Pub Date : 2021-07-06DOI: 10.5772/INTECHOPEN.98562
Tiago G. Goto, Hossein Rostami Najafabadi, Guilherme C. Duran, E. K. Ueda, A. K. Sato, Thiago de C. Martins, R. Y. Takimoto, H. Gohari, A. Barari, M. Tsuzuki
This chapter is related to several aspects of optimization problems in engineering. Engineers usually mathematically model a problem and create a function that must be minimized, like cost, required time, wasted material, etc. Eventually, the function must be maximized. This function has different names in the literature: objective function, cost function, etc. We will refer to it in the chapter as objective function. There is a wide range of possibilities for the problems and they can be classified in different ways. At first, the values of the parameters can be continuous, discrete (integers), cyclic (angles), intervals, and combinatorial. The result of the objective function can be continuous, discrete (integers) or intervals. One very difficult class of problems have continuous parameters and discrete objective function, this type of objective function has very weak sensibility. This chapter shows the versatility of the simulated annealing showing that it can have different possibilities of parameters and objective functions.
{"title":"Versatility of Simulated Annealing with Crystallization Heuristic: Its Application to a Great Assortment of Problems","authors":"Tiago G. Goto, Hossein Rostami Najafabadi, Guilherme C. Duran, E. K. Ueda, A. K. Sato, Thiago de C. Martins, R. Y. Takimoto, H. Gohari, A. Barari, M. Tsuzuki","doi":"10.5772/INTECHOPEN.98562","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.98562","url":null,"abstract":"This chapter is related to several aspects of optimization problems in engineering. Engineers usually mathematically model a problem and create a function that must be minimized, like cost, required time, wasted material, etc. Eventually, the function must be maximized. This function has different names in the literature: objective function, cost function, etc. We will refer to it in the chapter as objective function. There is a wide range of possibilities for the problems and they can be classified in different ways. At first, the values of the parameters can be continuous, discrete (integers), cyclic (angles), intervals, and combinatorial. The result of the objective function can be continuous, discrete (integers) or intervals. One very difficult class of problems have continuous parameters and discrete objective function, this type of objective function has very weak sensibility. This chapter shows the versatility of the simulated annealing showing that it can have different possibilities of parameters and objective functions.","PeriodicalId":340860,"journal":{"name":"Optimization Problems in Engineering [Working Title]","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127439002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-17DOI: 10.5772/intechopen.98384
Ju Qiu, Chaofeng Liu
The abrupt and explosive nature of flutter is a dangerous failure mode, which is closely related to the structural modes. In this work, the principal goal of the study is to produce the model, which is used very accurately for flutter predictions. Mode correctness of the model can correct the test deflects by the optimization technique----Sequential Quadratic Programming (SQP). The optimization of two finite element models for two flight conditions, transonic and supersonic speeds, had the different objectives which were defined by the nonlinear and linear eigenvector errors. The first and second frequencies were taken as constraints. And the stiffness of the rotation shaft was also restricted to some limits. The stiffness of the rudder axle was defined as design variables. Experiments were performed for considering springs both in plunge and in torsion of the rudder shaft. When the comparison between experimental information and analyzed calculations is described, generally excellent agreement is obtained between experimental and calculated results, and aeroelastic instability is predicted that agrees with experimental observations. Comments are also given concerning improvements of the flutter speed to be made to the model with changing stiffness of the rudder axle. Most importantly, V&V Method is used to provide the confidence in the results from simulation in this paper. Firstly, it introduces experimental data from Ground Vibration Test to build up or modify the Finite Element Model, during the Verification phase, which makes simulated models closer to the real world and guarantees satisfaction of final computed results to requirements, such as airworthiness. Secondly, the flutter consequence is validated by wind tunnel test. These enhancements could find potential applications in industrial problems.
{"title":"Verification and Validation of Supersonic Flutter of Rudder Model for Experiment","authors":"Ju Qiu, Chaofeng Liu","doi":"10.5772/intechopen.98384","DOIUrl":"https://doi.org/10.5772/intechopen.98384","url":null,"abstract":"The abrupt and explosive nature of flutter is a dangerous failure mode, which is closely related to the structural modes. In this work, the principal goal of the study is to produce the model, which is used very accurately for flutter predictions. Mode correctness of the model can correct the test deflects by the optimization technique----Sequential Quadratic Programming (SQP). The optimization of two finite element models for two flight conditions, transonic and supersonic speeds, had the different objectives which were defined by the nonlinear and linear eigenvector errors. The first and second frequencies were taken as constraints. And the stiffness of the rotation shaft was also restricted to some limits. The stiffness of the rudder axle was defined as design variables. Experiments were performed for considering springs both in plunge and in torsion of the rudder shaft. When the comparison between experimental information and analyzed calculations is described, generally excellent agreement is obtained between experimental and calculated results, and aeroelastic instability is predicted that agrees with experimental observations. Comments are also given concerning improvements of the flutter speed to be made to the model with changing stiffness of the rudder axle. Most importantly, V&V Method is used to provide the confidence in the results from simulation in this paper. Firstly, it introduces experimental data from Ground Vibration Test to build up or modify the Finite Element Model, during the Verification phase, which makes simulated models closer to the real world and guarantees satisfaction of final computed results to requirements, such as airworthiness. Secondly, the flutter consequence is validated by wind tunnel test. These enhancements could find potential applications in industrial problems.","PeriodicalId":340860,"journal":{"name":"Optimization Problems in Engineering [Working Title]","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123270779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-04DOI: 10.5772/INTECHOPEN.98240
C. Venkateswarlu
Stochastic optimization methods are increasingly used for optimizing processes that are difficult to solve by conventional techniques. These methods are widely employed to optimize the processes which have higher dimensionality with severe nonlinearities. Different methods of this kind include the genetic algorithm (GA), simulated annealing (SA), differential evolution (DE), ant colony optimization (ACO), tabu search (TS), particle swarm optimization (PSO), artificial bee colony (ABC) algorithm, and cuckoo search (CS) algorithm. Among these methods, tabu search (TS) is a potential tool used to find a feasible optimal solution from a finite set of solutions. The memory used in TS will remember the current best solution and it also enables the TS to track the last solutions while guiding the search moves. The capability of memory and strategic adaptation features of TS enable it to make use of good solutions and also search for new feasible regions in the search space. TS has been successfully applied to solve a wide spectrum of optimization problems in different disciplines. This chapter describes the TS algorithm in detail and its applications to chemical and environmental processes, specifically, dynamic optimization of a copolymerization reactor and inverse modeling of a biofilm reactor. In dynamic optimization of copolymerization reactor, the meta heuristic Tabu search (TS) is designed and applied to determine the optimal control policies of a styrene–acrylonitrile (SAN) copolymerization reactor. In inverse modeling of biofilm reactor, the tabu search is designed and applied to determine the parameters of kinetic and film thickness models as consequence of the validation of the mathematical models of the process with the aid of measured data acquired from an experimental fixed bed anaerobic biofilm reactor used in the treatment of pharmaceutical industry wastewater. For both the cases, optimization by Tabu search is carried out by suitably formulating the desired objective functions and the problems are solved by encoding the variables and parameters using real floating point numbers. The results explain the efficacy of TS for optimal control of polymerization reactor and inverse modeling of biofilm reactor.
{"title":"A Metaheuristic Tabu Search Optimization Algorithm: Applications to Chemical and Environmental Processes","authors":"C. Venkateswarlu","doi":"10.5772/INTECHOPEN.98240","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.98240","url":null,"abstract":"Stochastic optimization methods are increasingly used for optimizing processes that are difficult to solve by conventional techniques. These methods are widely employed to optimize the processes which have higher dimensionality with severe nonlinearities. Different methods of this kind include the genetic algorithm (GA), simulated annealing (SA), differential evolution (DE), ant colony optimization (ACO), tabu search (TS), particle swarm optimization (PSO), artificial bee colony (ABC) algorithm, and cuckoo search (CS) algorithm. Among these methods, tabu search (TS) is a potential tool used to find a feasible optimal solution from a finite set of solutions. The memory used in TS will remember the current best solution and it also enables the TS to track the last solutions while guiding the search moves. The capability of memory and strategic adaptation features of TS enable it to make use of good solutions and also search for new feasible regions in the search space. TS has been successfully applied to solve a wide spectrum of optimization problems in different disciplines. This chapter describes the TS algorithm in detail and its applications to chemical and environmental processes, specifically, dynamic optimization of a copolymerization reactor and inverse modeling of a biofilm reactor. In dynamic optimization of copolymerization reactor, the meta heuristic Tabu search (TS) is designed and applied to determine the optimal control policies of a styrene–acrylonitrile (SAN) copolymerization reactor. In inverse modeling of biofilm reactor, the tabu search is designed and applied to determine the parameters of kinetic and film thickness models as consequence of the validation of the mathematical models of the process with the aid of measured data acquired from an experimental fixed bed anaerobic biofilm reactor used in the treatment of pharmaceutical industry wastewater. For both the cases, optimization by Tabu search is carried out by suitably formulating the desired objective functions and the problems are solved by encoding the variables and parameters using real floating point numbers. The results explain the efficacy of TS for optimal control of polymerization reactor and inverse modeling of biofilm reactor.","PeriodicalId":340860,"journal":{"name":"Optimization Problems in Engineering [Working Title]","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125867560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-28DOI: 10.5772/INTECHOPEN.97677
A. Salas, S. El-Tantawy
Oscillators are omnipresent; most of them are inherently nonlinear. Though a nonlinear equation mostly does not yield an exact analytic solution for itself, plethora of elementary yet practical techniques exist for extracting important information about the solution of equation. The purpose of this chapter is to introduce some new techniques for the readers which are carefully illustrated using mainly the examples of Duffing’s oscillator. Using the exact analytical solution to cubic Duffing and cubic-quinbic Duffing oscillators, we describe the way other conservative and some non conservative damped nonlinear oscillators may be studied using analytical techniques described here. We do not make use of perturbation techniques. However, some comparison with such methods are performed. We consider oscillators having the form x¨+fx=0 as well as x¨+2εẋ+fx=Ft, where x=xt and f=fx and Ft are continuous functions. In the present chapter, sometimes we will use f−x=−fx and take the approximation fx≈∑j=1Npjxj, where j=1,3,5,⋯N only odd integer values and x∈−AA. Moreover, we will take the approximation fx≈∑j=0Npjxj, where j=1,2,3,⋯N, and x∈−AA. Arbitrary initial conditions are considered. The main idea is to approximate the function f=fx by means of some suitable cubic or quintic polynomial. The analytical solutions are expressed in terms of the Jacobian and Weierstrass elliptic functions. Applications to plasma physics, electronic circuits, soliton theory, and engineering are provided.
{"title":"Analytical Solutions of Some Strong Nonlinear Oscillators","authors":"A. Salas, S. El-Tantawy","doi":"10.5772/INTECHOPEN.97677","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.97677","url":null,"abstract":"Oscillators are omnipresent; most of them are inherently nonlinear. Though a nonlinear equation mostly does not yield an exact analytic solution for itself, plethora of elementary yet practical techniques exist for extracting important information about the solution of equation. The purpose of this chapter is to introduce some new techniques for the readers which are carefully illustrated using mainly the examples of Duffing’s oscillator. Using the exact analytical solution to cubic Duffing and cubic-quinbic Duffing oscillators, we describe the way other conservative and some non conservative damped nonlinear oscillators may be studied using analytical techniques described here. We do not make use of perturbation techniques. However, some comparison with such methods are performed. We consider oscillators having the form x¨+fx=0 as well as x¨+2εẋ+fx=Ft, where x=xt and f=fx and Ft are continuous functions. In the present chapter, sometimes we will use f−x=−fx and take the approximation fx≈∑j=1Npjxj, where j=1,3,5,⋯N only odd integer values and x∈−AA. Moreover, we will take the approximation fx≈∑j=0Npjxj, where j=1,2,3,⋯N, and x∈−AA. Arbitrary initial conditions are considered. The main idea is to approximate the function f=fx by means of some suitable cubic or quintic polynomial. The analytical solutions are expressed in terms of the Jacobian and Weierstrass elliptic functions. Applications to plasma physics, electronic circuits, soliton theory, and engineering are provided.","PeriodicalId":340860,"journal":{"name":"Optimization Problems in Engineering [Working Title]","volume":"148 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116398462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-19DOI: 10.5772/INTECHOPEN.97054
Satadru Roy, W. Crossley, Samarth Jain
Several complex engineering design problems have multiple, conflicting objectives and constraints that are nonlinear, along with mixed discrete and continuous design variables; these problems are inherently difficult to solve. This chapter presents a novel hybrid approach to find solutions to a constrained multi-objective mixed-discrete nonlinear programming problem that combines a two-branch genetic algorithm as a global search tool with a gradient-based approach for the local search. Hybridizing two algorithms can provide a search approach that outperforms the individual algorithms; however, hybridizing the two algorithms, in the traditional way, often does not offer advantages other than the computational efficiency of the gradient-based algorithms and global exploring capability of the evolutionary-based algorithms. The approach here presents a hybridization approach combining genetic algorithm and a gradient-based approach with improved information sharing between the two algorithms. The hybrid approach is implemented to solve three engineering design problems of different complexities to demonstrate the effectiveness of the approach in solving constrained multi-objective mixed-discrete nonlinear programming problems.
{"title":"A Hybrid Approach for Solving Constrained Multi-Objective Mixed-Discrete Nonlinear Programming Engineering Problems","authors":"Satadru Roy, W. Crossley, Samarth Jain","doi":"10.5772/INTECHOPEN.97054","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.97054","url":null,"abstract":"Several complex engineering design problems have multiple, conflicting objectives and constraints that are nonlinear, along with mixed discrete and continuous design variables; these problems are inherently difficult to solve. This chapter presents a novel hybrid approach to find solutions to a constrained multi-objective mixed-discrete nonlinear programming problem that combines a two-branch genetic algorithm as a global search tool with a gradient-based approach for the local search. Hybridizing two algorithms can provide a search approach that outperforms the individual algorithms; however, hybridizing the two algorithms, in the traditional way, often does not offer advantages other than the computational efficiency of the gradient-based algorithms and global exploring capability of the evolutionary-based algorithms. The approach here presents a hybridization approach combining genetic algorithm and a gradient-based approach with improved information sharing between the two algorithms. The hybrid approach is implemented to solve three engineering design problems of different complexities to demonstrate the effectiveness of the approach in solving constrained multi-objective mixed-discrete nonlinear programming problems.","PeriodicalId":340860,"journal":{"name":"Optimization Problems in Engineering [Working Title]","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133901326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-28DOI: 10.5772/INTECHOPEN.96458
B. Hichem, M. Faouzi
The multimodel approach is a research subject developed for modeling, analysis and control of complex systems. This approach supposes the definition of a set of simple models forming a model’s library. The number of models and the contribution of their validities is the main issues to consider in the multimodel approach. In this chapter, a new theoretical technique has been developed for this purpose based on a combination of probabilistic approaches with different objective function. First, the number of model is constructed using neural network and fuzzy logic. Indeed, the number of models is determined using frequency-sensitive competitive learning algorithm (FSCL) and the operating clusters are identified using Fuzzy K- means algorithm. Second, the Models’ base number is reduced. Focusing on the use of both two type of validity calculation for each model and a stochastic SVD technique is used to evaluate their contribution and permits the reduction of the Models’ base number. The combination of FSCL algorithms, K-means and the SVD technique for the proposed concept is considered as a deterministic approach discussed in this chapter has the potential to be applied to complex nonlinear systems with dynamic rapid. The recommended approach is implemented, reviewed and compared to academic benchmark and semi-batch reactor, the results in Models’ base reduction is very important witch gives a good performance in modeling.
{"title":"An Optimization Procedure of Model’s Base Construction in Multimodel Representation of Complex Nonlinear Systems","authors":"B. Hichem, M. Faouzi","doi":"10.5772/INTECHOPEN.96458","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.96458","url":null,"abstract":"The multimodel approach is a research subject developed for modeling, analysis and control of complex systems. This approach supposes the definition of a set of simple models forming a model’s library. The number of models and the contribution of their validities is the main issues to consider in the multimodel approach. In this chapter, a new theoretical technique has been developed for this purpose based on a combination of probabilistic approaches with different objective function. First, the number of model is constructed using neural network and fuzzy logic. Indeed, the number of models is determined using frequency-sensitive competitive learning algorithm (FSCL) and the operating clusters are identified using Fuzzy K- means algorithm. Second, the Models’ base number is reduced. Focusing on the use of both two type of validity calculation for each model and a stochastic SVD technique is used to evaluate their contribution and permits the reduction of the Models’ base number. The combination of FSCL algorithms, K-means and the SVD technique for the proposed concept is considered as a deterministic approach discussed in this chapter has the potential to be applied to complex nonlinear systems with dynamic rapid. The recommended approach is implemented, reviewed and compared to academic benchmark and semi-batch reactor, the results in Models’ base reduction is very important witch gives a good performance in modeling.","PeriodicalId":340860,"journal":{"name":"Optimization Problems in Engineering [Working Title]","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126251149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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