Single-Sensor-Based Structural Response Reconstruction Using a Novel Modal Response Estimation Method

Structural response reconstruction based on empirical mode decomposition in time domain

Abstract. Smart materials with sensors can monitor the structure's performance under external loading circumstances. They may also monitor internal deformations or damages caused by environmental factors such as temperature, humidity, etc. As a result, the sensors are linked to structural health monitoring to create automated systems for structural monitoring, inspection, and damage identification. The formulation of this review article was prompted by a growing interest in structural health monitoring and the need to ensure structure safety to detect problems early and avert collapse. The structure, measurement methods, and potential of sensors such as fiber optic, piezoelectric, corrosion, ceramic, and self-sensing cement composite utilized in the health monitoring of concrete structures are discussed in this review paper. This review also includes a brief and comparative analysis of various sensors, as well as the optimal number and location of sensors. The study exposed that choosing a suitable sensor is critical for accurate sensing and long-term structure monitoring. The sensor can detect physical (stress, strain) and chemical (corrosion) variables that affect the structure's endurance. Despite significant advances in damage monitoring approaches utilizing sensors, the study suggests that efficient sensor deployment remains problematic. The review revealed that the type of parameter to be monitored (stress, strain, humidity, etc.) and the structural and climatic conditions in which the sensor will be used determine the sensor's selection. As a result, a self-sensing cement composite based on carbon nanofiber (CNF) has been developed, which has good durability and compatibility with concrete structures. However, increasing the amount of CNF lowers the composite's compressive and flexural strength due to particle agglomeration. As a result, the review covers several sensors used in structural health monitoring with their measurements, applications, benefits, and limitations.

This paper provides an analytical proof and the theoretical development of the idea of using the torsional vibration measurements for a system-level condition monitoring of the drivetrain system. The method relies on modal parameter estimation of the drivetrain system by using the torsional measurements and subsequent monitoring of the variations in the system eigenfrequencies and normal modes. Angular velocity error function extracted from encoder outputs at both input and output of drivetrain is used to estimate modal parameters including natural frequencies and damping coefficients. In the proposed condition monitoring approach, it is shown that any abnormal deviation from the reference values of the drivetrain system dynamic properties can be translated into the progression of a specific fault in the system. In order to extract the condition monitoring features, local sensitivity analysis is engaged to establish a relationship between different categories of drivetrain faults with the system dynamic properties and the amplitude of torsional response, which helps with both to identify the state of the progressive faults and to localize them. Local sensitive analysis shows that abnormal deviations in stiffness and moment of inertia due to the presence of faults result in considerable changes in natural frequencies and modal responses which can be measured and used as fault detecting features by using the proposed analytical approach. Sensitivity analysis is also employed along with the estimated modal frequency for estimation of modal damping from the amplitude of response at the natural frequencies and their subsequent use for estimation of undamped natural frequencies which are later used in the proposed condition monitoring approach. The proposed approach is computationally inexpensive and can be implemented without additional instrumentation. Two test cases, using 10 MW simulated and 1.75 MW operational drivetrains have been demonstrated.

Modal identification performs one of the most important roles in structural dynamics analysis and structural health monitoring, especially when the input excitations are not measurable. Most of the traditional blind source separation approaches can only handle determined or overdetermined blind modal identification, where the number of observed sensors is equal to or greater than the number of active modes. When the number of observed sensors is less than the number of active modes, new methods to perform underdetermined blind modal identification should be considered. To tackle this issue, a novel operational modal identification method based on an enhanced sparse component analysis with optimized clustering is proposed. Firstly, a robust K-means clustering with differential evolution algorithm is put forward to estimate the mode shape matrix utilizing the sparse property of observed mixtures. Secondly, the modal responses are recovered by the least squares method from the incomplete knowledge of the mode shape matrix and the system outputs. Subsequently, the modal responses are transformed into a time domain through time-frequency transformation, where the modal parameters are extracted. Finally, numerical simulation and experimental verification demonstrate that in both the determined and underdetermined case, the proposed method can perform accurate and robust parameter identification of structural systems.

Sensor placement optimization plays a key role in structural health monitoring (SHM) of large mechanical structures. Given the existence of an effective damage identification procedure, the problem arises as to how the acquisition points should be placed for optimal efficiency of the detection system. The global multiobjective optimization of sensor locations for structural health monitoring systems is studied in this paper. First, a laminated composite plate is modelled using Finite Element Method (FEM) and put into modal analysis. Then, multiobjective genetic algorithms (GAs) are adopted to search for the optimal locations of sensors. Numerical issues arising in the selection of the optimal sensor configuration in structural dynamics are addressed. A method of multiobjective sensor locations optimization using the collected information by Fisher Information Matrix (FIM) and mode shape interpolation is presented in this paper. The sensor locations are prioritized according to their ability to localize structural damage based on the eigenvector sensitivity method. The proposed method presented in this paper allows to distribute the points of acquisition on a structure in the best possible way so as to obtain both data of greater modal information and data for better modal reconstruction from a minimum point interpolation. Numerical example and test results show that the proposed method is effective to distribute a reduced number of sensors on a structure and at the same time guarantee the quality of information obtained. The results still indicate that the modal configuration obtained by multiobjective optimization does not become trivial when a set of modes is used in the construction of the objective function. This strategy is an advantage in experimental modal analysis tests, since it is only necessary to acquire signals in a limited number of points, saving time and operational costs.

An operational modal response method for application to the structure health and integrity of pipelines is investigated. The modal response characteristics of externally supported pipe structures are quantified through flow Reynolds number (Red) variation. Pipe flow turbulence and the resulting hydrodynamic pressure fluctuations on the interior pipe wall provide the structural forcing mechanism, and signals from wall-mounted accelerometers provide the system response. During experiments, the Reynolds number is varied from 51,000 to 154,000. Over this Reynolds number range, the pipe flow turbulence was found sufficient enough to excite the structure at frequencies up to 400 Hz. Modal response characteristics obtained through Reynolds number variation were found to be in agreement with results from impact hammer modal testing. The in-situ modal response method developed was applied to two different structural health monitoring investigations, one involving loss-of-material and the other involving loss-of-fluid. The loss-of-material scenario simulated the process of external pipe wall corrosion, and the developed method was able to detect material loss as small as 1.4%. The loss-of-fluid scenario simulated a small leak. Despite the low operating pressure of 0.024 MPa, the methodology was able to detect fluid loss as low as 0.1% of the bulk flow rate. The developed method has the potential to offer in-situ continuous pipeline health monitoring that relies on the continuous changes (flow rate, product viscosity, product density) that are inherent to an operational pipeline system.

Robust optimal sensor placement for operational modal analysis based on maximum expected utility

Detecting damage at the earliest possible stage is the most desirable feature of any structural health monitoring scheme, for its successful practical implementation in the field. Particularly, for a small damage in its incipient stage, the minor changes in the dynamic characteristics of the structures, alter only some specific modal responses. Hence the damage features present in the modal response of only some limited modes due to the minor incipient damage will not get highlighted in the measured raw dynamic signatures. Also, the presence of environmental variability (EOV), which alter the dynamic characteristics and signature, mask the existence of the minor incipient damage from diagnosis, while using conventional damage diagnostic algorithms. In this paper, a new online health monitoring technique is proposed to handle the EOV and locate the minor damage in the structure. In the proposed online SHM scheme, we use the cointegration technique to handle the EOV. During online monitoring, the cointegrating vectors are obtained from the recent healthy data denoted as ‘baseline data’, collected from the structure. Subsequently, these vectors are used to filter out the confounding effects of EOV of the current data. During damage diagnosis with the current data, if the state of the structure is found to be healthy, then the ‘baseline data’ is updated with the current data along with their corresponding freshly evaluated cointegrating vectors. We later employ the blind source separation (BSS) technique on the cointegrated time series, free from EOV, to decompose the dynamic response into modal responses. Then we employ an automated algorithm proposed in this paper, on the decomposed signals (i.e. modal responses) in order to identify and isolate the modal responses with the damage features. Finally, the location of the damage is identified using a damage index, formulated with the isolated modal responses. Numerical simulation studies and experimental studies are carried out to test and evaluate the proposed online damage diagnostic technique and their capability in identifying minor/incipient damage like small cracks considering environmental variability with measurement noise.

Structural response reconstruction based on the modal superposition method in the presence of closely spaced modes

The basic hypothesis of a structural health monitoring (SHM) system is that the global parameters like stiffness, mass, and damping of a structure are modified by damage and so the dynamic response. Nevertheless, in the case of subtle incipient damage, the changes in the dynamic characteristics of the structures developed in the structure alter only a few modal responses that too in a very mild manner, while all other modal responses remain intact. The damage features present in the modal responses of those few modes will be hidden in the measured total raw dynamic signatures. Often they get buried in the measurement noise. Keeping this in view, in this paper, a hybrid damage diagnostic algorithm combining a multivariate analysis technique called blind source separation (BSS) with time series analysis to identify and locate the minor cracks in structures is proposed. BSS decomposes the measured acceleration time-history responses into modal responses. We use an automated algorithm to isolate the modal responses which are sensitive to the presence of minor/subtle damages. These isolated modal responses are then reconstructed using the mixing matrix to obtain a new time-history data which is enriched with the minor damage features. The presence and spatial location of damage are obtained by processing the reconstructed time-history data using autoregressive–autoregressive with exogenous input (AR-ARX) model, using a Density Function of Probability (PDF), of the prediction errors. Both the numerical simulation studies and experimental studies are carried out to test and evaluate the proposed damage diagnostic algorithm and their capability in identifying minor/incipient damage like subtle cracks under noisy measurements.

A method of sensor placement for the purpose on-orbit modal identification and test-analysis correlation is presented. The method is an extension of the Effective Independence method presented in past work to include the effects of a general representation of measurement noise. Sensor noise can be distributed nonuniformly throughout the structure as well as correlated between sensors. The only restriction is that the corresponding noise covariance intensity matrix is positive definite. The technique presented offers a fast and efficient approach for reducing a relatively large initial candidate sensor location set to a much smaller optimum set which retains the linear independence of the target modes and maintains the determinant of the Fisher Information Matrix resulting in improved modal response estimates. The noise covariance intensity matrix which has been introduced into the method can be thought of as a sensor weighting matrix which modifies the shape of the target modes. The mode shape coefficients are modified based upon the noise levels at the sensor locations. Inclusion of the noise model results in higher ranking of sensor locations with low noise levels and suppression of sensor locations with high noise levels. A criterion is also presented which can be used during the course of the sensor placement analysis to determine how many sensors are required to maintain a desired level of signal-to-noise ratio over all the target modes. Simple numerical examples are presented which clearly demonstrate the ideas and trends presented in the paper.

3D torsional experimental strain modal analysis for structural health monitoring using piezoelectric sensors

Suppression of several different modal responses in split-path transmissions by mesh phasing

The aim of this study is to propose a new output-only system identification technique using a virtual 1-DOF mass tuner(VMT) which is analogous to the tuned mass damper and has a characteristics to amplify the response of the measured acceleration responses of building structure. The VMT is a kind of modal filter that its response is maximized in the range of the natural frequency of a structure, and damping ratio of the structure can be identified using the response ratio of VMT at the different damping ratios consisting the VMT. Also, it is shown that the modal parameters can be precisely estimated if the VMT were applied to the mode response separated with mode decomposition method in the state space. For the verification of the proposed technique, the identification process is applied to the measured acceleration responses from 40 story steel frame structure when typhoon approached to the building. From the numerical simulation, it is found that the modal responses are well separated in the state space, the modal parameters are precisely identified with the proposed modal property estimation method.

PurposeThe purpose of this paper is to further validate a wireless sensor system developed at Clarkson University for structural monitoring of highway bridges. The particular bridge monitored employs a fiber reinforced polymer (FRP) panel system which is fairly innovative in the field of civil engineering design. The superstructure was monitored on two separate occasions to determine a change in structural response and see how the structural system performs over time.Design/methodology/approachA series of wireless sensor units was deployed at various locations of the steel superstructure, to measure both the modal response from acceleration measurements as well as quasi‐static and dynamic strain response. Ambient and forced loading conditions were applied to measure the response. Data results were compared over two separate periods approximately nine months apart.FindingsThe first eight mode shapes were produced from output‐only system identification providing natural frequencies ranging from approximately 6 to 42 Hz. The strain response was monitored over two different testing periods to measure various performance characteristics. Neutral axis, distribution factor, impact factor and end fixity were determined. Results appeared to be different over the two testing periods. They indicate that the load rating of the superstructure decreased over the nine month period, possibly due to deterioration of the materials or composite action.Research limitations/implicationsThe results from the two testing periods indicate that further testing needs to be completed to validate the change in response. It is difficult to say with certainty that the significant change in response is due to bridge deterioration and not other factors such as temperature effects on load rating. The sensor system, however, proved to provide high quality data and responses indicating its successful deployment for load testing and monitoring of highway infrastructure.Originality/valueThe paper provides a depiction of the change in structural behavior of a bridge superstructure using a wireless sensor system. The wireless system provided high‐rate data transmission in real time. Load testing at two different points in time, eight months apart, showed a significant change in bridge behavior. The paper provides a practical and actual physical load test and rating during these two periods for quantifiable change in response. It is shown that the wireless system is capable of infrastructure monitoring and that possible deterioration is expected with this particular bridge design. Additionally, the load testing occurred during different seasons, which could create cause for temperature effects in load rating. This can provide a basis for future performance monitoring techniques and structural health monitoring.