus removal task. Then, a MTO problem is modeled for WWTP. Third, a multi-task particle swarm optimization algorithm, based on the adaptive knowledge transfer method, is developed to cope with the above MTO problem. Then, the optimal set-points can be obtained in WWTP. Finally, the effectiveness of the proposed AMTO strategy is verified by comparing with other optimization strategies. The results demonstrate that the proposed AMTO strategy can achieve multiple tasks optimization in parallel and the optimal operation of WWTP. [ABSTRACT FROM AUTHOR]

Data-driven methods are widely used in wastewater treatment processes (WWTPs). However, disturbances are not fully considered during the control process, which may affect the stable operation of WWTPs. To address this issue, a data-driven robust model predictive control (DRMPC) method is proposed for WWTPs with disturbances. First, an interval type-2 fuzzy neural network (IT2FNN), which has high robust performance to disturbances, is used to identify dynamic behavior of WWTPs. Second, based on IT2FNN, a robust stabilizing controller is developed to weaken the influence of disturbances on control performance and stability. Third, the proposed controller ensures constraint satisfaction and input-to-state stability (ISS). Finally, the feasibility of DRMPC strategy is verified on the benchmark simulation model No. 1 (BSM1). The experimental studies indicate that the proposed DRMPC is capable of running stably and tracking accurately. [Display omitted] • Identify dynamic behavior of WWTPs by using IT2FNN. • Reduce the influence of disturbances on control performance and stability via the DRMPC algorithm. • The proposed controller ensures constraint satisfaction and input-state stable (ISS). • The feasibility of DRMPC strategy is verified on the benchmark simulation model No. 1 (BSM1). [ABSTRACT FROM AUTHOR]

Abstract: An approach, named extended extreme learning machine (ELM), is proposed for training the weights of a class of hierarchical feedforward neural network (HFNN). Unlike conventional single-hidden-layer feedforward networks (SLFNs), this hierarchical ELM (HELM) is based on the hierarchical structure which is capable of hierarchical learning of sequential information online, and one may simply choose hidden layers and then only need to adjust the output weights linking the hidden layer and the output layer. In such HELM implementations, the extended ELM provides better generalization performance during the learning process. Moreover, the proposed extended ELM method is efficient not only for HFNNs with sigmoid hidden nodes but also for HFNNs with radial basis function (RBF) hidden nodes. Finally, the HELM is applied to the activated sludge wastewater treatment processes (WWTPs) for predicting the water qualities. Experimental results and the performance comparison demonstrate the effectiveness of the proposed HELM. [Copyright &y& Elsevier]

Highlights: [•] NMMPC has two loops: the first loop deals with the control of DO and the second one is taking care of the nitrate. [•] The multivariate analysis of the process behavior can be obtained to avoid undesired interactions. [•] The errors between the set-point values and the control output remain within the range of ±0.05mg/L (±2.5%) – . [•] The errors of the set-point values and the control output can be kept within the range of ±5% – . [ABSTRACT FROM AUTHOR]

Gradient-based algorithms are commonly used for training radial basis function neural network (RBFNN). However, it is still difficult to avoid vanishing gradient to improve the learning performance in the training process. For this reason, in this paper, an accelerated second-order learning (ASOL) algorithm is developed to train RBFNN. First, an adaptive expansion and pruning mechanism (AEPM) of gradient space, based on the integrity and orthogonality of hidden neurons, is designed. Then, the effective gradient information is constantly added to gradient space and the redundant gradient information is eliminated from gradient space. Second, with AEPM, the neurons are generated or pruned accordingly. In this way, a self-organizing RBFNN (SORBFNN) which reduces the structure complexity and improves the generalization ability is obtained. Then, the structure and parameters in the learning process can be optimized by the proposed ASOL-based SORBFNN (ASOL-SORBFNN). Third, some theoretical analyses including the efficiency of the proposed AEPM on avoiding the vanishing gradient and the stability of SORBFNN in the process of structural adjustment are given, then the successful application of the proposed ASOL-SORBFNN is guaranteed. Finally, to illustrate the advantages of the proposed ASOL-SORBFNN, several experimental studies are examined. By comparing with other existing approaches, the results show that ASOL-SORBFNN performs well in terms of both learning speed and prediction accuracy. [ABSTRACT FROM AUTHOR]

Different time scales are inevitable for the controlled variables of wastewater treatment process (WWTP), which may degrade the operation performance or even destroy the stability of the closed-loop system. In this paper, a hierarchical nonlinear model predictive control (HNMPC) strategy is developed to deal with the different time scales of controlled variables to improve the operation performance of WWTP. The main merits of HNMPC are three-fold. First, a hierarchical control structure is developed to obtain reasonable control laws. Then, the controlled variables with different time scales can be tracked by different level controllers. Second, a gradient method is developed to solve the hierarchical optimization problem of HNMPC to reduce the computational cost. Then, the fast response of HNMPC can be achieved to improve the operation performance. Third, the stability of HNMPC is proved in theory. Then, the corresponding stability conditions are given to guide the practical application. Finally, the testing results on the benchmark simulation model verify that the proposed HNMPC can achieve suitable operation performance in terms of control accuracy. • In this work, a hierarchical nonlinear model predictive control (HNMPC) strategy is developed to deal with the different time scales of control variables to improve the operation performance of wastewater treatment process. • Firstly, a hierarchical control structure is developed to obtain reasonable control laws. Then, the control variables with different time scales can be tracked by different level controllers. • Secondly, a gradient method is developed to solve the hierarchical optimization problem of HNMPC to reduce the computational cost. Then, the fast response of HNMPC can be achieved to improve the operation performance. • Thirdly, the stability of HNMPC is proved in theory. Then, the corresponding stability conditions are given to guide the practical application. [ABSTRACT FROM AUTHOR]

Abstract: It has been shown extensively that the dynamic behaviors of a neural system are strongly influenced by the network architecture and learning process. To establish an artificial neural network (ANN) with self-organizing architecture and suitable learning algorithm for nonlinear system modeling, an automatic axon–neural network (AANN) is investigated in the following respects. First, the network architecture is constructed automatically to change both the number of hidden neurons and topologies of the neural network during the training process. The approach introduced in adaptive connecting-and-pruning algorithm (ACP) is a type of mixed mode operation, which is equivalent to pruning or adding the connecting of the neurons, as well as inserting some required neurons directly. Secondly, the weights are adjusted, using a feedforward computation (FC) to obtain the information for the gradient during learning computation. Unlike most of the previous studies, AANN is able to self-organize the architecture and weights, and to improve the network performances. Also, the proposed AANN has been tested on a number of benchmark problems, ranging from nonlinear function approximating to nonlinear systems modeling. The experimental results show that AANN can have better performances than that of some existing neural networks. [Copyright &y& Elsevier]

Abstract: This paper presents a flexible structure Radial Basis Function (RBF) neural network (FS-RBFNN) and its application to water quality prediction. The FS-RBFNN can vary its structure dynamically in order to maintain the prediction accuracy. The hidden neurons in the RBF neural network can be added or removed online based on the neuron activity and mutual information (MI), to achieve the appropriate network complexity and maintain overall computational efficiency. The convergence of the algorithm is analyzed in both the dynamic process phase and the phase following the modification of the structure. The proposed FS-RBFNN has been tested and compared to other algorithms by applying it to the problem of identifying a nonlinear dynamic system. Experimental results show that the FS-RBFNN can be used to design an RBF structure which has fewer hidden neurons; the training time is also much faster. The algorithm is applied for predicting water quality in the wastewater treatment process. The results demonstrate its effectiveness. [Copyright &y& Elsevier]

An optimal control method based on continuous-time continuous-state Hopfield neural network (CTCSHNN) is proposed for time-varying multivariable systems. The equivalence is built theoretically between receding-horizon linear quadratic (LQ) performance index and energy function of CTCSHNN, and the CTCSHNN is constructed to solve the above LQ optimization control problems. Moreover, the rolling optimization strategy is adopted to form closed-loop control structure that includes CTCSHNN so, the dynamic infinite-horizon optimization control is realized for multivariable time-varying systems. As an example, a second order time-varying system is simulated. Simulation results show the effectiveness and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

One of the major obstacles in using deep belief network (DBN) is the structure design. Numerous studies, both empirically and theoretically, show that choosing suitable structure can improve the performance of DBN. In this paper, a self-organizing DBN (S-DBN), based on the information relevance strategy (IRS), was proposed to design the structure of DBN. For this IRS, the maximal information coefficient was designed to measure the input and output information relevance of hidden neurons. Meanwhile, the mutual information was introduced to measure the information relevance among the hidden layers. Then, a novel self-organizing strategy was developed to grow and prune both the hidden neurons and layers during the training process. Moreover, a contrastive divergence algorithm was used to adjust the parameters of S-DBN. Finally, several benchmark problems were used to illustrate the effectiveness of S-DBN. The experimental results demonstrate that the proposed S-DBN owns better performance for classification problems and modeling nonlinear systems than some existing methods. [ABSTRACT FROM AUTHOR]

Interval type-2 fuzzy neural network (IT2FNN) has attracted considerable interest for modeling nonlinear dynamic systems in recent years. However, this promising technique is confronting the problem that constructing a suitable IT2FNN is a potential challenge ignored by most researchers. To solve this problem, a self-constructing interval type-2 fuzzy neural network (SC-IT2FNN), based on the cooperative strategies, is proposed in this paper. The main contributions of this paper are: First, a comprehensive evaluation algorithm (CEA), cooperating with the parameter optimization, is developed to design the structure of SC-IT2FNN to enhance its generalization performance. Second, a hierarchical optimization mechanism, cooperating with the nonlinear and linear parameters of SC-IT2FNN, is proposed to accelerate its learning speed. Third, the convergence of SC-IT2FNN is theoretically analyzed in detail to ensure its successful applications. Finally, several benchmark nonlinear systems and a real application are utilized to evaluate the effectiveness of SC-IT2FNN. The results demonstrate that our proposed SC-IT2FNN significantly improve the modeling performance in terms of high accuracy and compact structure. [ABSTRACT FROM AUTHOR]

Fault detection is important in the operation of wastewater treatment process (WWTP). In this paper, to ensure the process safety and effluent qualities, an intelligent fault detection (IFD) method, based on self-organizing type-2 fuzzy-neural-network (SOT2FNN) and intelligent identification method, was developed to detect and identify different types of sludge bulking. The main advantages of IFD are as follows. First, a data-driven framework, based on a data-driven model and an intelligent identification algorithm, was developed to facilitate the fault diagnosis. Second, a SOT2FNN, based on the intensity of information transmission algorithm and adaptive second-order algorithm, was designed to predict the sludge volume index (SVI) with high accuracy to provide necessary information for process monitoring. Third, an intelligent identification method, using the target-related identification algorithm (TRIA), was proposed to extract the correlation information to identify the types of sludge bulking. Finally, simulations and experimental examples were provided to confirm the effectiveness of the proposed IFD method. [ABSTRACT FROM AUTHOR]

Prediction of bulking sludge is a matter of growing importance around the world. In this study, to detect bulking sludge of wastewater treatment process (WWTP), an intelligent detection method, using a self-organizing recurrent radial basis function neural network (SORRBFNN) and a cause variables identification (CVI) algorithm, was developed to detect the fault points and the fault variables of bulking sludge. For this intelligent detection method, first, the structure and parameters of SORRBFNN were updated by an information-oriented algorithm (IOA) and an improved Levenberg-Marquardt (LM) algorithm to improve the prediction accuracy of the sludge volume index (SVI) from the water qualities. Second, the CVI algorithm was designed to allow a quick revealing of the cause variables of bulking sludge with high accuracy. And the intelligent detection method was tested on the measured data from a real WWTP. Experimental results confirmed the attractiveness and effectiveness of the proposed intelligent detection method. [ABSTRACT FROM AUTHOR]

Accurate control of dissolved oxygen (DO) concentration is the key to ensuring the quality of effluent from the wastewater treatment process (WWTP). However, the delay disturbance caused by the hydraulic retention time (HRT) hinders the accurate control of DO concentration. To solve this problem, an event-triggered recursive least squares-based sliding mode control (ETRLS-SMC) is proposed to overcome the obstacles caused by the delay disturbance for accurate control of DO concentration. First, a differential equation with a delay disturbance term is established to describe the dynamic process of the system. Then, the delay disturbance is explicitly depicted to lay the foundation for the controller design considering delay disturbance variables. Second, an RLS identification algorithm is used to online obtain the model parameters of the system. In particular, an event-triggered mechanism is designed to reduce the number of model updates with guaranteed accuracy. Third, combined with the ETRLS identification algorithm, an SMC method is introduced to control the DO concentration with delay disturbance variables. Then, the control law is computed to achieve stable control of the system. Finally, the performance of ETRLS-SMC is verified on the benchmark simulation model 1 (BSM1). The results show that the proposed method can reduce ISE by 0.0014 and 0.0128 when the threshold is 2.5% in two cases, including the reference value being fixed and changed, compared with the case without considering the delay disturbance. The results of trigger mechanism test further demonstrate the effectiveness of event-triggered mechanism. [ABSTRACT FROM AUTHOR]

Interval Type-2 fuzzy-neural-network (IT2FNN) has been widely used to model nonlinear systems. In current IT2FNN-based schemes, however, one of the main drawbacks is that the structure of IT2FNN is hard to be determined. In this paper, a self-organizing interval Type-2 fuzzy-neural-network (SOIT2FNN) is introduced via considering the structure adjustment and the parameters learning process simultaneously. Two main contributions of SOIT2FNN are summarized: Firstly, an intensity of information transmission algorithm, which can evaluate the independent component contributions of fuzzy rules, is introduced to optimize the structure of SOIT2FNN. Secondly, an adaptive second-order algorithm, which can obtain fast convergence, is developed to adjust the parameters of SOIT2FNN. To demonstrate the merits of SOIT2FNN, several benchmark nonlinear systems and a real world application are examined with comparisons against other existing methods. Moreover, a statistical analysis of the performance results indicates that the proposed SOIT2FNN performs better and is more suitable for modeling nonlinear systems than some existing methods. [ABSTRACT FROM AUTHOR]

Data-driven models (DDMs) are widely developed for monitoring wastewater treatment processes (WWTPs). However, DDMs, derived from invalid or noisy datasets, may fail to capture the dominant features of WWTPs and further result in inferior monitoring results. To solve this issue, a dynamic–static model is designed to monitor WWTPs. Primarily, the operational status of WWTPs is divided by a receding condition partition strategy, which can prevent the mutual interference of fluctuations among different operational conditions. As to the operational conditions without invalid datasets, the dynamic features of WWTPs are extracted by a dynamic intelligent model (DIM). DIM is built using an interval type-2 fuzzy neural network to mimic the dynamic relationship between process variables accurately. Meanwhile, the unreliable results caused by invalid datasets are compensated by a static statistical model. This model is developed to describe static properties using historical datasets, which are copied to execute the monitoring of WWTPs with a similarity discrimination mechanism. Finally, the proposed dynamic–static model is validated by several experiments in terms of total nitrogen removal under multiple operational conditions. The experimental results illustrate that the proposed model can ensure continuous and reliable monitoring of WWTPs. • In this work, a dynamic–static model is designed to monitor WWTPs. • The operational status of WWTPs is divided by a receding condition partition strategy. • As to the operational conditions without invalid datasets, the dynamic features of WWTPs are extracted by a dynamic intelligent model. • The unreliable results caused by invalid datasets are compensated by a static statistical model. [ABSTRACT FROM AUTHOR]

Multi-objective optimal control is often used to deal with conflicting objectives of the wastewater treatment process (WWTP) to ensure its operational safety and reliability. However, the existing multi-objective optimal control methods mainly analyze the optimization process and control process independently, which may make the set-points fluctuate largely and hard to track, thereby degrading the control and operation performance of WWTP. To solve this problem, a multi-objective integrated optimal control (MIOC) strategy is proposed for WWTP in this paper. The integrated optimal control structure is established by the multi-objective model predictive control framework to achieve the coordinated optimization and control solution. In the integrated optimal control structure, first, a comprehensive cost function with operation indices and tracking errors is designed to deal with the conflicting objectives. Second, a multi-gradient algorithm is employed to evaluate the dynamic set-points and control laws. Third, the stability analysis of MIOC is given to prove the proposed method can stabilize the system. Meanwhile, the proposed MIOC method is tested in the Benchmark Simulation Model No. 1 to demonstrate that it can achieve suitable operation performance with satisfactory control accuracy. [Display omitted] • Proposed a multi-objective integrated optimal control strategy for wastewater treatment process. • Designed an integrated optimal control structure for a wastewater treatment process with the multi-objective model predictive control framework. • Developed a comprehensive cost function and a multi-gradient algorithm. • The integrated optimal control strategy can improve the control performance and operation performance of wastewater treatment process. [ABSTRACT FROM AUTHOR]

Efficient and accurate decision is essential to avoid sludge bulking and ensure the stable operation of wastewater treatment process (WWTP). However, due to the strong nonlinear characteristic, time-varying characteristic and changeable triggering causes of sludge bulking, the decision performance is not optimistic. In this paper, an intelligent decision method combining recursive kernel principal component analysis (RKPCA) and Bayesian network (BN) is proposed to accurately detect the occurrence, identify the root causes and severity level, and provide the restraining measures for sludge bulking. The proposed intelligent decision method consists of three main parts. First, a RKPCA model based on the sliding window mechanism is proposed to extract the nonlinear and time-varying characteristics of WWTP. Then, the proposed RKPCA can assist the decision method to detect the sludge bulking with high accuracy. Second, a mean reconstruction contribution of RKPCA (MRC-RKPCA) method is designed to preliminarily isolate all candidate faulty relevant variables of sludge bulking. Then, the MRC-RKPCA method is able to provide the relationship between the sludge bulking and the corresponding faulty variables for the decision method. Third, a decision model using BN is developed to determine the root causes and the severity of sludge bulking through reverse and forward inference, and provide corresponding restraining measures. Then, the proposed decision method can obtain accurate strategies to suppress the sludge bulking. Finally, the proposed intelligent decision method was applied for a real WWTP. The results demonstrate the proposed intelligent decision method can obtain better decision performance than some existing methods. [ABSTRACT FROM AUTHOR]