Prestressed anchorage device piezoelectric array arrangement device and damage monitoring system and method

Abstract

The invention relates to a prestressed anchorage device piezoelectric array arrangement device and a damage monitoring system and method. The device comprises a measuring ring framework, a measuring ring fixing and adjusting nut, an ultrasonic probe and a piezoelectric probe pressure adjusting nut, the measuring ring framework is of an annular structure, the inner diameter of the measuring ring framework is matched with the outer diameter of a prestressed anchorage device, and mounting holes are evenly distributed in the annular structure. The measuring ring fixing and adjusting nuts are distributed along the outer ring of the measuring ring framework at equal intervals and used for fixing the measuring ring framework to the periphery of the prestressed anchorage device. The ultrasonic probe is mounted in a mounting hole of the measuring ring framework through a piezoelectric probe pressure adjusting nut; the piezoelectric probe pressure adjusting nut is used for pushing the ultrasonic probe to press the surface of the pre-stressed anchorage device, and flexible pre-tightening is achieved through the belleville spring. Piezoelectric array alternating excitation and multi-path analysis can achieve damage positioning of the circumferential position of the anchorage device, force value correction can be achieved under the condition that damage exists, and the monitoring precision of the damage of the prestressed anchorage device is improved.

Description

Technical Field

[0001] This invention relates to the field of prestressed anchor monitoring technology, and in particular to a piezoelectric array arrangement device, damage monitoring system and method for prestressed anchors. Background Technology

[0002] Prestressed anchorages are crucial components in prestressed concrete structures, responsible for prestress transfer and anchorage. Their service condition directly impacts the overall structural performance and safety margin. During long-term service, anchorages may be affected by factors such as temperature and humidity changes, corrosive media, load cycles, and relaxation, leading to degradation phenomena such as prestress loss, localized corrosion, and crack propagation. Therefore, developing monitoring methods capable of rapidly identifying the stress state and localized damage of anchorages is of great significance for bridge, tunnel, and building construction projects. Existing technologies for anchorage monitoring mainly employ resistance strain gauges, fiber optic gratings, and embedded force sensors to estimate anchorage force by directly measuring local strain or force values. However, these sensors typically require pre-embedding during structural construction or fixed installation on the anchorage surface, limiting their placement and making implementation difficult on existing structures. Furthermore, limitations in space and installation conditions restrict the number of sensors, hindering multi-point distributed monitoring and resulting in insufficient sensitivity to damage such as localized corrosion and contact degradation in the porous structure of anchorages.

[0003] To address these issues, some studies have employed piezoelectric ceramic (PZT) electromechanical impedance technology, measuring impedance changes under high-frequency excitation to reflect local stiffness variations. While this method is highly sensitive to contact damage, its application in practical anchorages faces challenges such as difficult installation, non-reusable bonding methods, inconsistent coupling forces, difficulties in multi-point placement, and susceptibility to temperature and environmental noise at high frequencies. Therefore, it struggles to meet the engineering requirements for rapid on-site deployment and array-based monitoring. Furthermore, some studies have utilized piezoelectric sensors to actively transmit swept-frequency signals, analyzing the frequency response function, power spectral density, peak amplitude, and other characteristics of the received signals to characterize stiffness changes on structural surfaces or interfaces. These methods can reflect local damage in general metal structures or contact components, but when applied to complex-shaped, space-constrained prestressed anchorages, they still suffer from inconvenient sensor placement, poor consistency among multiple sensors, difficulty in using response differences for reliable positioning, and difficulty in distinguishing between damage and anchorage force changes. In particular, the lack of existing technologies for the synchronous placement of multiple piezoelectric sensors tailored to the porous geometry of anchorages makes array-based monitoring difficult to achieve.

[0004] Traditional prestressed anchorage monitoring methods often rely on adhesive bonding or single-point clamping of sensors, which are inconvenient to install and have unstable coupling, making it difficult to ensure the consistency of signals from multiple measurement points and affecting monitoring accuracy. Existing methods generally lack array signal processing mechanisms for multiple sensors, making it impossible to extract physically meaningful indicators from the signals by utilizing the correlation between multi-point responses. Furthermore, the rough contact interface between the anchorage end and the anchor plate can change reflected or transmitted waves when damaged by corrosion or contact degradation, easily leading to misjudgments and affecting monitoring reliability. Therefore, traditional prestressed anchorage monitoring methods often suffer from low monitoring accuracy and reliability due to inconvenient sensor installation, lack of array signal processing mechanisms, and difficulty in distinguishing between damage and force change signals. Summary of the Invention

[0005] Based on this, in order to solve the above-mentioned technical problems, a piezoelectric array arrangement device, a damage monitoring system and method for prestressed anchors are provided, which can improve the monitoring accuracy and reliability of prestressed anchor damage.

[0006] A piezoelectric array arrangement device for prestressed anchors, the device comprising a measuring ring frame, a measuring ring fixing and adjusting nut, an ultrasonic probe, and a piezoelectric probe pressure adjusting nut, wherein:

[0007] The measuring ring skeleton is a ring structure with an inner diameter matching the outer diameter of the prestressed anchor, and mounting holes are evenly distributed on the ring structure.

[0008] The measuring ring fixing adjustment nuts are evenly distributed along the outer ring of the measuring ring skeleton, and are used to fix the measuring ring skeleton to the outer periphery of the prestressed anchor, restricting the axial and circumferential movement of the measuring ring skeleton;

[0009] The ultrasonic probe is installed in the mounting hole of the measuring ring skeleton through the piezoelectric probe pressure adjusting nut, forming a circumferentially distributed piezoelectric sensor array;

[0010] The ultrasonic probe includes a probe sleeve, a piezoelectric head, a butterfly spring, and a pressure sensor; the piezoelectric head includes a front contact cover plate, a piezoelectric element, and a rear metal cover plate.

[0011] The piezoelectric probe pressure adjusting nut is used to push the ultrasonic probe to press against the surface of the prestressed anchor, and the butterfly spring is used to achieve flexible pre-tightening.

[0012] In one embodiment, the measuring ring skeleton is made of metal; the piezoelectric probe pressure adjusting nut is used to adjust the contact pressure between the piezoelectric head and the surface of the prestressed anchor.

[0013] In one embodiment, the pressure sensor is a thin-film pressure sensor used to monitor the contact pressure between the piezoelectric head and the surface of the prestressed anchor in real time.

[0014] In one embodiment, the piezoelectric element is a piezoelectric ceramic disc with a silver electrode coated on the back. The positive and negative electrodes are led out through a double-shielded cable, the outer layer of which is covered with aluminum foil and braided copper wire.

[0015] A prestressed anchorage damage monitoring system, the system comprising:

[0016] The signal excitation and acquisition module is used to apply an excitation signal to the piezoelectric element in at least one ultrasonic probe and simultaneously acquire the received signals of the piezoelectric element in each ultrasonic probe.

[0017] The signal processing module is used to estimate the power spectral density of the received signal and extract the PSD peak features;

[0018] The feature relationship establishment module is used to establish the PF curve between the PSD peak value and the prestress, as well as the PP curve between the PSD peak values ​​of different sensors;

[0019] The damage identification module is used to determine whether there is local damage based on the PP curve and to correct the PSD peak value of the abnormal sensor.

[0020] The prestress estimation module inverts the current anchoring force based on the corrected PSD peak value and the PF curve.

[0021] In one embodiment, the signal excitation and acquisition module supports a rotating excitation mode, in which each piezoelectric element is used as an excitation source in turn, and the remaining piezoelectric elements are used as receivers to form a multipath signal matrix.

[0022] In one embodiment, the system further includes a damage localization module for constructing a damage impact matrix that reflects the influence of different damage locations on the multipath signal features in the multipath signal matrix; and for solving the damage location vector using a sparse inversion algorithm based on the deviation between the current signal features and the healthy baseline features.

[0023] A method for monitoring damage to prestressed anchors includes installing a piezoelectric sensor array, such as a piezoelectric array arrangement device, on the outer periphery of the prestressed anchor to form a piezoelectric sensor array. The method comprises:

[0024] Different levels of prestress were applied to the prestressed anchorage, and echo signals from each pressure sensor were collected. The power spectral density (PSD) of the echo signals was estimated using the Welch method, and the PSD peak value was extracted.

[0025] Establish the mapping relationship PF curve between the PSD peak value of each pressure sensor and the prestress, and obtain the PSD peak value mapping relationship PP curve between different pressure sensors when there is no damage, and save the fitting parameters and confidence intervals;

[0026] Based on the PP curve, determine whether the current PSD peak value combination of each pressure sensor falls within the confidence interval. If it exceeds the confidence interval, determine that the corresponding pressure sensor has local damage. Based on the PP curve, predict the corrected PSD peak value of the abnormal pressure sensor in the undamaged state.

[0027] Substitute the corrected PSD peak value into the corresponding PF curve to obtain the current anchoring force estimate, and output the anchoring force estimate and damage alarm information.

[0028] In one embodiment, the PF curve is a linear or nonlinear regression model; the PP curve is a linear or reversible transformation mapping relationship; when multiple pressure sensors are abnormal, the median or weighted average method is used to robustly correct the PSD peak value of the abnormal pressure sensors.

[0029] In one embodiment, the method further includes:

[0030] The pressure sensor's multipath PSD peak value under non-damage conditions was acquired by using a rotating excitation method, and the average value of each multipath PSD peak value was calculated as the baseline vector.

[0031] The multipath PSD peak values ​​of the pressure sensor under various damage states are collected, the change relative to the baseline vector is calculated, and the various changes are combined column-wise to construct a damage influence matrix.

[0032] Based on the damage influence matrix, the damage intensity vector is solved by the L1 regularized sparse inversion algorithm with non-negative constraints, and the damage location and intensity are determined according to the damage intensity vector.

[0033] The aforementioned piezoelectric array arrangement device, damage monitoring system, and method for prestressed anchors, through a ring-shaped measuring ring frame and an adjustable ultrasonic probe structure, enable multiple ultrasonic probes to achieve rapid positioning and maintain stable contact on the outer periphery of the anchor. The geometric relationship between the probes is determined by the measuring ring frame, and the contact pressure is jointly controlled by the adjustment mechanism and pressure sensors, thereby reducing deviations caused by manual arrangement and improving the repeatability and long-term stability of measurements. Through the correlation between multiple pressure sensors, abnormalities caused by damage and characteristic fluctuations caused by force changes can be distinguished, improving the reliability of monitoring results. Utilizing the spatial sensitivity of the multi-point array formed by the piezoelectric sensor array, damage location in the circumferential position of the anchor can be achieved, and synchronous changes at multiple locations can be distinguished, thereby improving the monitoring accuracy of prestressed anchor damage. Attached Figure Description

[0034] Figure 1 This is an application environment diagram of a prestressed anchor piezoelectric array arrangement device in one embodiment;

[0035] Figure 2This is a schematic diagram of the prestressed anchor piezoelectric array arrangement device in one embodiment;

[0036] Figure 3 This is a schematic diagram of the measuring ring skeleton structure in one embodiment;

[0037] Figure 4 This is a schematic diagram of the ultrasonic probe structure in one embodiment;

[0038] Figure 5 This is a schematic diagram of the ultrasonic probe sleeve structure in one embodiment;

[0039] Figure 6 This is a schematic diagram of a butterfly spring structure in one embodiment;

[0040] Figure 7 This is a schematic diagram of the pressure sensor structure in one embodiment;

[0041] Figure 8 This is a schematic diagram of the piezoelectric head structure in one embodiment;

[0042] Figure 9 This is a schematic diagram of the piezoelectric probe structure in one embodiment;

[0043] Figure 10 This is a schematic diagram of the various adjusting nuts in one embodiment;

[0044] Figure 11 This is a schematic diagram of the anchoring system and ultrasonic propagation in one embodiment;

[0045] Figure 12 This is a schematic diagram of the structure of a reflected wave testing system in one embodiment;

[0046] Figure 13 This is a schematic diagram of a method for establishing a database of a healthy anchoring system and monitoring damage in one embodiment.

[0047] Figure 14 This is a schematic diagram illustrating the functional relationship (i.e., PF curve) between the peak value of the PSD signal received by sensors B and C and the load in one embodiment.

[0048] Figure 15 This is a schematic diagram illustrating the functional relationship (i.e., the PP curve) between the peak values ​​of the PSD signals received by sensors B and C in one embodiment.

[0049] Figure 16 This is a schematic diagram showing the comparison between the estimated prestress value obtained from the PSD peak value of the signals received by sensors B and C and the true value of the loading in one embodiment.

[0050] Figure 17 This is a schematic diagram illustrating the correction of the peak value of the PSD signal received by sensor C in one embodiment. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0052] In one embodiment, such as Figures 1-10 As shown, a piezoelectric array arrangement device for prestressed anchors is provided. The device includes a measuring ring frame 100, a measuring ring fixing and adjusting nut 200, an ultrasonic probe 300, and a piezoelectric probe pressure adjusting nut 400. The components work together to form a circumferential piezoelectric sensor array adapted to the prestressed anchor 500, ensuring stable coupling between the sensor and the anchor surface and effective signal transmission.

[0053] The measuring ring skeleton 100 is a ring structure with an inner diameter matching the outer diameter of the prestressed anchor 500, and mounting holes are evenly distributed on the ring structure. The measuring ring fixing adjustment nuts 200 are evenly distributed along the outer ring of the measuring ring skeleton 100, and are used to fix the measuring ring skeleton 100 to the outer periphery of the prestressed anchor 500, restricting the axial and circumferential movement of the measuring ring skeleton 100. The ultrasonic probe 300 is installed in the mounting hole of the measuring ring skeleton 100 through the piezoelectric probe pressure adjustment nut 400, forming a circumferentially distributed piezoelectric sensor array. The ultrasonic probe 300 includes a probe sleeve, a piezoelectric head, a butterfly spring, and a pressure sensor. The piezoelectric head includes a front contact cover plate, a piezoelectric sheet, and a rear metal cover plate. The piezoelectric probe pressure adjustment nut 400 is used to push the ultrasonic probe 300 to press against the surface of the prestressed anchor 500, and achieves flexible pre-tightening through the butterfly spring.

[0054] like Figure 1 As shown, in this embodiment, a typical five-hole wedge-type prestressed anchor 500, along with a matching anchor plate 510 and a measuring ring frame 100, constitute the prestressed anchoring system. The steel strand is a Φ15.2mm seven-strand steel strand, and the tension range is set to 0–120kN. The anchor-anchor plate interface is a rough contact surface, and its contact characteristics change with the prestress, resulting in variations in the reflected wave amplitude and spectral energy. This forms the physical basis for the tests in this embodiment. A jack loading device is used to apply different prestress levels, allowing for testing every 10kN. The measuring ring frame 100 is installed around the prestressed anchor 500, forming a five-point circumferential array. The main structure is made of metal.

[0055] In one embodiment, the measuring ring frame 100 is made of metal; the piezoelectric probe pressure adjusting nut 400 is used to adjust the contact pressure between the piezoelectric head and the surface of the prestressed anchor 500.

[0056] like Figure 2 , Figure 3 As shown, the measuring ring frame 100 is an integral ring structure, made of 45# steel or 304 stainless steel by turning and milling, possessing sufficient rigidity and durability. It can maintain its shape stability under strong pre-tightening force on the engineering site, without deformation or loosening. The inner diameter of the measuring ring frame 100 is precisely matched with the outer diameter of the prestressed anchor to be monitored, ensuring the fit between the measuring ring frame 100 and the outer circumference of the prestressed anchor. Multiple mounting holes are evenly distributed on the ring structure, the number of which is consistent with the number of holes in the prestressed anchor (e.g., 5 holes for a 5-hole anchor), and the circumferential spacing of the mounting holes is equal, ensuring that the subsequent ultrasonic probes 300 can be evenly arranged around the circumferential area of ​​the prestressed anchor, achieving full coverage monitoring of the area around each anchor hole. The measuring ring frame 100 serves as the load-bearing foundation of the entire device, providing a stable installation reference for other components, while ensuring the spatial positioning accuracy between the ultrasonic probes 300.

[0057] like Figure 2 , Figure 3 As shown, the measuring ring fixing adjustment nuts 200 are equidistantly distributed along the outer ring of the measuring ring skeleton 100. In this embodiment, there are three measuring ring fixing adjustment nuts 200, evenly arranged at 120° intervals, and high-strength bolts of M6 or M8 specifications are selected. The core function of the measuring ring fixing adjustment nuts 200 is to lock the measuring ring skeleton 100 as a whole onto the outer circumferential surface of the prestressed anchor. By tightening the measuring ring fixing adjustment nuts 200, the inner end of the nut is tightly abutted against the outer circumference of the anchor, generating a radial locking force, thereby limiting the displacement of the measuring ring skeleton 100 in the axial (steel strand tensioning direction) and circumferential (circular tangential direction) directions of the anchor, preventing slippage due to vibration, load changes, and other factors during monitoring, and providing a reliable position reference for the stable operation of the ultrasonic probe 300.

[0058] The ultrasonic probe 300 is an integrated functional module and is the core component for signal transmission and reception. It is installed in the mounting hole of the measuring ring frame 100 through the piezoelectric probe pressure adjustment nut 400. Multiple ultrasonic probes 300 are evenly distributed around the circumference of the measuring ring frame 100 to form a complete piezoelectric sensor array (e.g., a five-hole anchor corresponds to 5 ultrasonic probes, covering the entire circumferential area of ​​the anchor).

[0059] like Figure 4 As shown, the internal structure of the ultrasonic probe includes a probe sleeve 310, a pressure sensor 320, a butterfly spring 330, and a piezoelectric head 340. All components are coaxially assembled to ensure uniform and stable force transmission. The probe sleeve 310 is a cylindrical hollow structure made of wear-resistant metal material. It serves as the outer shell of the ultrasonic probe 300, protecting the internal components and guiding the assembly direction. Its outer diameter matches the inner diameter of the mounting hole in the measuring ring frame 100, allowing it to move axially along the mounting hole. In this embodiment, the probe sleeve 310 structure is as follows: Figure 5As shown; the structure of the disc spring 330 is as follows Figure 6 As shown.

[0060] In one embodiment, the pressure sensor 320 is a thin-film pressure sensor used to monitor the contact pressure between the piezoelectric head 340 and the surface of the prestressed anchor in real time. The structure of the pressure sensor 320 is as follows: Figure 7 As shown, it includes a metal gasket 321 and a thin-film pressure sensor 322.

[0061] In one embodiment, the piezoelectric element is a piezoelectric ceramic disc with a silver electrode coated on the back. The positive and negative electrodes are led out through a double-shielded cable, the outer layer of which is covered with aluminum foil and braided copper wire.

[0062] The structure of the piezoelectric head 340 is as follows: Figure 8 As shown, the piezoelectric head 340 is the core of signal conversion, and is composed of a front contact cover plate 341, a piezoelectric sheet 342, and a rear metal cover plate 343 stacked sequentially. The front contact cover plate is made of a metal material with moderate hardness and directly contacts the surface of the prestressed anchor, ensuring effective transmission and reflection of ultrasonic waves while protecting the piezoelectric sheet from mechanical damage. The piezoelectric sheet is a commercially available piezoelectric ceramic disc with a diameter of 10–12 mm and a thickness of 0.3–0.5 mm. A silver electrode is coated on the back, and the positive and negative electrodes are led out through a shielded wire. It can generate ultrasonic vibration under the action of an excitation signal and convert the ultrasonic signal reflected from the anchor interface into an electrical signal. The shielded wire is a double-shielded cable, with an outer layer covered with aluminum foil and braided copper wire to reduce external electromagnetic interference. The rear metal cover plate is used to fix the position of the piezoelectric sheet, optimize stress distribution, and improve the vibration stability of the piezoelectric sheet. Qualitative analysis: A disc spring, made of spring steel with a stable elastic coefficient, is positioned between the probe sleeve and the piezoelectric head. Its function is to achieve flexible pre-tensioning, avoiding coupling instability caused by rigid contact between the piezoelectric head and the anchor surface. Simultaneously, its own elastic deformation compensates for contact deviations caused by installation errors or minor unevenness on the anchor surface, ensuring the fit between the piezoelectric head and the anchor surface. A pressure sensor, a thin-film type, is installed between the disc spring and the piezoelectric head. It monitors the contact pressure between the piezoelectric head and the anchor surface in real time and feeds the pressure signal back to the external control terminal. This provides operators with a basis for adjusting the contact state, preventing damage to the piezoelectric element due to excessive pressure or coupling failure due to insufficient pressure.

[0063] like Figure 9As shown, the piezoelectric probe pressure adjusting nut 400 is threaded to fit the mounting hole of the measuring ring skeleton 100 and is sleeved on the outside of the probe sleeve of the ultrasonic probe 300 to adjust the contact pressure between the ultrasonic probe 300 and the anchor surface. Specifically, by tightening the piezoelectric probe pressure adjusting nut 400, the probe sleeve is pushed to move axially along the mounting hole towards the anchor, thereby causing the piezoelectric head to abut against the anchor surface. As the nut is continuously tightened, the disc spring is compressed, generating an elastic preload. The pressure sensor provides real-time feedback on the contact pressure value, and the operator can adjust the contact pressure to a preset range based on the feedback data to ensure that the coupling state of all ultrasonic probes 300 is consistent, providing a guarantee for the consistency of subsequent signal acquisition. When it is necessary to disassemble or adjust the device, the piezoelectric probe pressure adjusting nut 400 is loosened from the adjusting nut mounting hole 901, the disc spring returns to its original position, and the ultrasonic probe 300 separates from the anchor surface. The operation is convenient and the device can be reused. The piezoelectric probe pressure adjusting nut 400 and the measuring ring fixing adjusting nut 200 are as follows... Figure 10 As shown.

[0064] In this embodiment, the measuring ring frame 100 is first fitted onto the outer periphery of the prestressed anchor 500 and locked in place by the measuring ring fixing adjusting nut 200, thus completing the overall positioning. Then, the ultrasonic probe 300 is inserted into the mounting hole of the measuring ring frame 100, and the piezoelectric probe pressure adjusting nut 400 is tightened to push the ultrasonic probe 300 into contact with the anchor surface. Finally, based on the values ​​fed back by the pressure sensor, the pressure adjusting nuts 400 of each piezoelectric probe are finely adjusted to ensure that the contact pressure of all ultrasonic probes 300 reaches a consistent range, completing the array arrangement. The entire assembly process requires no adhesive, is simple to operate, can be quickly completed on-site, and can be reused for monitoring different anchors after disassembly, demonstrating strong adaptability.

[0065] In one embodiment, a prestressed anchorage damage monitoring system is provided, comprising:

[0066] The signal excitation and acquisition module is used to apply an excitation signal to the piezoelectric element in at least one ultrasonic probe and simultaneously acquire the received signals of the piezoelectric element in each ultrasonic probe.

[0067] The signal processing module is used to estimate the power spectral density of the received signal and extract the PSD peak features;

[0068] The feature relationship establishment module is used to establish the PF curve between the PSD peak value and the prestress, as well as the PP curve between the PSD peak values ​​of different sensors;

[0069] The damage identification module is used to determine whether there is local damage based on the PP curve and to correct the PSD peak value of the abnormal sensor.

[0070] The prestress estimation module inverts the current anchoring force based on the corrected PSD peak value and the PF curve.

[0071] In this embodiment, a prestressed anchor damage monitoring system is constructed based on the piezoelectric array arrangement device. This system can effectively distinguish between signal differences caused by changes in anchoring force and local damage, and achieve accurate monitoring of the anchor's health status. Through modular design, the system ensures the efficiency, accuracy, and reliability of the monitoring process by having each module work collaboratively.

[0072] Specifically, the prestressed anchorage damage monitoring system mainly includes a signal excitation and acquisition module, a signal processing module, a feature relationship establishment module, a damage identification module, and a prestress estimation module. These modules are connected sequentially via data transmission lines to form a closed-loop monitoring process: the signal excitation and acquisition module outputs excitation signals to the piezoelectric array and acquires echo data; the signal processing module extracts effective features; the feature relationship establishment module constructs a quantization mapping model; the damage identification module judges the damage state based on the model and corrects abnormal features; and finally, the prestress estimation module inverts the anchorage force and outputs the monitoring results.

[0073] The signal excitation and acquisition module is the core of the system's data acquisition. It mainly consists of an ultrasonic signal generator and receiver, a fast channel converter, and a synchronization control unit. Its core function is to apply a preset excitation signal to the piezoelectric element in at least one ultrasonic probe and simultaneously acquire the received signals from the piezoelectric elements in all ultrasonic probes, providing raw data for subsequent analysis. Based on the sensitive frequency band of the anchor-anchor plate interface contact stiffness change, a sweep frequency signal of 10Hz to 1MHz is selected as the excitation signal. This frequency band can effectively cover the differences in ultrasonic propagation characteristics corresponding to changes in interface contact state, ensuring the signal's sensitivity to changes in anchoring force and local damage. The amplitude of the excitation signal is kept constant to avoid the stability of feature extraction being affected by signal intensity fluctuations.

[0074] It supports two flexible excitation modes: single-point excitation mode and rotating excitation mode, to adapt to different monitoring scenarios. Single-point excitation mode selects one ultrasonic probe in the array as the excitation source (e.g., sensor A in a five-hole anchor array), with the remaining probes acting as receivers. This mode is suitable for conventional anchoring force monitoring scenarios, balancing monitoring efficiency and accuracy. Rotating excitation mode uses all ultrasonic probes in the array sequentially as excitation sources, with the remaining probes acting as receivers (e.g., a five-hole anchor array can form 20 propagation paths). This mode is suitable for damage localization scenarios, improving the accuracy of damage identification through multi-path signals.

[0075] The signal excitation and acquisition module employs multi-channel synchronous acquisition technology with an acquisition rate set at 200kHz to ensure time consistency of received signals across all channels and avoid characteristic deviations caused by acquisition delays. At least two acquisitions are performed under each load condition, and the average value is taken as the valid data for that condition, reducing the impact of random noise on signal quality. Furthermore, a fast channel converter enables efficient transmission of excitation and received signals, and double-shielded cables reduce external electromagnetic interference, ensuring that high-frequency signals are not distorted during transmission.

[0076] In one embodiment, the signal excitation and acquisition module supports a rotating excitation mode, in which each piezoelectric element is used as an excitation source in turn, and the remaining piezoelectric elements are used as receivers to form a multipath signal matrix.

[0077] The signal processing module receives the raw time-domain signal transmitted from the signal excitation and acquisition module. Its core function is to transform the raw signal into quantitative features reflecting the anchor interface contact state through signal preprocessing and feature extraction, providing a foundation for subsequent model building and monitoring analysis. Specifically, the signal processing module first filters the received time-domain signal to remove low-frequency drift and high-frequency interference, retaining effective signal components related to the interface contact state. Then, it normalizes the signal to eliminate the influence of amplitude differences between different channels, improving the comparability of features. The Welch method is used to estimate the power spectral density of the preprocessed time-domain signal. Through segmented overlap and windowing, the variance of the spectral estimation is effectively reduced, improving the smoothness and reliability of the spectral curve. Specifically, the time-domain signal from the signal processing module is divided into multiple overlapping segments. Each segment is subjected to a Hanning or Hamming window and then a Fourier transform. The power spectra of each segment are then averaged to obtain the final PSD curve. In the PSD curve, the frequency band most sensitive to the change in the contact stiffness of the anchor interface is selected, and the peak value in this frequency band is extracted as the core feature quantity. The peak value directly reflects the energy change of the ultrasonic reflected wave and is positively correlated with the contact stiffness of the anchor-anchor plate interface. Thus, it can indirectly characterize the magnitude of the anchoring force and the interface damage state.

[0078] The feature relationship establishment module, based on the PSD peak characteristics extracted by the signal processing module, establishes two types of key mapping relationship curves: the PF curve (PSD peak value - prestress relationship) and the PP curve (PSD peak value relationship between different sensors). This provides quantitative model support for subsequent damage identification and anchoring force inversion. The PF curve describes the quantitative relationship between the PSD peak value of a single sensor and the anchoring force under healthy conditions. A series of known levels of prestress can be applied to the anchor using loading devices such as jacks. For each prestress level, the PSD peak value of the sensor is obtained through the signal excitation and acquisition module and the signal processing module. With prestress as the abscissa and PSD peak value as the ordinate, a linear or nonlinear regression method is used to fit the curve, resulting in the PF curve model. The confidence interval of the fitted curve is calculated and saved as an error reference for subsequent anchoring force inversion. A separate PF curve needs to be established for each ultrasonic probe to ensure the accuracy of force value inversion for sensors at different locations.

[0079] The Prestress-Proof (PP) curve describes the stable correlation between the peak PSD values ​​of different sensors under healthy conditions. In the absence of damage, the peak PSD values ​​of each sensor exhibit a consistent trend with changes in anchoring force; therefore, a stable mapping relationship exists between the peak PSD values ​​of any two sensors. Specifically, the PP curve establishment process can be as follows: Based on the peak PSD data of each prestressing level under healthy conditions collected during the database establishment phase; select any two sensors, using the peak PSD value of one sensor as the x-axis and the peak PSD value of the other sensor as the y-axis, and fit them using a linear or reversible transformation method to obtain their PP curve models, and calculate the confidence interval as the basis for subsequent damage assessment. For an array of N sensors, N×(N-1) / 2 sets of PP curves can be established, forming a multi-dimensional sensor correlation model and improving the reliability of damage identification.

[0080] The damage identification module is the core of accurate damage assessment. Its core function is to establish PP curves based on feature relationships, determine whether there is local damage to the anchorage, and correct abnormal PSD peak values ​​caused by damage, eliminating interference from damage on anchorage force inversion. Specifically, during online monitoring, the current PSD peak values ​​of each sensor are acquired in real time. Any one or more corresponding PP curves are selected, and it is determined whether the current PSD peak combination falls within the confidence interval of the PP curve. If the PSD peak combinations of all sensors are within the confidence interval of their respective PP curves, the anchorage is considered to be in a healthy state, and signal changes are only caused by changes in anchorage force. If the PSD peak value of a certain sensor, combined with the PSD peak values ​​of healthy sensors, exceeds the confidence interval of the PP curve, local damage is determined to exist in the circumferential region of the anchorage corresponding to the abnormal sensor. When a sensor is determined to have an abnormal PSD peak value due to damage, the abnormal peak value needs to be corrected based on the PP curve to obtain its theoretical PSD peak value under undamaged conditions, ensuring the accuracy of anchorage force inversion.

[0081] In one embodiment, a prestressed anchorage damage monitoring system further includes a damage location module for constructing a damage influence matrix to reflect the influence of different damage locations on the multipath signal characteristics in the multipath signal matrix; and solving for the damage location vector using a sparse inversion algorithm based on the deviation between the current signal characteristics and the healthy baseline characteristics.

[0082] The prestress estimation module, based on the PSD peak value corrected by the damage identification module, combines it with the PF curve constructed by the feature relationship module to inversely calculate the current anchorage force and output the final monitoring result. Specifically, the corrected PSD peak value is substituted into the PF curve model corresponding to the sensor, and the estimated current anchorage force is obtained by solving the equation. If the PF curve is a nonlinear model, a numerical iteration method can be used to solve it to ensure inversion accuracy. The final output includes the estimated anchorage force and uncertainty; damage alarm information, including damage location (corresponding to the placement area of ​​the abnormal sensor) and damage judgment confidence level; and original PSD data and feature extraction results for subsequent traceability analysis. The output results are simultaneously saved in the form of a visual interface and data files, facilitating real-time viewing and subsequent data review by engineers.

[0083] In one embodiment, a method for monitoring damage to prestressed anchorages is provided, wherein a piezoelectric array arrangement device for prestressed anchorages is installed on the outer periphery of the prestressed anchorage to form a piezoelectric sensor array, the specific process including:

[0084] Different levels of prestress were applied to the prestressed anchorage, and echo signals from each pressure sensor were collected. The power spectral density (PSD) of the echo signals was estimated using the Welch method, and the PSD peak value was extracted.

[0085] Establish the mapping relationship PF curve between the PSD peak value of each pressure sensor and the prestress, and obtain the PSD peak value mapping relationship PP curve between different pressure sensors when there is no damage, and save the fitting parameters and confidence intervals;

[0086] Based on the PP curve, determine whether the current PSD peak value combination of each pressure sensor falls within the confidence interval. If it exceeds the confidence interval, determine that the corresponding pressure sensor has local damage. Based on the PP curve, predict the corrected PSD peak value of the abnormal pressure sensor in the undamaged state.

[0087] Substitute the corrected PSD peak value into the corresponding PF curve to obtain the current anchoring force estimate, and output the anchoring force estimate and damage alarm information.

[0088] In one embodiment, the PF curve is a linear or nonlinear regression model; the PP curve is a linear or reversible transformation mapping relationship; when multiple pressure sensors are abnormal, the median or weighted average method is used to robustly correct the PSD peak value of the abnormal pressure sensors.

[0089] In one embodiment, a prestressed anchor damage monitoring method may further include a multi-damage localization process, specifically including: acquiring multi-path PSD peak values ​​of the pressure sensor in a non-damaged state using a rotating excitation method, and calculating the average value of each multi-path PSD peak value as a baseline vector; acquiring multi-path PSD peak values ​​of the pressure sensor in each damaged state, calculating the change relative to the baseline vector, and combining each change value column-wise to construct a damage influence matrix; based on the damage influence matrix, solving for the damage intensity vector using an L1 regularized sparse inversion algorithm with non-negative constraints, and determining the damage location and intensity according to the damage intensity vector.

[0090] In one embodiment, such as Figure 11 As shown, taking a five-hole anchor as an example, the steel strands pass sequentially through the anchor and anchor plate to form the anchoring system. The anchor and anchor plate jointly bear the tension of the steel strands, forming a rough contact interface for ultrasonic propagation between them. This device is installed on the outer periphery of the anchor. The constructed reflected wave testing system is shown below. Figure 12 As shown, in addition to the prestressed anchor piezoelectric array arrangement device, it also includes an ultrasonic signal excitation and receiver / synchronous acquisition module 121, a fast channel converter 122, and a data processing unit 123. The exciter applies a sweep frequency or broadband excitation signal to a certain piezoelectric probe. The signal acts on the rough contact interface between the anchor and the anchor plate, and the reflected echo is received by other probes in the array. The acquisition module realizes multi-channel synchronous acquisition, ensuring the time consistency of the signals from each sensor. The acquired data is input into the computer for signal processing via a control program.

[0091] To achieve signal feature extraction and prestress identification, this embodiment also provides a signal processing and feature extraction method: the Welch method is used to estimate the power spectral density (PSD) of the time-domain signal received by each sensor, and the peak value or local peak value in the frequency band is selected as the feature quantity of the sensor so that the feature quantity can reflect the change of the energy of the interface reflected wave.

[0092] In one embodiment, such as Figure 13 As shown, a method for establishing a database and monitoring damage in a healthy anchoring system is proposed. During the database establishment phase under healthy structural conditions, multiple data acquisitions are performed under different tension conditions. A functional relationship (PF curve) between prestress and peak PSD value is established for each sensor, and the fitting parameters and their confidence intervals are recorded. Based on the same healthy data, a PSD peak value relationship (PP curve) is established between different sensors to reflect the inherent correlation between multi-point responses.

[0093] During the online monitoring phase, the current PSD peak values ​​of each sensor in the array are compared. If the current characteristics of one or more sensors deviate from the confidence interval of the corresponding PP curve, it is determined that there may be local damage or contact degradation near that location. For sensors identified as abnormal, the current characteristic values ​​and PP curves of normal sensors are used to predict the characteristic values ​​that the sensor should have in a healthy state. These predicted values ​​are then used as correction values ​​and substituted into the PF curve to estimate the current anchoring force, thus avoiding the influence of abnormal signals caused by damage on force value identification. If multiple sensors are abnormal, robust correction can be performed by taking the median or weighted average of the predicted values ​​from multiple reference sensors.

[0094] Specifically, during the online monitoring phase, a rapid deployment device with 5 PZT piezoelectric arrays can be arranged around the anchor head to form an array; the received signal is recorded for each tension force (or load condition), and then the PSD of each sensor is estimated using Welch; the peak value (max PSD) or local peak amplitude is used as a feature; and the feature P is recorded under multiple known force values. sd For each sensor, perform regression (linear or nonlinear) to obtain the PF function: , where P sd The peak value is the power spectral density estimate from Welch; P zero is the zero point of the test curve; a and b are curve fitting parameters; F is the axial force of the anchor rod, preserving the confidence interval (e.g., 95% or 99% CL).

[0095] Next, under healthy conditions, the PSD characteristics (such as P) of two sensors are analyzed. B With P C They usually have a stable relationship (linear or invertible transformation): P C =h(P) BThe system fits the data using regression and saves the confidence intervals. Multiple PP pairs can be established for multi-sensor systems (or the overall linkage can be modeled using multidimensional covariance / PCA).

[0096] Then comes the online detection and correction process, which specifically includes collecting the current PSD features P B P C P D P E ; Inspection (P B P C If the error falls within the confidence interval of PP (or the residual / Mahanobis distance / outlier score is calculated), and exceeds this range, local damage is considered to have occurred (near the deviating sensor); if an anomaly is found in sensor i (e.g., P), it indicates a problem. C (High / Low), predict the P value that the sensor should have under "no damage" conditions using the relationship between the value of health sensor B and PP. C，corr =h(P) B ), put P C，corr Substitute the PF curve to estimate the tension.

[0097] If multiple sensors are abnormal, a robust method is used, such as using the median or weighted average of multiple correction values, or extreme value removal. At the same time, the estimated tension (with uncertainty), damage alarm (location, confidence level), and raw PSD are output and saved for posterior analysis.

[0098] In one embodiment, the installation steps of a prestressed anchor piezoelectric array arrangement device are as follows:

[0099] Place the measuring ring on the outer periphery of the anchor and tighten it with the measuring ring fixing adjusting nut to ensure close contact with the anchor.

[0100] Tighten the pressure adjusting nuts of the five piezoelectric probes (containing five piezoelectric sensors A~E) in sequence to make each probe contact the outer surface of the anchor.

[0101] Read the output of each pressure sensor and adjust the contact pressure to the range of 15±2N;

[0102] Check the positions, pressure output, and contact stability of the five probes to complete the array arrangement.

[0103] In one embodiment, such as Figure 12 As shown, a single-point excitation and multi-point reception method is adopted. One probe (piezoelectric sensor A) is selected as the excitation source, and the excitation signal is a frequency sweep signal of 10Hz to 1MHz. The remaining four probes (piezoelectric sensors B to E) simultaneously receive the echo signals. The data acquisition system adopts multi-channel synchronous acquisition with a sampling rate of 200kHz. Each force level is repeatedly acquired twice, and the average value is used for subsequent analysis.

[0104] When performing Welch power spectral density extraction and PF / PP curve establishment, the first step is to perform Welch PSD estimation on the time-domain signal for each channel; then, the PSD peak value is extracted in the most sensitive frequency band to form a sequence of eigenvalues; such as Figure 14 As shown, PF curves representing the PSD peak value versus prestress relationship for each sensor are established at force levels of 0, 10, 20, ..., 120 kN (taking sensors B and C as examples); Figure 15 As shown, under healthy conditions, PP curves are established between each sensor to describe the internal correlation of the array (taking sensors B and C as examples).

[0105] like Figure 14 As shown, during the loading process, the peak PSD values ​​of piezoelectric sensors B and C both exhibit a monotonically decreasing trend with increasing force. A set of verification data was generated by re-controlling the loading and unloading of the prestress, as shown below. Figure 16 As shown, the PSD peak value is substituted into the PF curve to invert the prestress, and compared with the reading of the loading device, the error is controlled within ±3%.

[0106] The prestressed anchor piezoelectric array arrangement device in this embodiment can realize multi-point arrangement of anchors in the circumference and can accurately identify the prestress state under different force levels.

[0107] In one embodiment, a rotating excitation strategy is used to monitor damage to prestressed anchorages. A piezoelectric array rapid probe ring is installed on the outer periphery of the five-hole anchorage and fixed with adjusting nuts. The contact pressure of each probe is adjusted to 15±2N to ensure consistent probe contact. To simulate circumferential damage to the anchorage, sandpaper is used to treat localized areas of the anchor plate surface in some tests to simulate corrosion, localized wear, or contact degradation.

[0108] Specifically, five probes are used sequentially as excitation sources; during each excitation, the remaining four probes act as receivers, forming 20 propagation paths, each with different sensitivities to damage; the excitation signal is a frequency sweep signal with constant amplitude (10Hz–1MHz); throughout this process, the acquisition system maintains synchronization across all channels. Next, Welch PSD estimation is performed on the time-domain echoes of all 20 paths; the PSD peak value of each path is extracted to form a 20-dimensional feature vector; under healthy conditions, data from multiple force levels are acquired to form a multi-channel health database.

[0109] In this embodiment, micro-damage is created by sanding the surface area of ​​the anchor near sensor C with sandpaper, simulating corrosion or localized wear. Figure 17 As shown, check (P) B P C Does it fall within the confidence interval of PP? C A high reading indicates damage to the circumferential region of sensor C; for example... Figure 17As shown, the damage point is characterized by the relationship between the value of health sensor B and PP, and the force value is inverted by substituting it into the corresponding PF curve.

[0110] When performing multiple damage localizations and force identifications, the main tasks involve constructing a damage influence matrix, online monitoring and damage localization, damage correction, and force value inversion. Specifically, to establish a response model of the array signal to different damage locations, this embodiment conducts calibration experiments under healthy conditions and known damage conditions. After extracting the power spectral density features of the multipath signals, a damage influence matrix is ​​constructed. When constructing the damage influence matrix, five controllable micro-damages are sequentially created in the circumferential region of the anchor, corresponding to five potential damage locations m=1, 2, ..., 5. For each damage location m, the peak power spectral density (PSD) values ​​of 20 propagation paths are obtained through alternating excitation of the piezoelectric array, forming a feature vector. Next, under healthy conditions (no damage), the peak PSD values ​​of the same 20 paths were recorded, and the average of these values ​​was taken multiple times as the baseline vector. Then, for each lesion site, the change in peak PSD relative to the healthy state is calculated: The feature change vectors corresponding to the five damage locations are combined column-wise to obtain the damage influence matrix: ; where matrix A d The m-th column describes the typical response pattern of the array's 20 paths when the damage occurs at location m.

[0111] When the anchorage is in an unknown health state, damage location and force value inversion are completed by real-time acquisition of array signals and comparison with the damage influence matrix. Specifically, during online monitoring and damage location, the PSD peak vector is first obtained through 20 paths under the current working condition: The response bias was obtained by comparing it with the healthy baseline: The deviation vector is considered as a linear combination of the damage influence matrix and the damage intensity vector x, and solved using sparse constraints: ;in, This represents the inferred damage intensity vector. This represents the regularization parameter, which controls sparsity and can be determined through offline cross-validation or the L-curve method. Representing the L1 norm improves the sparsity of the solution and makes damage localization more stable. When a certain element satisfies: That is, to determine that damage has occurred in the m-th circumferential region, where the threshold can be determined by the 95% upper confidence limit of the health test data.

[0112] Based on the detected damage location, the force value is retrieved after correction for the abnormal channel. Specifically, for the channel identified as being affected by damage (channel j), its linear mapping relationship with the healthy channel (channel i) in the healthy state is utilized: Based on current observations Calculate the corrected PSD peak value: If multiple health channels are referenced, a weighted average can be used for robust correction. ;in, Let be the standard deviation of the PP relationship residuals, and R be the reference channel set.

[0113] If the PF relationship is a nonlinear model P=f(F), the anchoring force can be calculated by back-calculating the peak value of the corrected PSD: In this embodiment, .

[0114] Through the above steps, this embodiment can identify the location of circumferential damage to the anchor by using alternating excitation and multipath analysis, and can achieve force correction under the condition that damage exists.

[0115] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0116] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A piezoelectric array arrangement device for prestressed anchors, characterized in that, The device includes a measuring ring frame, a measuring ring fixing and adjusting nut, an ultrasonic probe, and a piezoelectric probe pressure adjusting nut, wherein: The measuring ring skeleton is a ring structure with an inner diameter matching the outer diameter of the prestressed anchor, and mounting holes are evenly distributed on the ring structure. The measuring ring fixing adjustment nuts are evenly distributed along the outer ring of the measuring ring skeleton, and are used to fix the measuring ring skeleton to the outer periphery of the prestressed anchor, restricting the axial and circumferential movement of the measuring ring skeleton; The ultrasonic probe is installed in the mounting hole of the measuring ring skeleton through the piezoelectric probe pressure adjusting nut, forming a circumferentially distributed piezoelectric sensor array; The ultrasonic probe includes a probe sleeve, a piezoelectric head, a butterfly spring, and a pressure sensor; the piezoelectric head includes a front contact cover plate, a piezoelectric element, and a rear metal cover plate. The piezoelectric probe pressure adjusting nut is used to push the ultrasonic probe to press against the surface of the prestressed anchor, and the butterfly spring is used to achieve flexible pre-tightening.

2. The prestressed anchor piezoelectric array arrangement device according to claim 1, characterized in that, The measuring ring frame is made of metal; the piezoelectric probe pressure adjusting nut is used to adjust the contact pressure between the piezoelectric head and the surface of the prestressed anchor.

3. The prestressed anchor piezoelectric array arrangement device according to claim 1, characterized in that, The pressure sensor is a thin-film pressure sensor used to monitor the contact pressure between the piezoelectric head and the surface of the prestressed anchor in real time.

4. The piezoelectric array arrangement device for prestressed anchors according to claim 1, characterized in that, The piezoelectric element is a piezoelectric ceramic disc with a silver electrode coated on the back. The positive and negative electrodes are led out through a double-shielded cable, the outer layer of which is covered with aluminum foil and braided copper wire.

5. A prestressed anchorage damage monitoring system based on the device described in any one of claims 1-4, characterized in that, The system includes: The signal excitation and acquisition module is used to apply an excitation signal to the piezoelectric element in at least one ultrasonic probe and simultaneously acquire the received signals of the piezoelectric element in each ultrasonic probe. The signal processing module is used to estimate the power spectral density of the received signal and extract the PSD peak features; The feature relationship establishment module is used to establish the PF curve between the PSD peak value and the prestress, as well as the PP curve between the PSD peak values ​​of different sensors; The damage identification module is used to determine whether there is local damage based on the PP curve and to correct the PSD peak value of the abnormal sensor. The prestress estimation module inverts the current anchoring force based on the corrected PSD peak value and the PF curve.

6. The prestressed anchorage damage monitoring system according to claim 5, characterized in that, The signal excitation and acquisition module supports a rotating excitation mode, which allows each piezoelectric element to act as an excitation source in turn, while the remaining piezoelectric elements act as receivers, forming a multi-path signal matrix.

7. The prestressed anchorage damage monitoring system according to claim 6, characterized in that, The system also includes a damage localization module, which is used to construct a damage impact matrix to reflect the influence of different damage locations on the multipath signal features in the multipath signal matrix; and to solve for the damage location vector by using a sparse inversion algorithm based on the deviation between the current signal features and the healthy baseline features.

8. A method for monitoring damage to prestressed anchorages, comprising installing a piezoelectric array arrangement device as described in any one of claims 1-4 on the outer periphery of the prestressed anchorage to form a piezoelectric sensor array, characterized in that, The method includes: Different levels of prestress were applied to the prestressed anchorage, and echo signals from each pressure sensor were collected. The power spectral density (PSD) of the echo signals was estimated using the Welch method, and the PSD peak value was extracted. Establish the mapping relationship PF curve between the PSD peak value of each pressure sensor and the prestress, and obtain the PSD peak value mapping relationship PP curve between different pressure sensors when there is no damage, and save the fitting parameters and confidence intervals; Based on the PP curve, determine whether the current PSD peak value combination of each pressure sensor falls within the confidence interval. If it exceeds the interval, determine that the corresponding pressure sensor has local damage. Based on the PP curve, predict the corrected PSD peak value of the abnormal pressure sensor in the undamaged state. Substitute the corrected PSD peak value into the corresponding PF curve to obtain the current anchoring force estimate, and output the anchoring force estimate and damage alarm information.

9. The method for monitoring damage to prestressed anchorages according to claim 8, characterized in that, The PF curve is a linear or nonlinear regression model; the PP curve is a linear or reversible transformation mapping relationship; when multiple pressure sensors are abnormal, the median or weighted average method is used to robustly correct the PSD peak value of the abnormal pressure sensors.

10. The method for monitoring damage to prestressed anchorages according to claim 8, characterized in that, The method further includes: The pressure sensor's multipath PSD peak value under non-damage conditions was acquired by using a rotating excitation method, and the average value of each multipath PSD peak value was calculated as the baseline vector. The multipath PSD peak values ​​of the pressure sensor under various damage states are collected, the change relative to the baseline vector is calculated, and the various changes are combined column-wise to construct a damage influence matrix. Based on the damage influence matrix, the damage intensity vector is solved by the L1 regularized sparse inversion algorithm with non-negative constraints, and the damage location and intensity are determined according to the damage intensity vector.

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