Structural Response Measurements Research Articles

Frequency Response-Based Indirect Load Identification Using Optimum Placement of Strain Gages and Accelerometers

This paper presents an approach for indirect identification of dynamic loads acting on a structure through measurement of structural response at a finite number of optimally selected locations. Using the concept of frequency response function (FRF), the structure itself is considered as a load transducer. Two different types of sensors are investigated to measure the structural response. These include a use of accelerometers that leads to the identification of the displacement mode shapes. The second measurement approach involves a use of strain gages since strain measurements are directly related to imposed loads. A use of mixed strain-acceleration measurements is also considered in this work. Optimum sensor locations are determined herein using the D-optimal design algorithm that provides most precise load estimates. The concepts of indirect load identification, strain frequency response function (SFRF), displacement frequency response function (DFRF), along with the optimal locations for sensors are used in this paper. The fundamental theory for strain-based modal analysis is applied to help estimate imposed harmonic loads. The similarities and differences between acceleration-based load identification and strain-based load identification are discussed through numerical examples.

Motion Transmissibility for Load Identification Based on Optimum Sensor Placement

Knowledge on loads acting on a structure is important for analysis and design. There are many applications in which it is difficult to measure directly the dynamic loads acting on a component. In such situations, it may be possible to estimate the imposed loads through a measurement of the system output response. Load identification through output response measurement is an inverse problem that is not only ill‐conditioned but, in general, leads to multiple solutions. Therefore, additional information such as the number and locations of the imposed loads must be provided ahead of time in order to allow for a unique solution. This paper focuses on cases where such information is not readily available and uses the concept of motion transmissibility for the identification of loads applied to a structure. The identification of loads through measurement of structural response at a finite number of optimally selected sensor locations is investigated. Optimum sensor locations are identified using the D‐optimal design algorithm to provide the most precise load estimates based on acceleration measurements using accelerometers. Simulation results for multi‐degree‐of‐freedom (MDOF) discrete and continuous systems are presented to illustrate the proposed technique. It is seen that the proposed approach is effective in determining not only the number of applied loads as well as their locations but also the magnitude of applied loads.

Wind Load and Structural Parameters Estimation from Incomplete Measurements

The extended minimum variance unbiased estimation approach can be used for joint state/parameter/input estimation based on the measured structural responses. However, it is necessary to measure the structural displacement and acceleration responses at each story for the simultaneous identification of structural parameters and unknown wind load. A novel method of identifying structural state, parameters, and unknown wind load from incomplete measurements is proposed. The estimation is performed in a modal extended minimum variance unbiased manner, based on incomplete measurements of wind‐induced structural displacement and acceleration responses. The feasibility and accuracy of the proposed method are numerically validated by identifying the wind load and structural parameters on a ten‐story shear building structure with incomplete measurements. The effects of crucial factors, including sampling duration and the number of measurements, are discussed. Furthermore, the practical application of the developed inverse method is evaluated based on wind tunnel testing results of a 234 m tall building structure. The results indicate that the structural state, parameters, and unknown wind load can be identified accurately using the proposed approach.

Particle Filter Based Monitoring and Prediction of Spatiotemporal Corrosion Using Successive Measurements of Structural Responses.

Prediction of structural deterioration is a challenging task due to various uncertainties and temporal changes in the environmental conditions, measurement noises as well as errors of mathematical models used for predicting the deterioration progress. Monitoring of deterioration progress is also challenging even with successive measurements, especially when only indirect measurements such as structural responses are available. Recent developments of Bayesian filters and Bayesian inversion methods make it possible to address these challenges through probabilistic assimilation of successive measurement data and deterioration progress models. To this end, this paper proposes a new framework to monitor and predict the spatiotemporal progress of structural deterioration using successive, indirect and noisy measurements. The framework adopts particle filter for the purpose of real-time monitoring and prediction of corrosion states and probabilistic inference of uncertain and/or time-varying parameters in the corrosion progress model. In order to infer deterioration states from sparse indirect inspection data, for example structural responses at sensor locations, a Bayesian inversion method is integrated with the particle filter. The dimension of a continuous domain is reduced by the use of basis functions of truncated Karhunen-Loève expansion. The proposed framework is demonstrated and successfully tested by numerical experiments of reinforcement bar and steel plates subject to corrosion.

Identifying nonlinear characteristics of model-free MR dampers in structures with partial response data

MR dampers have been widely applied in passive and semi-active vibration control over the past decades. The modeling of hysteretic behavior of structural components is a prerequisite for optimal performances of MR dampers and the predication of nonlinear dynamic responses of structures subjected to severe dynamic loads. However, it is hard to establish proper mathematical models for the nonlinear hysteretic behaviors of MR dampers in service due to the complexities of nonlinearities and the degradations of the construction materials. Consequently, it is strongly desired to develop model-free methodologies for the nonlinear hysteretic performance identification with no assumption on the nonlinear hysteretic models of MR dampers. In this paper, a novel method is proposed for this purpose. Firstly, the MR dampers are in the linear state when the structure is under the weak external excitations, the restoring force of the MR dampers is only provided by linear stiffness and viscous damping of MR dampers, the structural physical parameters can be estimated based on the extended Kalman filter (EKF) approach. Then, MR dampers are in the nonlinear state when the structure is under the strong external excitations. The nonlinear restoring forces from MR dampers in a structure are treated as ‘unknown fictitious inputs’ to the corresponding structural systems without MR dampers. The recent Kalman filter with unknown input (KF-UI) algorithm developed by the authors is adopted for the simultaneous identification of the corresponding structural systems and the ‘unknown fictitious inputs’. No real information about the structure is needed, so the proposed method is capable of identifying hysteretic restoring forces of MR dampers by the direct use of partial structural dynamic response measurements, which are usually available from an employed structural health monitoring (SHM) system. To validate the performances of the proposed method, some numerical simulation examples of identifying nonlinear hysteretic restoring forces of MR dampers in different models are used.

Structural nonlinearity and mass identification with a nonparametric model using limited acceleration measurements

Structural nonlinearity identification is critical for post-event damage detection or condition evaluation of engineering structures after strong dynamic excitation such as earthquake where structural nonlinear behaviour should be considered. Structural nonlinear restoring force provides direct indicator describing structural damage initiation and development procedure. Considering the availability of structural dynamic response measurement and the difficulty in defining a parametric model for structural nonlinearity and in estimating structure mass accurately in practice, in this article, a time-domain structural nonlinear restoring force and mass identification approach for multi-degree-of-freedom structures under incomplete excitation using limited acceleration measurements but without using any parametric models of structural nonlinear restoring force is proposed. At first, a memory fading extended Kalman filter with a weighted globl iteration (MF-EKF-WGI) is used to identify the location of nonlinearities and then a Chebyshev polynomial nonparametric model is introduced to model the nonlinear restoring force. The unscented Kalman filter is used to identify the structural responses and the parameters of the Chebyshev polynomial to describe structural nonlinearity. Numerical and experimental studies with a four-storey frame model structure equipped with a magnetorheological damper, which is employed to mimic structural nonlinear behaviour, under impact excitations are carried out to validate the performance of the proposed approach using acceleration measurements at certain degrees of freedom. Numerical and experimental results show that the proposed approach is capable of identifying both structural nonlinear restoring force and mass with acceptable accuracy even with a very rough initial mass estimation. The proposed time-domain identification approach can be used to detect structural damage initiation and development process and to evaluate energy consumption quantitatively of engineering structures under dynamic loadings.

Synthesis of Cross-Correlation Functions of Partial Responses and the Extended Kalman Filter Approach for Structural Damage Detection Under Ambient Excitations

It is still necessary to investigate the detection of structural damage under ambient excitations since the excitations are random and unmeasured while measurement noises are inevitable. In this paper, a method based on the synthesis of cross-correlation functions of partial structural responses and the extended Kalman filter (EKF) approach is proposed for the identification and damage detection of structures under ambient excitations, in which both independent stationary and non-stationary white noise excitations in the product models are discussed. First, the equations of cross-correlation functions of structural responses are established when the ambient excitations are independent stationary white noise processes. Then, the EKF approach is utilized to identify structural parameters and cross-correlation functions using partial measurements of structural acceleration responses. Structural damage is detected based on the degradations of the identified structural element stiffness parameters. Finally, the proposed method is extended to deal with independent non-stationary white noise excitations in the product models. The numerical simulation examples of the ASCE structural health monitoring benchmark building subject to ambient excitation, a moment resisting frame model under white noise excitation, and a cantilever beam model under multiple independent non-stationary excitations are used to validate the feasibility of the proposed method. It is shown that the method is not sensitive to measurement noises. Also, a lab experimental study of the identification of a multi-story shear structure is investigated to further illustrate the applicability of the proposed method.

Identification of wind loads on super-tall buildings by Kalman filter

An inverse method based on the discrete time Kalman filter is developed to simultaneously estimate the unknown wind-induced responses and wind loads of high-rise buildings using limited response measurements. The accuracy and effectiveness of the presented estimation method are assessed based on both wind tunnel test results and field measurements of wind effects on a super-tall building. The wind-induced responses obtained by wind tunnel test are used to identify the wind loads on the super-tall building and evaluate the effects of crucial factors, such as covariance matrix of noise, initial estimation error, noise in measurements, modelling errors of structural dynamic properties and number of vibration modes, on the identification results. In addition, the wind loads are also estimated based on the field measured displacements during Typhoon Neoguri. Comparisons between the identified wind loads from the field measured displacements and the wind tunnel test results are made to verify the applicability of the inverse technique. The results of this study illustrate that the proposed inverse method is an efficient tool for predicting the wind loads on super-tall buildings from limited measurements of structural responses.

Structural response measurement of shape memory polymer components using digital image correlation method

Shape memory polymer (SMP) can actively deform under a certain external stimuli and maintain the deformation after the stimuli is removed. When the corresponding stimulus is applied again, it can return to its initial state. Due to their high strength, low density and high rigidity, SMP and its composites are getting increasing attention. The study of their mechanical behavior is critical for the design of composite materials. However, due to the anisotropic and viscoelastic properties of SMP composite, it is difficult to carry out a comprehensive study of structural response of SMP and its composite structures through traditional experimental methods. In this paper, the full-field displacement and strain of disc, beam and ring structures based on SMP and its composites were investigated by digital speckle correlation method, which is important for the comprehensive study of mechanical behavior and fabrication of SMP composites.

Assessment of the sound reduction index of building elements by near field excitation through an array of loudspeakers and structural response measurements by laser Doppler vibrometry

At low frequencies the assessment of the sound reduction index of building elements in the laboratory according to the standard ISO 10140-2:2010 is burdened by a large variation in the measurement results. This is due to the fact that at low frequencies the acoustic field is not sufficiently diffuse.This paper discusses a measurement procedure in which a diffuse field is created in the source room by means of an array of loudspeakers positioned closely to the building insulation element under test. This procedure exploits the acoustic near field of the loudspeaker array.The problems related to the breakdown of the diffuse field assumption of the receiving room are eliminated by measuring the structural response of the building insulation element under test by means of laser Doppler vibrometry and the application of the Rayleigh integral to compute the radiated sound power. The sound reduction index is determined from the ratio of the incident sound power, created by the loudspeaker array, and the radiated sound power.The measurement approach is validated by means of a measurement of the sound reduction index of a single layer glazing. Comparisons are made with an analytical model and with a standardized ISO 10140-2:2010 measurement. Although the method offers clear, strong points in terms of removing room acoustic effects from the measurements in the lower frequency range, a point of concern is the measurement effort.

Integrated multi‐type sensor placement and response reconstruction method for high‐rise buildings under unknown seismic loading

SummaryStructural health monitoring system has been implemented on high‐rise buildings to provide real‐time measurement of structural responses for evaluating their serviceability, safety, and sustainability. However, because of the complex structural configuration of a high‐rise building and the limited number of sensors installed in the building, the complete evaluation of structural performance of the building in terms of the information directly recorded by a structural health monitoring system is almost impossible. This is particularly true when seismic‐induced ground motion is unknown. This paper thus proposes an integrated method that enables the optimal placement of multi‐type sensors on a high‐rise building on one hand and the reconstruction of structural responses and excitations using the information from the optimally located sensors on the other hand. The structural responses measured from multi‐type sensors are fused to estimate the full state of the building in the modal coordinates using Kalman filters, from which the structural responses at unmeasured locations and the seismic‐induced ground motion can be reconstructed. The optimal multi‐type sensor placement is simultaneously achieved by minimizing the overall estimation errors of structural responses at the locations of interest to a desired target level. A numerical study using a simplified finite element model of a high‐rise building is performed to illustrate the effectiveness and accuracy of the proposed method. The numerical results show that by using 3 types of sensors (inclinometers, Global Positioning System, and accelerometers), the proposed method offers an effective way to design a multi‐type sensor system, and the multi‐type sensors at their optimal locations can produce sufficient information on the response and excitation reconstruction.

Hybrid motion sensing and experimental modal analysis using collocated smartphone camera and accelerometers

State-of-the-art multisensory technologies and heterogeneous sensor networks propose a wide range of response measurement opportunities for structural health monitoring (SHM). Measuring and fusing different physical quantities in terms of structural vibrations can provide alternative acquisition methods and improve the quality of the modal testing results. In this study, a recently introduced SHM concept, SHM with smartphones, is focused to utilize multisensory smartphone features for a hybridized structural vibration response measurement framework. Based on vibration testing of a small-scale multistory laboratory model, displacement and acceleration responses are monitored using two different smartphone sensors, an embedded camera and accelerometer, respectively. Double-integration or differentiation among different measurement types is performed to combine multisensory measurements on a comparative basis. In addition, distributed sensor signals from collocated devices are processed for modal identification, and performance of smartphone-based sensing platforms are tested under different configuration scenarios and heterogeneity levels. The results of these tests show a novel and successful implementation of a hybrid motion sensing platform through multiple sensor type and device integration. Despite the heterogeneity of motion data obtained from different smartphone devices and technologies, it is shown that multisensory response measurements can be blended for experimental modal analysis. Getting benefit from the accessibility of smartphone technology, similar smartphone-based dynamic testing methodologies can provide innovative SHM solutions with mobile, programmable, and cost-free interfaces.

Predicting the seismic performance of typical R/C healthcare facilities: emphasis on hospitals

Reinforced concrete (RC) type of buildings constitutes an important part of the current building stock in earthquake prone countries such as Albania. Seismic response of structures during a severe earthquake plays a vital role in the extent of structural damage and resulting injuries and losses. In this context, this study evaluates the expected performance of a five-story RC healthcare facility, representative of common practice in Albania, designed according to older codes. The design was based on the code requirements used in this region during the mid-1980s. Non-linear static and dynamic time history analyses were conducted on the structural model using the Zeus NL computer program. The dynamic time history analysis was conducted with a set of ground motions from real earthquakes. The building responses were estimated in global levels. FEMA 356 criteria were used to predict the seismic performance of the building. The structural response measures such as capacity curve and inter-story drift under the set of ground motions and pushover analyses results were compared and detailed seismic performance assessment was done. The main aim of this study is considering the application and methodology for the earthquake performance assessment of existing buildings. The seismic performance of the structural model varied significantly under different ground motions. Results indicate that case study building exhibit inadequate seismic performance under different seismic excitations. In addition, reasons for the poor performance of the building is discussed.

Malfunction diagnosis of sensors based on correlation of measurements

Structural health monitoring (SHM) is a type of on-site characterization of a real-world full-scale structure that is subjected to the real-world load cases. The fundamental element of SHM is the structural response measurements by sensors, the reliability of which is significant for safety assessment and other SHM applications. The paper proposed a method to diagnosis the fault in sensors using the correlation of measurements. The correlation of the variations of the measurements is examined using the sliding time windows, which is the principle to determine the fault in the sensors. The strain measurements from the SHM system of a real world structure, Shenzhen Bay Stadium, are performed to simulate the faults in sensors and to verify the effectiveness of the proposed method.

Time-Varying Wind Load Identification Based on Minimum-Variance Unbiased Estimation

A minimum-variance unbiased estimation method is developed to identify the time-varying wind load from measured responses. The formula derivation of recursive identification equations is obtained in state space. The new approach can simultaneously estimate the entire wind load and the unknown structural responses only with limited measurement of structural acceleration response. The fluctuating wind speed process is investigated by the autoregressive (AR) model method in time series analysis. The accuracy and feasibility of the inverse approach are numerically investigated by identifying the wind load on a twenty-story shear building structure. The influences of the number and location of accelerometers are examined and discussed. In order to study the stability of the proposed method, the effects of the errors in crucial factors such as natural frequency and damping ratio are discussed through detailed parametric analysis. It can be found from the identification results that the proposed method can identify the wind load from limited measurement of acceleration responses with good accuracy and stability, indicating that it is an effective approach for estimating wind load on building structures.

Sparse and low-rank methods in structural system identification and monitoring

This paper presents sparse and low-rank methods for explicit modeling and harnessing the data structure to address the inverse problems in structural dynamics, identification, and data-driven health monitoring. In particular, it is shown that the structural dynamic features and damage information, intrinsic within the structural vibration response measurement data, possesses sparse and low-rank structure, which can be effectively modeled and processed by emerging mathematical tools such as sparse representation (SR), and low-rank matrix decomposition. It is also discussed that explicitly modeling and harnessing the sparse and low-rank data structure could benefit future work in developing data-driven approaches towards rapid, unsupervised, and effective system identification, damage detection, as well as massive SHM data sensing and management.

Automated modal parameter-based anomaly detection under varying wind excitation

Wind-induced operational variability is one of the major challenges for structural health monitoring of slender engineering structures like aircraft wings or wind turbine blades. Damage sensitive features often show an even bigger sensitivity to operational variability. In this study a composite cantilever was subjected to multiple mass configurations, velocities and angles of attack in a controlled wind tunnel environment. A small-scale impact damage was introduced to the specimen and the structural response measurements were repeated. The proposed damage detection methodology is based on automated operational modal analysis. A novel baseline preparation procedure is described that reduces the amount of user interaction to the provision of a single consistency threshold. The procedure starts with an indeterminate number of operational modal analysis identifications from a large number of datasets and returns a complete baseline matrix of natural frequencies and damping ratios that is suitable for subsequent anomaly detection. Mahalanobis distance-based anomaly detection is then applied to successfully detect the damage under varying severities of operational variability and with various degrees of knowledge about the present operational conditions. The damage detection capabilities of the proposed methodology were found to be excellent under varying velocities and angles of attack. Damage detection was less successful under joint mass and wind variability but could be significantly improved through the provision of the currently encountered operational conditions.

Relevance feature selection of modal frequency-ambient condition pattern recognition in structural health assessment for reinforced concrete buildings

Modal frequency is an important indicator for structural health assessment. Previous studies have shown that this indicator is substantially affected by the fluctuation of ambient conditions, such as temperature and humidity. Therefore, recognizing the pattern between modal frequency and ambient conditions is necessary for reliable long-term structural health assessment. In this article, a novel machine-learning algorithm is proposed to automatically select relevance features in modal frequency-ambient condition pattern recognition based on structural dynamic response and ambient condition measurement. In contrast to the traditional feature selection approaches by examining a large number of combinations of extracted features, the proposed algorithm conducts continuous relevance feature selection by introducing a sophisticated hyperparameterization on the weight parameter vector controlling the relevancy of different features in the prediction model. The proposed algorithm is then utilized for structural health assessment for a reinforced concrete building based on 1-year daily measurements. It turns out that the optimal model class including the relevance features for each vibrational mode is capable to capture the pattern between the corresponding modal frequency and the ambient conditions.

Identification of model-free structural nonlinear restoring forces using partial measurements of structural responses

Identification of nonlinear structural system is an important but challenging task for structural health monitoring. Due to the complexities of structural nonlinearities, it is hard to establish proper mathematical models for some structural nonlinear behaviors. Moreover, only partial structural responses can be measured in practice; it is essential to conduct identification of nonlinear structural systems using only partial measurements of structural responses. To cope with these issues, an algorithm is proposed in this article for the identification of some model-free structural nonlinear restoring forces using only partial measurements of structural responses. First, an equivalent linear structural system is introduced for the identification of the locations of structural nonlinearities. Then, a model-free structural nonlinear restoring force is approximated by a power series polynomial. The unknown coefficients of the power series polynomials together with other structural parameters are identified by the extended Kalman filter so that the characteristics of the behaviors of the model-free of nonlinear restoring forces can be identified. Some numerical examples including the identification of two nonlinear multi-story shear frames and a planar nonlinear truss with different structural nonlinear restoring forces are used to validate the proposed algorithm.

A Computationally Efficient Algorithm for Real‐Time Tracking the Abrupt Stiffness Degradations of Structural Elements

AbstractReal‐time structural identification and damage detection are necessary for on‐line structural damage detection and optimal structural vibration control during severe loadings. Frequently, structural damage can be reflected in the stiffness degradation of structural elements. In this article, a time‐domain three‐stage algorithm with computational efficiency is proposed for real‐time tracking the onsets, locations, and extents of abrupt stiffness degradations of structural elements using measurements of structural acceleration responses. Structural dynamic parameters before damage are recursively estimated in stage I. Then, the time instants and possible locations of degraded structural elements are detected by tracking the errors between the measured data and the corresponding estimated values in stage II. Finally, the exact locations and extents of stiffness degradations of structural elements are determined by solving simple constrained optimization problems in stage III. Both numerical examples and an experimental test are used to validate the proposed algorithm for real‐time tracking the abrupt stiffness degradations of structural elements in linear or nonlinear structures using measurements of structural acceleration responses polluted by noises.