Cross-model Cross-mode Research Articles

A New Stochastic Model Updating Method Based on Improved Cross-Model Cross-Mode Technique.

This paper proposes a new stochastic model updating method to update structural models based on the improved cross-model cross-mode (ICMCM) technique. This new method combines the stochastic hybrid perturbation-Galerkin method with the ICMCM method to solve the model updating problems with limited measurement data and uncertain measurement errors. First, using the ICMCM technique, a new stochastic model updating equation with an updated coefficient vector is established by considering the uncertain measured modal data. Then, the stochastic model updating equation is solved by the stochastic hybrid perturbation-Galerkin method so as to obtain the random updated coefficient vector. Following that, the statistical characteristics of the updated coefficients can be determined. Numerical results of a continuous beam show that the proposed method can effectively cope with relatively large uncertainty in measured data, and the computational efficiency of this new method is several orders of magnitude higher than that of the Monte Carlo simulation method. When considering the rank deficiency, the proposed stochastic ICMCM method can achieve more accurate updating results compared with the cross-model cross-mode (CMCM) method. An experimental example shows that the new method can effectively update the structural stiffness and mass, and the statistics of the frequencies of the updated model are consistent with the measured results, which ensures that the updated coefficients are of practical significance.

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.

An improved model reduction-modal based method for model updating and health monitoring of an offshore jacket-type platform

Numerous constructed jacket platforms in the Persian Gulf require continuous monitoring due to aging which poses a significant hazard to the environment. The main aim of this study is to sketch a health monitoring system to address the problem of limitations and shortcomings of sensor networks and also to solve the localization problem. In order to achieve this goal, experimental modal analysis (EMA) is performed on a physical model of an offshore jacket platform to develop a numerically updated finite element model. Both traditional and improved Cross-Model Cross-Mode (CMCM) iteration algorithms are employed for this purpose and different model order reduction methods are compared in terms of their effects on the structural dynamic behavior of the case-study (SPD8 jacket platform). A new formulation is also proposed for the first time to compare the results of damage scenarios using both iteration algorithms. The effectiveness of the methodology in practical cases is also assessed by considering various numbers of sensors. According to the results, the improved iteration technique eliminates the detrimental impacts of the model reduction procedure on the proposed methodology, and physical parameters such as length, type, and location of a member play significant roles in the success of a damage detection scenario.

An improved model updating technique based on modal data

A novel technique of model updating named improved cross-model cross-mode (ICMCM) is presented. It is based on extracted modal data and to avoid a rank deficient problem and a biased solution of the derived linear equations, this method changes the form of coefficient matrix and adds more independent equations on the basis of the original cross-model cross-mode (CMCM) method. Truncated singular value decomposition is utilized for possible solutions. Results of two numerical investigations, including model updating of a simply-supported beam and damage detection on a jacket platform, indicate better accuracy and stability of the proposed technique. A comparative rank study reveals that this improved technique handles more unknowns with the same amount of extracted modes. Several damage cases are considered with modal data contaminated by noise. Results affected by noise level, extracted mode combinations, and different damage cases are discussed. Monte Carlo simulations show that even mode shapes contaminated with up to 3% added noise, it would still be possible to obtain satisfactory results with proper selected modes.

Developing a SIM strategy for offshore jacket platforms based on the FE model updating and a novel simplified method

Lack of data of the jacket structures may result in a high uncertainty about the structures ability to endure harsh marine environmental conditions. An experimental measurement from structural behavior under harsh marine environmental conditions is necessary to reduce this uncertainty in practical structural monitoring process of jacket structures. As an alternative, a novel and robust simplified methodology based on the empirical investigation could be a practical approach of better understanding the structures integrity. Hence, these methodologies are often termed as model reduction schemes. In this article, model reduction schemes include simplified platform model and static reduction. This work introduces a structural integrity assessment strategy for jacket structures based on the finite element (FE) model updating and a novel simplified method. Hereof, model reducing and model updating procedure is established based on a novel optimization technique. Since the number of measured degrees of freedom is most of the time restricted in practice, this paper represents a methodology using the cross model cross mode (CMCM) method in combination with an iterative procedure which uses limited, spatially incomplete modal information. One of the important advantages associated with the proposed method is that measuring the rotational degrees of freedoms, which is most of the time very expensive and inaccurate, is not needed.This research is an empirical study on a laboratory model of a jacket structure with the aim of establishing Refined Simplified FE Model (i.e. RSM) to conduct damage detection. The studied jacket structure is a reduced scale 2D frame fabricated and tested at the Laboratory of Modal Analysis of the Tabriz University, Iran. Hereof, experimental vibration tests are accomplished on a physical 2D platform model to record dynamic responses and acquire dynamic features of damaged structure. In addition to eliminate the uncertainty effects in the damage detection results, RSM technique is employed because of practical considerations and also this technique provides a fast damage zone diagnosis procedure. Also, improved reduction scheme is utilized based on static reduction scheme to carry out damage detection in jacket structure. Improved reduction technique eliminates the bad influence of model reduction procedure on the proposed new methodology. The results demonstrate that the presented new technique is completely successful in conducing damage identification in jacket structures.

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.

Developing a robust simplified method for structural integrity monitoring of offshore jacket-type platform using recorded dynamic responses

Designing of the updated models for the damage diagnosis purposes is an important topic in mechanical and structural engineering due to its application in structural health monitoring. In the modeling of complex dynamic systems, the approaches for reducing the discretization error may fail to enhance the confidence in simulation based predictions when the dynamical systems exhibit significant changeability in the description of the numerical model due to model uncertainty. This work is an experimental research on a laboratory model of a jacket structure with the target of establishing a baseline finite element (FE) model for long-term structural health monitoring for this type of structures. Experimental vibration tests are performed on a hydro elastic physical platform model to obtain dynamic characteristics. Moreover, this research represents an algorithm based on the cross model cross mode (CMCM) method in combination with an iterative procedure along with introducing a simplified method that is named Pseudo simplified (PS) model technique. This technique is capable of damage diagnosis with limited, spatially incomplete modal data. Such techniques are paid more attention for marine structures due to their application in facilitating the difficulties through the health monitoring procedures.The proposed new technique (PS) provides a fast damage zone identification process. For this propose, we evaluated the selection procedure of the inactive degrees of freedom in process of the model reduction with a reasonable criterion by using the sensitivity analysis of system response under base excitation. Meanwhile, the FE model updating based on the empirical model utilized to overcome the uncertainty in modeling. The major problem inherent to dynamic analysis is that it is time-consuming, expensive and a high computational burden is involved. Therefore, development of such methodologies would be extremely useful to spread out technologies that can be applied for offshore platform in service with saving of both time and cost.

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.

Model Simplification for Offshore Platforms Using Model Refinement Scheme

Offshore jacket platforms have been widely used in offshore oil and gas exploitation under hostile ocean environments. Finite element models of such structures need to have many degrees of freedom (DOFs) to represent the geometrical detail of complex structures, which leads to more computing power when performing the analysis and what’s more, the incompatibility in the number of degrees of freedom to the experimental models. Therefore, there is a need to simplify the analytical model by reducing the DOFs and in the process, making the essential eigen-properties agree with those of the experimental model is desired. In this paper, a scaled physical experimental model of an offshore jacket platform is simplified using the recently developed model refinement scheme. Mathematically, the procedure to implement the model refinement technique is an application of cross-model cross-mode (CMCM) method for model updating. The master degrees of freedom are chosen according to the placement of accelerometers in the experiment. Upon the completion of the refinement, the improved reduced jacket platform model matches the dynamic characteristics of the experimental model quite well.

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.

New iterative method for model updating based on model reduction

Model reduction technique is usually employed in model updating process. Here, a new iterative method associating the model updating method with the model reduction technique is investigated. Using the traditional iterative method, the errors resulted from replacing the reduction matrix of the experimental model with that of the finite element (FE) model are not fully considered, which needs more iterations and computing time. In order to reduce the errors produced in the replacement, a new iterative method is proposed based on the traditional method, in which the correction term related to the errors is added. The comparisons between the traditional iterative method and the proposed iterative method are shown by model updating examples of solar panels and both of these two iterative methods combine the cross-model cross-mode (CMCM) method and the succession-level approximate reduction (SAR) technique. The results indicate that the convergence rate and the computing time of the new method are significantly superior to those of the traditional iterative method with or without noise.

An improved model updating method of reduced-models for finite element model

Most of exiting model updating methods based on the substructure matrices did not consider the effect of model reduction process on model updating which led to the updating results could not become more and more accurate with the improvement of the model reduction precision and the convergence rate was greatly reduced. In order to solve this problem, this paper analyses the basic reason about this problem, and proposes an improved model updating method of reduced-models, named as improved reduced cross-model cross-mode (IRCMCM) method. The proposed method eliminates the disadvantageous effect by adding a correction term to the model updating formula and employing an iterative process. The results obtained by the referenced method and IRCMCM method are compared by numerical examples of satellite’s plates, which indicate the model updating results are more accurate by using the proposed method, and the model updating precision becomes better with the precision of the model reduction upgraded and the convergence rate is improved to a large extent at the same time.

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.

Refinement of reduced-models for dynamic systems

A refinement procedure for the reduced models of structural dynamic systems is presented in this article. The refinement procedure is to “tune” the parameters of a reduced model, which could be obtained from any traditional model reduction scheme, into an improved reduced model. Upon the completion of the refinement, the improved reduced model matches the dynamic characteristics – the chosen structural frequencies and their mode shapes – of the full order model. Mathematically, the procedure to implement the model refinement technique is an application of the recently developed cross-model cross-mode (CMCM) method for model updating. A numerical example of reducing a 5-DOF (degree-of-freedom) classical mass-spring (or shear-building) model into a 3-DOF generalized mass-spring model is demonstrated in this article.

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.