multiobjective optimization

Non-destructive damage detection methods analyze the output data collected from sensors to track the changes in the dynamic characteristics of the structure and detect the occurrence of damages. continuous recording and analysis of data to be aware of its safety and serviceability requires a network of sensors that are selected optimally and intelligently. Saving the cost of equipping the structure with this optimal sensor network, along with reducing damage detection error, has turned the issue of selecting the number and location of sensors into an optimization problem from an economic and functional point of view. Model order reduction methods along with optimization tools can play an effective role in selecting the master degrees of freedom. These methods divide the degrees of freedom of the structure into two groups of master and slave degrees of freedom. The master degrees of freedom appear in the process of calculating the mode shapes and natural frequencies, and the slave degrees of freedom are excluded from the equations. Finally, using the transfer matrix, the complete mode shapes are calculated using the mode shapes of the master degrees of freedom. In this paper, considering the key role of modal parameter recognition in structural damage detection, the performance and accuracy of different methods of dynamical model order reduction in the optimal sensor placement problem was studied. The 2d truss stucture and two-dimensional shear frame are modeled and analyzed. The sensor placement should be considered in such a way that the mode shape identification is done with sufficient accuracy and proper recognition. One of the effective tools in order to achieve this goal is to use the capabilities of metaheuristic optimization algorithms along with the capability of dynamic model reduction methods in the stage of identifying the mode shapes and before identifying the damages of structure. Combining model order reduction methods with metaheuristic optimization algorithms so that the selection of appropriate degrees of freedom for sensor installation (master degrees of freedom) leads to the most accurate identification of structural modes shapes is one of the main objectives of this study. The objective functions selected based on modal assurance criteria (MAC) and Fisher information matrix (FIM) and the capabilities of multi objective particle swarm optimization algorithm (MOPSO) to achieve the optimal number and proper arrangement of sensors are used to better identify the structural mode shapes and proper arrangement of sensors and obtained for system identification purposes. The results report better performance of SEREP and IDC methods in selection of master degrees of freedom and identifying the mode shapes of 2d truss and shear frame structures. According to the modeling and analysis performed for optimal placement of sensors using different model reduction methods, it can be concluded that the improved dynamic condensation (IDC) method is more accurate than other methods in identifying shear frame mode shapes and gives a smaller maximum non-diagonal MAC matrix element. Also, as the number of sensors increases due to the addition of information to the Fisher matrix, the Fisher matrix determinant increases and second objective function decreases. On the other hand, by reducing the number of available sensors, a limited number of modes can be detected. In this case, the best way to receive the structural modal information would be to place more available sensors on the lower and upper floors of the shear frame. Eventually, it can be concluded that the use of IDC and SEREP methods to select master degrees of freedom for sensor installation leads to better identification of modal parameters of the structure. Therefore, the capabilities of these methods can be used to identify damage in structures with a limited number of sensors.

The main problem of water resources planning is the inappropriate allocation between different consumers. Water allocation planning is a complex, multi-variable, and multi-constraint problem, which requires advanced optimization methods to be solved. Classical optimization methods are facing some limitations such as being trapped in local optimum points, and difficulties in handling different variables. In this paper two of these methods including particle swarm optimization, PSO and multiobjective non-dominated sorting genetic algorithms, NGGAII were explored and their efficiency in optimization water reservoir operation problems is compared. Dealing with the necessary of multiobjective programing accuracy, two single objective models was developed separately using PSO to verify the NSGAII results.

Tanks in water distribution networks are used to store water for emergency conditions, fire flow demand and demand oscillations controll. Construction of tanks spends a lot of money and therefore using whole volume of tanks is essential while operation. Otherwise, if tank volume will be more or less than what is required during operation, tank reliability is reduced. Accordingly, in this paper, a new relationship for tank reliability according to water level variation in tanks is defined. Therefore, maximum water level in tanks is defined as the decision variable. The definition of tank reliability is as follows. At first, the values of maximum level for each tank is computed such a way that optimal use is provided from balancing volume of tanks. In fact, for these maximum level values, maximum reliability is acheived for each tank. Now if during optimization process, a value lower than these computed maximum level is selected for decision variables, tank reliability is reduced. To compute the value of tank reliability, the values of tank water level for the selected decision variables is devided by the values of tank water level for maximum tank reliability. Also, because water level variation can effect on pressure and water age in demand nodes, this effect is investigated by considering hydraulic and quality reliability. In fact, variation of water level in tanks changes node demand pressures and in result actual node demands. Also, variation of water level or on the other hand variation of storage volume affects on water age in demand nodes. Besides, in order to investigate the simultaneous effect of water level variation on hydraulic and quality reliability, a relationship is also defined for integrated reliability. Definition of integrated reliability is to investigate whether there is optimum maximum tank level values that both hydraulic and quality reliability is improved simultaneusly while tank construction costs is minimum. Optimal management of tanks in water distribution networks to provide required water of consumers with desired quality is of high importance. To acheive this, optimization is defined as a powerful tool. In this paper, by focusing on operation phase, multiobjective optimization of water distribution performance is performed in which tank costs is considered as the first objective and tank reliability, node hydraulic reliability, node water age reliability and integrated reliability is considered as the second objective. Ant colony algorithm is codified in Microsoft Visual C for optimization due to its simplicity and high performance. The validity of the edited algorithm is tested on mathematical functions and proved to be applicable on water distribution networks. The created trade-off curve from multiobjective optimization helps the decision makers to select the top choice based on the importance of their own criterion whether it is hydraulic or quality.

Stiffness and strength of a structure are two vital and important parameters. Always designers try to find a method to produce equilibrium between these. Recent decade's investigations focused on optimization of stiffness. In these structures we can not ensure that structure has adequate strength or not. So survey of strength is a very important topic. To maximize the strength we have to minimize the maximum stress of the structures. In all of old researches stress is a constraint rather than objective in the optimization processes. Although this may guarantee the stress within a prescribed constraint (generally less than some limit), it cannot always make the maximum stress a minimum. In optimization of a single criterion (stiffness or strength), other criteria can not be maximum. Hence, multicriteria optimization is a logical method. In this research, we use Evolutionary Structural Optimization (ESO) method for size optimization to maximize stiffness and strength of structures. To obtain global criteria, we use weighting method and weight factors. A linear combination of both weighted criteria produces global criteria. In order to calculate suitable weight factors for any structure that we use in research, we examined different value of these and optimize the structures for this values. By comparison of the results, we select the best value of weight factors that can optimize strength and stiffness of the structure. This research has two important a) Thickness distribution at different positions of structure according to stiffness or strength alone does not optimize other criteria in order to have a structure with optimum stiffness and strength; we have to optimize two criteria simultaneously.b) Programming ESO method for multicriteria optimization is very easy and simple. We used a MATLAB code for the FE analysis and a loop for repeating the optimization procedure. Optimization of stiffness alone does not lead to a structure with adequate and vice versa. In order to have a structure with adequate stiffness and strength, we have to optimized the these criteria simultaneously. ESO is a very easy method for multicriteria optimization and programming. We optimize topology of the structures in this research.