Field Of Structural Health Monitoring Research Articles

Lamb wave based damage imaging in variable thickness plates

The researches on Lamb wave based damage localization for constant thickness plates have been widely investigated in the field of structural health monitoring, while the issue of Lamb wave based damage imaging in variable thickness plates is rarely addressed. This is because the Lamb wave propagation characteristics in plates with varying thickness is more complex than that with constant thickness. In this study, a Lamb wave based damage imaging method using a sensor array is proposed for damage localization in variable thickness plates. In the process of point-by-point imaging within the interested imaging area, a signal back-propagation operator based on a Lamb wave propagation model can deal with the problem of dispersion compensation for Lamb waves propagating in variable thickness plates. The Lamb wave propagation model, which is based on the assumption that Lamb waves propagating in a variable thickness plate can be seen as that propagating in a sequence of short and constant thickness plates with different thicknesses, can predict Lamb wave response waveform in variable thickness plates. Numerical simulations and experiments on aluminum plates with linearly varying thicknesses are implemented, and the imaging results validate the effectiveness of the proposed method.

Robust elastic wave sensing system with disordered metasurface and deep learning

Elastic wave sensing is a crucial information acquisition technology with extensive applications in structural health monitoring, nondestructive testing, and other fields. However, traditional elastic wave sensing systems face challenges such as poor performance, high power consumption, and limited adaptability in complex environments. Here, a robust elastic wave sensing system integrating disordered metasurface and deep learning is demonstrated, enhancing the sensing performance in the environments with harsh noise or unknown signals. The scheme fully utilizes the complementary advantages of disordered metasurface and deep learning in physical encoding and intelligent decoding respectively. The meticulously designed disordered metasurface efficiently encodes elastic waves, and a single sensor acquires the encoding signals, enabling low-power information acquisition. The deep learning model performs adaptive and rapid intelligent decoding of the encoding signals, achieving efficient and robust information sensing while overcoming the sensing limitations of traditional compressed sensing in complex scenarios with low SNR and unknown signals. A series of experimental results demonstrate that, even under severe noise interference (known signal SNR≥−15dB, unknown signal SNR≥−7dB), the system can sense location information in elastic waves with a millisecond-level sensing speed and an accuracy above 90%. Furthermore, the successful application of the sensing system in vibration-tracking imaging and mechanical reading–writing further validates its practicability and robustness. This work may open up new avenues for the potential application of intelligent sensing in the fields of structural health monitoring, nondestructive testing, and human–machine interaction.

Study on Strain Field Reconstruction Method of Long-Span Hull Box Girder Based on iFEM

The box girder’s condition significantly impacts the safety and overall performance of the entire ship because it is the primary stress component of the hull construction. This work used experimental research on the long-span hull box girder based on IFEM (Inverse Finite Element Method) technology to ensure the structural safety of the hull box girder. Due to the limitations of conventional experiments in this technical field, such as their reliance on finite element data and lack of input from physical tests, numerous research methods combining the strain sensing data from physical tests with the strain data from virtual sensors were conducted. The strain fields of the top plate, side plate, and bottom plate were each reconstructed in turn, and the verifier measuring points in the physical model test were used to assess the accuracy of the reconstruction results. The findings demonstrate that the top plate, side plate, and bottom plate reconstructions had relative errors of 0.24–7.86%, 0.75–8.13%, and 3.31–2.52%, respectively. This enables the reconstruction of the strain field of the long-span hull box girder using physical test data and promotes the use of iFEM technology in the field of structural health monitoring of large marine structures.

Study of Large Strain OFDR Sensor Based on Inclined Transfer Structure

In the fields of structural health monitoring, civil engineering safety monitoring, aerospace and other fields, the key challenge is to increase the range of strain measurements to solve with the information monitoring of large strains. Reducing the strain sensitivity of the sensor is an important way to solve the problem of small sensor ranges. In this paper, the inclined transfer structure is proposed to achieve large strain distributed optical fiber sensing. When the fiber is axially stretched directly to fracture, the inclined transfer structure is used to increase the strain measurement range of the system. The theoretical relationship between the strain monitored by single mode fiber sensors and the matrix strain is established. It is experimentally verified that the inclined transfer structure using polypropylene material as the matrix achieves the strain measurement from 36667[Formula: see text][Formula: see text] at sensing spatial resolution of 8[Formula: see text]mm, 10[Formula: see text]nm wavelength tuning range of the laser source and [Formula: see text] inclined angle, obtaining a good linear fit of more than 0.99. One hour stability of less than 11[Formula: see text]pm is obtained, corresponding to the strain of 9[Formula: see text][Formula: see text].

Study of factors affecting the magnetic sensing capability of shape memory alloys for non-destructive evaluation of cracks in concrete: Using response surface methodology (RSM) and artificial neural network (ANN) approaches

Currently, the field of structural health monitoring (SHM) is focused on investigating non-destructive evaluation techniques for the identification of damages in concrete structures. Magnetic sensing has particularly gained attention among the innovative non-destructive evaluation techniques. Recently, the embedded magnetic shape memory alloy (MSMA) wire has been introduced for the evaluation of cracks in concrete components through magnetic sensing techniques while providing reinforcement as well. However, the available research in this regard is very scarce. This study has focused on the analyses of parameters affecting the magnetic sensing capability of embedded MSMA wire for crack detection in concrete beams. The response surface methodology (RSM) and artificial neural network (ANN) models have been used to analyse the magnetic sensing parameters for the first time. The models were trained using the experimental data obtained through literature. The models aimed to predict the alteration in magnetic flux created by a concrete beam that has a 1 mm wide embedded MSMA wire after experiencing a fracture or crack. The results showed that the change in magnetic flux was affected by the position of the wire and the position of the crack with respect to the position of the magnet in the concrete beam. RSM optimisation results showed that maximum change in magnetic flux was obtained when the wire was placed at a depth of 17.5 mm from the top surface of the concrete beam, and a crack was present at an axial distance of 8.50 mm from the permanent magnet. The change in magnetic flux was 9.50 % considering the aforementioned parameters. However, the ANN prediction results showed that the optimal wire and crack position were 10 mm and 1.1 mm, respectively. The results suggested that a larger beam requires a larger diameter of MSMA wire or multiple sensors and magnets for crack detection in concrete beams.

3DGEN: a framework for generating custom-made synthetic 3D datasets for civil structure health monitoring

The availability of high-quality datasets is increasingly critical in the field of computer vision-based civil structural health monitoring, where deep learning approaches have gained prominence. However, the lack of specialized datasets for such tasks poses a significant challenge for training a reliable model. To address this challenge, a framework, 3DGEN, is proposed to swiftly generate realistic synthetic 3D datasets which can be targeted for specific tasks. The framework is based on diverse 3D civil structural models, rendering them from various angles and providing depth information and camera parameters for training neural networks. By employing mathematical methods, such as analytical solutions and/or numerical simulations, deformation of civil engineering structures can be generated, ensuring a reliable representation of their real-world shapes and characteristics in the 3D datasets. For texture generation, a generative 3D texturing method enables users to specify desired textures using plain English sentences. Two successful experiments are conducted to (1) assess the efficiency of generating the 3D datasets using two distinct structures, (2) train a monocular depth estimation network to perform 3D surface reconstruction with the generated dataset. Notably, 3DGEN is not limited to 3D surface reconstruction; it can also be used for training neural networks for various other tasks. The code and dataset are available at: https://github.com/YANDA-SHAO/Beam-Dataset-SE

Accelerometer static state detection (SSD)-assisted GNSS/accelerometer bridge monitoring algorithm

Abstract In the field of structural health monitoring (SHM), a loosely coupled (LC) Kalman filtering algorithm that accounts for baseline drift errors is commonly used to integrate GNSS data with accelerometer data. In the LC algorithm, the baseline drift errors are considered unknown parameters that need to be estimated. In scenario of continuous float solutions, the estimation of baseline drift error is often inaccurate, leading to the divergence of monitoring results. Theoretically, as a type of motion sensor, accelerometers are expected to qualitatively determine the priori state of bridges, whether dynamic or static. Utilizing the inherent characteristics of accelerometers and the principle of zero-velocity detection in integrated navigation, we originally propose a bridge static state detection (SSD) method based on low-cost accelerometer, and introduces this prior SSD information as a constraint in GNSS/accelerometer LC algorithm, called SSD-LC bridge monitoring algorithm. Through a simulation platform and real-world bridge monitored tests, the effectiveness of our proposed SSD method has been verified. Furthermore, our proposed SSD-LC bridge monitoring algorithm can effectively mitigate the divergence problem in baseline drift estimation that occurs with continuous GNSS float solutions in traditional algorithms, which can effectively avoid misjudgments and false alarms in bridge monitoring during GNSS anomalies.

Reliability Assessment of Fiber Optic Shape Sensing

Fiber optic shape sensing is a promising technology capable of enriching the field of Structural Health Monitoring (SHM), with many potential applications that expand the uses of distributed optical fiber sensors. The operational principle is based on the simultaneous strain acquisition from several optical fiber cores deployed in a single sensing cable (or multicore fiber). The parallel strain traces of these cores can be combined to extract curvature and torsion distributions along the sensing cable, that can be used for the three-dimensional reconstruction of the underlying shape. This study evaluates the reliability of fiber optic shape sensing for damage detection through the use of a model-assisted probability of detection framework specifically developed to simulate a carbon fiber-reinforced polymers specimen under quasi-static loading monitored by distributed optical fiber sensors based on Rayleigh backscattering. Specifically, we compare the performance of a traditional distributed optical fiber strain sensor with the one of a hypothetical distributed shape sensing cable (or multicore fiber). To perform this comparison, we redefine the damage index definition, which is usually based on the measured strain values, to make it compatible with shape sensing, where it can be defined in terms of curvature and torsion. With these preliminary results, we aim to evaluate whether shape sensing technology can be employed for damage detection to detect damage-related deformation, whether we can obtain better results compared to traditional optical fiber sensor applications, and discuss how damage metrics need to be modified. In future activities, these aspects will be further investigated taking into account other case studies and shape sensing configurations.

3D Vibration Analysis using Phase-Based Displacement Estimation and Stereo Cameras

Non-contact sensors are increasingly integral to the field of Structural Health Monitoring (SHM), with camera being widely utilized due to their high spatial resolution and cost-effectiveness in measuring structural displacements. Phase-based optical flow (POF) techniques have proven valuable for accurate and computationally efficient 2D vibration measurements. However, these techniques are typically confined to single-camera systems and encounter challenges in measuring vibrations in out-of-plane directions. Previous research on 3D vibration measurement has predominantly centered on pixel intensity-based techniques using stereo camera systems. Although these methods demonstrate high performance in calculating global strains and stresses, they are less suitable for accurate vibration measurement. To address these limitations, this study proposes a novel 3D vibration measurement approach that integrates POF within the context of stereo camera systems. 2D vibrations are extracted by applying Complex Gabor filters to stereo images, and subsequently, 3D vibration measurements are estimated through camera calibration and triangulation, using computed camera internal and external parameters. To validate the method, modal analysis experiments are conducted on an aluminum plate. The 3D vibration measurement results are compared with those obtained through 3D Digital Image Correlation (DIC) and contact sensors and the accuracy is demonstrated.

Evaluating Unmanned Aerial Vehicles for Vibrational Analysis: Exploiting Integrated Capabilities of Nano-Drones as Nodes in a WSN

Addressing the aging infrastructure challenge in both civil and industrial sectors has spurred the development of advanced sensor technologies and novel inspection methodologies, significantly contributing to the field of Structural Health Monitoring (SHM). While conventional sensors, such as structure-mounted accelerometers, have demonstrated high effectiveness, their deployment may be difficult or even impossible in high-risk environments like post-seismic areas, where the installation procedure hampers the operators' safety. Hence, this study aims to evaluate the characteristics of a novel sensing platform compatible with autonomous deployment for vibration inspection of infrastructures. In particular, we explore the use of Unmanned Aerial Vehicles (UAVs), with a specific focus on nano-drones, as a viable and promising solution due to their compact size and cost-effectiveness. In particular, Crazyflie 2.1 nano-drones are exploited as reference platforms, given their characteristics in terms of versatility and electrical parameters. The objective is to utilize the on-drone MEMS-based Inertial Measurement and Microcontroller Unit (IMU and MCU) to perform, at the same time, both flight control and navigation, and vibration inspection. This approach eliminates the need for additional hardware, going beyond other successful drone applications in SHM, such as visual inspections, sensors deployment, and distance measurements. The proposed solution is validated through a comparison with commercial sensors for SHM. Multiple drones can be combined to deploy wireless sensor networks in hard-to-reach locations, ready for vibration monitoring with minimal software adjustments, offering a novel approach to SHM. The results indicate that the Crazyflie drone is capable of detecting even small variations in the dynamic response of a beam, with a maximum deviation of 1% compared to commercially available counterparts designed for SHM purposes.

A Study on XANNs for Analyzing Failures in Guided Ultrasonic Wave-based Damage Localization

In the field of Structural Health Monitoring (SHM) using Guided Ultrasonic Waves (GUW), machine learning (ML) approaches for data analysis are becoming increasingly popular. Especially, deep learning with artificial neural networks (ANN) has proven effective due to its ability to process a large amount of data. ANN are commonly employed in damage localization tasks, where, with appropriate training, they deliver good results. However, a significant challenge persists in the application of ANN, namely, their "black-box" nature, which hinders the investigation of decision processes within the ANN and makes it difficult to understand why an ANN model fails under certain inputs. In the present work, an already introduced explainable artificial neural network (XANN) approach will be utilized to investigate when and why a trained XANN model fails with given inputs. The Open Guided Wave (GUW) platform's data is employed to train and test a XANN model designed to predict the location of artificial damage. Subsequently, individual inputs are modified (simulating malfunctions in specific sensor paths), and the impact on decision processes within the XANN architecture is examined. The aim of this study is to investigate and enhance the resilience and explainability of ANN approaches in the SHM domain.

Design of self-healing materials for the integration of structural health monitoring (SHM^2)

Integration of the complementary fields of structural health monitoring in self-healing materials (SHM2) has the potential to transform the traditional engineering concepts of fail safe and damaged tolerant design. Structural health monitoring seeks to embed and automate sensing capabilities within structures to determine their state and to detect degradation or damage. Once degradation or damage is detected, additional decisions and potential action are required. Reducing operational envelopes can prevent further damage accumulation or catastrophic failure or repairs can be performed to correct the degradation. Typical repair requires active involvement of personnel and potentially down time. Self-healing materials seek to avoid maintenance needs and down time through the creation of structures and materials with an imbued capability to repair damage. Together SHM^ 2 has the potential to create a closed loop where damage is detected using embedded sensors and automated analysis that can then initiate self-healing. The highly structured and controlled nature of self-healing materials presents an opportunity to design structures that additionally support health monitoring capabilities. This paper presents recent research and results informing the design of shape memory alloy (SMA) fiber reinforced metal matrix composites (MMCs) to optimize self-healing capabilities and structural health monitoring (SHM^2). Fiber pull tests were performed to analyze the strength of the interface between the SMA fibers and matrix allowing for sizing to complement both composite design and healing capabilities. Analysis was performed to understand complex failure mechanisms occurring at the interface between detwinning shape memory alloys and the metal matrix. And novel composite design was performed to support both the self-healing and damage detection capabilities of the material structure.

A radar transducer for unidirectionally emitting and steering SH guided wave

It is of practical importance to emit a pure wave mode, focus its energy along a given direction, and then steer the wave beam in guide-wave-based structural health monitoring (SHM) because it can quickly scan the overall structure. Such a goal is usually realized using a two-dimensional (2D) phased array, which requires many transducer elements and expensive electronics. This work proposed a radar transducer (RD-T) for unidirectionally emitting and steering the fundamental shear horizontal wave (SH0 wave). The proposed RD-T consists of an annular metasubstrate and several rectangular thickness-shear (d15) piezoelectric wafers. The metasubstrate is designed to provide the required phase gradient for unidirectionally emitting and sensing a pure SH0 wave, so no extra time delay is required for driving the RD-T. The beam steering is obtained by activating the subunits one by one. The SH0 wavefields generated by the subunit are described by a theoretical model and the effects of dimension parameters are analyzed. Finite element simulations and experiments are conducted to examine the performances of the RD-T. Both simulated and experimental results indicate that from 200 kHz to 270 kHz, the RD-T can unidirectionally emit an SH0 wave with a high SNR (signal-to-noise ratio) and steer the wave beam along different directions. The performance of the RD-T on damage detection is then investigated by pulse-echo experiments. It can be found that the RD-T can successfully distinguish symmetric defects and locate defects with an acceptable error. Compared with the traditional 2D phased array, the RD-T can realize 360° scanning of the overall structure more efficiently, exhibiting great potential in the field of SHM.

Transfer learning via intermediate structures

Recent advances have been made in the field of population-based structural health monitoring (PBSHM), which seeks to share valuable information across a population to improve inferences regarding the health states of the members. However, enabling knowledge transfer between structures with highly disparate features (i.e., heterogeneous populations) is an ongoing challenge. The current work proposes a technique for knowledge transfer within a heterogeneous population, via intermediate structures that help bridge the gap in information between the structures of interest. The transformation from the source to the intermediate and target domains is based on geodesic flows, to incrementally map between changes in geometric and statistical properties. The proposed technique is demonstrated using simulated lumped-mass systems.

Guided Wave Phased Array Ultrasonic Imaging for Thin Plate Inspection

This study focuses on the application of phased array ultrasonic testing with guided waves for Structural Health Monitoring (SHM) in thin plates. Addressing the limitations of conventional ultrasonic testing efficiently by inspecting thin, long structures. This study employs phased array technology to thin isotropic plates at high frequency(2MHz), thereby elevating imaging and defect detection in structural components. Through the utilization of the full matrix capture (FMC) scanning approach in 3-D finite element (FE) simulations, A0 and S0 modes were generated on steel plates with through-hole geometries. The process involved capturing reflected signals to form an FMC matrix that includes all A-scan signals. Subsequently, the total focusing method (TFM) algorithm was applied to FMC data for the reconstruction of focused images of A0 and S0 modes separately. A key improvement in our approach is integrating a time-domain filtering method into the FMC data. This enhancement addresses the dispersive nature of guided waves, thus improving the accuracy in identifying defect locations and sizes within the images. Our finite element simulations on steel specimens, with varied through-hole locations, revealed the method's potential in accurately imaging defects located deeper within the structure. Additionally, the study expanded to evaluate the efficacy of phased array ultrasonic testing (PAUT) in SHM, particularly in conjunction with guided waves to study the flaw detection sensitivity of the defect through the TFM algorithm on isotropic steel plates up to wavelength(λ)/16. This whole analysis considered crucial factors such as ultrasonic wave mode, frequency, and group velocity for the structure under inspection. This study represents a significant contribution to the field of SHM, introducing a sophisticated, real-time monitoring methodology that promises to enhance structural integrity assessment. Keywords: SHM, PAUT, GW, FMC, TFM FE Simulations, Time Domain Filtering, Ultrasonic Testing.

Spatiotemporal energy regulation strategy for enhancing SNR and spatial resolution in the damage detection with SH0 waves

The fundamental shear horizontal (SH0) wave, which can be generated by electromagnetic acoustic transducers (EMATs), is widely used in the structural health monitoring fields owing to its non-dispersive nature and the ability to detect over long distances. However, current SH0 wave methods hardly achieve the excellent signal-to-noise ratio (SNR) of the echo signals and satisfactory spatial resolution to defects due to the co-restriction between them. To address these issues, a spatiotemporal energy regulation strategy (STERS) is proposed in this paper to optimize energy distribution in the temporal and spatial dimensions. First, spatiotemporal pulse compression technology (STPCT) is proposed to improve both SNR and spatial range resolution for defect detection. Second, a staggered dual-exciter employing two sets of excitation signals is designed to improve the spatial azimuth resolution. Besides, a double sidelobe suppression algorithm (DSSA) is proposed to suppress sidelobe issues arising from the application of STPCT, thereby further improving the performance of STPCT. Finally, multiple simulations and experiments are executed to demonstrate the advantages of the proposed damage detection system. Results show that our methods can achieve comprehensive improvement in SNR, spatial range resolution, spatial azimuth resolution, and sidelobe suppression ability.

Damage identification in sandwich structures using Convolutional Neural Networks

The increasing complexity of structures and materials, coupled with ever more stringent demands for safety and cost reduction in maintenance operations, has driven the need to develop advanced techniques for structural integrity monitoring, known as Structural Health Monitoring (SHM). In this context, this study investigates the use of image processing techniques of mode shapes in a composite sandwich panel, employing various Convolutional Neural Network (CNN) models, with the purpose of identifying damage. The main objective is to classify the type of damage, whether it is in the core, at the interface, or in the laminate, followed by the precise location of the flaw and determination of damage dimensions in terms of length and width. To achieve these goals, the finite element method was used to create a representative database, and subsequently, an efficient data management system and model implementation were established to optimize computational costs. The results obtained show that, in the classification task, a high accuracy in damage type identification (99%) was achieved, even when images had high levels of noise. Regarding the regression task for damage localization, satisfactory results were obtained, while the dimensioning of damage length proved acceptable, albeit with some limitations, and inclination identification presented challenges. This study represents a significant advancement in the field of SHM and explores both the advantages and limitations of using Convolutional Neural Networks for this purpose. The results obtained provide valuable insights for the practical application of these techniques in the detection and assessment of damage in sandwich structures, thus contributing to enhancing the safety and efficiency of maintaining such structures.

Mn-doped 0.67BiFeO3-0.33BaTiO3 ceramic sensor for high-temperature structural health monitoring

Real-time monitoring of structural health status is very important for supersonic aircraft, since the long-term operation in harsh service environments, such as high temperatures, can cause potential damage. Structural health monitoring (SHM) based on lamb wave has been approved to be a critical technique for the reliable operation of supersonic aircraft, but is limited by the operating temperature of conventional piezoelectric sensors, which makes it difficult to meet the high-temperature monitoring requirements. The BiFeO3–BaTiO3 ceramics exhibit excellent piezoelectric properties and high Curie temperature (Tc), making them promising for high-temperature SHM of supersonic aircraft. Here, we fabricated a piezoelectric sensor using 0.67BiFeO3-0.33BaTiO3-0.25%molMnO2 (BF33BTMN-025) ceramic, which exhibits a piezoelectric charge constant (d33) of 135 pC/N at room temperature and a Tc of 448 °C. The BF33BTMN-025 ceramic sensor operates effectively at temperatures up to 200 °C and maintains stable damage monitoring sensitivity as well. Compared with Pb(Zr, Ti)O3 (PZT), BaTiO3 (BTO) and other piezoelectric sensors commonly used in SHM field, the BF33BTMN-025 ceramic sensor has a higher operating temperature and a comparable sensitivity. Our work demonstrates that the BF33BTMN-025 ceramic sensor can be employed as piezoelectric sensor for high-temperature SHM, which has a wide application potential in the field of real-time monitoring of supersonic aircraft.

Structural displacement measurement using deep optical flow and uncertainty analysis

Displacement serves as a crucial indicator in the field of structure health monitoring for assessing the condition of civil engineering structures. Computer vision is commonly employed for this purpose due to its cost-effectiveness and convenience. Traditional non-contact computer vision methods, such as optical flow, have been applied to obtain the displacement of bridges. However, real-time monitoring remains challenging due to the computational complexity involved. Therefore, optical flow based on deep learning (referred to as deep optical flow) has gained significant attention. Its main advantage lies in its ability to achieve real-time displacement monitoring, which is of great significance. Furthermore, the accuracy of deep optical flow is comparable to that of traditional optical flow methods for displacement measurement. In this paper, the deep optical flow, RAFT-GOCor, is proposed and applied to extract the displacement of structures, then Bayesian RAFT-GOCor based on Monte Carlo dropout is also presented and applied to analyze the uncertainty of the displacement. The algorithms are verified by laboratory simulated experiments and field bridge loading test. The results indicate that both deep optical flow and uncertainty analysis are feasible methods for measuring structural displacement.

Applying matrix regularization to identification of traffic-induced equivalent loads and multi-vehicle weight on beam-like bridge

Identification of traffic-induced forces is an important topic in the field of bridge structural health monitoring (B-SHM). It can provide reliable data to support the great demand for monitoring and evaluating the working conditions of bridges. Bridges may serve under consistent moving vehicles and this requires that the methods of moving force identification (MFI) should be applicable under circumstances such as multiple-vehicle loading and long-term monitoring. Centering on cases containing multiple vehicles, this study proposed a matrix regularization-based method for the identification of traffic-induced equivalent loads and multi-vehicle weights. Herein, multiple moving forces in the spatial domain are converted into a certain number of equivalent loads which virtually act at fixed locations on the bridge as a kind of coordinate transformation. The MFI problem then can be transformed into tasks of identifying some concentrated forces. To solve the problem of equivalent load identification, the structural input-output relationship is firstly reorganized in a matrix-matrix-matrix form with the help of segmentation via time windows and consideration of unknown structural initial conditions. Then the matrix regularization with a sparse penalty term is introduced to formulate an identified equation so that, it can ensure the strong noise robustness of the identified results. Finally, the total weight of multiple vehicles can be empirically estimated from the sum of the identified equivalent loads. Numerical simulations and model experiments are performed to verify the proposed method's performance. The effects of vehicle speeds, measuring noise, number of modal orders, number of vehicles, and vehicle spacings are investigated. The illustrated results show that the proposed method turns out to be effective and precise in identifying the traffic-induced equivalent loads and the weight of multiple vehicles.