Identificación Robusta de Sistemas no Lineales mediante Algoritmos Evolutivos

[EN] The identification process of the parameters of a nominal model and its uncertainty, when it is used for Robust Control, is known as Parametric Robust Identification (RI). A possible approach to RI, which is appropriate when noise statistical properties unknown and/or model error invalidate statistical approaches, is the deterministic one (Set Membership Estimation). This deterministic approach assumes that identification error (IE), differences between the simulated outputs of the model and the measured outputs of the process, although unknown, will be bounded. Therefore, the objective is to estimate the parameters set of a model which keeps the identification error bounded by a certain norm and bound. This set is known as the feasible parameter set (FPS). For linear in their parameters models, the FPS is, if it exists, a convex polytope. In nonlinear models, the polytope can be non-convex even disjoint. In this thesis a RI methodology, which permits to estimate any kind of FPS in nonlinear models when IE is bounded by several norms simultaneously, is presented. This methodology converts the RI problem into a multimodal optimization problem with optimal global infinities, which constitute the FPS. For its optimization a specific evolutionary algorithm e-GA has been developed, to characterize the FPS by means of a discrete set of models FPS^* adequately distributed along the FPS. The methodology comes accompanied by a procedure that makes easy the determination of bounds, associated to the norms of the IE, in order to guarantee an FPS\neq\emptyset. For that, the Pareto Front information, which is obtained by means of minimization norms of the IE in a multobjective context is used. To solve the multobjective problem an evolutionary algorithm e-MOGA has been developed. In addition, a nominal model of restricted interpolated projection which belongs to the FPS is proposed. It is optimal in both identification and estimation errors in the parameter space. The RI of three nonlinear models, with real data, is presented as application examples of the proposed methodology: a thermal process, a model which shows the blockage that produces a given drug on the ionic currents of a cardiac cell and a greenhouse climate model (temperature and humidity) with roses hydroponic crop.[ES] Al proceso de identificación de los parámetros de un modelo nominal y su incertidumbre para su utilización en Control Robusto se le conoce como Identificación Robusta Paramétrica (IR). Un posible enfoque para abordar la IR, que resulta apropiado cuando el desconocimiento de las propiedades estadísticas del ruido y/o la dinámica no modelada invalidan los enfoques estocásticos, es el determinístico (Set Membership Estimation). Este enfoque asume que el error de identificación (EI), diferencia entre las salidas medidas de proceso y las simuladas del modelo, aunque es desconocido, está acotado. De ahí que, bajo este enfoque, se persiga la determinación del conjunto de parámetros que consiguen mantener el EI acotado para una determinada norma y cota. Dicho conjunto es conocido como el conjunto de parámetros factibles (FPS). Cuando el modelo es lineal respecto de sus parámetros, el FPS, si existe, es un politopo convexo. En modelos no lineales dicho politopo puede ser no convexo e incluso inconexo. En esta tesis se presenta una metodología de IR que permite determinar FPS, de cualquier tipo, en modelos no lineales cualesquiera, acotando el EI simultáneamente mediante varias normas. La metodología transforma el problema de IR en un problema de optimización multimodal con infinitos óptimos globales, los cuales constituyen el FPS. Para su optimización se ha desarrollado un algoritmo evolutivo (EA) específico e-GA, que caracteriza el FPS mediante un conjunto discreto de modelos FPS* adecuadamente distribuido a lo largo del FPS. La metodología viene acompañada de un procedimiento que facilita la determinación de las cotas, asociadas a las normas que acotan el EI, para asegurar que FPS no se aun conjutno vacío. Para ello, se utiliza la información que genera el frente de Pareto resultante de la minimización simultánea de las normas mediante una optimización multiobjetivo.Para resolver este problema de optimización se ha desarrollado el algoritmo evolutivo e-MOGA. Adicionalmente, se propone como modelo nominal un modelo de proyección interpolada restringida que, pertenenciendo al FPS, resulta óptimo respecto del error de identificación y respecto del error de estimación en el espacio de parámetros. Como ejemplos de aplicación de la metodología propuesta se presenta la IR, con datos reales, de los parámetros de tres modelos no lineales: un sistema térmico, un modelo que refleja el bloqueo que produce un determinado fármaco sobre las corrientes iónicas de una célula cardíaca y el modelo climático de un invernadero (temperatura y humedad) con cultivo hidropónico de rosas.[CA] Al procés d'identificació dels paràmetres d'un model nominal i la seua incertesa per a la seua utilització en Control Robust se'l coneix com a Identificació Robusta Paramètrica (IR). Un possible enfocament per a abordar l'IR, que resulta apropiat quan el desconeixement de les propietats estadístiques del soroll i/o la dinàmica no modelada invaliden els enfocaments estocàstics, és el determinístic (Set Membership Estimation). Aquest enfocament assumeix que l'error d'identificació (EI), diferència entre les eixides mesurades del procés i les simulades del model, encara que és desconegut, està acotat. Davall aquest enfocament, es persegueix la determinació del conjunt de paràmetres que aconsegueixen mantenir l'EI acotat per a una determinada norma i cota. Dit conjunt és conegut com el conjunt de paràmetres factibles (FPS). Quan el model és lineal respecte dels seus paràmetres, el FPS, si existeix, és un politop convex. En models no lineals dit politop pot ser no convex i fins i tot inconnex. En aquesta tesi es presenta una metodologia d'IR que permet determinar FPS, de qualsevol tipus, en models no lineals qualsevol, acotant l'EI simultàniament mitjançant diverses normes. La metodologia transforma el problema d'IR en un problema d'optimització multimodal amb infinits òptims globals, els quals constitueixen el FPS. Per a la seua optimització s'ha desenvolupat un algoritme evolutiu (EA) específic e-GA, que caracteritza el FPS mitjançant un conjunt discret de models FPS^* adequadament distribuït al llarg del FPS. La metodologia ve acompanyada d'un procediment que facilita la determinació de les cotes, associades a les normes que acoten l'EI, per a assegurar que FPS\neq\emptyset. Per a això, s'utilitza la informació que genera el front de Pareto resultant de la minimització simultània de les normes mitjançant una optimització multiobjetiu. Per a la resoldre, el problema multiobjectiu s'ha desenvolupat l'algoritme evolutiu e-MOGA. Addicionalment, es proposa com a model nominal un model de projecció interpolada restringida que, pertanyent al FPS, resulta òptim respecte de l'error d'identificació i respecte de l'error de estimació en l'espai de paràmetres. Com a exemples d'aplicació de la metodologia proposada es presenta l'IR, amb dades reals, dels paràmetres de tres models no lineals: un sistema tèrmic, un model que reflecteix el bloqueig que produeix un determinat fàrmac sobre els corrents iònics d'una cèl·lula cardíaca i el model climàtic d'un hivernacle (temperatura i humitat) amb cultiu hidropònic de roses.Herrero Durá, JM. (2006). Identificación Robusta de Sistemas no Lineales mediante Algoritmos Evolutivos [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/13139

New optimal controller tuning method for an AVR system using a simplified Ant Colony Optimization with a new constrained Nelder-Mead algorithm

[EN] In this paper, an optimal gain tuning method for PID controllers is proposed using a novel combination of a simplified Ant Colony Optimization algorithm and Nelder¿Mead method (ACO-NM) including a new procedure to constrain NM. To address Proportional-Integral-Derivative (PID) controller tuning for the Automatic Voltage Regulator (AVR) system, this paper presents a meta-analysis of the literature on PID parameter sets solving the AVR problem. The investigation confirms that the proposed ACO-NM obtains better or equivalent PID solutions and exhibits higher computational efficiency than previously published methods. The proposed ACO-NM application is extended to realistic conditions by considering robustness to AVR process parameters, control signal saturation and noisy measurements as well as tuning a two-degree-of-freedom PID controller (2DOF-PID). For this type of PID, a new objective function is also proposed to manage control signal constraints. Finally, real time control experiments confirm the performance of the proposed 2DOF-PIDs in quasi-real conditions. Furthermore, the efficiency of the algorithm is confirmed by comparing its results to other optimization algorithms and NM combinations using benchmark functions.This work was supported by the Vanier Canada Graduate Scholarship, the Michael Smith Foreign Study Supplements Program from the Natural Sciences and Engineering Research Council of Canada and by the Ministerio de Economia y Competitividad (Spain), project DPI2015-71443-R. It was also supported by the Bourse Mobilite Etudiante from Ministere de l'Education du Quebec, the CEMF Claudette MacKay-Lassonde Graduate Engineering Ambassador Award and the SWAAC Bourseau merite pour etudiantes de cycles superieurs.Blondin, MJ.; Sanchís Saez, J.; Sicard, P.; Herrero Durá, JM. (2018). New optimal controller tuning method for an AVR system using a simplified Ant Colony Optimization with a new constrained Nelder-Mead algorithm. Applied Soft Computing. 62:216-229. https://doi.org/10.1016/j.asoc.2017.10.007S2162296

Control-Oriented Modeling of the Cooling Process of a PEMFC-Based u-CHP System

[EN] Micro-combined heat and power systems (¿-CHP) based on proton exchange membrane fuel cell stacks (PEMFC) are capable of supplying electricity and heat for the residential housing sector with a high energy efficiency and a low level of CO2 emissions. For this reason, they are regarded as a promising technology for coping with the current environmental challenges. In these systems, the temperature control of the stack is crucial, since it has a direct impact on its durability and electrical efficiency. In order to design a good temperature control, however, a dynamic model of the ¿-CHP cooling system is required. In this paper, we present a model of the cooling system of a PEMFC-based ¿-CHP system, which is oriented to the design of the temperature control of the stack. The model has been developed from a ¿-CHP system located in the laboratory of our research team, the predictive control and heuristic optimization group (CPOH). It is based on first principles, dynamic, non-linear, and has been validated against the experimental data. The model is implemented in Matlab/Simulink and the adjustment of its parameters was carried out using evolutionary optimization techniques. The methodology followed to obtain it is also described in detail. Both the model and the test data used for its adjustment and validation are accessible to anyone who wants to consult them. The results show that the model is able to faithfully represent the dynamics of the ¿-CHP cooling system, so it is appropriate for the design of the stack temperature controlThis work was supported in part by the Ministerio de Economia y Competitividad, Spain, under Grant DPI2015-71443-R and Grant RTI2018-096904-B-I00, and in part by the Local Administration Generalitat Valenciana under Project GV/2017/029Navarro-Giménez, S.; Herrero Durá, JM.; Blasco, X.; Simarro Fernández, R. (2019). Control-Oriented Modeling of the Cooling Process of a PEMFC-Based u-CHP System. IEEE Access. 7:95620-95642. https://doi.org/10.1109/ACCESS.2019.2928632S9562095642

Design and Experimental Validation of the Temperature Control of a PEMFC Stack by Applying Multiobjective Optimization

[EN] The current environmental challenges require the implementation of environmentally friendly energy production systems. In this context, proton exchange membrane fuel cell stacks (PEMFC) represent, due to their high electrical efficiency and their low level of CO2 emissions, a promising alternative technology. However, there are still many technical aspects that need to be improved before they become a commercial reality. One of them is the temperature control of the stack, since its electrical efficiency and its lifetime depend on the performance of this control. In this work, we design a multiloop PID control of the temperature of a PEMFC stack and validate it experimentally. The stack is the prime mover of a micro combined heat and power system (micro-CHP). For this task, we use a previously developed nonlinear model and apply a multiobjective optimization methodology. To assess its performance, the PID control is compared to a second PID control designed with a linearized model. The results show, on the one hand, the importance of having a nonlinear model valid in a wide operation range for the correct design of the temperature control of a PEMFC stack and, on the other hand, the advantages of applying a multiobjective optimization methodology to this problem.This work was supported in part by the Spanish Ministry of Science, Innovation, and Universities under Grant RTI2018-096904-B-I00, and in part by the Generalitat Valenciana Regional Government under Project AICO/2019/055.Navarro-Giménez, S.; Herrero Durá, JM.; Blasco, X.; Simarro Fernández, R. (2020). Design and Experimental Validation of the Temperature Control of a PEMFC Stack by Applying Multiobjective Optimization. IEEE Access. 8:183324-183343. https://doi.org/10.1109/ACCESS.2020.3029321S183324183343

Multivariable controller design for the cooling system of a PEM fuel cell by considering nearly optimal solutions in a multi-objective optimization approach

[EN] This paper presents a design for the multivariable control of a cooling system in a PEM (proton exchange membrane) fuel cell stack. This system is complex and challenging enough: interactions between variables, highly nonlinear dynamic behavior, etc. This design is carried out using a multiobjective optimization methodology. There are few previous works that address this problem using multiobjective techniques. Also, this work has, as a novelty, the consideration of, in addition to the optimal controllers, the nearly optimal controllers nondominated in their neighborhood (potentially useful alternatives). In the multiobjective optimization problem approach, the designer must make decisions that include design objectives; parameters of the controllers to be estimated; and the conditions and characteristics of the simulation of the system. However, to simplify the optimization and decision stages, the designer does not include all the desired scenarios in the multiobjective problem definition. Nevertheless, these aspects can be analyzed in the decision stage only for the controllers obtained with a much less computational cost. At this stage, the potentially useful alternatives can play an important role. These controllers have significantly different parameters and therefore allow the designer to make a final decision with additional valuable information. Nearly optimal controllers can obtain an improvement in some aspects not included in the multiobjective optimization problem. For example, in this paper, various aspects are analyzed regarding potentially useful solutions, such as (1) the influence of certain parameters of the simulator; (2) the sample time of the controller; (3) the effect of stack degradation; and (4) the robustness. Therefore, this paper highlights the relevance of this in-depth analysis using the methodology proposed in the design of the multivariable control of the cooling system of a PEM fuel cell. This analysis can modify the final choice of the designer.This study was supported in part by the Ministerio de Ciencia, Innovacion y Universidades (Spain) (grant no. RTI2018-096904-B-I00) and by the Generalitat Valenciana regional government through project AICO/2019/055.Pajares-Ferrando, A.; Blasco, X.; Herrero Durá, JM.; Simarro Fernández, R. (2020). Multivariable controller design for the cooling system of a PEM fuel cell by considering nearly optimal solutions in a multi-objective optimization approach. Complexity. 2020:1-17. https://doi.org/10.1155/2020/8649428S1172020Gunantara, N. (2018). A review of multi-objective optimization: Methods and its applications. Cogent Engineering, 5(1), 1502242. doi:10.1080/23311916.2018.1502242Engau, A., & Wiecek, M. M. (2007). Generating ε-efficient solutions in multiobjective programming. European Journal of Operational Research, 177(3), 1566-1579. doi:10.1016/j.ejor.2005.10.023Loridan, P. (1984). ?-solutions in vector minimization problems. Journal of Optimization Theory and Applications, 43(2), 265-276. doi:10.1007/bf00936165White, D. J. (1986). Epsilon efficiency. Journal of Optimization Theory and Applications, 49(2), 319-337. doi:10.1007/bf00940762Pajares, A., Blasco, X., Herrero, J. M., & Reynoso-Meza, G. (2018). A Multiobjective Genetic Algorithm for the Localization of Optimal and Nearly Optimal Solutions Which Are Potentially Useful: nevMOGA. Complexity, 2018, 1-22. doi:10.1155/2018/1792420Schutze, O., Vasile, M., & Coello, C. A. C. (2011). Computing the Set of Epsilon-Efficient Solutions in Multiobjective Space Mission Design. Journal of Aerospace Computing, Information, and Communication, 8(3), 53-70. doi:10.2514/1.46478Pajares, A., Blasco, X., Herrero, J. M., & Reynoso-Meza, G. (2019). A New Point of View in Multivariable Controller Tuning Under Multiobjective Optimization by Considering Nearly Optimal Solutions. IEEE Access, 7, 66435-66452. doi:10.1109/access.2019.2915556Fredriksson, A., Forsgren, A., & Hårdemark, B. (2011). Minimax optimization for handling range and setup uncertainties in proton therapy. Medical Physics, 38(3), 1672-1684. doi:10.1118/1.3556559Lee, J., & Johnson, G. E. (1993). Optimal tolerance allotment using a genetic algorithm and truncated Monte Carlo simulation. Computer-Aided Design, 25(9), 601-611. doi:10.1016/0010-4485(93)90075-yAndújar, J. M., & Segura, F. (2009). Fuel cells: History and updating. A walk along two centuries. Renewable and Sustainable Energy Reviews, 13(9), 2309-2322. doi:10.1016/j.rser.2009.03.015Mehta, V., & Cooper, J. S. (2003). Review and analysis of PEM fuel cell design and manufacturing. Journal of Power Sources, 114(1), 32-53. doi:10.1016/s0378-7753(02)00542-6De las Heras, A., Vivas, F. J., Segura, F., Redondo, M. J., & Andújar, J. M. (2018). Air-cooled fuel cells: Keys to design and build the oxidant/cooling system. Renewable Energy, 125, 1-20. doi:10.1016/j.renene.2018.02.077Kandlikar, S. G., & Lu, Z. (2009). Thermal management issues in a PEMFC stack – A brief review of current status. Applied Thermal Engineering, 29(7), 1276-1280. doi:10.1016/j.applthermaleng.2008.05.009Yan, Q., Toghiani, H., & Causey, H. (2006). Steady state and dynamic performance of proton exchange membrane fuel cells (PEMFCs) under various operating conditions and load changes. Journal of Power Sources, 161(1), 492-502. doi:10.1016/j.jpowsour.2006.03.077Maghanki, M. M., Ghobadian, B., Najafi, G., & Galogah, R. J. (2013). Micro combined heat and power (MCHP) technologies and applications. Renewable and Sustainable Energy Reviews, 28, 510-524. doi:10.1016/j.rser.2013.07.053Notter, D. A., Kouravelou, K., Karachalios, T., Daletou, M. K., & Haberland, N. T. (2015). Life cycle assessment of PEM FC applications: electric mobility and μ-CHP. Energy & Environmental Science, 8(7), 1969-1985. doi:10.1039/c5ee01082aMartinez, S., Michaux, G., Salagnac, P., & Bouvier, J.-L. (2017). Micro-combined heat and power systems (micro-CHP) based on renewable energy sources. Energy Conversion and Management, 154, 262-285. doi:10.1016/j.enconman.2017.10.035Elmer, T., Worall, M., Wu, S., & Riffat, S. B. (2015). Fuel cell technology for domestic built environment applications: State of-the-art review. Renewable and Sustainable Energy Reviews, 42, 913-931. doi:10.1016/j.rser.2014.10.080Hawkes, A., Staffell, I., Brett, D., & Brandon, N. (2009). Fuel cells for micro-combined heat and power generation. Energy & Environmental Science, 2(7), 729. doi:10.1039/b902222hEllamla, H. R., Staffell, I., Bujlo, P., Pollet, B. G., & Pasupathi, S. (2015). Current status of fuel cell based combined heat and power systems for residential sector. Journal of Power Sources, 293, 312-328. doi:10.1016/j.jpowsour.2015.05.050Strahl, S., & Costa-Castelló, R. (2017). Temperature control of open-cathode PEM fuel cells. IFAC-PapersOnLine, 50(1), 11088-11093. doi:10.1016/j.ifacol.2017.08.2492Zhang, G., & Kandlikar, S. G. (2012). A critical review of cooling techniques in proton exchange membrane fuel cell stacks. International Journal of Hydrogen Energy, 37(3), 2412-2429. doi:10.1016/j.ijhydene.2011.11.010Navarro Gimenez, S., Herrero Dura, J. M., Blasco Ferragud, F. X., & Simarro Fernandez, R. (2019). Control-Oriented Modeling of the Cooling Process of a PEMFC-Based $\mu$ -CHP System. IEEE Access, 7, 95620-95642. doi:10.1109/access.2019.2928632Herrero, J. M., García-Nieto, S., Blasco, X., Romero-García, V., Sánchez-Pérez, J. V., & Garcia-Raffi, L. M. (2008). Optimization of sonic crystal attenuation properties by ev-MOGA multiobjective evolutionary algorithm. Structural and Multidisciplinary Optimization, 39(2), 203-215. doi:10.1007/s00158-008-0323-7Bristol, E. (1966). On a new measure of interaction for multivariable process control. IEEE Transactions on Automatic Control, 11(1), 133-134. doi:10.1109/tac.1966.1098266Blasco, X., Herrero, J. M., Sanchis, J., & Martínez, M. (2008). A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Information Sciences, 178(20), 3908-3924. doi:10.1016/j.ins.2008.06.010Schmittinger, W., & Vahidi, A. (2008). A review of the main parameters influencing long-term performance and durability of PEM fuel cells. Journal of Power Sources, 180(1), 1-14. doi:10.1016/j.jpowsour.2008.01.07

A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization

[EN] In a multi-objective optimization problem, in addition to optimal solutions, multimodal and/or nearly optimal alternatives can also provide additional useful information for the decision maker. However, obtaining all nearly optimal solutions entails an excessive number of alternatives. Therefore, to consider the nearly optimal solutions, it is convenient to obtain a reduced set, putting the focus on the potentially useful alternatives. These solutions are the alternatives that are close to the optimal solutions in objective space, but which differ significantly in the decision space. To characterize this set, it is essential to simultaneously analyze the decision and objective spaces. One of the crucial points in an evolutionary multi-objective optimization algorithm is the archiving strategy. This is in charge of keeping the solution set, called the archive, updated during the optimization process. The motivation of this work is to analyze the three existing archiving strategies proposed in the literature (ArchiveUpdateP(Q,epsilon)D(xy), Archive_nevMOGA, and targetSelect) that aim to characterize the potentially useful solutions. The archivers are evaluated on two benchmarks and in a real engineering example. The contribution clearly shows the main differences between the three archivers. This analysis is useful for the design of evolutionary algorithms that consider nearly optimal solutions.This work was supported in part by the Ministerio de Ciencia, Innovacion y Universidades (Spain) (grant number RTI2018-096904-B-I00), by the Generalitat Valenciana regional government through project AICO/2019/055 and by the Universitat Politecnica de Valencia (grant number SP20200109).Pajares-Ferrando, A.; Blasco, X.; Herrero Durá, JM.; Martínez Iranzo, MA. (2021). A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization. Mathematics. 9(9):1-28. https://doi.org/10.3390/math9090999S1289

A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization

[EN] New challenges in engineering design lead to multiobjective (multicriteria) problems. In this context, the Pareto front supplies a set of solutions where the designer (decision-maker) has to look for the best choice according to his preferences. Visualization techniques often play a key role in helping decision-makers, but they have important restrictions for more than two-dimensional Pareto fronts. In this work, a new graphical representation, called Level Diagrams, for n-dimensional Pareto front analysis is proposed. Level Diagrams consists of representing each objective and design parameter on separate diagrams. This new technique is based on two key points: classification of Pareto front points according to their proximity to ideal points measured with a specific norm of normalized objectives (several norms can be used); and synchronization of objective and parameter diagrams. Some of the new possibilities for analyzing Pareto fronts are shown. Additionally, in order to introduce designer preferences, Level Diagrams can be coloured, so establishing a visual representation of preferences that can help the decision-maker. Finally, an example of a robust control design is presented - a benchmark proposed at the American Control Conference. This design is set as a six-dimensional multiobjective problem. (c) 2008 Elsevier Inc. All rights reserved.Partially supported by MEC (Spanish Government) and FEDER funds: Projects DPI2005-07835, DPI2004-8383-C03-02 and GVA-026.Blasco, X.; Herrero Durá, JM.; Sanchís Saez, J.; Martínez Iranzo, MA. (2008). A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Information Sciences. 178(20):3908-3928. https://doi.org/10.1016/j.ins.2008.06.010S390839281782

WH-MOEA: A Multi-Objective Evolutionary Algorithm for Wiener-Hammerstein System Identification. A Novel Approach for Trade-Off Analysis Between Complexity and Accuracy

[EN] Several approaches have been presented to identify Wiener-Hammerstein models, most of them starting from a linear dynamic model whose poles and zeros are distributed around the static non- linearity. To achieve good precision in the estimation, the Best Linear Approximation (BLA) has usually been used to represent the linear dynamics, while static non-linearity has been arbitrarily parameterised without considering model complexity. In this paper, identification of Wiener, Hammerstein or Wiener-Hammerstein models is stated as a multiobjective optimisation problem (MOP), with a trade-off between accuracy and model complexity. Precision is quantified with the Mean-Absolute-Error (MAE) between the real and estimated output, while complexity is based on the number of poles, zeros and points of the static non- linearity. To solve the MOP, WH-MOEA, a new multiobjective evolutionary algorithm (MOEA) is proposed. From a linear structure, WH-MOEA will generate a set of optimal models considering a static non-linearity with a variable number of points. Using WH-MOEA, a procedure is also proposed to analyse various linear structures with different numbers of poles and zeros (known as design concepts). A comparison of the Pareto fronts of each design concept allows a more in-depth analysis to select the most appropriate model according to the user¿s needs. Finally, a complex numerical example and a real thermal process based on a Peltier cell are identified, showing the procedure¿s goodness. The results show that it can be useful to consider the simultaneously precision and complexity of a block-oriented model (Wiener, Hammerstein or Wiener- Hammerstein) in a non-linear process identification.This work was supported in part by the Ministerio de Ciencia, Innovación y Universidades, Spain, under Grant RTI2018-096904-B-I00-AR, and in part by the Salesian Polytechnic University of Ecuador through a Ph.D. scholarships granted to J. Zambrano.Zambrano, J.; Sanchís Saez, J.; Herrero Durá, JM.; Martínez Iranzo, MA. (2020). WH-MOEA: A Multi-Objective Evolutionary Algorithm for Wiener-Hammerstein System Identification. A Novel Approach for Trade-Off Analysis Between Complexity and Accuracy. IEEE Access. 8:228655-228674. https://doi.org/10.1109/ACCESS.2020.3046352228655228674

Analyzing the Nearly Optimal Solutions in a Multi-Objective Optimization Approach for the Multivariable Nonlinear Identification of a PEM Fuel Cell Cooling System

[EN] In this work, the parametric identification of a cooling system in a PEM (proton exchange membrane) fuel cell is carried out. This system is multivariable and nonlinear. In this type of system there are different objectives and the unmodeled dynamics cause conflicting objectives (prediction errors in each output). For this reason, resolution is proposed using a multi-objective optimization approach. Nearly optimal alternatives can exist in any optimization problem. Among them, the nearly optimal solutions that are significantly different (that we call nearly optimal solutions nondominated in their neighborhood) are potentially useful solutions. In identification problems, two situations arise for consideration: 1) aggregation in the design objectives (when considering the prediction error throughout the identification test). When an aggregation occurs in the design objectives, interesting non-neighboring (significantly different) multimodal and nearly optimal alternatives appear. These alternatives have different trade-offs in the aggregated objectives; 2) new objectives in decision making appear. Some models can, with similar performance in the design objectives, obtain a significant improvement in new objectives not included in the optimization phase. A typical case of additional objectives are the validation objectives. In these situations, nearly optimal solutions nondominated in their neighborhood play a key role. These alternatives allow the designer to make the final decision with more valuable information. Therefore, this work highlights, as a novelty, the relevance of considering nearly optimal models nondominated in their neighborhood in problems of parametric identification of multivariable nonlinear systems and shows an application in a complex problem.This work was supported in part by the Ministerio de Ciencia, Innovacion y Universidades, Spain, under Grant RTI2018-096904-B-I00, and in part by the Generalitat Valenciana Regional Government under Project AICO/2019/055.Pajares-Ferrando, A.; Blasco, X.; Herrero Durá, JM.; Salcedo-Romero-De-Ávila, J. (2020). Analyzing the Nearly Optimal Solutions in a Multi-Objective Optimization Approach for the Multivariable Nonlinear Identification of a PEM Fuel Cell Cooling System. IEEE Access. 8:114361-114377. https://doi.org/10.1109/ACCESS.2020.3003741S114361114377

Nonlinear Robust Identification using Evolutionary Algorithms. Application to a Biomedical Process

[EN] This work describes a new methodology for robust identification (RI), meaning the identification of the parameters of a model and the characterization of uncertainties. The alternative proposed handles non-linear models and can take into account the different properties demanded by the model. The indicator that leads the identification process is the identification error (IE), that is, the difference between experimental data and model response. In particular, the methodology obtains the feasible parameter set (FPS, set of parameter values which satisfy a bounded IE) and a nominal model in a non-linear identification problem. To impose different properties on the model, several norms of the IE are used and bounded simultaneously. This improves the model quality, but increases the problem complexity. The methodology proposes that the RI problem is transformed into a multimodal optimization problem with an infinite number of global minima which constitute the FPS. For the optimization task, a special genetic algorithm (epsilon-GA), inspired by Multiobjective Evolutionary Algorithms, is presented. This algorithm characterizes the FPS by means of a discrete set of models well distributed along the FPS. Finally, an application for a biomedical model which shows the blockage that a given drug produces on the ionic currents of a cardiac cell is presented to illustrate the methodology. (C) 2008 Elsevier Ltd. All rights reserved.Partially supported by MEC (Spanish government) and FEDER funds: Projects DP12005-07835, DP12004-8383-CO3-02 and Generalitat Valenciana (Spain) Project GVA-026.Herrero Durá, JM.; Blasco, X.; Martínez Iranzo, MA.; Ramos Fernández, C.; Sanchís Saez, J. (2008). Nonlinear Robust Identification using Evolutionary Algorithms. Application to a Biomedical Process. Engineering Applications of Artificial Intelligence. 21(8):1397-1408. https://doi.org/10.1016/j.engappai.2008.05.001S1397140821