damage detection in flexible structures is a research field and an industrial favorite. If damages in structures, air crafts and ships are not detected and repaired, they will possibly collapse. damage detection in flexible structures using vibration signals and in particular modal test data is the most suitable method. This method is in fact an NOT technique. In this we will present an analytical method for damage detection in .undamped flexible structures using modal data (natural frequencies. and mode shapes). Reviewing past theories, eigenvalue and igenmode, sensitivity equations are used to derive a system of equations .relating the shifts in natural frequencies/mode-shapes to elemental physical parameters. damage detection is then carried out by solving the extracted system of equations. Also, modal expansion and Nelson method are examined and the better method of solving for eigenmode perturbation is chosen. It is recommended that in solving for repeated eigenmode perturbation with generalized inverse techniques, orthogonally condition between theoretical mode shapes must be satisfied. The presented mathematical relations are applicable for trusses, beams and frames but the principles of the theory is general. Finally an experimental investigation is carried out and the position of a crack in a frame with this theory detected.

This paper proposes a method for Structural damage detection through the sensitivity analysis of modal shapes in the calculation of modal strain energy (MSE). For this purpose, sensitivity equations were solved to determine the strain energy based on dynamic data (i.e., modal shapes). An objective function was then presented through the sensitivity-based MSE to detect Structural damage. Due to the nonlinearity of sensitivity equations, the objective function of the proposed formulation can be minimized through the shuffled shepherd optimization algorithm (SSOA). The first few modes were employed for damage detection in solving the inverse problem. The proposed formulation was evaluated in a few numerical examples under different conditions. The numerical results indicated that the proposed formulation was efficient and effective in solving the inverse problem of damage detection. The proposed method not only minimized sensitivity to measurement errors but also effectively identified the location and severity of Structural damage.

In recent years, damage identification of structures becomes more attractive for researchers in order to quantify the condition of Structural system during service life. Moreover, identifying the damage location and severity is very important after disasters such as earthquake and terrorist attak. Structures can also be damaged by normal activity such as corrosion, aging, fatique, wind, waveload, etc. Therefore, the Structural health monitoring is an emerging field to ensure good performance of structures. In this paper, identification of the location and severity of damages in structures are studied by analytical method using artificial bee colony optimization (ABC). In the analytical method, the mass and stiffness matrices of structure can be determined by the finite element procedure. Considering the stiffness matrix of healthy structure and that of the damage structure, the location and severity of the damage can be determined. It is assumed that the global mass matrix remains unchanged after the damage occurs in the structure. The natural frequencies and mode shapes of damaged structure can be obtained by measurement. In the study, the damage characteristics are known. Then by applying the eigenvalue equation, the stiffness matrix is determined for damaged structure. Finding the location of damage is introduced as an inverse problem. The conventional methods are very expensive and time consuming, while meta-heuristic methods are capable to solve complex optimization problems. Swarm intelligence algorithm introduces the collective behavior of social insects colonies to solve optimization problems. Artificial bee colony algorithm is an evolutionary computing method, which was developed, based on the intelligent foraging behavior of honeybee swarm. Each food source is considered as a possible solution. The location and quality of the nectar from the flower is related to the damage properties and fitness function, respectively. The dimension of every artificial employed bee is equal to the number of member of the structure. Then quality value of the food source is evaluated by the fitness function. The best fitness value is memorized in each search. When the fitness value is improved after a predefined iteration, the new possible solution will be considered. In the ABC process, the number of food source, the limit and the maximum cycle number are three control parameters. In the optimization problem, applying a proper objective function is one of the indispensable part of the process. Since the Structural damage detection is a highly nonlinear problem, a proper objective function can detect the damage accurately and quickly. There are various methods for damage detection, which generally can be classified into two categories, static and dynamic method. Because of the efficiency of the dynamic method, the objective function is selected based on the dynamic technique, which utilizes the eigenvalue problem. In the mathematical equation of the objective function, the mass and stiffness matrix of healthy structure is defined by finite element method. The natural frequencies and mode shapes obtained by the measurement or modeling the structure. The stiffness matrix of damaged structure is determined with the optimization algorithm to minimize the objective function. In a measurement test, the used sensors cannot detect all of the degrees freedom of a structure, therefore the obtained information in measurement include a limited number of frequencies or mode shapes. In addition, to avoid a time consuming process, it may be decided to utilize only a limit number of frequencies obtained by the measurement. The system equivalent reduction expansion process (SEREP), which is an accurate and efficient technique of model reduction, is utilized in the paper. Moreover, the damage detection is examined through three numerical examples, plane and space truss and palne frame, each one has two damage scenarios, which include noisy measurement data. The results indicate that the proposed method is a powerfull procedure to detect damages in structures.

In this paper, a new method is introduced for recognition, location, and severity of damage in engineering stochastic structures, based on Autoregressive Moving Average (ARMA) parametric model and fuzzy classification. The important aspect of the proposed method is the fuzzy viewpoint on stochastic Structural damage diagnosis, which uses estimated ARMA parameters as feature vector. Moreover, the proposed method eliminates the optimization stage in finding membership functions parameters of fuzzy system by substituting the variances of estimated ARMA parameters directly as tuning parameters in membership functions. Another important aspect of the proposed method is the inessentiality to measure the excitation input force applied to the structure. A finite element model of a frame for diagnosing damage, wherein the damage is modeled by different stiffness reduction and location, is considered as a case study. After obtaining satisfactory results from numerical simulations, the proposed method is applied to a simply supported beam as an experimental laboratory structure, where the spring connected to the structure in different locations with different stiffness is considered as the damaged object. The results are considerably satisfactory.

damage identification in structures is one of the most important problems in Structural engineering because early damage detection prevents a catastrophic event in structures. In this paper, a new damage identification method proposed based on a short time load excitement and dynamic time history response of structures as a damage index. To solve the equation of motion of structure, the state space method was used. To identify damage in different structures, cascade-forward network has been used. In the training process of machine, the time history of dynamic responses used as input and damage states as output. The novelty of present method is the application of time history responses of structure under short time loading excitation to train cascade-forward network. To show the efficiency of presented method, three examples consist of a frame, bending plate and beam structures has been investigated. The obtained results reveal that proposed method is viable in detecting damage in different structures.

Structures suffer local damages due to various reasons. If these damages are not identified, they could be aggravated by natural disasters such as earthquakes or artificial factors such as unprincipled excavations, leading to total destruction of the structure. As a result, health monitoring in structures and their elements is regarded as one of the most significant research topics in civil, mechanical, and aerospace engineering. A damage detection method is to process the time or frequency domain of Structural responses. In this context, wavelet transform is one of the processing methods for both time and frequency domains, and many studies have utilized it to investigate Structural health monitoring. In this paper, a comprehensive review was conducted on the published studies. Besides, damage detection was performed by considering the vibration mode shapes of a defective cantilever, which were used as wavelet-transform input signals. The diagram of the detail coefficients resulting from the wavelet analysis of the input signal presented the maximum and minimum values in the defective positions. These findings support the efficiency of using wavelet transform in damage detection. Further, the sensitivity of damage detection based on wavelet transform to the severity of damages showed that with the rise in damage severity in a location, a larger relative jump occurs in the output signal of all modes.

Structural damage detection technique helps to locate and detect damage that occurred in a structure by using the observed changes of its dynamic and static characteristics. The existing approaches proposed in this area can be divided into two main groups: the dynamic damage detection methods using dynamic data and the static damage detection methods using static data (static displacement, static strain etc.). As the static equilibrium equation is only related to the Structural stiffness, accurate static displacement and strain data, it can be obtained rapidly and cheaply. For the reasons stated, the static damage detection methods have attracted more attention in recent years This paper presents a non-destructive global Structural damage detection and assessment algorithm using static data. A set of static forces is applied to a set of degrees of freedom and the static responses (displacements) are measured at another set of DOFs. Some simultaneous equations characterized from Changes in the static response which Structural damage caused. The method is determined damage as a change in the Structural stiffness parameter. Genetic Algorithms are powerful tools for solving large optimization problems. Optimization is considered to minimize objective function involve difference between the load vector of damaged and healthy structure. As mentioned above the static damage identification methods have many advantages, but some difficulties still exist. The main problems the first of all is, the information used in the static damage identification methods is less than in the dynamic identification, which makes it more difficult to get the ideal identification result. For example, the angular displacement or rotational freedom is difficult to determine. Second, the effects of the damage may be concealed due to the limited load paths. Lastly, the static data provide only the local Structural damage information, and the measured static data are very limited. So it is important to achieve the best damage identification and if the best result is obtained it means that the method is Reliable. damage defined by several scenarios included single scenario and multiple scenarios. For example in plane truss scenario two means: 40% damage in element No. 2 and 60% damage in element No. 10. Numerical results in this paper for a plane arch bridge and a plane truss show the ability of this method in detecting damage in given structures. Also Figures show damage detections in multiple damage scenarios have really nice answer. Even existence of noise in the measurements doesn’t reduce the accuracy of damage detections method in these structures.

Structural Health Monitoring (SHM) as a process in order to implement a damage detection strategy and assess the condition of structure plays a key role in Structural reliability. In this paper, we aim to present a methodology for online detection of damages which may occur during a strong ground excitation. In this regard, Empirical Mode Decomposition (EMD) is superseded by Ensemble Empirical Mode Decomposition (EEMD) in the Hilbert Huang Transformation (HHT). Albeit analogous, EEMD brings about more appropriate Intrinsic Mode Functions (IMFs) than EMD. IMFs are employed to assess the first mode frequency and mode shape. Afterward, Artificial Neural Network (ANN) is applied to predict story acceleration based on previously measured values. Because ANN functions precisely, any congruency between predicted and measured acceleration indicates onset of damage. Then, another ANN method is applied to estimate the stiffness matrix. Though the first mode shape and frequency are calculated in advance, the process essentially requires an inverse problem to be solved in order to find stiffness matrix, which is done by ANN. This algorithm is implemented on moment-resisting steel frames, and the results show that the proposed methodology is reliable for online prediction of Structural damage.