Abstract
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.
 Keywords: Offshore platform, Access bridge, Damage detection, Improved modal strain energy, Stubbs index.

INTRODUCTION

One of the most important components of marine platforms is the access bridges between them. In addition to being used for the passage of personnel, these bridges are also the place for the passage of facilities. Due to the location in the corrosive environment of the sea and also the possibility of various damages to these members that cause huge financial and life losses, it is very important to check and control the health of these structures.
To monitor the health of structures, various methods are used. One of the methods used in this regard is visual inspection, which leads to obtaining important information about the health of the structure. In addition to its special advantages, this method requires a lot of time and money. Also, due to the unavailability of some sections of the structure, it is not possible to detect the damage in them using visual inspection, and it is not possible to detect the internal damage of the structure and its origin using visual inspection. For this reason, in recent years, a lot of attention has been paid to non-destructive damage identification methods to increase safety and ensure the existing condition of the structure. One of these methods is to use the vibration characteristics of the structure to evaluate the damage at the structure level, which is used as a complementary solution next to visual inspections. In all vibration-based damage detection methods, the structure's modal characteristics (natural frequency, mode shape, and modal damping) are a function of its physical characteristics. Therefore, by using the change in the static or dynamic response of the structures, the change in their physical characteristics and as a result the structural damage can be identified in the initial stages, the maintenance costs of the structure can be reduced and the failure of the structure can be prevented.
The studies conducted in the past show the high accuracy and ability of the modal strain energy method in detecting damage in marine structures. Considering the long operational life of the country's offshore platforms and the existence of possible damages in these platforms, as well as the importance of access bridges between offshore platforms, in this article a comparison between the accuracy of different damage detection methods, including the Stubbs index method, the improved strain energy method and the new recommended method has been done by the authors to use this method in the identification of real damages in marine platforms. In the Stubbs index method, as the primary method based on modal strain energy, only the shape of the structure's vibration modes has been used to identify damage. In the improved method, by using the natural frequencies of the structure, a more accurate estimate has been provided to identify the damage in the structures. This research tries to provide better results, especially for multiple damages in structures with a large number of members, by improving the improved method.

METHOD AND MATERIAL

When an elastic object is subjected to a force, tension is created in it, the object changes its shape and the state of its various points changes compared to the initial state. Changing the point of effect of forces applied to the body causes some work to be done when they are applied. The aforementioned work, which is accompanied by the change of shape of the object in the state of tension, causes the storage of some energy in the form of elastic energy in the object, which is called strain energy. Modal strain energy is a situation where no force is applied to the structure and the structure is in a state of free vibration, and the modal strain energy of each member can be obtained by dynamic analysis and solving the presented relationships. Damage in a structure usually causes a decrease in the stiffness of the structure and does not affect the mass matrix of the structure.
In this part, using the modal strain energy method, the damage in the structure has been identified. This damage is defined by reducing the stiffness (reduction of the elastic modulus) of the member and the finite element model of the structure is written in MATLAB software. So, for example, the presence of 20% damage in member number 15 causes the difficulty level of that member to reach 80% of the initial state. Validation of the results was done by comparing the assumed amount of damage and the amount of damage obtained from the written program.
The structure has 100 members and is modeled as a bending frame. The 4 connection points of the structure to the marine platform are modeled as girders. The rows and columns related to the supports have been removed from the mass and stiffness matrices of the structure. The elastic modulus (E) is equal to 210 GPa and the density of steel is equal to 7850 kg/m3.

DISCUSSION AND CONCLUSION

With the passing of the service life of marine structures, the need to monitor their health is felt to identify the place of damage under the structures. The communication bridge between marine platforms is of great importance considering that it is the place where personnel and pipelines pass. However, it has been less studied in previous studies. In this research, using the modal strain energy method, which is one of the most suitable methods for non-destructive damage identification in structures, single and multiple damages were identified in the communication bridge in a marine platform, and the results of the three Stubbs index methods, the strain energy method The improved modal and the new method presented by the authors were compared with each other. It was also tried to include different modes of damage; members whose failure causes more damage. The results obtained from this article are:
Considering that the average error for the accuracy of identifying the location of damage in the Stubbs index, the improved method and the new method are 3.55, 2.82 and 2.21% respectively, so the new method can identify the location of damage in the structure with more accuracy.

Comparison of the results of different modes shows that the average damage location error decreases with increasing damage severity.
In the case of minor and small injuries that are in the initial stages of formation and growth, as well as large and highly developed injuries, the new method can identify the location of the injury with a high ability.
The accuracy of damage location using the modal strain energy method is higher in horizontal members than in restrained members.
The accuracy of this method is higher for members that are on a horizontal plane than for members that connect the upper and lower members.
The accuracy of identifying the damage location increases by moving away from the supports.
The new method identifies the location of the damage in the structure with higher accuracy and it is recommended to use this method instead of Stubbs index and improved modal strain energy methods.


ACKNOWLEDGEMENT

The authors would like to thank the Iranian Offshore Oil Company (IOOC) for providing the drawings of the access bridge of the Foroozan Oil complex.