Damage identification in framed structures using natural frequencies

Nowadays, structural health monitoring has attracted much attention, due to the construction of important and complex structures and their safety. One branch of structural health monitoring is damage detection, estimating the location and extent of eventual damages in the structural systems. In this study, an efficient method is introduced to determine the location and extent of damage in the frame, beam and truss structures using time domain response and an optimization algorithm. First of all, the structural damage detection problem is formulated as a standard optimization problem. So that, the optimization objective function is defined by using the acceleration of damaged structures and analytical model acceleration. The acceleration is obtained using Newmark method. Damage is simulated by reducing the elasticity modulus of structural members. Then, damage problem converted to an optimization problem are solved by teaching–learning-based optimization (TLBO) algorithm therefore, the exact location and extent of damage in structure can be determined. In order to show the capabilities of the proposed approach for identifying structural damage, four illustrative test examples are considered with considering measurement noise effect. The results clearly show that the proposed method is as a powerful method to detect multiple damage in structures.

Composite structures are generally more susceptible to impact damage than non-composite structures, and early identification of damage is the primary goal of structural health monitoring (SHM). If such damage remains undetected or reaches a critical size, it can lead to sudden collapse and catastrophic failure. Modern SHM methods aim to preserve the integrity of composite structures through continuous inspection, monitoring, and damage assessment, including detection, localization, quantification, classification, and prognosis. These methods use sensor-based technologies to assess vibration, extension, and acoustic and thermal emission. This paper provides a review of various computational methods including physics-based methods (signal processing techniques, modal analysis, and finite element model updating) and optimization methods (inverse problems, particle swarm optimization, topology optimization, genetic algorithms, time series analysis, and hybrid techniques), alongside machine learning methodologies employing neural networks as well as deep learning for damage identification in composite structures. These computational and learning-based techniques are widely applied in the development of algorithms, optimization strategies, and hybrid frameworks for SHM. The review further summarizes the applications, advantages, and limitations of each method according to structure type and damage characteristics. The key emphasis of this review is on integrating computational approaches, as well as machine learning, to enhance the efficiency of damage identification. The conclusion is drawn based on an overview of the literature, focusing on the contributions of different computational methods and machine learning for damage identification in composites.

Considering the issue of misjudgment in railway bridge damage identification, a method combining the step-by-step damage detection method with the statistical pattern recognition is proposed to detect the structural damage of a railway continuous girder bridge. The whole process of damage identification is divided into three identification sub-steps, namely, damage early warning, damage location, and damage extent identification. The multi-class pattern classification algorithm of C-support vector machine and the regression algorithm of ε-support vector machine are engaged to identify the damage location and damage extent, respectively. For verifying the proposed method, both of the proposed method and the optimization method are used to deal with the measured data obtained from a specific railway continuous girder model bridge. The results show that the proposed method can not only identify the damage location correctly, but also obtain the damage extent which is consistent with the experimental results accurately. By uncoupling finite element analysis and damage identification, normalizing the index, and seeking the separation hyper plane with maximum margin, the proposed method has more favorable advantages in generalization and anti-noise. As a result, it has the ability to identify the damage location and extent, and can be applied to the damage identification in real bridge structures.

Background: Structural damage identification is a very important subject in the field of civil, mechanical and aerospace engineering according to recent patents. Optimal sensor placement is one of the key problems to be solved in structural damage identification. Methods: This paper presents a simple and convenient algorithm for optimizing sensor locations for structural damage identification. Unlike other algorithms found in the published papers, the optimization procedure of sensor placement is divided into two stages. The first stage is to determine the key parts in the whole structure by their contribution to the global flexibility perturbation. The second stage is to place sensors on the nodes associated with those key parts for monitoring possible damage more efficiently. With the sensor locations determined by the proposed optimization process, structural damage can be readily identified by using the incomplete modes yielded from these optimized sensor measurements. In addition, an Improved Ridge Estimate (IRE) technique is proposed in this study to effectively resist the data errors due to modal truncation and measurement noise. Two truss structures and a frame structure are used as examples to demonstrate the feasibility and efficiency of the presented algorithm. Results: From the numerical results, structural damages can be successfully detected by the proposed method using the partial modes yielded by the optimal measurement with 5% noise level. Conclusion: It has been shown that the proposed method is simple to implement and effective for structural damage identification.

This paper proposes a novel method for structural damage identification that integrates the power spectral density (PSD) of structural acceleration responses with densely connected convolutional networks (DenseNet). The method transforms the training object of the DenseNet into a numerical matrix (PSD matrix) for structural damage identification. Leveraging transfer learning, the DenseNet models are initially trained on simulated data and further fine‐tuned using experimental data to enhance robustness and generalization. Results demonstrate that frequency‐domain signals processed by PSD significantly enhance model performance, achieving lower mean squared error (MSE), higher Pearson’s correlation coefficient ( R value), and reduced mean absolute error (MAE) compared to time‐domain signals. The effectiveness of this method was verified on a six‐story frame structure. This study underscores the efficacy of transfer learning in bridging the gap between simulated and real‐world data, thereby facilitating effective structural health monitoring and damage identification.

As sensor monitoring technology continues to evolve, structural online monitoring and health management have found numerous applications across various fields. However, challenges remain concerning the real-time diagnosis of structural damage and the accuracy of dynamic reliability predictions. In this paper, a structural online damage identification and dynamic reliability prediction method based on Unscented Kalman Filter (UKF) is presented. Specifically, in the Wiener degradation process with random effects on structural performance, the structural damage identification is initially realized using UKF. Following that, the EM algorithm is employed for estimating the performance model parameters. Eventually, dynamic reliability prediction is realized based on conditional probability. The simulation results indicate that the method effectively estimates the damage state during the structure’s use while providing accurate, real-time, and dynamic reliability predictions for the system.

Structural nonlinear damage identification based on Bayesian optimization GNAR/GARCH model and its experimental study

Recently, the authors proposed computationally attractive algorithms to determine the location and extent of structural damage for undamped structures assuming damage results in a localized change in stiffness properties. The algorithms make use of a finite-element model and a subset of measured eigenvalues and eigenvectors. The developed theories approach the damage location and extent problem in a decoupled fashion. First, a theory is developed to determine the location of structural damage. With location determined, a damage extent theory is then developed. The damage extent algorithm is a minimum rank perturbation, which is consistent with the effects of many classes of structural damage on a finite-element model. In this work, the concept of the minimum rank perturbation theory (MRPT) is adopted to determine the damage extent on the mass properties of an undamped structure. In addition, the MRPT is extended to the case of proportionall y damped structures. For proportionally damped structures, the MRPT is used to find the damage extent in any two of the three structural property matrices (mass, damping, or stiffness). Finally, illustrative case studies using both numerical and actual experimental data are presented. HE advent of the Space Shuttle has prompted considerable attention to the design and control of large space structures. Due to the large size and complexity of envisioned structures, as well as the use of advanced materials to reduce structural weight, it may become necessary to develop a structural health monitoring system to detect and locate structural damage as it occurs. From experience gained in the machinery health monitoring field, one would expect the vibration signature of the structure, either frequency response functions and/or modal parameters, to provide useful information in determining the location and extent of structural damage. Assume that a refined finite element model (FEM) of the structure has been developed before damage has occurred. By refined, we mean that the measured and analytical modal properties are in agreement. Next, assume that at a later date some form of structural damage has occurred. If significant, the damage will result in a change in the structures modal parameters. The question is: can the discrepancy between the original FEM modal properties and postdamage modal properties be used to ascertain structural damage? Most prior work in damage detection has used the general framework of FEM refinement (system identification) in the development of damage assessment algorithms. The motivation behind the development of FEM refinement techniques is based on the need to validate engineering FEMs before their acceptance as the basis for final design analysis. The standard problem has been to seek a refined FEM that is as close to the original FEM and whose modal properties are in agreement with those that are measured subject to various constraints such as symmetry and sparsity preservation. A considerable amount of work in this area has been

Purpose Aiming at the problems of high cost, high risk and traffic impact of in situ load testing of Bridges after fire, this paper proposes a fire bridge structural damage identification method based on a fire dynamics simulator (FDS)-Kriging model modification and a unit modal strain energy damage index, so as to effectively assess the damage of bridge structures after fire. Determine whether it can continue to be used and whether it affects driving safety. Design/methodology/approach Propose a fire bridge structural damage identification method to establish the FDS-Kriging model correction. Findings The finite element model of the fire bridge modified using FDS-Kriging approach can reflect the actual situation of the bridge structure more accurately, and the damage location and degree identified by the modal strain energy method are consistent with the actual bridge. Therefore, the effectiveness of the proposed method has been verified, and a new strategy for fire bridge damage identification has been provided. Research demonstrates that the finite element model of the fire-damaged bridge, modified using the FDS-Kriging method, can more accurately reflect the actual structural state. Moreover, the damage location and severity identified via the modal strain energy method align well with the actual bridge conditions. Thus, the effectiveness and engineering applicability of the proposed method are validated, offering a comprehensive new strategy and technical support for the integrated performance evaluation, damage identification and reliability analysis of fire-damaged bridges. Originality/value By determining the finite element correction interval and combining it with the Kriging model, the method realizes the fine correction of the finite element model of the fire bridge. Structural damage identification is carried out by using the unit modal strain energy damage index. This verifies the effectiveness and engineering applicability of the proposed method, which offers a novel approach and technical support for the comprehensive performance evaluation, damage identification and reliability analysis of fire-damaged bridges.

In this paper, we improved the particle swarm optimization (PSO) algorithm with inertial weight by adopting the sigmoid function. The IPSO is applied to structural damage identification in frame structures. Firstly the theoretical background of the improved PSO (IPSO) algorithm is presented. Secondly, we use a suite of four famous benchmark functions to evaluate the algorithm performance. Some comparative studies on single and multi-damage of a 2-story rigid frame structure have been carried out. The results of the numerical simulation demonstrate that the approach can detect the structural damage with higher accuracy.

The present research aims to develop an effective and applicable structural damage detection method. A damage identification approach using only the changes of measured natural frequencies is presented. The structural damage model is assumed to be associated with a reduction of a contribution to the element stiffness matrix equivalent to a scalar reduction of the material modulus. The computational technique used to identify the damage from the measured data is described. The performance of the proposed technique on numerically simulated real concrete girder bridge is evaluated using imposed damage scenarios. To demonstrate the applicability of the proposed method by employing experimental measured natural frequencies this technique is applied for the first time to a simply supported reinforced concrete beam statically loaded incrementally to failure. The results of the damage identification procedure show that the proposed method can accurately locate the damage and predict the extent of the damage using high-frequency (here beyond the 4th order) vibrational responses.

This study presents a modal-based damage detection technique for framed structures. A framed structure is tested using a vibration-based method and the mode shapes corresponding to undamaged and damaged states of the structure are obtained. The damage to the framed structure is induced by reducing the stiffness of columns at a particular storey and tested using the shaking table. The corresponding finite element (FE) model was verified for its natural frequency with the experimental model. Moreover, a series of studies were performed by concentrating the damage to a smaller scale by including spot damage on the framed structure and varying the damage location and intensity. The model was analysed using finite element software for these tests and mode shape slope differences and mode shape curvature differences were generated. Derivatives of mode shape slopes were plotted and correlated with the damage location. Mode shape slope is discontinuous and becomes a maximum value close to the damaged location. Mode shape curvatures also show a maximum difference near the damaged location. Finite element model, as well as the experimental investigation, shows the competence of the proposed approach in structural damage identification.

The accuracy of structural damage identification is affected by the uncertainties in the vibration measurements and the finite element modeling. This paper proposes a novel approach based on sparse deep belief network (DBN) for structural damage identification with uncertain and limited data. Vibration characteristics, that is, natural frequencies and mode shapes, are extracted as the input to the network, while the output are the damage locations and severities of the structure. DBN is chosen to train the generated data sets and identify structural damages. Restricted Boltzmann Machines (RBMs) are used as building blocks to composite a DBN. To further enhance the capacity of the RBMs, an arctan-based sparse constraint is utilized to enable the hidden units to become sparse. This is achieved by adding an arctan norm constraint on the whole of the hidden units' activation probabilities. Numerical and experimental studies are conducted to verify the accuracy and performance of the proposed method. Undetermined damage identification is conducted, in which the quantity of input modal data is less than that of the system parameters to be identified. The identification results show that the proposed sparse DBN based on arctan can identify the damage effectively, and its accuracy is better than those obtained by other methods, even when the modeling uncertainty and the measurement noise exist and only limited data is available.

A methodology is presented for detecting structural damage in elastic structures by nondestructive means. Measured modal test data along with a correlated analytical structural model are used to locate potentially damaged regions using residual modal force vectors and to conduct a weighted sensitivity analysis to assess the extent of mass and/or stiffness variations, where damage is characterized as a stiffness reduction. The current approach is unique among other approaches in that it accounts for (1) variations in system mass, system stiffness, and mass center (locations), (2) perturbations of both the natural frequencies and modal vectors, and (3) statistical confidence factors for the structural parameters and potential experimental instrumentation error. Moreover, this procedure can be used with either full or reduced models. A wide variety of numerical examples are presented that show that the current method provides a precise indication of both the location and the extent of structural damage.

A hybrid evidence-genetic method of determining the location and extent of multiple structural damages by using genetic algorithms is presented. The method makes use of the combination information of natural frequencies and mode shapes. First the damage detection strategy is to localize the damage sites by using an evidence theory, which can perfectly integrate the damage identification information coming from both natural frequencies and mode shapes; then, an improved genetic algorithm is proposed to determine the damage extent. A cantilever beam is analyzed as a numerical example to compare the performance of the proposed method with other methods. Simulation results show that identification results of the evidence theory are better than those both of the frequency MDLAC method and the mode shape MDLAC method, and the improved genetic algorithm is also more accurate and effective than the simple genetic algorithms. Therefore, the hybrid evidence-genetic method is very effective for the identification of multiple structural damages.