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In view of the demand for accurate modal identification, and based on the characteristics of free vibration response, this paper introduces a new window function for Fourier Transform called the Power–Exponential window. The Power–Exponential window addresses the characteristics of free vibration response. It significantly enhances the accuracy of modal identification by improving the spectral properties of structural response. The proposed window function consists of exponential and power terms. This study focuses on the additional damping and frequency-domain differentiation introduced by the Power–Exponential window function. The exponential term weakens the boundary effect related to the time-domain truncation and suppresses the spectral leakage. Moreover, it can be interpreted in clear physical terms as providing additional damping to the signal. The power term in the window function corresponds to frequency domain differentiation, and it alleviates the spectral broadening that arises due to the additional damping. Furthermore, the analytical expression for the response spectrum confirms that the Power–Exponential window not only aligns the peak response frequency with the damped natural frequency but also establishes an explicit linear relationship between the actual structural damping ratio and the identification result from the half power bandwidth method. Both contribute to an improved accuracy and usability of certain frequency-domain modal identification methods. The influence of the Power–Exponential window parameters on modal parameter identification is analyzed, and the optimal selection principle and suggested parameter values are proposed. Finally, numerical simulations and an experimental frame model test are conducted to verify the accuracy and validity of modal parameter identification based on the Power–Exponential window.

Słowa kluczowe:
Modal identification, Window function, Frequency domain, Spectrum leakage, Fourier Transform (FT)

Streszczenie:
Vehicle–road coupled system is inherently time–varying, and its responses are traditionally calculated using time–domain methods which involves significant computational effort. Aiming to improve the efficiency of response calculation for the coupled system, this paper proposes a fast calculation method in frequency domain, based on the newly developed moving frequency response function (FRF). Firstly, considering the vibration characteristics of an infinitely long road, the road response is straightforwardly expressed using the road impulse response function (IRF). Subsequently, the concept of the road moving IRF is proposed and derived with respect to the moving observation points. The moving FRF is then obtained by applying Fourier transform, which allows the responses of the road moving observation points to be established in frequency domain for fast calculation under moving loads. Furthermore, by analyzing the vehicle–road coupled vibrations, based on the vehicle FRF and road moving FRF, a formula for the vehicle–road coupling force is derived in frequency domain, along with an expression for the responses at the vehicle–road contact points. Finally, the approach is illustrated in numerical simulations of vehicle–road coupled systems, and its computational efficiency and accuracy are verified through comparison with currently popular methods.

Słowa kluczowe:
vehicle-road coupled vibration, frequency domain, frequency response function, impulse response function, numerical simulations

Streszczenie:
Accurate vehicle parameter information plays an important role in assessing the conditions of roads and bridges, along with the corresponding maintenance. This study considered a vehicle parameter identification method based on a vehicle frequency response function (FRF). First, the vehicle FRF was deduced with respect to the displacements of the vehicle-road contact points, thereby building the relationships among the FRF, vehicle responses, and road profile in the frequency domain. Next, using the responses of vehicles passing over on-road bumps of known size, a direct estimation of the vehicle FRF was described. Then, a combination of Tikhonov regularization and a shape function method was used to update the estimated vehicle FRF by removing the singular data owing to the direct computation of the vehicle FRF. Subsequently, the modifying factors of the vehicle parameters were iteratively identified based on a sensitivity analysis of the estimated FRF to the vehicle parameters. A numerical simulation for vehicle parameter identification was performed to test the effectiveness of the proposed methods, considering a 5% Gaussian noise pollution and the influences of different driving speeds. At last, field tests of a vehicle passing over bumps were performed for the verification of vehicle parameter identification

Słowa kluczowe:
vehicle parameter identification, frequency response function, Tikhonov regularization, shape function method

Streszczenie:
Accurate information about vehicle parameters and road roughness is of great significance in vehicle dynamic analysis, road driving quality, etc. In this study, a method for estimating vehicle parameters and road roughness was developed using the measured vehicle responses from field tests which is efficient, economical, and accurate. First, the full-vehicle model was introduced. Then, vehicle modal parameters were identified using the consequent free responses of a vehicle passing over bumps. Second, the expression of the vehicle frequency response function (FRF) with respect to the wheel contact point was derived from the vehicle equation of motion, and a road roughness estimation method based on the vehicle FRF was developed. Third, field tests in which the vehicle passes over bumps were performed for vehicle model identification. Finally, field tests for road roughness estimation were carried out using a calibrated vehicle to verify the effectiveness of the proposed methods.

Słowa kluczowe:
road roughness, vehicle parameters, modal identification, frequency response function (FRF), vehicle response

Streszczenie:
Many mode decomposition methods suffer from aliasing effects and modal distortion. This paper proposes a constrained mode decomposition (CMD) method that directly addresses these problems. The CMD is based on a linear combination of structural-free responses. The decomposed response is thus ensured to have a physical meaning and to satisfy the structural equation of motion, which improves the accuracy of mode decomposition and identification. The decomposition aim is to obtain a single-mode response. The CMD defines the corresponding natural frequency as the target frequency, while other natural frequencies are defined as constrained frequencies. The proposed method combines the measured physical responses in such a way that the constrained frequency components are selectively suppressed, while the amplitude of the target frequency component is selectively retained above a predefined level. The result is the intended single-mode free response, which can be used to clearly extract the corresponding modal parameters. For well-separated modes, the criterion for selective suppression is based on the fast Fourier transform (FFT) peak amplitude. For separation of closely spaced modes, a criterion based on FFT derivative is proposed to avoid modal distortion. The accuracy and applicability of the CMD method is tested in a numerical simulation and using a four-story lab frame structure. The experimental data are used to verify the effectiveness of the proposed CMD method and to compare it with two other widely used mode decomposition methods.

Słowa kluczowe:
frequency-domain response, linear combination, mode decomposition, peak characteristics, structural health monitoring (SHM)

Streszczenie:
A novel criterion, based on additional virtual masses estimated in multiple tests and the Bayesian theory, is proposed in this paper to improve the efficiency and precision of damage identification. Initially, a method is proposed that uses the experimentally measured frequency-domain response and a predetermined target frequency to estimate the required additional virtual mass. The proposed mass estimation method is flexible with respect to the frequency band of excitation, which can be thus selected according to practical engineering constraints. Furthermore, a new objective function based on the residual between the theoretical and experimental virtual masses is proposed. The objective function avoids calculating the structural modes through Eigen decomposition of the structural mass and stiffness matrices, and it thus improves the computational efficiency. Thirdly, based on the theoretical frequency response function of the finite element model, explicit formulas are derived for quick calculation of the additional masses and their sensitivities with respect to damage factors. In the next step, randomness and the influence of measurement noise are considered, and the approach is formulated in the probabilistic Bayesian framework. Finally, numerical simulations of a simply supported beam, a 3D truss structure and a 3D building, as well as an experimental 3-story frame, are used to verify the effectiveness of the proposed methods. The results clearly indicate that identified damage factors are close to real values, and thus acceptable in engineering.

Słowa kluczowe:
structural health monitoring (SHM), damage identification, additional virtual mass, sensitivity analysis, Bayesian theory

Streszczenie:
Damage of bridge cables is mainly manifested as the decrease in cable forces. These forces are affected by the boundary conditions, cable length, cable stiffness, and cable appendages, making it hard to identify the cable forces. Based on the substructure isolation method, this study proposes an approach for cable force identification to judge cable damage by adding virtual supports to each cable so that the cables share the same length and boundary conditions. The cable forces can then be identified according to the relationship between the natural frequency and cable forces. The basic concept is that the boundary sensors are transformed into virtual supports by a linear combination of the convolution of measured responses to achieve the zero boundary response. A finite element model of a suspension bridge was used to validate the proposed method in a simulation. When the virtual supports were added to the cables, the relationship between the cable forces and the natural frequency was almost linear, and the cable damage could be successfully identified with 5% noise. Finally, the effectiveness of the proposed method was verified experimentally, and the natural frequency of the isolated cable substructure was confirmed to be a highly sensitive damage indicator.

Słowa kluczowe:
cable damage, cable forces, natural frequency, structural health monitoring (SHM), substructure isolation method, virtual supports

Streszczenie:
Damage identification methods based on structural modal parameters are influenced by the structure form, number of measuring sensors and noise, resulting in insufficient modal data and low damage identification accuracy. The additional virtual mass method introduced in this study is based on the virtual deformation method for deriving the frequency-domain response equation of the virtual structure and identify its mode to expand the modal information of the original structure. Based on the initial condition assumption that the structural damage was sparse, the damage identification method based on sparsity with l1 and l2 norm of the damage-factor variation and the orthogonal matching pursuit (OMP) method based on the l0 norm were introduced. According to the characteristics of the additional virtual mass method, an improved OMP method (IOMP) was developed to improve the localization of optimal solution determined using the OMP method and the damage substructure selection process, analyze the damage in the entire structure globally, and improve damage identification accuracy. The accuracy and robustness of each damage identification method for multi-damage scenario were analyzed and verified through simulation and experiment.

Słowa kluczowe:
structural health monitoring (SHM), damage identification, virtual mass, sparse constraint, IOMP method

Streszczenie:
Road roughness is an important factor in road network maintenance and ride quality. This paper proposes a road-roughness estimation method using the frequency response function (FRF) of a vehicle. First, based on the motion equation of the vehicle and the time shift property of the Fourier transform, the vehicle FRF with respect to the displacements of vehicle–road contact points, which describes the relationship between the measured response and road roughness, is deduced and simplified. The key to road roughness estimation is the vehicle FRF, which can be estimated directly using the measured response and the designed shape of the road based on the least-squares method. To eliminate the singular data in the estimated FRF, the shape function method was employed to improve the local curve of the FRF. Moreover, the road roughness can be estimated online by combining the estimated roughness in the overlapping time periods. Finally, a half-car model was used to numerically validate the proposed methods of road roughness estimation. Driving tests of a vehicle passing over a known-sized hump were designed to estimate the vehicle FRF, and the simulated vehicle accelerations were taken as the measured responses considering a 5% Gaussian white noise. Based on the directly estimated vehicle FRF and updated FRF, the road roughness estimation, which considers the influence of the sensors and quantity of measured data at different vehicle speeds, is discussed and compared. The results show that road roughness can be estimated using the proposed method with acceptable accuracy and robustness.

Słowa kluczowe:
structural health monitoring, road roughness, vehicle response, frequency response function, Fourier transform

Streszczenie:
Adding a virtual mass is an effective method for damage identification. It can be used to obtain a large amount of information about structural response and dynamics, thereby improving the sensitivity to local damage. In the current research approaches, the virtual mass is determined first, and then the modal characteristics of the virtually modified structure are identified. This requires a wide frequency band excitation; otherwise the crucial modes of the modified structure might be out of the band, which would negatively influence the modal analysis and damage identification. This paper proposes a method that first determines the target frequency and then estimates the corresponding value of the additional virtual mass. The target frequency refers to the desired value of the natural frequency after the virtual mass has been added to the structure. The virtual masses are estimated by tuning the frequency response peaks to the target frequencies. First, two virtual mass estimation methods are proposed. One is to directly calculate the virtual mass, using the frequency‐domain response at the target frequency point only, whereas the second method estimates the mass using a least‐squares fit based on the frequency‐domain response around the target frequency. Both proposed methods utilize merely a small part of the frequency domain. Therefore, an impulse, a simple harmonic, or a narrow spectral excitation can be used for damage identification. Finally, a numerical simulation of a simply supported beam and experiments of a frame structure and a truss structure are used to verify the effectiveness of the proposed method.

Słowa kluczowe:
damage identification, frequency response, structural health monitoring (SHM), virtual distortion method (VDM), virtual mass

Streszczenie:
In practical civil engineering, structural damage identification is difficult to implement due to the shortage of measured modal information and the influence of noise. Furthermore, typical damage identification methods generally rely on a precise Finite Element (FE) model of the monitored structure. Pointwise mass alterations of the structure can effectively improve the quantity and sensitivity of measured data, while the data fusion methods can adequately utilize various kinds of data and identification results. This paper proposes a damage identification method that requires only approximate FE models and combines the advantages of pointwise mass additions and data fusion. First, an additional mass is placed at different positions throughout the structure to collect the dynamic response and obtain the corresponding modal information. The resulting relation between natural frequencies and the position of the added mass is sensitive to local damage, and it is thus utilized to form a new objective function based on the modal assurance criterion (MAC) and l1-based sparsity promotion. The proposed objective function is mostly insensitive to global structural parameters, but remains sensitive to local damage. Several approximate FE models are then established and separately used to identify the damage of the structure, and then the Dempster-Shafer method of data fusion is applied to fuse the results from all the approximate models. Finally, fractional data fusion is proposed to combine the results according to the parametric probability distribution of the approximate FE models, which allows the natural weight of each approximate model to be determined for the fusion process. Such an approach circumvents the need for a precise FE model, which is usually not easy to obtain in real application, and thus enhances the practical applicability of the proposed method, while maintaining the damage identification accuracy. The proposed approach is verified numerically and experimentally. Numerical simulations of a simply supported beam and a long-span bridge confirm that it can be used for damage identification, including a single damage and multiple damages, with a high accuracy. Finally, an experiment of a cantilever beam is successfully performed.

Słowa kluczowe:
structural health monitoring (SHM), damage identification, adding mass, data fusion, objective function, modal assurance criterion (MAC)

Streszczenie:
Structural damage identification plays an important role in providing effective evidence for the health monitoring of bridges in service. Due to the limitations of measurement points and lack of valid structural response data, the accurate identification of structural damage, especially for large-scale structures, remains difficult. Based on additional virtual mass, this paper presents a damage identification method for bridges using a vehicle bump as the excitation. First, general equations of virtual modifications, including virtual mass, stiffness, and damping, are derived. A theoretical method for damage identification, which is based on additional virtual mass, is formulated. The vehicle bump is analyzed, and the bump-induced excitation is estimated via a detailed analysis in four periods: separation, free-fall, contact, and coupled vibrations. The precise estimation of bump-induced excitation is then applied to a bridge. This allows the additional virtual mass method to be used, which requires knowledge of the excitations and acceleration responses in order to construct the frequency responses of a virtual structure with an additional virtual mass. Via this method, a virtual mass with substantially more weight than a typical vehicle is added to the bridge, which provides a sufficient amount of modal information for accurate damage identification while avoiding the bridge overloading problem. A numerical example of a two-span continuous beam is used to verify the proposed method, where the damage can be identified even with 15% Gaussian random noise pollution using a 1-degree of freedom (DOF) car model and 4-DOF model.

Słowa kluczowe:
structural health monitoring, damage identification, vehicle bump, additional virtual mass, bridge

Streszczenie:
Damage identification for liquid–solid coupling structures remains a challenging topic due to the influence of liquid and the limitation of experimental conditions. Therefore, the adding mass method for damage identification is employed in this study. Adding mass to structures is an effective method for damage identification, as it can increase not only the experimental data but also the sensitivity of experimental modes to local damage. First, the fundamental theory of the adding mass method for damage identification is introduced. After that, the method of equating the liquid to the attached mass is proposed by considering the liquid–solid coupling. Finally, the effectiveness and reliability of damage identification, based on adding mass for liquid–solid coupling structures, are verified through experiments of a submerged cantilever beam and liquid storage tank.

Słowa kluczowe:
structural health monitoring, damage identification, liquid-solid coupling, adding mass, sensitivity

Streszczenie:
Adding virtual masses to a structure is an efficient way to generate a large number of natural frequencies for damage identification. The influence of a virtual mass can be expressed by Virtual Distortion Method (VDM) using the response measured by a sensor at the involved point. The proper placement of the virtual masses can improve the accuracy of damage identification, therefore the problem of their optimal placement is studied in this paper. Firstly, the damage sensitivity matrix of the structure with added virtual masses is built. The Volumetric Maximum Criterion of the sensitivity matrix is established to ensure the mutual independence of measurement points for the optimization of mass placement. Secondly, a method of sensitivity analysis and error analysis is proposed to determine the values of the virtual masses, and then an improved version of the Particle Swarm Optimization (PSO) algorithm is proposed for placement optimization of the virtual masses. Finally, the optimized placement is used to identify the damage of structures. The effectiveness of the proposed method is verified by a numerical simulation of a simply supported beam structure and a truss structure.

Słowa kluczowe:
damage identification, sensor optimization, virtual distortion method (VDM), particle swarm optimization (PSO) algorithm, sensitivity

Streszczenie:
This research proposes a damage identification approach for storage tanks that is based on adding virtual masses. First, the frequency response function of a structure with additional virtual masses is deduced based on the Virtual Distortion Method (VDM). Subsequently, a Finite Element (FE) model of a storage tank is established to verify the proposed method; the relation between the added virtual masses and the sensitivity of the virtual structure is analyzed to determine the optimal mass and the corresponding frequency with the highest sensitivity with respect to potential damages. Thereupon, the damage can be localized and quantified by comparing the damage factors of substructures. Finally, an experimental study is conducted on a storage tank. The results confirm that the proposed method is feasible and practical, and that it can be applied for damage identification of storage tanks.

Słowa kluczowe:
damage identification, storage tanks, sensitivity analysis, frequency

Streszczenie:
Damage identification based on modal parameters is an important approach in structural health monitoring (SHM). Generally, traditional objective functions used for damage identification minimize the mismatch between measured modal parameters and the parameters obtained from the finite element (FE) model. However, during the optimization process, the repetitive calculation of structural modes is usually time-consuming and inefficient, especially for large-scale structures. In this paper, an improved objective function is proposed based on certain characteristics of the peaks of the frequency response function (FRF). Traditional objective functions contain terms that quantify modal shapes and/or natural frequencies. Here, it is proposed to replace them by the FRF of the FE model, which allows the repeated full modal analysis to be avoided and thus increases the computational efficiency. Moreover, the efficiency is further enhanced by employing the substructural virtual distortion method (SVDM), which allows the frequency response of the FE model of the damaged structure to be quickly computed without the costly re-analysis of the entire damaged structure. Finally, the effectiveness of the proposed method is verified using an eight-story frame structure model under several damage cases. The damage location and extent of each substructure can be identified accurately with 5% white Gaussian noise, and the optimization efficiency is greatly improved compared with the method using a traditional objective function.

Słowa kluczowe:
structural health monitoring (SHM), damage identification, substructure, virtual distortion method (VDM), frequency response

Streszczenie:
In vibration-based damage identification, a common problem is that modal information is not enough and insensitive to local damage. To solve this problem, an effective method is to increase the amount of modal information and enhance the sensitivity of the experimental data to the local damage. In this paper, a damage identification method based on additional virtual masses and Bayesian theory is proposed. First, the virtual structure with optimal additional mass and high sensitivity to local damage is determined through sensitivity analysis, and then a large number of virtual structures can be obtained by adding virtual masses; thus, a lot of modal and statistical information of virtual structures can be obtained. Second, the Bayesian theory is used to obtain the posterior probability distribution of the damage factor when structural a priori information is considered. Third, by finding the extreme value of the probability density function, the damage factor is derived based on the a priori information and the statistical information of virtual structures. Finally, the effectiveness of the proposed method is verified by numerical simulations and experiments of a 3-story frame structure. Experimental and numerical results show that the proposed method can be used to identify the damage severity of each substructure and thus damaged substructures can be localized and quantified; the error in damage factor is basically within 5%, which shows the accuracy of the proposed method. The proposed method can not only provide the structural damage localization and quantification result (i.e., the damage factor), but also the probability distribution of the damage factor; moreover, it has high sensitivity to damage and high accuracy and efficiency.

Słowa kluczowe:
Structural health monitoring, Damage identification, Bayesian theory, Virtual distortion method (VDM), Virtual mass

Streszczenie:
A damage identification method based on additional virtual masses was proposed aiming at storage tanks' features of space-symmetry, dense lower-order modes and being insensitive to local damages. Firstly, magnitudes of additional masses were determined through sensitivity analysis of storage tanks' structural modes. Then based on the virtual deflection method (VDM), the tanks' frequency responses after attaching additional virtual masses were constructed and their natural frequencies were identified with the original structures' excitation time histories and the original structures' corresponding positions' acceleration response time histories. Furthermore, using the tanks' features of space-symmetry, their damage positions were preliminarily determined according to the distribution law of their natural frequencies after attaching virtual masses. The sensitivity analysis of the tanks' finite element model was used to solve iteratively damages' level. Finally, the tanks' finite element models were used to perform numerical simulations and correctly predict their damage locations and levels. The effectiveness of this proposed method was verified.

Słowa kluczowe:
storage tanks, damage identification, sensitivity analysis, frequency

Streszczenie:
This paper proposes a frequency-domain method of substructure identification for local health monitoring using substructure isolation method (SIM). The first key step of SIM is the numerical construction of the isolated substructure, which is a virtual and independent structure that has the same physical parameters as the real substructure. Damage identification and local monitoring can be then performed using the responses of the simple isolated substructure and any of the classical methods aimed originally at global structural analysis. This paper extends the SIM to frequency domain, which allows the computational efficiency of the method to be significantly increased in comparison to time domain. The mass-spring numerical model is used to introduce the method. Two aluminum beams with the same substructure are then used in experimental verification. In both cases the method performs efficiently and accurately.

Słowa kluczowe:
structural health monitoring (SHM), damage identification, substructuring frequency domain, boundary

Streszczenie:
Structural health monitoring (SHM) has become a hot and intensively researched field in civil engineering. Thereinto, damage identification play an important role in maintaining structural integrity and safety. Many effective methods have been proposed for damage identification. However, accurate global identification of large real-world structures is not easy due to their complex and often unknown boundary conditions, nonlinear components, insensitivity of global response to localized damages, etc. Furthermore, global identification often requires lots of sensors and involves large number of unknowns. This is costly, rarely feasible in practice, and usually yields severely ill-conditioned identification problems. Substructuring approach is a possible solution: substructuring methods can focus on local small substructures; they need only a few sensors placed on the substructure and yield smaller and numerically much more feasible identification problems. This paper proposed an improved substructure method using local free response for substructure damage identification. The virtual supports are constructed by Substructure Isolation Method (SIM) using the linear combination of the substructural responses. The influence of the global errors is isolated by adding the virtual supports on the main degree of freedoms (DOFs) of the substructure. Through the correlation analysis, the substructural modes are selected and used for damage identification of the substructure. A plain model of cable stayed bridge is used for the verification of the proposed method.

Słowa kluczowe:
structural health monitoring (SHM), damage identification, substructure, cable stayed bridge, free response

Streszczenie:
This paper presents a parameter estimation method for Structural Health Monitoring based on the combined measured structural global frequencies and structural local frequencies. First, the global test is experimented to obtain the low order modes which can reflect the global information of the structure. Secondly, the mass is added on the member of structure to increase the local dynamic characteristic and to make the member have local primary frequency, which belongs to structural local frequency and is sensitive to local parameters. Then the parameters of the structure can be optimized accurately using the combined structural global frequencies and structural local frequencies. The effectiveness and accuracy of the proposed method are verified by the experiment of a space truss.

Streszczenie:
This paper proposes a substructure isolation method, which uses time series of measured local response for online monitoring of substructures. The proposed monitoring process consists of two key steps: construction of the isolated substructure, and its identification. The isolated substructure is an independent virtual structure, which is numerically isolated from the global structure by placing virtual supports on the interface. First, the isolated substructure is constructed by a specific linear combination of time series of its measured local responses. Then, the isolated substructure is identified using its local natural frequencies extracted from the combined responses. The substructure is assumed to be linear; the outside part of the global structure can have any characteristics. The method has no requirements on the initial state of the structure, and so the process can be carried out repetitively for online monitoring. Online isolation and monitoring is illustrated in a numerical example with a frame model, and then verified in a cantilever beam experiment.

Streszczenie:
This paper presents a method for damage identification by adding virtual masses to the structure in order to increase its sensitivity to local damages. The main concept is based on the Virtual Distortion Method (VDM), which is a fast structural reanalysis method that employs virtual distortions or pseudo loads to simulate structural modifications. In this paper, the structure with an added virtual mass is called the virtual structure. First, the acceleration frequency response of the virtual structure is constructed numerically by the VDM using local dynamic data measured only by a single excitation sensor and a single acceleration sensor. Second, the value of the additional mass is determined via sensitivity analysis of the constructed frequency responses of the virtual structure with respect to damage parameters; only the natural frequencies with high sensitivity are selected. This process is repeated for all the considered placements of the virtual mass. At last, the selected natural frequencies of all the virtual structures are used together for damage identification of the real structure. A finite element (FE) model of a plane frame is used to introduce and verify the proposed method. The damage can be identified precisely and effectively even under simulated 5 % Gaussian noise pollution.

Słowa kluczowe:
Structural health monitoring (SHM), Damage identification, Virtual distortion method (VDM), Virtual mass, Sensitivity analysis

Streszczenie:
针对大型土木结构损伤识别优化效率低的问题，提出了子结构虚拟变形方法。虚拟变形方法是一种结构
快速重分析的方法，该方法利用单元的虚拟变形模拟结构的损伤，可以在不重新建立有限元模型的情况下，快速
计算出结构参数改变后的结构响应。该文基于虚拟变形法的基本思想，对子结构的刚度矩阵进行分解和对损伤后
结构运动方程进行整理，推导出利用子结构的虚拟变形刻画损伤的方法，扩展了虚拟变形方法的适用范围；并且
给出了虚拟变形和结构响应的相关性计算公式，通过相关性分析提取主要的虚拟变形，减少参与计算的子结构虚
拟变形的数目，提高计算效率；最后利用一个五十层框架的数值仿真验证方法的有效性

Streszczenie:
由于土木工程结构的复杂性、传感器测点的有限性以及局部损伤的不敏感性等问题，大型结构的模型修正存在一定困难。针对空间桁架结构，为克服上述问题，对其进行整体和局部的动力测试试验，然后联合实测的结构整体和局部动态信息进行模型修正：首先进行空间桁架整体的动力测试试验，获得反应整体特性的低阶模态；然后为了提高局部杆件的动态特性，在杆件上附加一定质量，获得附加质量后杆件的局部主频率，并在各类杆件中选取一定数目进行动态测试；最后联合所有实测结构整体的低阶模态和杆件的局部主频率，对空间桁架结构进行模型修正。修正后的模态参数与实测模态吻合良好，验证了方法的有效性。

Słowa kluczowe:
结构健康监测, 模型修正, 桁架, 频率, 振型

Streszczenie:
针对大型复杂结构的整体监测常常面临测量信息不足等困难,提出只利用局部动态响应进行子结构损伤识别的约束子结构方法。约束子结构方法是通过子结构响应的卷积组合限制子结构边界的响应为零,来实现施加虚拟支座,从而将子结构分离出整体,然后利用构造的相应子结构内部响应,进行子结构损伤识别。该文利用先分段提取结构响应的子时间序列,再延时排列Toeplitz矩阵的方式,使基于不同响应的构造约束子结构的方程具有相同表达式,统一了约束子结构方法的基本思想。通过测量悬臂梁的局部动力响应,利用局部响应的时间序列实现了子结构的快速准确地分离和识别,验证了方法的实用性和有效性。

Słowa kluczowe:
结构健康监测, 损伤识别, 子结构, 时间序列, 脉冲响应

Streszczenie:
针对土木工程中实测模态相对较少，很难进行大型结构的损伤识别的困难，提出附加虚拟支座的损伤识别方法。该方法利用约束子结构方法在结构上附加虚拟支座来增加结构形式的方法，增加识别模态的数量，从而实现结构的准确损伤识别。约束子结构方法的基本思想是通过响应的卷积组合为零将传感器转化为虚拟支座。将附加虚拟支座后的结构定义为虚拟结构，每个虚拟支座对应一个虚拟结构，那么在结构上不同位置附加虚拟支座，则可以获得多个虚拟结构的模态；联合所有虚拟结构和对应的频率即可准确快速的识别出整体结构的损伤。最后通过三层空间框架模型验证方法的有效性。

Słowa kluczowe:
结构健康监测, 损伤识别, 约束子结构方法, 灵敏度分析, 频率

Streszczenie:
This paper extends and studies experimentally the substructure isolation method. Local health monitoring is significant for large and complex structures, since it costs less and can be easily implemented compared with global analysis. In contrast to other substructuring methods, in which the substructure is separated from the global structure, but coupled to it via the interface forces, the substructure isolation method isolates the substructure into an independent structure by placing virtual fixed supports on the interface. Model updating or damage identification can be then performed locally and precisely using the constructed responses of the isolated substructure and any of the existing methods aimed originally at global identification. This paper discusses and further extends the approach to improve its performance in real applications. A new type of virtual interface support (free support) is proposed for isolation. Relaxation of the original requirements concerning the type and placement of the isolating excitations is discussed. Previously, the method relied on the linearity of the global structure; here, only the substructure is required to be linear, the global structure besides the substructure can be non-linear, yielding, changing or unknown. A damaged cantilever beam is used in the experimental study. Up to three modified global structures with the same substructure are used to test the robustness of the isolation with respect to unknown modifications and non-linearities of the outside structure. Two typical global health monitoring methods are applied at the substructural level. A comparison with the results obtained from a generic substructure separation method is offered.

Słowa kluczowe:
Structural Health Monitoring (SHM), substructure isolation method, substructural identification, virtual distortion method (VDM), local monitoring, virtual supports

Streszczenie:
针对大型复杂结构的整体监测常常面临测量信息不足等困难,提出只利用局部动态响应进行子结构损伤识别的局部主频率方法.子结构的局部主频率指：如果整体模态中含有以局部子结构位移为主的模态,即等价于在局部激励作用下,整体结构的振动主要体现为子结构的振动,并且主要以这阶局部模态振动为主,那么对应的该阶频率即定义为子结构的局部主频率.局部主频率主要反映子结构的局部特性,对子结构损伤的灵敏度高,所以只利用局部主频率就可以识别子结构.当子结构特征不明显时,提出通过附加质量使子结构具有局部主频率的有效方法.该文进行了大型空间桁架的局部动力测试试验,试验中通过附加质量使杆件子结构具有局部主频率,并能准确地识别出杆件损伤的位置和程度.

Słowa kluczowe:
结构健康监测, 损伤识别, 子结构, 模态分析, 频率响应

Streszczenie:
This contribution presents, discusses and illustrates the constrained mode decomposition (CMD) method. The CMD is a recently proposed method that extracts single mode components from measured multimodal free structural responses. These components can be then processed, in time domain or in frequency domain, for identification of modal parameters, and ultimately, for structural health monitoring. The aim of the CMD is thus similar to the aims of other well-known mode decomposition approaches, such as the empirical mode decomposition (EMD) or the variational mode decomposition (VMD). However, in contrast to the EMD, the CMD-processed responses retain the characteristics of the free response (satisfy the equation of motion of the same structure) and they have thus a clear, well-defined physical meaning. In comparison to the VMD, the formulation of the CMD is much simpler: the CMD combines linearly recorded structural responses in a way that simultaneously (1) amplifies the selected modal component and (2) constrains/suppresses other components. The amplification/suppression process is quantified in terms of the FRF peaks or, in case of closely spaced modes, in terms of FRF derivatives.

Słowa kluczowe:
mode decomposition, frequency domain, linear combination, FRF peak, structural health monitoring, modal identification

Streszczenie:
In this paper, a damage localization method based on additional virtual mass and dynamic test of simple harmonic excitation is proposed. Firstly, when additional masses are added to the structure, a large number of virtual structures can be constructed; then the virtual construction formula is derived in order to obtain the dynamic response of virtual structures without adding real mass. After dynamic test of simple harmonic excitation, the dynamic response of virtual structures can be obtained using the acceleration response and virtual construction formula. Furthermore, when the applied harmonic excitation frequency is close to the natural frequency of the structure, the structural response can reach a maximum by adding advisable mass and the mass value can be calculated. When the local structure is damaged, the extreme value and the corresponding position of the additional mass are found by adding mass at different positions in the structure. Thus, the approximate location of the damage is determined according to the results. Finally, the numerical simulation of the elastic foundation beam model simplified by track structure is carried out, and the results show that the damage can be localized.

Słowa kluczowe:
structural health monitoring, damage identification, slab track, virtual mass

Streszczenie:
This paper presents a damage identification method using virtual structure. The main concept is based on Virtual Distortion method (VDM), which belongs to a fast structural reanalysis method and employs the virtual distortions or virtual forces to simulate the structural modifications. In this paper, the structure with virtual mass, damping or stiffness is defined as virtual structure. Firstly, the frequency response of the virtual structure is constructed by VDM method; Secondly, the natural frequencies of virtual structure with additional masses or stiffness are estimated; At last, the estimated natural frequencies of the virtual structure are used for damage optimization of the structure. A numerical beam model is used to describe and verify the proposed method.

Streszczenie:
This paper presents the substructure isolation method, which a novel method for substructural analysis and structural health monitoring (SHM) at the local level. The motivation behind it are the facts that global SHM of large and complex structures is generally difficult and that often only small substructures are crucial and require monitoring. These facts suggest that there is a need for ways of applying global SHM approaches locally, which is impossible with typical substructuring methods. The paper offers an overview of the common substructuring approaches and describes the substructure isolation method. The method splits the task of local monitoring into two stages: (1) Isolation; the outside influences are numerically eliminated from the measured response of the substructure. (2) Local SHM; all methods aimed originally at global SHM can be used with the constructed response of the isolated substructure. Local analysis is possible in time domain as well as in frequency domain; in offline and in online time regimes. The method is illustrated in a numerical example and substantiated in an experimental study using a damaged cantilever beam; the robustness of the isolation with respect to unknown modifications of the outside structure is tested.

Słowa kluczowe:
Substructuring, Structural Health Monitoring, SHM, Damage identification, Local analysis

Streszczenie:
Substructure Isolation Method (SIM) is used for large substructure identification. It utilizes the responses of global structure to construct the responses of the isolated substructure, which is a virtual and independent structure with the same system parameters as the real substructure. Then, the substructure identification is carried out equivalently via the isolated substructure and flexibly by some of the existing identification methods which aim originally at the large structure. Therefore, the performance of the SIM offers the possibility that the large substructure can be identified. A numerical bridge model is used to verify the proposed method, which preforms efficiently and accurately.

Słowa kluczowe:
Structural Health Monitoring (SHM), Damage identification, Substructure, Interface force

Streszczenie:
This paper proposes a Substructure Isolation Method based on time series (SIM-TM) of measured local response and intended for local online monitoring of substructures. The method consists of two key steps: (numerical) construction of the isolated substructure, and local identification. The isolated substructure is an independent virtual structure, which is separated from the global structure with virtual supports placed in their interface. In the first step, the response of the isolated substructure is constructed by linear combinations of sub-time series of the measured local responses. Then, natural frequencies of the isolated substructure are identified based on the constructed response and used for local identification. The method has no requirements on the initial state of the structure. The isolation can be carried out time section by time section using the successive fragments of the measured responses, so that the approach can be used for online monitoring. A numerical frame model is used to verify the proposed online monitoring method.

Streszczenie:
This paper proposed a frequency domain method of substructure identification for local health monitoring. The substructure isolation method (SIM) consists of two steps: the first is the construction of isolated substructure which is the key of the method, and the second is damage identification of substructure. The isolated substructure is a virtual and independent structure, and it have the same physical parameters of the real substructure with the additional virtual supports on boundary, which is realized by operating the measured response. This paper extends the SIM method to frequency domain, which could make the method employ more measured response and compute more efficiently. A mass-spring numerical model is used to verify the theory of the SIM method, and a cantilever beam is experimented to test the method. The method preformed efficiently and accurately in the both numerical model and experiment.

Streszczenie:
This paper presents a Substructure Isolation method for substructural damage identification using time series of local measured response. Isolated Substructure is a virtual and independent structure which is numerically separated from the global structure by adding virtual supports on the substructure interface. The basic concept of the isolation method is that: first time series of substructural responses are divided into several sub-series with overlap; through the linear combination of all the sub-series, when the boundary response are constrained to zeros, the corresponding inner responses are the constructed responses of the Isolated Substructure; then the substructural damage identification can be performed equivalently by the modes of the Isolated Substructure which are identified from the constructed inner responses. Numerical model of a six-span truss and an experiment of a cantilever beam are used to validate the method. Both the isolation and damage identification are preformed very well using local measured responses.

Streszczenie:
A substructuring method is presented for substructure identification and local health monitoring. The concerned substructure is numerically separated from the global structure to be a so-called Isolated Substructure by adding virtual supports on the substructure interface. The isolated substructure is a small and independent structure; its virtual supports are constructed using the FFT of measured local responses of the global structure. The damage of the substructure can be then identified easily by any of the classical methods which perform well on global structures. An experiment of a cantilever beam, of which the upper part is chosen as the substructure, is used to validate the method.

Streszczenie:
This paper presents a substructuring method on damage identification using Local Primary Frequency (LPF).When a local excitation is applied on a concerned substructure, if the caused vibration mainly consists of only one single modal which represents most of the substructural distortion, then the corresponding frequency is defined as the substructural LPF. LPF reflects more information of the substructure and hence is more sensitivity to the substructural damage. Therefore, LPF can be used for substructural model updating and identification. However, generally substructures don’t own LPF. In this case, virtual supports constructed by Substructure Isolation Method are applied on the substructural boundary, such that it can enhance the constraint on the boundary, and decrease the influence from elements outside the substructure. In this way, the substructure sensitivity is enhanced and correspondingly the LPF of the substructure can be constructed. Numerical simulation of a three-story space frame structure testifies that substructural damages are identified effectively by this method.

Słowa kluczowe:
Structure Health Monitoring (SHM), Damage Identification, substructuring method, Substructure Isolation Method, Local Primary Frequency (LPF), Virtual Supports

Streszczenie:
This paper describes an effective method of substructure isolation for local structural health monitoring (SHM). In practice, often only a small part of a larger structure is critical and needs monitoring [1]. However, typical SHM methods require modeling or analysis of the global structure, which can be costly, time-consuming and error-prone. The proposed approach is based on the virtual distortion method [2]; the substructure is isolated from the entire structure by placing modeled fixed supports in all nodes of their mutual boundary. Therefore, given an excitation of the substructure and a measured response, the response of the substructure treated as fixed supported can be computed. Only experimental data are used for isolation, and no numerical modeling is required. A numerical experiment of damage identification in a frame-truss will be presented during the talk to validate the methodology at 5% rms measurement error level. It is omitted here due to space constraints.

Streszczenie:
This presentation considers a semi-active control method aimed at the reduction of structural vibrations in the presence of unknown structural damages. The control algorithm is developed using reinforcement learning [1], a machine learning technique characterized by an iterative trial-and-error interaction of the control agent with the controlled structure. A quasi-optimal control law is derived by observing and learning from the collected interaction experience. By being data-driven, this strategy bypasses the need for an analytical derivation of optimal control, which can be challenging in semi-active and nonlinear control systems [2]. The approach of double Deep Q Learning (DQN) with experience replay is used. It builds upon earlier results [3], but here the aim here is to promote control robustness in the presence of unknown structural damages. The control algorithm is ultimately encoded in the form of a trained artificial neural network with a custom architecture that involves a dedicated damage-identification branch.
The effectiveness of the approach is demonstrated using a numerical model of a structure subjected to a seismic-type random excitation. A semi-active tuned mass damper (TMD) is employed as the actuator, and the control signal affects its viscous damping properties. The reference baseline is provided by the optimally tuned, classical passive TMD.

Słowa kluczowe:
Structural control, Semi-active control, Structural health monitoring (SHM), Reinforcement learning, Machine learning

Streszczenie:
This contribution reviews a recently proposed control strategy for mitigation of vibrations based on the Prestress-Accumulation Release (PAR) approach [1]. The control is executed by means of semi-actively controllable truss-frame nodes. Such nodes have an on/off ability to transfer bending moments: they are able to temporary switch their operational characteristics between the truss-like and the frame-like behaviors. The focus is not on local energy dissipation in the nodes treated as friction dampers, but rather on stimulating the global transfer of vibration energy to high-order modes. Such modes are high-frequency and thus highly dissipative by means of the standard mechanisms of material damping. The transfer is triggered by temporary switches to the truss-like state performed at the moments of a high local bending strain. A sudden removal of a kinematic constraint releases the locally accumulated strain energy into high-frequency and quickly damped vibrations.
The first formulation investigated global control laws [1]. Recent approaches generalized it to decen-tralized control with a local-only feedback, which was tested in damping of free vibrations [2] as well as forced vibrations [3]. Recently, a global formulation was proposed that aims at a targeted energy transfer between specific vibration modes [4], and attempts were made to go beyond skeletal struc-tures [5]. Numerical and experimental results will be presented to confirm the high effectiveness of the approach in mitigation of free, forced random and forced harmonic vibrations.

Streszczenie:
Aiming at this characteristic that the cable force identification precision is influenced by factors such as stiffness, boundary conditions and length, especially when the length of cable is short, boundary conditions cannot be simplified as fixed or pinned directly. Therefore, the method of adding virtual supports on the structure was proposed for cable force identification. The method of adding virtual supports on cable is based on the Substructure Isolation, through the change rule of natural frequency realize the structure damage identification. The virtual supports were constructed by the Substructure Isolation method using the liner combination of responses. By adding virtual supports realized that the substructures of cable were constructed, using the method can be additional virtual support in different position of the cable and get more virtual structures, combined with the frequency variation law of all virtual structures, the damage identification of cable can be carried out quickly and accurately.

Streszczenie:
This paper proposes a Substructure Isolation Method (SIM) for online local health monitoring at the substructural level. The SIM [1] includes two key steps: isolation of the substructure, and its local identification. Isolated substructure is an independent virtual structure, which is isolated from the global structure with virtual supports placed in the interface DOFs. Its response is constructed by such a linear combination of time series of measured local responses that the desired boundary conditions are satisfied and all outside influences are removed. Given the combined response, the substructure is locally identified using any of the standard methods aimed originally at global analysis. This is unlike other substructuring methods, see e.g. [2,3], which require dedicated methods in order to deal simultaneously with structural damages and generalized interface forces.

The SIM has been originally [1] used in off-line analysis and required zero initial conditions. Here, it is used for local online monitoring by a repeated application to successively extracted measurement time series. Non-zero initial conditions are allowed; they are reflected in a free vibration component of the constructed responses of the isolated substructure.