No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Flexibility approach for damage identification of cantilever-type structures with bending and shear deformation
Abstract
Slender structures such as tall buildings and chimneys can be modeled as cantilevers with bending and shear deformation. A flexibility approach for damage identification of cantilever-type structures by utilizing the data of dynamic modes is proposed in this paper. An important advantage of the approach is that it only requires a small number of modes, so that it is convenient for practical application. The effectiveness of the approach is verified by numerical and experimental examples.
... Peng et al. [7] developed a method for determining the damage location of beam structures by using redistribution of static shear energy. Li et al. [8] proposed a flexible method for damage identification of cantilever structures, such as high-rise buildings and chimneys, using a few dynamic modal data. Koo et al. [9] proposed a damage quantification method for shear buildings based on the modal data measured by ambient vibration. ...
... Using Eqs. (7), (8), and (10) can be simplified as: ...
Shear-type structures are common structural forms in industrial and civil buildings, such as concrete and steel frame structures. Fault diagnosis of shear-type structures is an important topic to ensure the normal use of structures. The main drawback of existing damage assessment methods is that they require accurate structural finite element models for damage assessment. However, for many shear-type structures, it is difficult to obtain accurate FEM. In order to avoid finite element modeling, a model-free method for diagnosing shear structure defects is developed in this paper. This method only needs to measure a few low-order vibration modes of the structure. The proposed defect diagnosis method is divided into two stages. In the first stage, the location of defects in the structure is determined based on the difference between the virtual displacements derived from the dynamic flexibility matrices before and after damage. In the second stage, damage severity is evaluated based on an improved frequency sensitivity equation. The main innovations of this method lie in two aspects. The first innovation is the development of a virtual displacement difference method for determining the location of damage in the shear structure. The second is to improve the existing frequency sensitivity equation to calculate the damage degree without constructing the finite element model. This method has been verified on a numerical example of a 22-story shear frame structure and an experimental example of a three-story steel shear structure. Based on numerical analysis and experimental data validation, it is shown that this method only needs to use the low-order modes of structural vibration to diagnose the defect location and damage degree, and does not require finite element modeling. The proposed method should be a very simple and practical defect diagnosis technique in engineering practice.
... And it demonstrated higher sensitivity to structural defects compared to both above mentioned approaches. Several variations and extensions based on modal flexibility have been successfully applied for the assessment of structural damage [16][17][18]. ...
... The optimal hyperparameters results of the network attained by the BO for three damage scenarios is illustrated in Table 13. In addition, Tables 14,15,16,and Fig. 16 present the statistical results of damage assessment for three cases. Once more, the obtained damage ratios are detected by DINN with smallest error ratios. ...
In this work, an effective Damage-Informed Neural Network (DINN) is first developed to pinpoint the position and extent of structural damage. Instead of resolving the damage identification problem by conventional numerical methods, a Deep Neural Network (DNN) is employed to minimize the loss function which is designed by combining multiple damage location assurance criterion and flexibility matrices to guide the training process. In our computational framework, the parameters of the network, which include both weights and biases, are treated as new design variables instead of damage ratios. Therein, the training data consists only of a set of spatial coordinates of elements, whilst corresponding the damaged ratios of elements unknown to the network are factored into the output. To achieve the goal, the loss value is calculated relying on the predicted damage ratios with supporting Finite Element Analysis (FEA). Additionally, Bayesian Optimization (BO) algorithm is used to automatically tune hyperparameters of the network for enhancing reliability in damage identification. Several numerical examples for damage localization of truss and frame structures are investigated to evaluate the effectiveness and reliability of the suggested methodology. The obtained results point out that our model not only correctly locates the actual damage sites but also requires the least number of structural analyses and faster convergence rate compared with other algorithms.
... Ma trận độ mềm lần đầu được đề xuất bởi Bernan và cs [6] và đến nay vẫn được sử dụng rộng rãi. Một ví dụ cho việc sử dụng ma trận độ mềm là nghiên cứu được thực hiện bởi Li và cs [7], Dionisio [8]. Li và cs [7] đề xuất một biện pháp nhằm xác định hư hỏng trong các kết cấu mảnh như là nhà cao tầng, ống khói bằng cách giả thiết mô hình các kết cấu này như là một dầm mút thừa. ...
... Một ví dụ cho việc sử dụng ma trận độ mềm là nghiên cứu được thực hiện bởi Li và cs [7], Dionisio [8]. Li và cs [7] đề xuất một biện pháp nhằm xác định hư hỏng trong các kết cấu mảnh như là nhà cao tầng, ống khói bằng cách giả thiết mô hình các kết cấu này như là một dầm mút thừa. Hư hỏng trong mô hình số dầm liên tục hai nhịp và khung hai tầng được xác định chính xác nhờ sự thay đổi của ma trận độ mềm và tần số dao động riêng [9]. ...
Đánh giá sức khỏe công trình dựa vào phương pháp đo dao động thuộc nhóm phương pháp không phá hoại và có khả năng áp dụng trong thực tế. Việc nghiên cứu áp dụng sử dụng các phương pháp này là cần thiết, tạo điều kiện phát hiện sớm và khoanh vùng được vị trí hư hỏng. Dựa vào số liệu đo gia tốc, dạng dao động riêng của hệ sẽ được tìm thấy và sử dụng để xác định vị trí của hư hỏng trong kết cấu. Nếu như các phương pháp đánh giá sức khỏe công trình sử dụng dạng dao động riêng khi áp dụng cho kết cấu dạng bản thì cần phân tích hệ làm việc theo 2 phương với các phép toán phức tạp thì phương pháp sử dụng ma trận độ mềm chỉ tính độ mềm của hệ tại từng bậc tự do và sử dụng các phép tính tương tự với hệ kết cấu dạng dầm. Trong bài báo này, hệ số hư hỏng được tính toán từ sai khác ma trận độ mềm ở trạng thái hư hỏng và trạng thái nguyên được sử dụng để xác định vị trí hư hỏng của kết cấu dạng bản. Phương pháp được áp dụng trên mô hình số kết cấu bản giản đơn có một và hai vị trí hư hỏng. Kết quả là hệ số hư hỏng phản ánh hoàn toàn chính xác vị trí hư hỏng trên mô hình này. Với mô hình bản giản đơn trong phòng thí nghiệm, phương pháp sử dụng ma trận độ mềm xác định tương đối chính xác vị trí hư hỏng.
... Static responses are more sensitive to damage than dynamic responses [2,3], and the equipment used for static testing and for precise static displacement of structures can be obtained rapidly and economically [1]. However, there are two main drawbacks in the static damage identi cation methods: (1) Static testing provides less information compared to dynamic testing; (2) The e ect of damage on static responses for damage detection may be cryptic due to limited load paths [1]. ...
... Static responses are more sensitive to damage than dynamic responses [2,3], and the equipment used for static testing and for precise static displacement of structures can be obtained rapidly and economically [1]. However, there are two main drawbacks in the static damage identi cation methods: (1) Static testing provides less information compared to dynamic testing; (2) The e ect of damage on static responses for damage detection may be cryptic due to limited load paths [1]. ...
Damage detection and estimation in structures using incomplete static responses are presented in this study. In the proposed approach, damage location and severity is determined by solving an optimization problem using a pattern search algorithm. Therefore, an objective function is formulated using incomplete static responses. Because of limitations in using sensors and difficulties in sensing all degrees of freedom, the effect of using incomplete responses has been evaluated. The performance of the proposed method was evaluated using three numerical examples, namely, a simply supported beam, a three-story plane frame, and a plane bridge with and without noise in measured displacement and containing one or several damages. The results indicate that the proposed method is effective and robust in the detection and estimation of damage in spite of the incomplete responses.
... Examples of use of a dynamically measured flexibility matrix are the work of Li et al. [70] and Dionisio [32]. Li et al. [70] proposed an approach for damage identification in slender structures, such as tall buildings and chimneys, based on modelling them as cantilevers and utilising the flexibility matrix in a least squares solution approach. ...
... Examples of use of a dynamically measured flexibility matrix are the work of Li et al. [70] and Dionisio [32]. Li et al. [70] proposed an approach for damage identification in slender structures, such as tall buildings and chimneys, based on modelling them as cantilevers and utilising the flexibility matrix in a least squares solution approach. The method assumed that damage in each storey of a building could be represented by just two variables and thus only a minimal number of modes were needed for successful identification. ...
Vibration based condition monitoring refers to the use of in situ non-destructive sensing and analysis of system characteristics –in the time, frequency or modal domains –for the purpose of detecting changes, which may indicate damage or degradation. In the field of civil engineering, monitoring systems have the potential to facilitate the more economical management and maintenance of modern infrastructure. This paper reviews the state of the art in vibration based condition monitoring with particular emphasis on structural engineering applications.
... The number, location, and depth of the cracks on the beam can be identified using the displacement variance generated by the external force, and the method is still feasible under the interference signal [Kumar and Singh, 2022]. Some researchers evaluate the damage by comparing the change of flexibility matrices in the absence and presence of crack defects [Li et al., 1999;Stutz et al., 2005]. Moreover, a detection method using its power flow feature has been studied. ...
The vibration analysis of beams with cracks is an important problem in the structural dynamics community. In this study, a general model for the vibration analysis of a cracked beam with general boundary conditions was developed and investigated, emphasizing its vibration and power flow characteristics. The beam crack was introduced via torsional and translational coupling springs, which separated the beam structure into two segments, and the corresponding vibration characteristics were investigated via an energy-based formulation in conjunction with the Lagrangian procedure. A boundary-smoothed Fourier series was employed to construct the beam displacement field to avoid boundary differential discontinuities. Various crack statuses, including their depths or positions can be easily considered by adjusting the stiffness coefficient of the artificial springs. Several examples were presented to validate the effectiveness and accuracy of the proposed model. The modal characteristics and forced response of a cracked beam were predicted and analyzed, respectively, with a detailed depiction of the power flow around the crack. The results indicate that the presence of a crack has an important effect on the modal characteristics of an elastically restrained beam, as well as on the power flow distribution across the beam structure. This study can provide an effective tool for the dynamic analysis and power flow mechanism of beam structures with various cracks and complex boundary conditions.
... Pandey and Biswas [12] first proposed the idea of using changes in modal flexibility matrix for localizing damages in a beam structure, which has drawn significant attention. Since then, worldwide researchers have devoted a lot of effort to the development and application of damage diagnosis techniques based on modal flexibility for various types of structures [15,16,[17][18][19][20][21][22][23][24][25][26][27][28]. ...
Over the past decades, numerous damage diagnosis techniques based on modal flexibility have been studied and developed for various types of structures, but rarely for structures made of functionally graded (FG) materials. This paper aims to present the extensive applicability of a modal flexibility sensitivity-based damage index termed as MFBDI for damage identification of FG beams. The formulation of this damage index is based on the closed-form of modal flexibility sensitivity derived from the direct algebraic method. The applicability of the offered damage identification method is numerically demonstrated on a clamped-clamped FG beam and a two-span FG beam under (i) single and multiple damage cases, (ii) noise-polluted measurement data, and (iii) only the information of the first few incomplete modes. The identification results indicate that when the noise level added to the mode shape data is below 10%, the offered method can correctly localize the locations of damaged elements and approximately quantify their damage magnitudes in the FG beams. In addition, the influences of the number of used modes, damage magnitudes, and gradient index values are also investigated in the numerical simulations.
... Besides, the identified modal parameters of the actual structure may also be different from the numerical model. Therefore, a modified inversing method is employed to solve K, which is inspired by the flexibility approach for structural damage identification [32]. In this way, K can be determined under the condition that the vibrational parameters of fundamental modes should be consistent between the reduced order model and the actual structure. ...
This article reports a methodology for estimating dynamic wind forces on a steel lattice tower by using limited structural displacements. The methodology involves combining the modal state-space system model and a Kalman filter-based algorithm. For convenient application, the equivalent concentrated forces are taken as the inversing objects, representing the distributed wind forces on a lattice tower. The corresponding equivalent cantilever model of the lattice tower is utilized, in which the stiffness matrix is estimated by a modified flexibility approach. Based on the modal superposition principle, the dynamic wind forces in physical space are reconstructed using the identified input modal wind forces. The scheme of the dynamic wind force reconstruction is designed in detail. A typical transmission steel lattice tower is considered, and the aeroelastic wind tunnel experiments are performed. The performance and effectiveness of the proposed scheme are investigated based on numerical simulations and wind tunnel tests. It is indicated that the reconstructed dynamic wind forces can produce equivalent dynamic responses to the actual. Besides, it performs robustly on the effect of measurement noise. Although the modal force identification is sensitive to the modeling error of structural natural frequency, the effect can be judged according to the change in the power spectra of the identified modal force. The proposed inversing approach can serve as a useful tool to evaluate dynamic wind forces on steel lattice towers with limited response measurements.
... Hence, any change observed in the flexibility matrix can be interpreted as damage indication in the structure and further information on the damage location and its extent [50] . In the previous studies [51][52][53] , authors concluded that the advantage of using flexibility matrix is better than those using others in damage diagnose. ...
... For civil structures, both approaches can be used, though methods based on physical models are usually more popular because they can achieve all the five levels of damage identification and because of the strong experience of civil engineers in building reliable models. Among model-based strategies, 2 Shock and Vibration linear methods are well-established techniques that are based on simple assumptions: damage is a stiffness reduction which modifies the structural dynamic parameters such as vibration frequencies [5][6][7], mode shapes and their curvatures [8][9][10][11], flexibility matrix [12][13][14], and modal strain energy [15][16][17]. However, the accuracy of these methods in finding damage, especially at their first stage of inception, depends on the uncertainty of modal parameter identification and the variation of structural properties due to the environmental conditions [18][19][20][21][22]. ...
This paper discusses the monitoring of Palazzo Lombardia, one of the tallest high-rise buildings in Italy. First, the layout of the monitoring system is addressed for a general description of the sensors used. The paper provides details about how data coming from transducers are used. Special focus is put on the use of signals acquired by means of accelerometers, which are employed for the estimation of modal parameters through operational modal analysis. The procedure used for choosing the modal analysis algorithm and fixing the values of its main parameters is discussed in detail. The modal identification results on the first eight months of monitoring are discussed in the second part of the manuscript, together with a statistical analysis. This allows for a first model of the relationships between eigenfrequencies and environmental variables aiming at a general structural health monitoring procedure based on the evolution of the building’s modal parameters.
... Since then, many researchers have applied and developed various approaches based on modal flexibility for the diagnosis and assessment of structural damage. For example,Li et al. (1999)proposed a flexibility approach for damage identification of cantilever-type structures using the data from dynamic modes. Stutz, Castello, and Rochinha (2005) presented a flexibility-based continuum method for damage detection. ...
A Jaya algorithm was recently proposed for solving effectively both constrained and unconstrained optimization problems. In this article, the Jaya algorithm is further extended for solving the optimization-based damage identification problem. In the current optimization problem, the vector of design variables represents the damage extent of elements discretized by the finite element model, and a hybrid objective function is proposed by combining two different objective functions to determine the sites and extent of damage. The first one is based on the multiple damage location assurance criterion and the second one is based on modal flexibility change. The robustness and efficiency of the proposed damage detection method are verified through three specific structures. The obtained results indicate that even under relatively high noise level, the proposed method not only successfully detects and quantifies damage in engineering structures, but also shows better efficiency in terms of computational cost.
... Hence, any change observed in the flexibility matrix can be interpreted as damage indication in the structure and further information on the damage location and its extent [50] . In the previous studies [51][52][53] , authors concluded that the advantage of using flexibility matrix is better than those using others in damage diagnose. ...
The paper presents an efficient multi-stage optimization approach for damage detection in plate-like structures. In this approach, the damage identification process is achieved by minimizing an objective function established via flexibility changes of the structure. The vector of design variables represents correspondingly the damage extent of elements discretized by the finite element model. For analyzing the response of plate structures, the finite element model using 9-node quadratic quadrilateral elements is applied. For solving the optimization problem, a modified differential evolution (MDE) algorithm, which can help enhance the balance of global and local searches in each generation, is used for many stages of damage detection, in which the low damage variables in each stage are gradually eliminated after several generations to reduce the dimension of searching space and to increase the convergence rate of the problem. The efficiency of the proposed method is investigated through two numerical examples for isotropic and laminated composite plates. The obtained results indicate that the proposed method not only successfully detects the location and severity of multi-damage cases in the plate structures, but also show the better efficiency in term of computational cost.
... Proof of this is the review of damage detection methods through the change in modal properties presented in [26]. The relevant method are: Natural Frequency Based Methods [93], Mode Shape Based Methods [94][95][96][97][98], Mode Shape Curvature Based Methods [99][100][101][102][103], Strain Mode Shape Based Methods [71,[104][105][106][107][108], Dynamically Measured Flexibility Based Methods [109][110][111], and Neural Network Based Methods [112][113][114][115][116][117]. ...
Offshore Wind has become the most profitable renewable energy source due to the remarkable development it has experienced in Europe over the last decade. In this paper, a review of Structural Health Monitoring Systems (SHMS) for offshore wind turbines (OWT) has been carried out considering the topic as a Statistical Pattern Recognition problem. Therefore, each one of the stages of this paradigm has been reviewed focusing on OWT application. These stages are: Operational Evaluation; Data Acquisition, Normalization and Cleansing; Feature Extraction and Information Condensation; and Statistical Model Development. It is expected that optimizing each stage, SHMS can contribute to the development of efficient Condition-Based Maintenance Strategies. Optimizing this strategy will help reduce labor costs of OWTs׳ inspection, avoid unnecessary maintenance, identify design weaknesses before failure, improve the availability of power production while preventing wind turbines׳ overloading, therefore, maximizing the investments׳ return. In the forthcoming years, a growing interest in SHM technologies for OWT is expected, enhancing the potential of offshore wind farm deployments further offshore. Increasing efficiency in operational management will contribute towards achieving UK׳s 2020 and 2050 targets, through ultimately reducing the Levelised Cost of Energy (LCOE).
... Many damage identification algorithms are available in literature and most of them are based on the measurement of the structural vibrations coupled to a proper mechanical modelling. Linear methods are very popular because they are based on simple assumptions: damage is a stiffness reduction, which modifies the structural dynamic parameters such as vibration frequencies [3], [4], [5], mode shapes and their curvatures [6], [7], [8], [9] flexibility matrix [10], [11], [12], modal strain energy [13], [14], [15] and so on. The aim of these methods is the identification of one or more features, based on the dynamic parameters listed above, in order to define the presence of damage, its localization and its severity. ...
The challenge of identifying structural damage has gained a lot of attention among the research community during the last decades. Many damage identification algorithms are available in literature and most of them are based on vibration measurements. The accuracy of these methods depends on the measurement quality and especially on the number of sensors used to perform themonitoring activity. The need for a large number of devices does not complywith the economic advantage of an efficient structural maintenance based on remote monitoring. The purpose of this work is to explore the application of cameras to damage identification. The main advantage in using a camera is that every row or column in the pixel matrix can be considered a sensor on its own. This characteristic makes a camera an interesting device for damage detection, since it possible to estimate the structural dynamic behaviour on a continuous field by one single device at a reasonable price. In this work a camera will be used for the mode shape curvatures estimation of a cantilever beam with the final goal to identify damages in the structure. The results will show the efficacy of vision-based measurements for the monitoring purpose.
... Many damage identification algorithms are available in literature and most of them are based on the measurement of the structural vibrations eventually coupled to a proper mechanical modeling. Linear methods are very popular because they are based on simple assumptions: damage is a stiffness reduction, which modifies the structural dynamic parameters such as vibration frequencies [3][4][5], mode shapes and their curvatures [6][7][8][9] flexibility matrix [10][11][12], modal strain energy [13][14][15] and so on. The aim of these methods is the identification of one or more features, based on the dynamic parameters listed above, in order to define the presence of damage, its localization and its severity. ...
In this paper two methods for damage localization, the IDDM (Interpolation Damage Detecting Method), and the Modal Shape Curvature Method (MSCM) are applied to the same experimental case of a cantilever aluminum beam for which several different damage scenarios have been artificially reproduced in laboratory. IDDM is a new method recently proposed in literature which is on the definition of a damage-sensitive feature in terms of the accuracy of a spline function interpolating the Operational Displacement Shapes of the structure. This paper will present a comparison between the two methods on experimental data from a laboratory bench structure. Results show that, due to the small changes of the damage features induced by damage, both methods require a high-quality data set to provide a reliable damage localization even if the number of false alarms is slightly lower if the IDDM is applied.
... However, the flexibility matrix can be accurately estimated based on the first few modes because it is inversely proportional to the squares of natural frequencies. Li et al. [10] applied the flexibility approach to damage identification of cantilevertype structures. Stutz et al. [11] presented a flexibility-based continuum damage detection method. ...
An approach to identify damage of bridge utilizing modal flexibility and neural network optimized by particle swarm optimization (PSO) is presented. The method consists of two stages; modal flexibility indices are applied to damage localizing and neural network optimized by PSO is used to identify the damage severity. Numerical simulation of simply supported bridge is presented to demonstrate feasibility of the proposed method, while comparative analysis with traditional BP network is for its superiority. The results indicate that curvature of flexibility changes can identify damages with both single and multiple locations. The optimization of bias and weight for neural network by fitness function of PSO algorithm can realize favorable damage severity identification and possesses more satisfactory accuracy than traditional BP network.
... It should be noted here that the flexibility matrix, being the inverse of the stiffness matrix, can be similarly used for structural damage detection purposes, with an increase in flexibility being indicative of damage. Damage detection studies using the structural flexibility include those by Toksoy and Aktan [20], Pandey and Biswas [21], Mayes [22], Li et al. [23], Bernal [24], amongst others. Comparing the natural frequencies, mode shapes and modal flexibility, Zhao and DeWolf [25] found the modal flexibilities to be most sensitive to damage. ...
It is of interest to the modal testing and health monitoring community to quantify how an error in any identified mode shape propagates to the identified flexibility matrix. Here this problem is investigated in a probabilistic framework. The approach followed involves deriving analytical expressions to track how errors, due to random deviations between identified and “true” mode shapes, propagate to the Modal Assurance Criterion (MAC) and the Coordinate Modal Assurance Criterion (COMAC) values as well as the estimated flexibility matrix. The comparison of the expected values and variances of these errors identifies the inconsistency between the magnitude of errors in the MAC and COMAC values and the identified flexibility matrix. The analytical results are further validated via Monte Carlo simulations. Finally, two mode shape comparison criteria, termed as the Flexibility Proportional Modal Assurance Criterion (FPMAC) and the Flexibility Proportional Coordinate Modal Assurance Criterion (FPCOMAC), are proposed. These new criteria aim to mimic the expected error in the predicted flexibility matrix in a direct comparison of the identified and “true” mode shapes, and hence they can be used to complement MAC and COMAC in interpreting the analysis results.
... So, most of the damage detection methods are on the basis of the changes of dynamic characteristics and static responses (He et al., 2007). Static responses are more sensitive to damage than dynamic responses (Li et al, 1999& Hjelmstad et al., 1997 and the equipments of static testing, and precise static displacements of structures could be obtained rapidly and economically (He et al., 2007). However, there are two main drawbacks in the static damage identification methods: (1) Static testing provides less information as compared to dynamic testing; (2) The effect of damages on static responses for damage detection may be cryptic due to limited load paths (He et al., 2007). ...
... In those cases, the designed control scheme based on the nominal system may significantly degrade the performance or sometimes even destabilize the closed-loop system. Recently, there has been considerable interest in the field of structural damage or failure (Li et al., 1999;Sundaresan et al., 2002;Tseng and Naidu, 2002), especially for the case of crack initiation (Saavedra and Cuitino, 2001;Rajic et al., 2002) or delamination (Nam et al., 2000). Also equal research momentum has been focused on dealing with those problems by adopting several control design methodologies Boskovic and Mehra, 2002;Song et al., 2002). ...
This paper presents a real time adaptive active control system for vibration suppression of flexible structural systems with piezoelectric actuators–sensors. The system considered in this paper is a plate model with segmented piezoelectric actuators. An input–output model is developed for the identification of the systems, and on-line recursive identification scheme that is adequate to the proposed input–output model is used. An adaptive control method combined with model following control scheme is proposed for vibration suppression. An estimator is considered to exclude the effect of noise from the output signals. The proposed control strategy is successful in improving the dynamic characteristics of the structural systems. The experiments demonstrated the benefit of the proposed algorithm.
... Diversos métodos de estimación de la rigidez de estructuras consideran la masa del sistema como un valor conocido, generalmente proveniente de un modelo teórico (masas concentradas en los nodos, masas consistentes) 24,25,18,16,15 . El sistema de identificación de la rigidez requiere de una matriz de masa como información inicialM. ...
En este trabajo se presenta la aplicación de un método de estimación de la rigidez a estructuras de baja altura compuestas por muros de mampostería confinada. El método estima la rigidez a cortante (GA) y a flexión (EI), a partir del conocimiento de la matriz de masa y de una evaluación experimental previa, de la cual se hayan obtenido al menos dos frecuencias de vibración y sus respectivas formas modales. Una vez presentados los métodos de identificación de la rigidez y ajuste de la matriz de masa, se realizan simulaciones numéricas, que permiten establecer la sensibilidad de la estimación de la rigidez en función de diversas variables tales como el modelo de masa utilizado, la geometría de la estructura y la presencia de aberturas. Adicionalmente se propone una metodología para la cuantificación del cambio de rigidez ocurridos en una estructura compuesta por muros de mampostería confinada.
The presence of faults is common in engineering composite structures. Precise detection of faults prior to failure has been the focal point for researchers working in this domain. Detection of damage from the modal characteristics is an age-old promising technique besides the artificial intelligence techniques such as neural network (NN), Artificial neural network (ANN), recurrent neural network (RNN), and particle swarm optimization (PSO) methods. However, multiple detection techniques combined can give better results. In this regard, recurrent neural networks (RNN) and modified particle swarm optimization (mPSO) are combined to detect damages in a glass fiber reinforced polymer (GFRP) composite cantilever beam. The proposed hybrid model consists of two stages; indices of relative natural frequencies applied to locate crack parameters (position and severity) by recurrent neural network technique and optimization of the results (position and severity) by mPSO. The results illustrate this method can be implemented to predict multiple transverse cracks and their parameters in a composite beam, manifested in the change of natural frequencies where the error is limited to 0.97% only.
The bridges monitored within one cluster refer to several medium- and small-span beam bridges with similar structural characteristics located in a continuous elevated corridor. The variation in the strain monitoring data of these bridges comprehensively reflects diverse coupling effects. These complex coupling factors present great challenges for the damage diagnosis of bridges. To address this issue, a damage localization method for bridges monitored within one cluster is proposed based on a spatiotemporal correlation model of strain monitoring data between bridges. First, a deep learning architecture combining a convolutional neural network (CNN) with a long short-term memory (LSTM) network is established, which can reveal the complex time-varying mapping relationship between the strain monitoring data for similar bridges within one cluster to obtain an accurate spatiotemporal correlation model. Second, a strain prediction framework is presented that uses the proposed spatiotemporal correlation model after training. On this basis, the predicted and measured strains can be utilized to calculate a damage localization index that is not affected by complex coupling factors. Then, combined with abnormal diagnosis theory, the proposed index is implemented to accurately localize damage in all bridges within one cluster. Finally, the application of the proposed method to three actual bridges monitored within one cluster demonstrates the accuracy of the spatiotemporal correlation model and the effectiveness of structural damage localization.
The article proposes a new efficient two-stage approach for damage localization and quantification in shell structures using a modal flexibility sensitivity-based damage indicator abbreviated as MFBDI and a recently developed parameter-free optimization algorithm named golden ratio optimization method (GROM). In the first stage, the damage indicator MFBDI is employed to localize possible damage elements in the monitored shell structure. These possible damage elements also help define the search space of optimization problem in the next step. In the second stage, the GROM as a robust optimization solver is implemented to update the finite element (FE) model of the shell structure for refined localization of damage and quantification of its severity. The accuracy and efficiency of the proposed two-stage approach are demonstrated by two numerical simulation examples including a hypar shell and a spherical shell. The simultaneous influences of spatially-incomplete and inaccurate vibration data on damage prediction results are also taken into consideration. The obtained results reveal that the proposed approach can provide an efficient and accurate damage localization and quantification procedure for the studied shell structures.
The bridges monitored within one cluster refer to several medium- and small-span beam bridges with the same or similar structural characteristics located in a local road network, and these bridges suffer the similar traffic and environmental loads. It is still little research on how to detect the damage of all bridges monitored within one cluster utilizing the above-mentioned characteristics of these bridges. To address this issue, a method is proposed for the damage cross-detection between bridges monitored within one cluster by using the difference ratio of projected strain monitoring data under time-varying environmental temperatures. First, a damage feature is established by using the difference ratio of projected strain monitoring data obtained from the same cross-section position of any two bridges monitored within one cluster that have similar or identical structural characteristics. On this basis, the relationship between the statistical characteristics of the proposed damage feature and the degree of structural similarity between two bridges are discussed in detail. Second, a damage detection index is presented by calculating the subspace angle between two damage features. Then, combined with kernel density estimation and a cross-validation strategy, the proposed index is implemented to detect the damage of all bridges monitored within one cluster. Finally, numerical simulation examples are utilized to analyse and discuss the application limitations, noise resistance performance and structural damage sensitivity of the proposed method. Moreover, the effectiveness of the proposed method is also demonstrated by using the strain monitoring data obtained from actual bridges monitored within one cluster.
The post-earthquake repairability of self-centering buckling restrained braced frames (SCBFs) is usually evaluated based on structural performance indexes. From the view of the performance demands for SCBFs, further studies are urgently needed to discuss whether the self-centering brace (SCB) must be completely self-centering for the design of SCBFs. In this paper, 2-, 4-, 8-, 12-, and 16-story steel framed buildings were examined through nonlinear dynamic analyses to summarize the influence of the pretension forces of SCBs on the seismic responses of SCBFs. Numerical results illustrated that at a modest reduction of the pretension force, the SCBF satisfies both the demands on the seismic performance and the post-earthquake repairability of the building structures. The SCBF could more effectively exert the energy dissipation capacity of the self-centering brace and mitigate its floor acceleration response at a smaller pretension force. The self-centering ratio α for the design of the SCBFs is recommended to be between 0.6 and 1.0, where α is defined as the ratio between the pretension force of the self-centering system and the maximum strength of the energy dissipation system. Notably, the SCB with α = 0.6 was a partially self-centering brace, which meant that the self-centering brace was unnecessarily designed to be completely self-centering.
This study aims at comprehensively exploring and comparing four different methods of vibration-based damage detection in reinforced-concrete beams with three different support conditions. The methods chosen are Change in Flexibility (FC), Curvature Mode Shape (CMS), Modal Strain Energy Change Ratio (MSECR) and Principal Eigenvector of Modal Flexibility Change (PE). The parameters considered for this study are damage detection, localization, and quantification, for both single and multiple damage cases. The objective is to propose the most efficient method for both these cases. A beam of length 3.15m is analyzed using a self-developed finite element model-based program on MATLAB™ and damage is simulated by reductions in effective flexural rigidity. Based on the aforementioned parameters, it is found that the FC Method is most suitable for single damage detection while the MSECR method is most suitable for multiple damage detection.
Despite its importance in some structures, shear deformation is systematically neglected by most static structural system identification methods. This paper analyzes for the first time in the literature the effect of this deformation in the static inverse analysis of thin web bridges. This study is focused on the observability techniques. The most recent formulation found in the literature is based onthe Euler-Bernoulli beam theory. This formulation is unable to identify correctly the characteristics of a structure (such as flexural stiffness) when shear deformation is not negligible. To solve this problem, the observability method is updated according to Timoshenko's beam theory. This formulation uses an algebraic method which combines a symbolical and a numerical application. Thus, the updated observability formulation is able to obtain not only the flexural stiffness but also the shear one. Besides this, a parametric equation of the estimates is obtained for the first time in the literature. Some examples of growing complexity are used to illustrate the validity of the the proposed formulation formulation.
This article presents two methodologies for the identification of stiffness and flexibility matrices of framed building under shear behavior. Both methods require an initial (theoretical) value of the characteristic matrices, to be adjusted. They also require an experimental (real) modal frequency and its eigenvector. The mathematical formulae are presented. A four-story framed building is analyzed. Its initial stiffness are changed in order to represent seismic damage. Obtained results are exact, showing precision of both methodologies.
This article presents an identification method for the assessment of flexure and shear stiffness of shear wall buildings. Required data includes an initial (theoretical) model, the estimation of lumped mass values (by floor) and the experimental evaluation of one or two eigenvalues (modal frequency and its modal shapes). The method estimates stiffness whenever flexural (El) or shear (GA) values are relevant or are irrelevant. An initial formula includes both shear and flexural components. Furthermore, particular developments are carried out for particular cases of irrelevant shear or flexural deformations. Developed methods concern shear wall buildings with regular slabs . It's application allows the identification of the system's stiffness, and the presence of damage or changes in the initial stiffness. The method is applied for three numerical examples showing its simple implementation. Numeric errors are null.
The prepared catalysts containing 30, 50, 60 or 80% TS-1 were used to catalyze the propylene epoxidation to produce propylene oxide (PO) in a fixed bed reactor. TS-1 was the active site of the catalyst. The catalyst with 80% TS-1 had the highest activity and mechanical intensity. The selectivity of PO decreased and the utilization of H2O2 increased as the WHSV of propylene increased from 0.30 to 0.70/hr. The catalyst containing 80% TS-1 exhibited 97.8% H2O2 conversion, 86.4% PO selectivity, and 91.8% H2O2 utilization when the WHSV of propylene was 0.70/hr.
Titanosilicalite TS-1 has attracted more attention due to its excellent catalytic properties in partial oxidation of organic compounds. The studies of the synthesis of TS-1 have become a hotspot in catalytic field. This article summarizes the advances in this field. The factors affecting on the physicochemical properties of TS-1 are discussed, including the template, the titanium source, the silicon source, the base source and the crystallization conditions. The structure characteristics of TS-1 have been reviewed.
In this paper, structural damage identification algorithm was studied for the case with unknown input and incomplete output dynamic response information. Based on the hybrid inversion method for physical parameter identification in time domain, the change rate of element stiffness being defined as the damage factor, and the rectangular window method being introduced for removing the abnormal noise data, a hybrid inversion (damage detection and ground motion inversion) of structural damage indentification in time domain was proposed. A numerical simulation of 5-stories frame model was conducted. Considering the different lengths of rectangular window and the different noise levels, the identification result (damage identification accuracy and damage location) and convergence rate were compared. Simultaneously, the time-histories of ground motion inversion are compared with those of the real ground motion. The results show that the hybrid inversion algorithm established in the paper for structural damage identification and ground motion inversion is very effective. ©, 2015, Science and Technology Periodical Press. All right reserved.
This article presents an identification method for the assessment of stiffness coefficients due to shear (GA) and flexural (EI) behavior. The numerical evaluation is based on experimental data and considers the influence of various mass models. An additional methodology is included, allowing the evaluation of stiffness variations of a shear wall building. In the first step a non parametric method is employed for mass model identification, and an identification method is presented for the evaluation of the stiffness of shear wall structures, both requiring experimental data. The influence of various mass models is evaluated. A procedure employed in the evaluation of the stiffness variation of shear wall buildings is proposed, and a numerical example is evaluated, leading to satisfactory results. Conclusions and recommendations are included.
In the present paper, a method for identifying damage in a multi storeyed shear building structure is presented using minimum number of modal parameters of the structure. A damage at any level of the structure may lead to a major failure if the damage is not attended at appropriate time. Hence an early detection of damage is essential. The proposed identification methodology requires experimentally determined sparse modal data of any particular mode as input to detect the location and extent of damage in the structure. Here, the first natural frequency and corresponding partial mode shape values are used as input to the model and results are compared by changing the sensor placement locations at different floors to conclude the best location of sensors for accurate damage identification. Initially experimental data are simulated numerically by solving eigen value problem of the damaged structure with inclusion of random noise on the vibration characteristics. Reliability of the procedure has been demonstrated through a few examples of multi storeyed shear structure with different damage scenarios and various noise levels. Validation of the methodology has also been done using dynamic data obtained through experiment conducted on a laboratory scale steel structure.
It is important to explore efficient algorithms for the identification of both structural parameters and unmeasured earthquake ground motion. Recently, the authors proposed an algorithm for the identification of shear-type buildings and unknown earthquake excitation. In this paper, it is extended to the investigation of the identification of flexible buildings with bending deformation and the unmeasured earthquake ground motion. In the absolute co-ordinate system, the unmeasured ground motion can be treated as an unknown translational force and a bending moment at the 1st floor level of a flexible building. Structural unknown parameters above the 1st story of the building can be identified by the extended Kalman estimator and the 1st story stiffness and the unmeasured ground motion are subsequently estimated based on the least-squares estimation. The proposed algorithm is further extended to the identification of tall bending-type buildings based on substructure approach. Inter-connection effect between sub-buildings is treated as ‘additional unknown inputs’ to sub-buildings, which are estimated by the extended Kalman estimator without the measurements of rotational responses. Numerical examples demonstrate the identification of a multi-story, tall bending-type building and its unmeasured earthquake ground motions using only partial measurements of structural absolute responses.
This study presents a methodology for damage estimation in simply-supported beams. This method requires the mass matrix and two eigenvalues (modal frequency and its modal shapes). In the first step, the mathematical development is presented. Secondly, a methodology for the orthogonalization of experimental modal shapes is showed, to assure the orthogonality in between the experimental eigenvectors and the mass matrix. The modal frequency and modal shapes for the different damages conditions are obtained by a dynamic test into one simply-supported beam. The presented methodology is precise for damage estimation in the studied cases.
Resumen Se presenta la identificación del daño introducido en un modelo aporticado a escalada reducida, usando dos metodologías de evaluación, las cuales requieren de un ensayo experimental dinámico previo y de un modelo teórico inicial. Estas metodologías aprovechan la configuración de los edificios aporticados en la ecuación que rige el sistema. La primera de las metodologías se ocupa de la estimación de la rigidez, para ello se parte del conocimiento previo de los valores de masa de la estructura. La segunda metodología considera que no se conoce la matriz de masa del sistema. A continuación se describe el modelo ensayado, luego se detalla el procedimiento de ensayo dinámico realizado y la identificación que conduce a la obtención de los parámetros dinámicos correspondientes. Finalmente, se estiman los cambios de rigidez en la estructura ensayada, producidos por el daño, mediante la aplicación de las metodologías inicialmente expuestas. Los resultados obtenidos son satisfactorios. Summary This article presents the experimental evaluation of a reduced scale framed building model subjected to dynamic tests and controlled damage conditions. In the first part of this article, stiffness identification procedures are developed, and two methodologies are presented: when the mass matrix is known or when it is unknown. In this last case, the mass matrix must be identified before the stiffness matrix is assessed. The identification procedure requires an experimental essay as well as an analytical model to establish the initial undamaged condition of the structure. In the second part of this article, the frame building scale model and the performed experimental tests, leading to the dynamic identification of the structure, are described. Various controlled damage conditions of the structure are considered, and their dynamic properties are evaluated by experimental means. The proposed identification procedures are then applied and the results are discussed. Both methods prove to be suitable to successfully identify the damage location and the stiffness matrix of the structure under various damage conditions.
This paper proposes the concept of multidirectional-modal-parameter-based visual inspection with high-frame-rate (HFR) stereo video analysis as a novel active sensing methodology for determining the dynamic properties of a vibrating object. HFR stereo video is used for observing the 3-D vibration distribution of an object under unknown excitations in the audio-frequency range, and the projections of the vibration displacement vectors along multiple directions can be verified using output-only modal analysis that can estimate their modal parameters such as resonant frequencies and mode shapes. Through implementing a fast output-only modal parameter estimation algorithm on a 10000-fps stereo vision platform, we developed a real-time multidirectional-modal-parameter-based visual inspection system; it can measure the 3-D vibration displacement vectors of 30 points on a beam-shaped object from 512 × 96 pixel stereo images at 10000 fps and can determine its resonant frequencies and mode shapes along 72 different directions around its beam axis as its input-invariant modal parameters. To demonstrate the performance of our system in modal-parameter-based visual inspection, the asymmetric dynamic properties, caused by cracks, of several steel beams vibrating at dozens of hertz and having artificial cracks were inspected in real time by determining the modal parameters along 72 directions around their beam axes.
This paper presents an original method of estimating the location and severity of damage in a framed building based on experimental measurements of its fundamental vibration modes. Two procedures are presented: one usable when the mass matrix is known and the other usable when the mass matrix is unknown. Both require prior knowledge of the fundamental vibration modes of the undamaged structure, either through experimental tests or through an accurate analytical model. An important advantage of this method is that very few experimental data are needed. To study the accuracy of damage identification under noisy conditions, numerical simulations of a multi-storey, framed building were conducted. The new method was also tested by measuring the physical vibrations of a scale model under controlled damage conditions. Both variations of the method proved to be suitable, successfully identifying the location of damage and quantifying the stiffness reductions under various conditions.
Titanium silicalite-1 (TS-1) zeolites and films supported on porous α-Al2O3 tubes were prepared using TS-1 and silicalite-1 (Sil-1) seeds by hydrothermal synthesis. The structure and catalytic properties of the TS-1 powders and films were characterized by SEM, XRD, FT-IR, UV–vis and styrene partial oxidation by hydrogen peroxide. The results showed that TS-1 prepared from Sil-1 seeds were as active as TS-1 from nucleated and TS-1 seeded syntheses, in spite of the concerns about nonuniformity and dilution caused by the use of pure silica Sil-1 seeds. The Ti atoms were successfully incorporated as tetra-coordinated titanium in the zeolite framework and the phenylacetaldehyde selectivity correlates well with the infrared band for Ti–O–Si of the TS-1. Reaction over TS-1 film indicates that reactions occurred at the topmost layer of the film due to the slow diffusion in the zeolite pores.
In this paper, the flexibility method of damage identification for transmission tower based on Wigner-Ville Distribution (WVD) signal amplitude vector is forwarded. The damage coefficient equation involving modal parameters and damage parameters is firstly established, on the basis of the linear relation of flexibility matrix and structure parameters. Then, the mathematical deduction of WVD signal term reveals the function relation between WVD signal terms and modal parameters. Lastly, the damage coefficient equation is solved by substituting mode shape vector with the signal amplitude vector of response under suddenly unloading to identified the position and extent of structural damage. A numerical example demonstrates its accuracy for damage identification and excellent noisy immunity.
Shear damage may occur in the process of metal machining such as blanking and cutting, where localized shear deformation is developed. Experimental findings indicate that microscopic shear damage evolution in aluminium alloy 2024T3 (Al 2024T3) is a multi-stage mechanism, including particle cracking, micro-shear banding, matrix microcracking and coalescence of microcracks. This study is an attempt to use a set of equations to describe the multi-stage shear damage evolution in Al 2024T3. The shear damage variables in terms of multi-couple parameters of a power-law hardening material have been defined. An evolution curve of shearing damage has been calculated from experimental data. The values of the shear damage variable at different stages of damage have also been calculated. By making use of the findings, the relation between the microscopic shear damage evolution and the macroscopic shear response of the material has been discussed.
This article presents an identification method for the assessment of flexure and shear stiffness of shear wall buildings. Required data includes an initial (theoretical) model, the estimation of lumped mass values (by floor) and the experimental evaluation of one or two eigenvalues (modal frequency and its modal shapes). The method estimates stiffness whenever flexural (EI) or shear (GA) values are relevant or are irrelevant. An initial formula includes both shear and flexural components. Furthermore, particular developments are carried out for particular cases of irrelevant shear or flexural deformations. The method is applied for two numerical examples showing its simple implementation. The numeric errors are very small, in the order of 10 up to 10 in the case of structures with 5 up to 12 stories.
Detection of damage to structures has recently received considerable attention from the viewpoint of maintenance and safety assessment. In this respect, the vibration characteristics of buildings have been applied consistently to obtain a damage index of the whole building, but it has not been established as a practical method until now. It is reasoned that this is perhaps due to restrictions on the experiment, use of improper method, and lack of inspection opportunity for the structures. In addition, in the case of large-scale structures such as buildings, many variables to be considered for the analysis contribute to a large number of degrees of freedom, and this can also be a considerable problem for the analysis. A practical method for the detection of structural damage using the first natural frequency and mode shape of building is proposed in this paper. The effectiveness of the proposed method is verified by numerical analysis and experimental tests. From the results, it is observed that the severity and location of the damage can be estimated with a relatively small error by using modal properties of building. Copyright © 2004 John Wiley & Sons, Ltd.
An effective algorithm, which combined an adaptive real-parameter genetic algorithm with simulated annealing, is proposed to detect damage occurrence in beam-type structures. The proposed algorithm uses the displacements of static response and natural frequencies of modal analysis, which are obtained by finite element software ANSYS. There are three different kinds of beam structures to verify the performance of the proposed algorithm. These three cases have different boundary conditions and different damage scenarios. From the results, it is demonstrated that the proposed algorithm is efficient in flexural stiffness damage identification for beam-type structures under free of noise condition. Even under the case of noise, the results show that the searched solutions are still in reasonable precision.
Cette thèse présente trois méthodes pour l'identification des rigidités des structures d'usage commun dans l'ingénierie civile, à partir de données dynamiques expérimentales. La première méthode est développée pour des structures composées pour portiques. La deuxième méthode proposée est appliquée à des structures constituées pour des poutres isostatiques. La troisième est une méthodologie d'estimation des rigidités en flexion (EI) et au cisaillement (GA/γ) pour une structure constituée de murs dont les énergies de déformation en flexion et cisaillement peuvent être soit du même ordre de grandeur, soit l'une prépondérante par rapport à l'autre. Pour chaque méthode, des simulations numériques sont effectuées pour identifier les dommages structuraux ou les variations des rigidités, en termes de localisation et de magnitude de ces dommages. L'incidence et l'impact des erreurs et bruits sur les valeurs estimées des rigidités structurales sont analysés. Les méthodologies sont également appliquées pour localiser des dommages mécaniques ou des réductions de section sur modèles de laboratoire. A partir des concepts dynamiques de base et considérant une typologie donnée de structure, la thèse développe les concepts et formulations permettant d'identifier les rigidités résiduelles des structures considérées. Les méthodes peuvent être aisément mises en oeuvre pour déterminer les éventuels dommages (localisation et intensité) qui peuvent affecter une structure, par exemple après un séisme. Peu de mesures sont requises à cet effet : des essais de vibration libre et du matériel peu onéreux de mesures sont amplement suffisants dans le cas particulier des structures étudiées
The design characteristics of a passive or an active controller depend upon the mechanical properties of the structure to be controlled. If a change in mechanical properties accurs at any point in the structure, a corresponding adjustment should be made in the control system if the original control objectives are to be continually satisfied. Therefore, as part of the overall control program, it is practicable to nondestructively monitor changes in the mechanical properties of controlled structures. Furthermore, if it is possible to specify the probable location of the change in mechanical properties and estimate the magnitude of the change, such valuable information may provide the basis for decisions regarding recommendations concerning the future use of, or repairs to, the structure.
For the assessment of structural integrity, the use of system identification techniques has been studied by many investigators. Using the system identification techniques, the differences in structural dynamic characteristics between the undamaged and damaged structures are translated into the structural element stiffness changes, which reveal the structural damage. The method in this paper is based on the stiffness matrix correction technique using submatrices. The stiffness reduction factor (SRF) for each submatrix, which reveals the location and extent of stiffness damage, is obtained using a computationally efficient pseudoinverse solution. A planar truss example used by S.W Smith and S.L. Hendricks is employed to illustrate the method.
Nondestructive inspection of structures by modal analysis of vibration response is reported. The dependence of natural frequencies and modal damping coefficients on deterioration in structures is examined. The magnitude of change in natural frequencies is a function of the severity and of the location of deterioration in structures. Ratios of changes in natural frequencies normalized with respect to the largest frequency change are independent of severity for small deterioration and can serve to indicate the location of deterioration directly. Specific deterioration events have an associated characteristic ensemble of ratios of natural frequency changes that may be compiled in advance to form a data base for later interpretation of observed modal parameter changes. The modal analysis method is demonstrated in experiments on a welded steel frame exposed to fatigue loading, and on wire ropes damaged by sawcuts. The method holds promise as a condition monitoring tool for bridges and other skeletal structures.
This paper presents a structural diagnosis technique using "vibrational signature" analysis and the concept of strain mode shape (SMS). When a structure experiences a damage or change, a new state of force equilibrium is realized. This change of force distribution can be noted from the SMSs of the structure measured before and after the damage. The magnitude of the changes reflects the degree of forces redistributed. Since force redistribution is, in general, greatest near the damaged area. the location of damage is implicitly identified by the severity of the SMS change. A steel model frame was tested in the laboratory to substantiate this approach. Results show that locations of minor damage (specified change) in the frame can be pinpointed.
The need to monitor the dynamic characteristics of large structural systems for purposes of assessing the potential degradation of structural properties has been established. This paper develops a theory for assessing the occurrence, location, and extent of potential damage using on-orbit response measurements. Feasibility of the method is demonstrated using a simple structural system as an example.
Continuum modeling of large space structures is extended to the problem of detecting construction errors in large space structures such as the proposed space station. First-order dynamic sensitivity equations for structures involving eigenfrequencies, modal masses, modal stiffness, and modal damping are presented. Matrix equations relating changes in element parameters to dynamic sensitivities are summarized. The sensitivity equations for the entire dynamical system are rearranged as a system of algebraic equations with unknowns of stiffness losses at selected locations. The feasibility of the formulation is numerically demonstrated on a simply supported Euler-Bernoulli beam with simulated construction defects. The method is next extended to large space structures modeled as equivalent continua with simulated construction defects.
A general theory of non-destructive damage detection in structures The Netherlands: Nijho
- N Stubbs
Stubbs N. A general theory of non-destructive damage detection in structures. In: Structural Control, Proceedings of the Second International Symposium on Structural Control, The Netherlands: Nijho, Dordrecht, 1985. p. 694±713.
The identi®cation of earthquake-induced damage of reinforced concrete frames
- Li Hq
- Ou
- Jp
Li HQ, Ou JP. The identi®cation of earthquake-induced damage of reinforced concrete frames. J Harbin Univ Civil Engng Archit 1996;2:8±12 in Chinese.
A system identification technique with unknown input information
- Wang
Wang D, Haldar A. A system identi®cation technique with unknown input information. In: Schueller, Schinozuka, Yao, editors. Proceedings of the 6th International Conference On Struct. Safety and Reliability, Austria: ICOSSAR 93, 1994. p. 851±7.
The experimental research on the dynamic behaviour of structure models, Report No. 7 of the National Key Project on the detection and supervision system of high-rise buildings
- Li Gq Hao
- Hc
- Lu
Li GQ, Hao HC, Lu Y. The experimental research on the dynamic behaviour of structure models, Report No. 7 of the National Key Project on the detection and supervision system of high-rise buildings, 1996. in Chinese.
The research and application of inspection on high-rise buildings, Report no. 5 of the National Key Project on the detection and supervision system of high-rise buildings
- Li J Li
- Bs
Li GQ, Li J, Li BS. The research and application of inspection on high-rise buildings, Report no. 5 of the National Key Project on the detection and supervision system of high-rise buildings, December, 1995. in Chinese.
of the National Key Project on the detection and supervision system of high-rise buildings
- G Q Li
- H C Hao
- Y Lu
of the National Key Project on the detection and supervision system of high-rise buildings
- G Q Li
- J Li
- B S Li
The identification of earthquake-induced damage of reinforced concrete frames
- Li