This article introduces a novel method for distilling knowledge from complex models using fuzzy systems. The complex knowledge comes from a proposed hybrid NFN-LSTM model (teacher) composed of a long shor-term memory (LSTM) coupled to a neo-fuzzy neuron (NFN) structure. The proposed student model, the NFN-MOD, is an explainable Takagi–Sugeno fuzzy model that resembles modular characteristics to mimic the temporal memory of the LSTM part in the teacher model. The NFN-MOD is adaptable across many scenarios, including solo learning (without a teacher), with the estimation of a previously trained teacher, or training in parallel with the teacher. The complexity reduction of the student model is achieved through the pruning of its consequent parameters with the lowest L1-norm. Application of NFN-MOD in industrial case studies (sulfur recovery unit and cement manufacturing process) demonstrates the efficiency of NFN-MOD in distilling complex knowledge from the teacher model NFN-LSTM, with emphasis on parallel training and parameter pruning. In addition, a novel explainability analysis is introduced, which evaluates the influence of antecedent parameters of the student model in relation to the expected real system output.

Wildfires are complex phenomena with harmful consequences, ranging from environmental and property destruction to loss of human lives. In this sense, predicting wildfire behaviour is essential to mitigate its impacts and consequences. The Rothermel model is the most used fire rate of spread prediction model. However, input parameter uncertainty is a significant source of prediction error. In this paper, we propose the calibration of the input parameters of the fire propagation model by metaheuristic algorithms under a two-stage framework. The fire spread model consists on the Rothermel model in a two-dimensional approach for surface fires. The proposed calibration is performed in two stages iteratively repeated over time: (i) the calibration of the fire spread model's input parameters and (ii) the wildfire spread prediction using the calibrated input parameters. The calibration was performed by the genetic algorithm, differential evolution, and simulated annealing, which calibrates the surface-area-to-volume ratio, fuel bed depth, live fuel moisture and dead fuel moisture. The symmetric difference between the real and predicted fire map shapes was defined as the fitness function of all three metaheuristic algorithms. For validation, simulations were done on two prescribed fires. The results for the real and estimated fire behaviour were then compared and revealed that all the tested metaheuristic algorithms produce a better fit to the real fire's perimeter when compared to the uncalibrated Rothermel model. From the results, differential evolution provided the majority of best results when compared to genetic algorithm and simulated annealing algorithms in each scenario.

Abstract Machine Learning (ML) has attracted great interest in the modeling of systems using computational learning methods, being utilized in a wide range of advanced fields due to its ability and efficiency to process large amounts of data and to make predictions or decisions with a high degree of accuracy. However, with the increase in the complexity of the models, ML's methods have presented complex structures that are not always transparent to the users. In this sense, it is important to study how to counteract this trend and explore ways to increase the interpretability of these models, precisely where decision‐making plays a central role. This work addresses this challenge by assessing the interpretability and explainability of fuzzy‐based models. The structural and semantic factors that impact the interpretability of fuzzy systems are examined. Various metrics have been studied to address this topic, such as the Co‐firing Based Comprehensibility Index (COFCI), Nauck Index, Similarity Index, and Membership Function Center Index. These metrics were assessed across different datasets on three fuzzy‐based models: (i) a model designed with Fuzzy c‐Means and Least Squares Method, (ii) Adaptive‐Network‐based Fuzzy Inference System (ANFIS), and (iii) Generalized Additive Model Zero‐Order Takagi‐Sugeno (GAM‐ZOTS). The study conducted in this work culminates in a new comprehensive interpretability metric that covers different domains associated with interpretability in fuzzy‐based models. When addressing interpretability, one of the challenges lies in balancing high accuracy with interpretability, as these two goals often conflict. In this context, experimental evaluations were performed in many scenarios using 4 datasets varying the model parameters in order to find a compromise between interpretability and accuracy.

Electric vehicle physical parameters highly influence the modeling of its different systems. Although a simulation using data acquired from field tests can have satisfactory results, the parameters inaccuracy, due to either insufficient information or wear, can prevent a better performance. In this paper, 10 electric vehicle physical parameters are adjusted/calibrated by three metaheuristic algorithms: Particle Swarm Optimization, Genetic Algorithms, and Simulated Annealing. Moreover, tests on real short and long distance data sets were used in order to validate the proposed framework to EV model calibration. The results achieved indicate that parameter calibration is effective in the reduction of the modeling error.

Every year, wildfires cause significant losses and destruction around the globe. In order to attempt to reduce their damages, resources have been put into developing fire propagation prediction systems. In a real wildfire event, these systems provide the authorities with information about the fire propagation in the near future, thus allowing them to make better decisions. Wildfire spread prediction systems are based on fire propagation models, from which the most used and accepted model is the Rothermel model. However, given the complexity of the wildfire phenomena and the uncertainty of some of its input parameter values, the Rothermel model can produce misleading results of fire propagation. This paper uses 3 metaheuristic algorithms, genetic algorithm (GA), differential evolution (DE) and simulated annealing (SA), for calibration of input parameters from the Rothermel model. These algorithms were validated using 37 datasets containing data from controlled experimental fires. Results have shown that these algorithms provide a precise wildfire spread prediction accounting for the uncertainties in the model’s selected parameters.

Wastewater Treatment Plants (WWTPs) are complex structures, with nonlinear characteristics, that have strict quality criteria, and carry out the treatment using various resources, with special emphasis on electricity. The optimization of WWTPs is a necessity to achieve sustainability. This work proposes the use of metaheuristic algorithms to optimize the functioning of a WWTP. Genetic Algorithm, Particle Swarm Optimization, and Simulated Annealing are used to minimize the aeration energy consumption prediction by an artificial neural network. The optimization framework aims dynamically adjusts the reference value for the proportional-integral (PI) controller. The proposed approach was able to dynamically adjust the oxygen pumping requirement and thus reduce the electricity consumption compared to the default PI controller adopted by the Benchmark Simulation Model no. 2 (BSM2).

Prediction of key variables is an important part of the monitoring, control, and optimization of industrial processes, since it is important to anticipate certain behaviors so that the correct actions can be taken. To assess which algorithm is best suited to the prediction of a number of key variables at various stages of wastewater treatment plants (WWTP), five computational algorithms were researched: Artificial Neural Network, Long Short-Term Memory, deep learning Transformer model, Adaptive Neuro-Fuzzy Inference System, and Gaussian Mixture Model. With these models, techniques already well established in the state-of-the-art are evaluated, as well as more recent methods that have been exhibiting good performance in variable prediction regression problems. These algorithms were evaluated in four WWTP case studies, in which the objective is to predict the following key variables: total suspended solids, nitrate and nitrite, ammonia and ammonium, and biochemical oxygen demand. The learning process of each algorithm was performed using extensive tests in order to select the input variables, and define the topologies and hyper-parameters of the presented models by cross-validation. The results indicate that it is possible to adequately predict the four variables, and the best results were achieved by the Transformer algorithm, which presents the lower error values in the considered metrics.

This paper proposes a methodology for iterative learning of multi-input multi-output (MIMO) fuzzy models focusing on dynamic system identification. The first step of the proposed method is the learning of the antecedent part of the fuzzy system, which is learned iteratively, where fuzzy rules can be added or merged based on the presented novelty detection and similarity criteria defined by a recursive extension of the Gath-Geva clustering algorithm. Then, the consequent part consists in the direct implementation of a non-recursive fuzzy approach that uses global least squares, Observer Kalman Filter Identification (OKID) and the Eigensystem Realization Algorithm (ERA). The proposed method is validated using experimental data from a real quadrotor aerial robot, a nonlinear dynamic system. Using quantitative performance metrics, the proposed method is compared with Hammerstein-Wiener models (H.-W.), nonlinear autoregressive models with exogenous input (NARX), and state-space models using subspace method with time-domain data (N4SID), other MIMO system identification techniques. The proposed method achieved better results compared to other techniques, showing the importance and versatility of learning based on novelty detection for MIMO problems.

This paper proposes an iterative learning approach to learn a fuzzy system composed of a sum of multiple univariate zero-order Takagi-Sugeno (T-S) fuzzy systems. The learning algorithm is based on the backfitting algorithm, and new fuzzy rules are iteratively added based on a novelty detection criterion, which gives the novelty degree of a new data by a value between zero and one, allowing an easier rule creation threshold's definition. In order to validate the performance of the proposed approach, 10 benchmark data sets are used to compare the proposed approach with two well-known state-of-the-art methods, the Extreme Learning Machine (ELM), and the Support Vector Regression (SVR), and with the GAM-ZOTS approach, which model is similar to the proposed approach. From the results, it is concluded that the proposed approach outperforms ELM, SVR and GAM-ZOTS in almost all data sets.

A proof of concept of a purely virtual test platform for critical cyberphysical systems in closed-loop is presented in this work. An H∞direct adaptive fuzzy controller is formulated to tackle the wheel slip tracking problem in Antilock-Braking System over a CAN network. A Lyapunov function for the nonlinear control system is derived using the Riccati equation solution in order to prove stability and robustness with respect to network-induced delays, data packet losses, and model uncertainty. Simulation results show that high performance and robustness are achieved.

The paper proposes a methodology to self-evolve an online fuzzy logic controller (FLC). The proposed methodology does not require any initialization at all, it can start with an empty set of fuzzy control rules or with a simple collection of fuzzy control rules obtained from an expert operator. The FLC design is online, using only the input/output data obtained during the normal operation of the system while it is being controlled. The FLC is composed of a simple structure, where each input variable has its own set of fuzzy control rules, and is evaluated individually by the proposed methodology avoiding the high increase in the number of fuzzy control rules. The FLC structure and their antecedent and consequent parameters are both online modified by the proposed methodology. Only simple information about the system and controller is need, specifically the universe of discourse of the input and output variables, an information that is mandatory to control any process. The performance of the proposed methodology is tested on a simulated continuous-stirred tank reactor (CSTR) system where the results show that the proposed methodology has the capability of designing the FLC in order to successfully controlling the CSTR system by evolving/modifying the FLC structure when unknown regions of operation are reached (unknown for the controller).

This paper proposes a method for adaptive identification and predictive control using an online sequential extreme learning machine based on the recursive partial least-squares method (OS-ELM-RPLS). OL-ELM-RPLS is an improvement to the online sequential extreme learning machine based on recursive least-squares (OS-ELM-RLS) introduced in [1]. Like in the batch extreme learning machine (ELM), in OS-ELM-RLS the input weights of a single-hidden layer feedforward neural network (SLFN) are randomly generated, however the output weights are obtained by a recursive least-squares (RLS) solution. However, due to multicollinearities in the columns of the hidden-layer output matrix caused by the presence of redundant input variables or by a large number of hidden-layer neurons, the problem of estimation the output weights can become ill-conditioned. In order to circumvent or mitigate such ill-conditioning problem, it is proposed to replace the RLS method by the recursive partial least-squares (RPLS) method. The identification methodology is proposed for two application problems: (1) construction of a inferential model, and (2) the learning of a model for the Generalized predictive control (GPC) algorithm. The integration of the proposed adaptive identification method with the GPC results in an adaptive predictive control methodology. To validate and demonstrate the performance and effectiveness of the proposed methodologies, they are applied on modeling of two public regression data sets and on control of the flow through a simulated valve.

The paper proposes a new framework to learn a Fuzzy Logic Controller (FLC), from data extracted from a process while it is being manually controlled, in order to control nonlinear industrial processes. The learning of the FLC is performed by a hierarchical genetic algorithm (HGA). First, the fuzzy c-means (FCM) clustering algorithm is applied to initialize the HGA population, in order to reduce the computational cost and increase the performance of the HGA. The HGA is composed by five hierarchical levels and it is an automatic tool since it does not require any prior knowledge concerning the structure (e.g. the number of rules) and the database (e.g. antecedent and consequent fuzzy sets) of the FLC, and concerning the selection of the adequate input variables and their respective time delays. After the extraction of the FLC by the proposed method, in order to obtain a better control results, if necessary, the learned FLC can be improved manually by using the information transmitted by a human operator, and/or the learned FLC could be easily applied to initialize the required fuzzy knowledge-base of adaptive controllers. In order to improve the results of the learned FLC, a direct adaptive fuzzy controller is applied. Moreover, the proposed method is applied on control of the dissolved oxygen in an activated sludge reactor within a simulated wastewater treatment plant. The results are presented, showing that the proposed method successfully extracted the parameters of the FLC.

A novel adaptive evolving Takagi-Sugeno (T-S) model identification method is investigated and integrated in a control architecture to control of nonlinear processes is investigated. The proposed system identification approach consists of two main steps: antecedent T-S fuzzy model parameters identification and consequent parameters identification. First, a new unsupervised fuzzy clustering algorithm (NUFCA) is introduced to combine the K-nearest neighbor and fuzzy C-means methods into a fuzzy modeling method for partitioning of the input-output data and identifying the antecedent parameters of the fuzzy system. Then, a recursive procedure using a particle swarm optimization (PSO) algorithm is exploited to construct an online fuzzy model identification and adaptive control methodology. For better demonstration of the robustness and efficiency of the proposed methodology, it is applied to the identification of a model for the estimation of the flour concentration in the effluent of a real-world wastewater treatment plant (WWTP), and identification and control, using a generalized predictive controller (GPC), of a real experimental setup composed of two coupled DC motors. The results show that the developed evolving T-S fuzzy model methodology can identify nonlinear systems satisfactorily and can be successfully used for a prediction model of the process for the GPC.

This work addresses the problem of controlling unknown and time varying plants for industrial applications. To deal with such problem several Self-Tuning Controllers with a Proportional Integral and Derivative (PID) structure have been chosen. The selected controllers are based on different methodologies, and some use implicit identification techniques (Single Neuron and Support Vector Machine) while the others use explicit identification (Dahlin, Pole placement, Deadbeat and Ziegler-Nichols) based in the Least Squares Method. The controllers were tested on a real DC motor with a varying load. The results have shown that all the tested methods were able to properly control an unknown plant with varying dynamics.

This paper proposes a new method for identification problems for industrial applications based on a Takagi-Sugeno (T-S) fuzzy model. The learning of the T-S model is performed from input/output data to approximate unknown nonlinear processes by a coevolationary genetic algorithm (GA). The proposed method is an automatic tool since it does not require any prior knowledge concerning the structure (e.g. the number of rules) and the database (e.g. antecedent fuzzy sets) of the T-S fuzzy model, and concerning the selection of the adequate input variables and their respective time delays. The proposed methodology is able to design all the parts of the T-S fuzzy prediction model and it is composed by five hierarchical levels. To validate and demonstrate the performance and effectiveness of the proposed algorithm, it is applied on Box-Jenkins benchmark problem.

The paper proposes an adaptive fuzzy predictive control method for industrial processes, which is based on the Generalized predictive control (GPC) algorithm. To provide good accuracy in the identification of unknown nonlinear plants, an online adaptive law is proposed to adapt a T-S fuzzy model. It is demonstrated that the tracking error remains bounded. The stability of closed-loop control system is studied and proved via the Lyapunov stability theory. To validate the theoretical developments and to demonstrate the performance of the proposed control, the controller is applied on a simulated laboratory-scale liquid-level process. The simulation results show that the proposed method has good performance and disturbance rejection capacity in industrial processes.

The paper proposes a stable indirect adaptive fuzzy predictive control, which is based on a discrete-time Takagi-Sugeno (T-S) fuzzy model and on the Generalized predictive control (GPC) algorithm. The T-S fuzzy model is used to approximate the unknown nonlinear plant, that to provide good accuracy in identification of unknown model parameters, three online adaptive laws are proposed. It is demonstrated that the tracking error remains bounded. The stability of closed-loop control system is studied and proved via the Lyapunov stability theory. To validate the theoretical developments and to demonstrate the performance of the proposed control, the controller is applied on a nonlinear simulated laboratory-scale liquid-level process. The simulation results show that the proposed method has a good performance and disturbance rejection capacity in industrial processes.

The paper proposes a new method to automatically extract all fuzzy parameters of a Fuzzy Logic Controller (FLC) in order to control nonlinear industrial processes. The learning of the FLC is performed from controller input/output data and by a hierarchical genetic algorithm (HGA). The algorithm is composed by a five level structure, where the first level is responsible for the selection of an adequate set of input variables. The second level considers the encoding of the membership functions. The individual rules are defined on the third level. The set of rules are obtained on the fourth level, and finally, the fifth level, selects the elements of the previous levels, as well as, the t-norm operator, inference engine and defuzzifier methods which constitute the FLC. To demonstrate and validate the effectiveness of the proposed algorithm, it is applied to control a simulated water tank level process.

The paper proposes an adaptive fuzzy predictive control method. The proposed controller is based on the Generalized predictive control (GPC) algorithm, and a recurrent fuzzy neural network (RFNN) is used to approximate the unknown nonlinear plant. To provide good accuracy in identification of unknown model parameters, an online adaptive law is proposed to adapt the consequent part of the RFNN, and its antecedent part is adapted by back-propagation method. The stability of closed-loop control system is studied and proved via the Lyapunov stability theory. A nonlinear lab oratory-scale liquid-level process is used to validate and demonstrate the performance of the proposed control. The simulation results show that the proposed method has good performance and disturbance rejection capacity in industrial processes and outperforms the PID and the classical GPC controllers.

The paper presents an adaptive fuzzy predictive control based on discrete-time Takagi-Sugeno (T-S) fuzzy model. The proposed controller is based on Generalized predictive control (GPC) algorithm, and a discrete-time T-S fuzzy model is employed to approximate the unknown nonlinear process. To provide a better accuracy in identification of unknown parameters of the model, it is proposed an on-line adaptive law which ensures that the tracking error remains bounded. The stability of closed-loop control system is proved/studied via the Lyapunov stability theory. To validate the theoretical developments and to demonstrate the performance of the proposed control is simulated as nonlinear system a laboratory-scale liquid-level process. The simulation results show that the proposed method has a good performance and disturbance rejection capacity in industrial process.