objective function

pavement management system (PMS) is the coordinate and regular process for doing all of the activities in roads. the main purpose of PMS is the prediction of pavement condition and the life cycle cost for determining the suitable time table. by true construction and management, we can provide a true decision making and sustainable maintenance for rehabilitation and reconstruction of the roads. The true construction and management. PMS is the economic method for maintenance of the one of the most important national funds. the aim of this research is that according to the uncertainty of the assigned budgets, the optimum management for M&R methods was done. at this research, the road of Khorramabad-dorood was selected as the case study. the objective function at this research is the promotion of the roads quality according to budget limitations. for calculations, GAMS software has been used. the results show that, how we can prioritize the budget among the several sections.

Engineering structures are prone to damage over their service life as a result of natural disaster so that damage spreading may lead to many casualties. In order to prevent these catastrophic events, early damage detection must be carried out. By considering these issues, numerous structural damage detection methods have been proposed by many researchers in the last few decades. Among all sorts of methods developed for damage detection in structures, vibration-based methods due to their simplicity and applicability are highly favored by many researchers. The basic conceptual of the vibration-based methods is that modal parameters (natural frequencies and their associated mode shapes) are functions of the physical properties of the structure (mass, damping, and stiffness). Therefore, changes in the physical properties will cause changes in the modal properties. A class of vibration-based methods is identified and damages are quantified using the model updating approach. In these methods, an objective function defined in terms of the discrepancies between the analytical model and real structural system is minimized as an optimization problem. In this paper, a novel model updating method is presented based on a structure’s main modal parameters (natural frequencies and their corresponding modal shapes). For this purpose, a hybrid vibration-based objective function is proposed to minimize the differences between the structure’s properties and the analytical model. A penalty function is integrated into the objective function to reduce the effects of noise in damage detection and uncertainties in the assessment procedure. The Teaching-Learning-Based Optimization (TLBO) algorithm is applied to solve this problem as an optimization problem. This algorithm is inspired by the traditional learning process of students in school. The two main stages of this algorithm are the effect of the teacher’s knowledge on student learning by the convergence strategy and students learning from each other by the divergence strategy. To evaluate the applicability of the proposed objective function in detecting the location and intensity of the damage, three numerical cases are considered. These cases include an 8-story shear frame, a continuous beam, and a spatial truss. Different challenges such as the effect of noise on measured data and the effect of the penalty-function on results of damage detection were considered. Furthermore, a comparative study is investigated between the proposed objective function and three other objective functions developed based the main model parameters. The results demonstrated that the proposed method is a reliable and stable technique in damage prognosis in structures.

Structural damage not only changes the dynamic characteristics of the structure, but also it may lead to complete destruction of the structure in some cases. Since early identification of damage can prevent such catastrophic events, structural health monitoring and damage detection has absorbed the attention of the civil, mechanical and aerospace engineers in the last decades. An effective health monitoring methodology not only can provide information about the global serviceability of the monitored structure, but also it can help the engineers to prepare cost-effective rehabilitation programs based on the obtained details about the health of the structure and its members. Different methods have been proposed for structural damage identification and estimation. Vibration-based methods consider the changes in the structural modal parameters, like natural frequencies and associated mode shapes, and/or their derivatives, like modal flexibility and residual force vector, for damage identification and quantification. Considering their acceptable sensitivity to wide-range of structural damages, vibration-based methods are considered as one of the most practical approaches for structural fault prognosis. Employing vibration parameters to define the damage detection problem as a model updating problem, is one of the well-known strategies that can return both the damage location and extent in different types of engineering structures. Such methods can be solved with optimization algorithms to find and report the structural damage in terms of the global extremums of a damage-sensitive objective function.
In this paper a new model updating approach for health monitoring and damage localization and quantification in engineering structures is presented. At first, a damage-sensitive objective function, which is based on the error function between the modal data of the monitored structure and its analytical model, is proposed. This objective function is formulated by means of the point-by-point matching strategy to minimize the difference between two models. Modal natural frequencies and the associated mode shape vectors are directly fed to the objective function and this can result in an easy assessment methodology to check the convergence rate of the function. Moreover, in such a case, the objective function uses the sensitivity of both these parameters for damage identification. The proposed inverse problem is solved using Moth-Flame Optimization (MFO) algorithm which has been inspired form spiral convergence of moths toward artificial lights. From mathematical point of view, updating the position of the moths with respect to the flames –which are the best solutions obtained during iterations–, reduces the probability of being trapped in the local extremum points and also, ensures the convergence of the algorithm to its global optimal solution. The applicability of the method was evaluated by studying different damage patterns on three numerical examples of engineering structures: a seven-story shear frame, a simple beam with 10 elements, and a planar truss with 29 elements. In all these studies, damages were simulated as reduction in the stiffness matrix of the damaged elements. Different issues, like noise effects, were considered and their impacts on the performance of the proposed method were investigated. Furthermore, comparative studies were carried out to discuss the advantages and drawbacks of the introduced method as well as the employed techniques. The obtained results indicate that the method is an effective strategy for vibration-based damage detection and localization in engineering structures.

In the last two decades, knowledge of the distribution of the ionospheric electron density considered as a major challenge for geodesy and geophysics researchers. To study the physical properties of the ionosphere, computerized ionosphere tomography (CIT) indicated an efficient and effective manner. Usually the value of total electron content (TEC) used as an input parameter to CIT. Then inversion methods used to compute electron density at any time and space. However, CIT is considered as an inverse ill-posed problem due to the lack of input observations and non-uniform distribution of TEC data. Many algorithms and methods are presented to modeling of CIT. For the first time, 2-dimensional CIT was suggested by Austin et al., (1988). They used algebraic reconstruction techniques (ART) to obtain the electron density. Since, other researchers have also studied and examined the CIT. Although the results of all studies indicates high efficiency of CIT, but two major limitations can be considered to this first, due to poor spatial distribution of GPS stations and limitations of signal viewing angle, CIT is an inverse ill-posed problem. Second, in most cases, observations are discontinuous in time and space domain, so it is not possible determining the density profiles at any time and space around the world.
In this paper, the method of residual minimization training neural network is proposed as a new method of ionospheric reconstruction. In this method, vertical and horizontal objective functions are minimized. Due to a poor vertical resolution of ionospheric tomography, empirical orthogonal functions (EOFs) are used as vertical objective function. To optimize the weights and biases in the neural network, a proper training algorithm is used. Training of neural networks can be considered as an optimization problem whose goal is to optimize the weights and biases to achieve a minimum training error. In this paper, back-propagation (BP) and particle swarm optimization (PSO) is used as training algorithms. 3 new methods have been investigated and analyzed in this research. In residual minimization training neural network (RMTNN), 3 layer perceptron artificial neural networks (ANN) with BP training algorithm is used to modeling of ionospheric electron density. In second method, due to the use of wavelet neural network (WNN) with BP algorithm in RMTNN method, the new method is named modified RMTNN (MRMTNN). In the third method, WNN with a PSO training algorithm is used to solve pixel-based ionospheric tomography. This new method is named ionospheric tomography based on the neural network (ITNN).
The GPS measurements of the Iranian permanent GPS network (IPGN) (1 ionosonde and 4 testing stations) have been used for constructing a 3-D image of the electron density. For numerical experimentation in IPGN, observations collected at 36 GPS stations on 3 days in 2007 (2007.01.03, 2007.04.03 and 2007.07.13) are used. Also the results have been compared to that of the spherical cap harmonic (SCH) method as a local ionospheric model and ionosonde data. Relative and absolute errors, root mean square error (RMSE), bias, standard deviations and correlation coefficient computed and analyzed as a statistical indicators in 3 proposed methods. The Analyzes show that the ITNN method has a high convergence speed and high accuracy with respect to the RMTNN and MRMTNN. The obtained results indicate the improvement of 0.5 to 5.65 TECU in IPGN with respect to the other empirical methods.
The GPS measurements of the Iranian permanent GPS network (IPGN) (1 ionosonde and 4 testing stations) have been used for constructing a 3-D image of the electron density. For numerical experimentation in IPGN, observations collected at 36 GPS stations on 3 days in 2007 (2007.01.03, 2007.04.03 and 2007.07.13) are used. Also the results have been compared to that of the spherical cap harmonic (SCH) method as a local ionospheric model and ionosonde data. Relative and absolute errors, root mean square error (RMSE), bias, standard deviations and correlation coefficient computed and analyzed as a statistical indicators in 3 proposed methods. The Analyzes show that the ITNN method has a high convergence speed and high accuracy with respect to the RMTNN and MRMTNN. The obtained results indicate the improvement of 0.5 to 5.65 TECU in IPGN with respect to the other empirical methods.

Due to high capacity and low energy consumption of Magneto-Rheological (MR) dampers، they are vastly being utilized to control seismic responses of structures. Presenting more precise methods for control algorithm، and including more realistic physical chara­­cteristics of MR dampers (e. g. nonlinearities، uncertainties and …) will help engineers to employ this kind of damper more efficiently. In order to achieve a controller that quickly and accurately determines the input voltages to the MR dampers، in this paper، a new strategy is proposed. The proposed strategy utilizes Adaptive Network based Fuzzy Inference System، (ANFIS) for optimal control of structures that are equipped with MR dampers. To obtain optimal time histories of demanded voltages، a new objective functional (J) that is a combination of some control criteria including reduction of relative drifts، absolute accelerations and absorbed energy is suggested. The optimization problem is such formulated that the set of equations of motions and equations representing the nonlinear model of MR dampers (here Bouc-Wen) are solved simultaneously. The optimization problem is solved by the enhanced method of steepest descend algorithm by Moharrami and Fayezi [3]. In this way، for a 15-storey building frame subjected to two deterministic earthquakes، the time histories of optimal input voltages of dampers are numerically computed. Next، the optimal voltages associated with the data on drifts، velocities and accelerations of stories are used as desired input- output data pairs to train the ANFIS as a quick and accurate controller. Three ANFISs were trained by different weights for drift (q1) and absolute acceleration (q2) data versus voltages. The weights of q1 and q2 controlling data were assumed to be (1،0)، (0،1) and (1، 0. 42) for ANFIS1، ANFIS2 and ANFIS3، respectively. Finally، to establish a context for assessment of the effectiveness of the proposed strategy in comparison with other conventional methods and to analyze the effects of weights in the objective functional، two numerical cases are presented. In the first case، the aforementioned 15-storey building frame is controlled against some earthquakes which were not applied for training process of ANFIS. Results show that ANFIS1 has decreased maximum and time-averaged relative drifts more than other control methods. In addition، this controller has somehow attenuated base shear similar to passive-on but has not been successful in reduction of absolute acceleration values. The ANFIS2 has controlled absolute accelerations better than other controllers whereas drifts have been reduced fairly well. By the ANFIS3، one can achieve reasonable decrease in all controlling criteria. Their values are between ANFIS1 and ANFIS2. It can be concluded that depending on the relative importance of control on drifts or accelerations of stories، one can chose proper weights for q1 and q2. In the second example، a benchmark six-storey building that is equipped with 2 dampers in the first، and 2 dampers in the second storey، has been controlled by the three proposed controllers. The results are compared with several conventional methods. The proposed strategy show more flexibility in reduction of the structural control criteria in comparison with some other conventional methods.