One way to diagnose damage in structures is to use their modal strain energy change index. Since occurrence of damage in parts of a structure, in addition to changing the modal strain energy of the damaged parts, also changes the modal strain energy of the healthy parts, in the vicinity of the main damaged elements, false damaged elements will appear, which makes it difficult to identify the main damaged elements. To solve this problem, in the present work a two-step method has been used to determine the location of the damage on the deck of a concrete bridge. In the first step, by finite element modelling and performing the modal analysis, the initial damage index of different parts of the bridge deck is determined based on modal strain energy changes, using a few vibration mode shapes. In the second step, using weight coefficients, the modified damage index for each element is calculated separately, minimizing the number of false damaged elements. The proposed method for calculating weight coefficients is simple and at the same time accurate. The efficiency of this method was investigated in several damage scenarios with an intensity of only 5% in different parts of the deck of bridge. The results showed that, while the initial damage index could not distinguish even 3 damaged elements in the bridge deck from the healthy elements, the modified damage index was able to identify up to 7 damaged elements in different parts of the bridge deck with good accuracy using only 2 mode shapes.

D a m a g e d e t e c t i o n a n d a s s e s s m e n t i n s t r u c t u r e s h a v e i n c r e a s i n g l y r e c e i v e d t h e a t t e n t i o n o f r e s e a r c h e r s, d u e t o t h e i r r o l e i n e c o n o m i c a l a s p e c t s a n d e m e r g e n c y m a n a g e m e n t a f t e r e a r t h q u a k e s. T h e m a j o r i t y o f s t u d i e s o n v a r i o u s m e t h o d s o f d a m a g e d e t e c t i o n r e l y o n t h e m e a s u r e d v i b r a t i o n r e s p o n s e p a r a m e t e r s o f s t r u c t u r e s, a s a r e s u l t o f t h e i r a p p l i c a b i l i t y t o l a r g e a n d c o m p l e x s t r u c t u r e s.W h i l e m o s t r e s e a r c h h a s c o n c e n t r a t e d o n o n e o r t w o d i m e n s i o n a l s t r u c t u r e s, t h e r e a r e f e w s t u d i e s a v a i l a b l e i n t h e l i t e r a t u r e o n t h r e e d i m e n s i o n a l s t r u c t u r e s. T h e p u r p o s e o f t h i s s t u d y i s t o a p p l y m e t h o d s b a s e d o n m o d a l p a r a m e t e r s t o t h r e e d i m e n s i o n a l r e i n f o r c e d c o n c r e t e f r a m e s. T o a c h i e v e t h i s o b j e c t i v e, n u m e r i c a l r e s u l t s a r e g e n e r a t e d f o r a 3D o n e s t o r y f r a m e w i t h f i v e d i f f e r e n t s c e n a r i o s o f d a m a g e. T h e a p p l i c a t i o n o f v i b r a t i o n m e t h o d s, e s p e c i a l l y ``m o d e s h a p e c u r v a t u r e'', a n d m e t h o d s b a s e d o n ``m o d a l s t r a i n e n e r g y'' i n d a m a g e l o c a l i z a t i o n, a r e a l s o i n v e s t i g a t e d. T o i m p l e m e n t t h e s e m e t h o d s r e q u i r e s o n l y a s m a l l n u m b e r o f m o d e s h a p e s i d e n t i f i e d f r o m b o t h d a m a g e d a n d b a s e l i n e s t r u c t u r e s. T h e m o d e s h a p e s a r e d i v i d e d a c c o r d i n g t o t h e i r d e g r e e s o f f r e e d o m i n o r d e r t o i m p r o v e t h e a c c u r a c y o f t h e m o d e s h a p e c u r v a t u r e i n d i c a t o r m e t h o d. I n a d d i t i o n, t h e a c c u r a c y o f t h e m o d a l s e n s i t i v i t y m e t h o d h a s b e e n i n v e s t i g a t e d f o r t w o b e h a v i o r a l m o d e s (a x i a l a n d f l e x u r a l) o f s t r u c t u r e s. F u r t h e r m o r e, t h e s t i f f n e s s m a t r i x h a s b e e n d e c o m p o s e d t o i t s c o m p o n e n t s (a x i a l a n d t r a n s v e r s a l t e r m s) i n m e t h o d s b a s e d o n m o d a l s t r a i n e n e r g y. I t s h o u l d b e n o t e d t h a t t h e a c c u r a c y o f t h e r e s u l t s i s r e l a t e d t o d a m a g e l o c a t i o n. O n t h e o t h e r h a n d, v a r i o u s k i n d s o f i n d i c e s u s e d i n t h i s s t u d y h a v e n o t i c e a b l e d i f f e r e n c e s i n e l e m e n t s, w h i c h a r e i n t h e p r o x i m i t y o f t h e p r i m a r y d a m a g e l o c a t i o n. T h e r e s u l t s r e v e a l t h a t t h e m o d e s h a p e c u r v a t u r e c h a n g e o f r o t a t i o n a l d e g r e e s o f f r e e d o m a n d m o d a l s t r a i n e n e r g y c h a n g e a s s o c i a t e d w i t h t h e a x i a l t e r m o f t h e s t i f f n e s s m a t r i x h a v e a n a c c e p t a b l e a c c u r a c y i n d a m a g e l o c a l i z a t i o n. I n a d d i t i o n, i t c a n b e c o n c l u d e d t h a t l o c a l i z a t i o n o f d a m a g e a t t h e b a s e o f c o l u m n s v i a i n d i c e s a p p l i e d i n t h i s s t u d y i s m o r e a c c u r a t e c o m p a r e d t o o t h e r l o c a t i o n s.

Bridges are exposed to various micro and small damages during their service life. Due to the importance and role of these structures in transportation on roads, timely detection of damages in them has a special place. This research presents an innovative and efficient method for diagnosing and estimating micro and small damages to bridges. The proposed method is based on the combination of spectral finite element and modal strain energy-based damage index to determine the location of damages in the first step. Then the support vector regression technique is used to estimate the severity of damages in the second step. A new eight-node element with spectral finite element characteristics is defined in OpenSees software. Then, micro and small damages are modeled in a single-span beam and a double-span steel beam with spring supports. In the first step, after modal analysis of the structures, the modal strain energy-based damage index is calculated to determine the location of the damages. In the second step, using the modal strain energy-based damage indices calculated in the previous step, the support vector regression networks are trained to estimate the severity of the damages. The results show very high accuracy and optimal performance of the proposed method.

Structural damage detection is based on that the dynamic response of structure will change because of damage. Hence, it is possible to estimate the location and severity of damage before and after the damage. In this study, damage detection issue based on modal parameters for an optimization problem using neural network and fuzzy genetic system offered and the effectiveness of these two methods in detecting the location and also the severity of the damage is assessed. For studying damage detection, the numerical model of the Crowchild bridge is made by its dynamic characteristics and has been used for various damage scenario detection. In the first method, the natural frequency, and in the second method, modal strain energy is selected as a damage indicator. Using simplified models to study the behavior of bridges due to their simplicity and acceptable accuracy is very common. The results show that the Genetic Fuzzy System can be more successful when a simplified model is used. Comparing the results of two failure detection methods shows that the fuzzy system is less sensitive to existing uncertainties.

A set of second-order differential equations (the initial value problem) is used to analyze the vibrations of structures. This method is based on changing the second-order differential equations to the eigenvalue problem, which is usually used for modal analysis of structures. This problem involves a matrix equation with mass and stiffness as coefficient matrices. Changes in some stiffness matrix arrays change eigenvalues ​​and eigenvectors, and changes in stiffness matrices indicate damage to one or more structural members. Therefore, identifying modified arrays is very useful for monitoring the health of structures. Modified stiffness array arrays can be obtained by comparing new eigenvalues ​​and eigenvectors with old ones. The Stubbs Index (Modal Strain Energy) Stubbs (MSE) uses only special vectors to identify injuries. In the improved modal strain energy method (IMSE) proposed by Lee et al., In addition to special vectors, special values ​​are also entered in relation to the damage index. In this research, a new injury index is presented with the development of the above two indicators, which show more accurate results than them. In this study, the health monitoring of a template platform structure of Forouzan Persian Gulf oil field is compared to compare the accuracy of these three indicators. The results show that the new method is more accurate than the Stubbs and IMSE indices, especially in the presence of multiple injuries.

Changes in modal strain energy of elements before and after damage is a robust damage detection index. However, in structures like double layer grids which have large number of elements, this method has some problems. First, In large structures this method needs more mode shapes to detect damage through modal strain energy method which in practice is difficult to determine. Second, this method introduce some healthy elements as damaged element. To overcome these problems, in this paper a two stage damage detection technique based on modal strain energy method is presented for detecting damage in double layer grids. First, the Modal Strain Energy Based Index (MSEBI) for each mode shape is determined. Then a data fusion technique based on Bayesian theory is used to combine MSEBI values obtained from each mode shape to find damaged elements. Then Charged System Search (CSS) optimization method which is a powerful optimization method is employed to optimize an objective function based on natural frequency to determine damage severity of damaged elements. To demonstrate the performance of the proposed method, a large double layer grid with 1536 elements and different single and multiple damage cases is considered. Numerical results show that the proposed method can successfully find damaged elements and their severities using only few first numbers of mode shapes and frequencies.

One of the challenges in the health monitoring of bridge structures is the "data" extraction from the structure. This is done by sensors in the structure. The layout and use of the fewest possible number of sensors, so as to provide the most needed data on structural status, has always been of interest. There are shortcomings in the methods used to determine the location of sensors in bridges, such as the use of one optimization indicator, determination of the number of sensors experimentally, high environmental noise, and a long calculation time. In order to overcome these shortcomings, a new MSE-MGA (Modal Strain Energy-Modified Genetic Algorithm) method is proposed in this study. In this method, two modal strain energy indices and modal contribution coefficient are used to reduce the noise effect of vehicles passing through. All the appropriate locations of the sensors are selected by these indices, and then the optimal number of sensors and their location are determined by using the genetic algorithm. The results show that increasing the number of sensors from a given optimal value has no effect on increasing the required data. Also, the simultaneous use of two optimization indices has resulted in the elimination of a large number of inappropriate points for sensor placement, resulting in a significantly reduced computational time. To investigate the performance and practical application of this method, a model of a steel bridge is modeled and the optimal number of sensors and their layout are determined.

Foroozan platform is one of the most important Iranian offshore facilities lies along the border of Iran and Saudi Arabia. As time passes by, the possibility of presence of some damage in the structural members of this platform increases. As a consequence of these damages, the operation of the platform may be disrupted and if the damage grows, especially in sensitive areas such as deck, joints or splash zone that are prone to failure, cause more damage in the future. This highlights the necessity of structural health monitoring of this platform. One of the most common structural health monitoring techniques is the modal strain energy-based damage index which is known as Stubbs index. In recent years, modifications have been made to original version of this index, one of which is to consider the natural frequencies in determining the location of damage. In this paper, using the improved modal strain energy method and considering the natural frequencies in determining the location of damage, the location and severity of damage in the Foroozan platform have been identified. One of the differences between this study and similar studies is the large number of elements of this real platform. The results showed that the improved method has a higher accuracy in locating the damage than the original method (Stubbs index). Also, single and multiple damages, with low and high intensity, were predicted with appropriate accuracy by this method.

The foundation of offshore wind turbines has various structures at different depths of the sea. At depths between 30 and 50 meters, jacket substructure is recommended as an economical solution for offshore wind turbines. During their life cycle, the substructures of offshore wind turbines are exposed to a couple of damage sources which can reduce their service life. This problem became more severe in sensitive areas such as deck, joints, or splash zone that are prone to failure. Modal strain energy (MSE) method is one of the non-destructive and practical methods in which the location and the severity of the damage is determined using changes in the dynamic properties of the structure. In recent years, some modifications have been made to the original version of this method, one of which is to consider modal frequencies in determining the location of damage. In this paper, the damage location and its severity are identified for members located in deck and splashing zone in tripod substructure of wind turbine using improved modal strain energy method (IMSE). The results showed that the improved method is more accurate in locating the damage than the original method (Stubbs index). Also, single and multiple damages, both with low and high intensity, were predicted with this method with appropriate accuracy.

The passage of personnel and the placement of facilities on the access stairs of offshore complexes have made it very important to identify damage to these components. The modal strain energy method is one of the non-destructive and practical methods that uses changes in the dynamic properties of the structure to identify the location and determine the severity of damage in the structure. In recent years, modifications have been made to the initial version of this method, one of which is to consider the natural frequencies in locating the damage. In this paper, using the improved modal strain energy method and considering natural frequencies, a new relationship is presented to more accurately identify the location of damage in the structure, and three different damage indices in the offshore platform access bridge structure are studied and compared. The results show that the average error to accurately identify the location of damage in the average Stubbs index, the improved method and the novel method are 3.55, 2.82, and 2.21 percent, respectively, so the novel method can more accurately identify the location of damage in the structure. Also, comparing the results of different cases shows that the average damage location error decreases with increasing damage severity. The accuracy of identifying the location of the damage also increases when moving away from the supports.