Cross-model Cross-mode Method Research Articles

Structural damage identification by a cross modal energy sensitivity based mode subset selection strategy

This paper presents a strategy specialized for modal energy (ME) based methods, including modal strain energy (MSE) and modal kinetic energy (MKE), to select the best mode subset prior to damage identification. The damages due to the changes in stiffness and mass of structural members are both considered. In order to apply the proposed scheme to a more general situation, the cross modal energy (CME) sensitivity instead of the usual ME sensitivity is derived and designated as a sensitivity index. According to this index, the mode combinations (MCs) that are more sensitive to stiffness and mass changes are retained, while the remaining MCs that complicate the process of damage detection are eliminated. One of the important applications of the proposed mode subset selection strategy (MSSS) is to optimize the Cross-model cross-mode (CMCM) system by eliminating some redundant equations, thereby improving the performance of the CMCM method and reducing the computational burden. Numerical and experimental studies are carried out to prove the effectiveness of the proposed scheme. The results show that the performance of the CMCM method has been significantly improved after adopting the MSSS.

Employing an improved cross model cross mode algorithm for damage detection of a steel offshore platform frame using experimental data

In this study, a modified cross model cross mode (CMCM) algorithm is developed to identify and localize the damage based on the changes made in modal physical parameters of a steel platform frame. The research is mostly focused on the first three stages of structural health monitoring due to their close relation to the structural dynamic characteristics and numerical modeling aspects. For this purpose, experimental modal analysis is implemented on a physical model of a 2D jacket platform frame. The finite element analysis is developed based on the recorded data to validate the proposed algorithm. The numerical model is updated employing the improved CMCM method and the results are compared to those of the traditional method. The effect of the noisy data on the performances of the improved method is also investigated. The results indicate the success of the proposed method in identifying the location and the severity of the damage. It is also concluded that the improved iterative methods include advantages such as time saving and higher accuracy in comparison with the traditional one.

Damage detection of shear buildings through structural mass-stiffness distribution

For structural damage detection of shear buildings, this paper proposes a new concept using structural element mass-stiffness vector (SEMV) based on special mass and stiffness distribution characteristics. A corresponding damage identification method is developed combining the SEMV with the cross-model cross-mode (CMCM) model updating algorithm. For a shear building, a model is assumed at the beginning based on the building's distribution characteristics. The model is updated into two models corresponding to the healthy and damaged conditions, respectively, using the CMCM method according to the modal parameters of actual structure identified from the measured acceleration signals. Subsequently, the structural SEMV for each condition can be calculated from the updated model using the corresponding stiffness and mass correction factors, and then is utilized to form a new feature vector in which each element is calculated by dividing one element of SEMV in health condition by the corresponding element of SEMV in damage condition. Thus this vector can be viewed as a damage detection feature for its ability to identify the mass or stiffness variation between the healthy and damaged conditions. Finally, a numerical simulation and the laboratory experimental data from a test-bed structure at the Los Alamos National Laboratory were analyzed to verify the effectiveness and reliability of the proposed method. Both simulated and experimental results show that the proposed approach is able to detect the presence of structural mass and stiffness variation and to quantify the level of such changes.

Structural model updating of an offshore platform using the cross model cross mode method: An experimental study

The present paper validates a recently developed cross model cross mode (CMCM) model updating method for an offshore platform structure by using experimental data. First, the CMCM model updating method, where a modal expansion technique is used to overcome the spatial incompleteness problem, is briefly summarized. One particularly novel development is that a simplified added-mass model of the surrounding water is proposed, and the updating coefficients are directly incorporated into the CMCM procedure. Next, a small-scale offshore platform is fabricated. Model tests are experimentally conducted for four cases, including two cases in air with and without deck mass and two cases in water under hammer and wave excitation. Finally, the first three orders of modal parameters are identified. The CMCM method in combination with the modal expansion technique is used to update the structural models. The results demonstrate that the present method is effective for the model updating of offshore platform structures with a minimal amount of lower-order, spatially incomplete experimental modal data.

Model updating and parameters estimation incorporating flexible joints and boundary conditions

Development of efficient model-updating and parameter estimation techniques is of great importance for civil structures. The present paper extends a recently developed cross-model cross-mode (CMCM) method for model updating and parameter estimation, when connectivity flexibility and boundary conditions are incorporated. First, the stiffness matrix of a beam member with semi-rigid joints at both ends is formulated, where the semi-rigid joints enable connections to be modelled as partially restrained. Second, boundary substructure elements are used to capture the stiffness and mass properties of the foundation. Finally, the model updating and parameter estimation of connection flexibility and boundary conditions are incorporated into the CMCM method. To validate the capability and effectiveness of the developed algorithm, numerical studies are conducted on a 2D bridge structure based on data generated from finite-element models. Numerical results demonstrate that the present method is effective for model updating and parameter estimation, when incorporating connectivity flexibility and boundary conditions.

Finite Element Model Updating of a Steel Jacket Scale Model

In this paper, the finite element model of a steel jacket scale model is updated using modal parameters identified by modal test. Updating parameters are selected based on sensitivity analysis by solving modal energies. And then, a two-steps updating process is carried out using different parameters and the Cross-Model Cross-Mode (CMCM) model updating method is applied in each step. Results indicate that with selection of updating parameters and sensitivity analysis, CMCM method can update the finite element model with physical meanings.

Fuzzy cross-model cross-mode method and its application to update the finite element model of structures

As a novel updating technique, cross-model cross-mode (CMCM) method possesses a high efficiency and capability of flexible selecting updating parameters. However, the success of this method depends on the accuracy of measured modal shapes. Usually, the measured modal shapes are inaccurate since many kinds of measured noises are inevitable. Furthermore, the complete testing modal shapes are required by CMCM method so that the calculating errors may be introduced into the measured modal shapes by conducting the modal expansion or model reduction technique. Therefore, this algorithm is faced with the challenge of updating the finite element (FE) model of practical complex structures. In this study, the fuzzy CMCM method is proposed in order to weaken the effect of errors of the measured modal shapes on the updated results. Then two simulated examples are applied to compare the performance of the fuzzy CMCM method with the CMCM method. The test results show that proposed method is more promising to update the FE model of practical structures than CMCM method.

Model Updating and Damage Detection Using Cross Model Cross Mode Method for 3D Frame Structures

For the health monitoring of civil structures, the study of finite element model updating or damage detection mainly focuses on undamped systems. Thus, their objective has been exclusively restricted to the correction of the mass and stiffness matrices. In contrast, this paper performs the model updating and damage detection for damped structures. A theoretical contribution of this paper is to extend the cross-model cross-mode (CMCM) method to simultaneously update the mass, damping and stiffness matrices of a finite element model when only few spatially incomplete, complex-valued modes are available. Numerical studies are conducted for a five-story frame structure with multiple damaged elements. The numerical results reveal that applying the CMCM method, together with an iterative Guyan reduction scheme, can yield good damage detection in general.

Employing incomplete complex modes for model updating and damage detection of damped structures

In the study of finite element model updating or damage detection, most papers are devoted to undamped systems. Thus, their objective has been exclusively restricted to the correction of the mass and stiffness matrices. In contrast, this paper performs the model updating and damage detection for damped structures. A theoretical contribution of this paper is to extend the cross-model cross-mode (CMCM) method to simultaneously update the mass, damping and stiffness matrices of a finite element model when only few spatially incomplete, complex-valued modes are available. Numerical studies are conducted for a 30-DOF (degree-of-freedom) cantilever beam with multiple damaged elements, as the measured modes are synthesized from finite element models. The numerical results reveal that applying the CMCM method, together with an iterative Guyan reduction scheme, can yield good damage detection in general. When the measured modes utilized in the CMCM method are corrupted with irregular errors, assessing damage at the location that possesses larger modal strain energy is less sensitive to the corrupted modes.

Using incomplete modal data for damage detection in offshore jacket structures

The development of robust techniques for early damage detection for offshore structures is crucial to avoid the possible catastrophe caused by structural failures. This article applies the cross-model cross-mode (CMCM) method for damage detection that is capable of identifying the damage to individual members of offshore jacket platforms, when limited, spatially incomplete modal data is available. Basically, the CMCM method is classified as a direct, physical property adjustment model updating method. Implementing this method requires only a few modes measured from the damaged structure. In dealing with spatial incompleteness, this paper investigates both model reduction and modal expansion techniques. Specifically, either Guyan (static condensation) or SEREP (system equivalent reduction expansion process) transformation matrix, between the master and slave degrees-of-freedom, is employed in the model reduction or modal expansion process. One theoretical development is an iterative procedure to compute the transformation matrix associated with the (unknown) damaged structure. Numerical studies are conducted for a jacket platform with multiple damaged members based on synthetic data generated from finite-element models. The results suggest that (i) Guyan scheme always outperforms SEREP, (ii) model reduction is always better than modal expansion, and (iii) the CMCM method in conjunction with iterative Guyan reduction approach yields the best damage location and severity estimate.

Simultaneous Mass, Damping, and Stiffness Updating for Dynamic Systems

different modes associated with the mathematical and experimental models, respectively. Two numerical examples are demonstrated: a 4-degree-of-freedom mass–spring–damper system and a 30-degree-of-freedom finite element model for a cantilever beam. The numerical updating by the cross-model cross-mode method is excellent for all system matrices when the measured modes are spatially complete and noise free. The cross-model cross-mode method, together with the Guyan reduction scheme, also performs reasonably well under a spatial incompleteness situation.

Cross-model cross-mode method for model updating

Model updating has become a common method to improve the correlation between finite-element models and measured data. This paper develops a direct, physical property adjustment model updating method, named as cross-model cross-mode (CMCM) method. This new method is capable of updating the mass and stiffness matrices simultaneously based on very limited measured mode shapes and modal frequencies. Two structural models, a shear building model and a three-dimensional frame structural model, are demonstrated in the numerical examples. Numerical results indicate that an excellent updating is achievable by applying the CMCM method.