Structural dynamic tomography and damage monitoring method using self-excitation wave

Abstract

The invention belongs to the technical field of structural damage monitoring, and particularly relates to a structural dynamic tomography and damage monitoring method using self-excitation waves, which comprises the following steps: S1, carrying out spatial discretization processing on a monitored object, and establishing a three-dimensional discrete model; arranging a plurality of sensors on a monitoring object; recording the space coordinates of each sensor; s2, applying external excitation to a known position, and inverting an initial wave velocity field in the monitoring object; s3, extracting self-excitation waves of the monitored object received by each sensor; s4, identifying the arrival time of each self-excitation wave signal on each sensor; the space coordinates of the wave source of each excitation wave signal are calculated through inversion; s5, synchronously updating the wave velocity field based on the space coordinates of the wave sources of the respective excitation waves, and processing to obtain a damage result of the monitored object; and S6, performing corresponding processing based on a damage result. According to the method, dynamic tomography and real-time monitoring of the damage position, range and evolution process can be realized.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of structural damage monitoring, and particularly relates to a method for structural dynamic tomography and damage monitoring by using self-excited waves. BACKGROUND

[0002] Structural damage monitoring is an important means to ensure the safety and service performance of engineering structures, and is widely used in the health diagnosis of key infrastructures such as bridges, tunnels, dams, high-rise buildings and aerospace. The core goal is to identify the possible micro-cracks, debonding, corrosion or material degradation in the structure by collecting the physical response information of the structure in real time or periodically, and to evaluate the location, range and severity of the damage, so as to provide a scientific basis for maintenance decision-making and prevent sudden structural failure accidents.

[0003] At present, traditional structural detection and imaging techniques mainly rely on active excitation methods such as ultrasonic detection and impact echo method. These methods excite elastic waves, ultrasonic waves and other waves to propagate in the structure by artificially applying external excitation (such as electric pulse, mechanical impact), and then use sensors to receive reflected or transmitted signals, and analyze the travel time, amplitude attenuation and other characteristics of the waves to determine the internal defects. However, such techniques generally have low detection efficiency, complex operation and high cost, and are difficult to achieve long-term and continuous online monitoring. In addition, the excitation device needs to be frequently laid and maintained, and has poor adaptability in complex or harsh environments, which limits its application in dynamically operating structures.

[0004] Further, existing tomography techniques based on active wave field mainly rely on a single physical parameter (such as average wave speed or attenuation coefficient) for inversion and reconstruction, which is difficult to fully reflect the material heterogeneity and complex wave propagation mechanism in multi-phase media (such as reinforced concrete, composite materials), resulting in insufficient imaging resolution, especially when multiple small-scale damages coexist or deep defects are identified. At the same time, although some studies attempt to use the self-vibration signals of the structure generated by environmental excitation (such as wind load, traffic vibration) for modal analysis to achieve passive monitoring, this method mainly reflects the changes in the overall dynamic characteristics of the structure (such as frequency drift, mode shape change), and has low sensitivity to local damage, making it difficult to achieve accurate positioning and quantitative evaluation.

[0005] Therefore, how to realize dynamic tomography and real-time monitoring of damage location, range and evolution process has become a problem to be solved. SUMMARY

[0006] In view of the deficiencies of the prior art, the present application provides a method for structural dynamic tomography and damage monitoring by using self-excited waves, which can realize excitation-free, dynamic tomography and real-time monitoring of damage location, range and evolution process.

[0007] To solve the above technical problems, the application adopts the following technical solutions:

[0008] A structural dynamic tomography and damage monitoring method using self-excited waves, comprising the following steps:

[0009] S1. Spatially discretizing the monitoring object to divide it into a plurality of three-dimensional discrete units, establishing a three-dimensional discrete model; arranging a plurality of sensors on the monitoring object and recording the spatial coordinates of each sensor to form a sensor array for collecting self-excited waves of the monitoring object from different directions, wherein the self-excited waves are elastic waves spontaneously generated during the damage or damage propagation process of the structure inside the monitoring object, and the energy carried by the self-excited waves is converted from the strain energy inside the structure;

[0010] S2. Collecting elastic wave propagation data by applying external excitation at a known position, and combining with the wave travel time information to invert the initial wave velocity field inside the monitoring object;

[0011] S3. Collecting the elastic wave signals generated inside the monitoring object under the service state of the monitoring object, and pre-processing the data obtained by the sensor array to extract the self-excited waves generated by the monitoring object received by each sensor;

[0012] S4. Identifying the arrival time of each self-excited wave signal at each sensor; determining whether it is the first time to perform damage analysis, i.e., determining whether it is the first batch of self-excited wave signals received by the sensor array after installation, from the structure inside; if so, combining the spatial coordinates of the sensors and the initial wave velocity field to invert and calculate the spatial coordinates of the wave sources of each excitation wave; if not, combining the spatial coordinates of the sensors and the wave velocity field calculated last time to invert and calculate the spatial coordinates of the wave sources of each excitation wave;

[0013] S5. Based on the spatial coordinates of the wave sources of each self-excited wave, synchronously solving and updating the wave velocity field inside the monitoring object to obtain the damage result of the monitoring object, wherein the damage result includes the damage range;

[0014] S6. Based on the damage result of the monitoring object, performing corresponding processing.

[0015] Compared with the prior art, the application has the following beneficial effects:

[0016] 1. Achieve long-term real-time monitoring without external continuous excitation. Compared with traditional active ultrasonic or shock echo technologies that rely on artificially applied excitation sources, this method fully utilizes the elastic wave signals spontaneously generated by the evolution of (micro)damage (such as crack initiation and propagation) during the service process of the structure as an information source, eliminating frequent dependence on external excitation devices. The "self-excited wave" in this method is an elastic wave spontaneously generated during damage or damage propagation within the structure, and its energy is converted from the strain energy within the structure. Therefore, the source of the self-excited wave is the precise location of damage such as cracks, and the self-excited signal naturally carries information about the damage location and its process. Based on this, excitation-free, real-time, and dynamic imaging and monitoring of internal structural damage can be achieved.

[0017] The system utilizes external excitation to calculate the initial wave velocity field of the entire structure or a local area. In the first monitoring stage, based on the initial wave velocity field and self-excited wave signals, a new wave velocity field and structural damage state under the current condition are reconstructed. Subsequently, the wave velocity field calculated in the previous stage is used as the initial state for the current analysis of the monitored object. The self-excited waves received in this stage are used to solve for the current wave velocity field inside the damaged structure and analyze the damage state. This process is implemented alternately and continuously to achieve long-term dynamic damage monitoring. This not only significantly reduces system operating costs and operational complexity but also makes continuous, long-term online monitoring possible, making it particularly suitable for large-scale infrastructures that are difficult to frequently require manual intervention or need 24 / 7 monitoring.

[0018] 2. Improved Damage Localization Accuracy and Imaging Resolution. In S2, this method obtains the initial wave velocity field inside the structure through initial external excitation inversion, as well as the updated wave velocity field calculated in subsequent stages, providing an accurate propagation medium model for the subsequent localization of self-excited wave sources. Compared to the homogeneous or simplified wave velocity assumptions often used in traditional tomography, this initial wave velocity field and its subsequent updated field more realistically reflect the heterogeneity of the material inside the structure, thus significantly improving the inversion accuracy of the wave source spatial coordinates in S4. Combining the three-dimensional discrete model with the spatial coverage of a multi-sensor array and the dynamic adjustment of the array, high-resolution localization and high-precision spatial distribution reproduction of multiple damage sources can be achieved.

[0019] 3、With the development of damage, the local wave speed continues to decrease. If the initial high wave speed model is still used, it will lead to the arrival time prediction deviation, and then cause the systematic outward shift or diffusion of the wave source positioning. This method updates the wave speed field in real time, so that the positioning model is always consistent with the current state of the structure, which can more sensitively capture small changes in the medium, identify new damage areas or expanding areas in time, and improve the early warning ability of the monitoring system. Such settings will feed the inversion results (current wave speed field) back to the front-end positioning module, forming a closed-loop processing flow of "perception → modeling → re-perception". This mechanism enables the system to have "memory" and "learning" capabilities: each imaging result provides more accurate prior information for the next analysis, avoiding model drift and error accumulation caused by independent event processing, enhancing the spatio-temporal consistency of multi-source event fusion analysis, and promoting the development of the monitoring system towards intelligence and autonomy.

[0020] 4、Enhance the recognition of weak signals and anti-interference ability. To solve the problem of weak self-excited wave signals that are easily overwhelmed by noise, the data preprocessing mechanism is introduced in S3 to effectively extract the true self-excited event signals. Through multi-sensor collaborative analysis and accurate identification of arrival time difference, combined with known sensor layout and wave speed field model, the reliability of signal feature extraction in low signal-to-noise ratio environment is improved, overcoming the defect of traditional technology that leads to large positioning deviation due to arrival time error and assuming wave speed as a constant value.

[0021] 5、Realize dynamic imaging and evolution tracking of damage. Unlike modal analysis methods or static imaging techniques that only reflect the overall state changes of the structure, this method is based on the spatial aggregation characteristics of a large number of self-excited wave sources (S5), which can dynamically reconstruct the expansion path and range changes of the damage area, and realize the construction of "point-to-surface" damage evolution map. This dynamic tomographic imaging capability based on physical mechanisms enables the development process of local damage to be visualized, making up for the shortcomings of existing technologies that cannot capture the dynamic behavior of damage.

[0022] 6、Suitable for comprehensive evaluation of complex structures and multiple damage scenarios. Through three-dimensional discrete modeling and parallel processing of multiple source signals, this method can identify multiple damage events simultaneously and distinguish their spatial positions and activity levels, especially suitable for health monitoring of heterogeneous, multiphase composite structures such as reinforced concrete and composite materials. Compared with traditional methods that can only identify single defects or overall stiffness degradation, it has stronger adaptability and comprehensive diagnosis.

[0023] In summary, this method can achieve high-precision, non-invasive, long-term real-time dynamic monitoring of internal damage in engineering structures, breaking through the limitations of traditional detection techniques in terms of excitation dependence, imaging resolution, and dynamic perception ability. It provides an intelligent and efficient new approach for structural health monitoring, achieving dynamic tomographic imaging and real-time monitoring of damage location, range, and evolution process.

[0024] Preferably, in S3, the preprocessing includes filtering, denoising and background interference suppression; and the self-excited wave signal caused by internal structural damage is screened out by threshold detection, energy mutation recognition or pattern classification method.

[0025] Such arrangement, the filtering, denoising and background interference suppression in the preprocessing step can effectively remove irrelevant components in the original signal, such as environmental noise, equipment electrical noise, etc. This not only improves the signal-to-noise ratio, making the subsequent analysis more accurate and reliable, but also reduces the influence of non-target information on the analysis results, ensuring the authenticity and purity of the signal. And using threshold detection, energy mutation recognition or pattern classification method to further screen the preprocessed signal, can accurately capture the weak changes caused by internal structural damage. These methods can customize parameters according to different types of damage characteristics, so as to effectively separate the damage signal from the complex background, significantly improving the recognition and positioning accuracy of the damage signal.

[0026] Preferably, in S4, for a self-excited wave received by a sensor, the calculation method of its arrival time is as follows:

[0027] 1) Signal preprocessing; the time when the amplitude of the self-excited wave first exceeds the preset threshold is taken as the threshold point, and a preset number of data points before and after the threshold point are selected as the data of the signal window to be analyzed;

[0028] 2) Autoregressive (AR) model modeling; noise segment and signal segment separation: select the middle point as the noise data and signal data, and calculate the order M1, M2 and coefficient of the AR model; determine the AR model coefficient through Yule-Walker equation, and minimize the prediction error variance;

[0029] 3) AIC calculation and segmentation point determination; select each data point in the signal window as the segmentation point in turn, and divide the data sequence in the window into two segments: noise segment and signal segment; for the segmentation point K, calculate the AIC value of the noise segment and the signal segment, and take the K with the minimum AIC(K) value as the arrival time; wherein, the calculation formula of AIC(K) value is:

[0030] AIC(K) = (K-M1)log(σ12) + (N-K-M2)log(σ22) + 2(M1+M2);

[0031] In the formula, σ12 and σ22 are the prediction error variances of the noise segment and the signal segment; N is the signal length.

[0032] This setup, through preset threshold windowing, improves the focus and computational efficiency of the analysis area. The first step determines the initial "candidate arrival region" by setting an amplitude threshold, and then uses this as the center to extract an analysis window containing data points before and after it, effectively narrowing the computational scope for subsequent modeling. Compared to modeling the entire signal segment, this strategy significantly reduces the computational burden while avoiding interference from far-field noise or irrelevant signal segments on model parameter estimation. This preprocessing mechanism achieves rapid focusing from global to local data, providing a high-quality data foundation for subsequent high-precision segmentation.

[0033] 2. Utilizing AR models to separately characterize the dynamic characteristics of noise and signal enhances the physical interpretability of the model. This scheme divides the window signal into two parts: "noise in the first part and signal in the second part," and establishes autoregressive (AR) models for each part. This effectively captures the stationary random characteristics of the noise segment and the structured dynamic changes of the signal segment. By solving the AR coefficients through the Yule-Walker equation and minimizing the prediction error variance, the optimal fit of the model to the statistical characteristics of each segment is ensured. This segmented modeling strategy fully considers the essential differences in the system response before and after the signal arrival, improving the model's ability to approximate the real physical process.

[0034] 3. Automatic identification of optimal breakpoints based on the AIC criterion avoids human intervention and improves interpretation consistency. The essence of arrival time is the boundary between noise and signal segments. This scheme introduces the AIC (Akaike Information Criterion) as an evaluation index for the breakpoint K, comprehensively considering both model fit (reflected by error variance) and model complexity (reflected by order penalty terms). By traversing all possible K values ​​and selecting the breakpoint that minimizes the total AIC, data-driven optimal breakpoint detection is achieved. This method does not rely on empirical thresholds or graphical interpretation, significantly improving the objectivity and repeatability of arrival time identification, and is particularly suitable for automated monitoring systems.

[0035] 4. Integrating model order selection and error control, balancing fitting accuracy and overfitting suppression. The AIC formula includes penalty terms for M1 and M2 (2(M1+M2)), achieving a balance between model fitting accuracy and complexity. If a split point leads to an excessively high model order or an insignificant decrease in error variance, its AIC value will increase due to the increased penalty term, thus eliminating it from the algorithm. This mechanism effectively prevents misjudgment of arrival time due to overfitting noise, enhancing the algorithm's robustness and anti-interference capability under low signal-to-noise ratio conditions.

[0036] Preferably, in S4, the process of calculating the position coordinates of a wave source includes:

[0037] Based on sensor S i coordinates (x) i ,y i ,zi ) and the wave source elastic wave arrival sensor S i The time t i According to the relationship between distance, time and wave velocity, a positioning equation group containing n equations is established:

[0038]

[0039] In the formula, t0 is the time when the elastic wave of the wave source occurs; i = 1, 2, 3, …, n, n is the number of sensors receiving signals; (x, y, z) is the wave source coordinate; V AE is the average wave velocity of the elastic wave propagating in the medium;

[0040] Based on the positioning equation group, an identity transformation is used to derive a monomial cubic equation with V as the unknown quantity:

[0041]

[0042] In the formula, the coefficients a, b, c and d are combined from the coefficients of the original equation group;

[0043] Solving the monomial cubic equation, the value of V AE is obtained, and is recorded as old V AE ; old V AE is substituted into the positioning equation group to obtain the wave source coordinate; according to the relative position of the wave source coordinate and the sensor s i , the ray tracing method is used to search for the wave propagation path in the initial wave velocity field or the wave velocity field calculated last time to determine all the cells through on the self-excited wave propagation path.

[0044] The ratio of the length of the propagation path in the cell to the total length of the entire path is used as the weight, and the wave velocity values of the cells through in the wave velocity field are used for weighted summation to obtain new V AE .

[0045] If the difference between the new and old V AE is greater than the preset threshold (i.e. the error limit), the new V AE is taken as the old V AE of the next round, substituted into the positioning equation group and solved to obtain the new source coordinate, and the above process is repeated to update the source coordinate solution and the wave velocity solution; if the difference between the new and old V AE is less than or equal to the preset threshold, the wave source coordinate obtained at present is taken as the actual wave source coordinate.

[0046] This setup involves several key aspects. First, based on the received wave signal time and the sensor's known position coordinates, and combined with the propagation speed of elastic waves in the medium, a set of n positioning equations is established. This method more accurately reflects the spatial relationship between the wave source and the sensor, thus improving positioning accuracy. A cubic equation with the average wave velocity as the unknown is derived through identity transformation, and the old average wave velocity value is obtained by solving it. This process avoids the difficulty of directly solving complex nonlinear equations, simplifies the calculation steps, and improves computational efficiency.

[0047] 2. This technical solution introduces an iterative optimization process, gradually approximating the true wave source location and wave velocity value through multiple iterations. Compared with a one-time solution method, this iterative optimization strategy can significantly improve the accuracy of the positioning results, especially when the wave velocity field is non-uniform.

[0048] 3. Based on the relative position of the wave source coordinates and the sensor, the ray tracing method is used to trace the wave propagation path in the wave velocity field, determining all elements passed through along the propagation path. This method can more accurately simulate the wave propagation process, further improving positioning accuracy. Furthermore, using the ratio of the propagation path's length within an element to the total path length as a weight, the wave velocity values ​​of these elements in the wave velocity field are weighted and summed to obtain a new average wave velocity value. This weighted summation method considers the influence of material properties and states within different elements on the wave velocity, making the calculation results more reasonable and accurate.

[0049] Preferably, in S5, the process of processing the damage results of the monitored object includes: integrating the spatial coordinates of the sources of each excitation wave into a three-dimensional point set, and calculating the minimum convex hull containing all position coordinates in the three-dimensional point set as the damage range of the monitored object.

[0050] This setup, which calculates the minimum convex hull containing the coordinates of all locations within a 3D point set as the damage extent, effectively defines the spatial region affected by the actual damage. This not only helps in understanding the actual impact range of the damage but also provides an important basis for subsequent maintenance decisions. Compared to traditional tomographic imaging techniques that rely on inversion and reconstruction based on a single physical quantity (such as wave velocity or attenuation coefficient), this method can define the damage boundary more clearly and accurately.

[0051] Furthermore, for structures with complex geometries or material compositions, such as reinforced concrete and composite materials, the minimum convex emboss algorithm can better adapt to the influence of internal heterogeneity by handling the spatial distribution of self-excited wave sources. Even in the presence of multiple small-scale damages, it can achieve comprehensive coverage and accurate assessment of the damage range by integrating the spatial coordinates of multiple weak signal sources, thus improving the ability to identify damage in complex structures.

[0052] Preferably, in S5, the process of synchronously solving, updating the wave velocity field in the monitoring object, and processing the damage result of the monitoring object comprises:

[0053] Assembling the arrival time of each sensor receiving the excited wave into a time vector T;

[0054] Calculating the elastic wave propagation path length from the wave source to each sensor and the line segment length of the path in the discrete unit it penetrates, to obtain a distance matrix A;

[0055] Solving the imaging equation AS=T using the time vector T and the distance matrix A to obtain a slowness vector S; the slowness vector S is composed of the slowness values of the elastic wave propagation in each discrete unit of the monitoring object, and each element of the vector S corresponds to the slowness value of a discrete unit; the slowness value is the reciprocal of the wave velocity v;

[0056] Based on the slowness vector S, determining the damage range of the monitoring object and the damage degree of each discrete unit in the damage range; and updating the wave velocity field in the monitoring object based on the slowness matrix.

[0057] Such a setting, 1, traditional tomography is mostly based on uniform grid and simplified propagation model, it is difficult to accurately reflect the real path and speed change of wave propagation in complex structure. The method constructs a distance matrix A by calculating the actual line segment length between each wave source and each sensor, and combines the measured arrival time to form a time vector T, to establish an accurate AS=T imaging equation. This way fully considers the propagation geometry of waves in heterogeneous media, improves the spatial resolution in the inversion process, so that the imaging result can more truly reflect the physical state inside the structure.

[0058] 2, the slowness (the reciprocal of the wave velocity) is taken as the core parameter representing the damage degree, which has clear physical meaning: material damage usually leads to the decrease of elastic modulus and the increase of internal micro-cracks, thus reducing the wave velocity and increasing the slowness. Therefore, the value of each discrete unit in the slowness vector S directly corresponds to its medium degradation degree, and the larger the value is, the more serious the damage is. This quantitative index based on physical mechanism is more scientific and interpretable than the traditional empirical judgment relying only on signal energy or event density, which helps to realize the grading evaluation and risk warning of damage.

[0059] 3, enhance the recognition ability of multi-source and complex damage. In actual engineering structures, damage often presents the characteristics of multiple points, dispersion or local aggregation. By constructing a global imaging equation and solving the slowness distribution of the whole region, this method can process data from multiple wave sources at the same time, and comprehensively invert the slowness field in the whole monitoring object, avoiding the information fragmentation problem caused by point-by-point positioning. Even in the case of multiple damage regions coexisting, it can clearly distinguish the abnormal degree of slowness in different regions, and effectively identify the main damage area and potential weak area.

[0060] Preferably, for each discrete unit within the damage range, the damage degree is calculated by the following formula:

[0061]

[0062] wherein v p is the wave speed, is the inverse of the slowness value of the discrete unit; D is the damage degree; E is the elastic modulus of the undamaged material; p is the material density; and m is the material Poisson's ratio.

[0063] In this way, by obtaining the wave speed (slowness) distribution of each discrete unit of the structure, the damage state and its distribution of the entire region can be intuitively understood.

[0064] Preferably, an algebraic reconstruction algorithm is used to solve the imaging equation AS = T; the calculation process of the algebraic reconstruction algorithm comprises:

[0065] Step 1, initialization: assigning an initial slowness value to all discrete units;

[0066] Step 2, iterative update: using the current slowness value, iterating for the ith propagation path to obtain an updated solution S; applying this solution to the i+1th path, continuing to iterate and obtaining a new modified solution; repeating the above process until all paths have completed one iteration;

[0067] Step 3, convergence check: evaluating whether the new solution S obtained by iteration meets the preset convergence criteria; if the new solution does not meet the convergence criteria, returning to step 2 for iteration again until the convergence condition is met and the final slowness vector S is obtained.

[0068] With such a setting, by introducing the algebraic reconstruction algorithm to solve the imaging equation, not only are the defects of traditional imaging methods such as high requirement for data completeness, weak noise resistance and difficulty in adapting to complex monitoring environments overcome, but also the advantages of iterative reconstruction in local sensitivity, prior information fusion and dynamic updating are fully utilized.

[0069] Preferably, in S6, based on the damage result of the monitoring object, a corresponding three-dimensional damage display diagram is generated in combination with the three-dimensional discrete model thereof; in the three-dimensional damage display diagram, different colors are used to represent the severity of damage.

[0070] In S6, the corresponding processing comprises: adjusting the positions of the sensors in the sensor array, increasing the number of sensors around the damage range area, to improve the spatial sampling density and the collection sensitivity of the self-excited wave signal in the local area of the damage range, and to enhance the monitoring capability of the damage evolution behavior, according to the damage range of the monitoring object determined in S5.

[0071] Traditional structural monitoring results are mostly output in the form of numerical values, graphs or two-dimensional slices, which are difficult to fully reflect the distribution characteristics of damage in three-dimensional space. The present scheme superimposes damage range and degree information onto the three-dimensional discrete model of the structure, generating a stereoscopic visualization image, allowing users to observe the spatial position, geometric shape and expansion trend of the damage from any angle, greatly enhancing the intuitive understanding of the internal state of complex structures. In addition, by setting a color gradient (such as blue→yellow→red) corresponding to low→medium→high damage degree, and using the high sensitivity of the human eye to color differences, rapid identification of damage severity is achieved. Compared to traditional imaging methods that rely solely on numerical values or gray scale changes, color three-dimensional display images can more clearly distinguish the degradation levels of different regions, making it easier for engineers to quickly locate key damage areas and make priority judgments.

[0072] In addition, the present method dynamically increases the number of sensors around the identified damage area, effectively improving the local spatial sampling density, making the wave field information collection of the damage area more intensive and detailed, thereby significantly improving the spatial resolution of damage positioning and imaging. Moreover, increasing the sensor arrangement near the damage area allows for closer capture of weak self-excited wave signals (such as acoustic emission signals generated by crack propagation, local loosening, etc.), improving the signal amplitude and signal-to-noise ratio, which is beneficial for the detection of early or minor damage. BRIEF DESCRIPTION OF DRAWINGS

[0073] In order to make the purpose, technical scheme and advantages of the invention clearer, the following will further describe the invention in detail with reference to the accompanying drawings, in which:

[0074] Figure 1 is a flowchart of the present method;

[0075] Figure 2 is a flowchart of the method implementation in Example 1;

[0076] Figure 3 is a schematic diagram of the self-excited wave (i.e. acoustic emission in the figure) phenomenon and its signal acquisition process in Example 1;

[0077] Figure 4 is a schematic diagram of the self-excited wave source (red node) and its adaptive mesh division in the discrete model in Example 2;

[0078] Figure 5 is a schematic diagram of determining the damage range based on the self-excited wave source and its (minimum convex) envelope in Example 2;

[0079] Figure 6 is a preparation schematic diagram of Example 1 in Example 3;

[0080] Figure 7 is a schematic diagram of determining the damage distribution range in Example 1 in Example 3;

[0081] Figure 8 Schematic diagram for real-time wave velocity field inversion of example 1 in embodiment three;

[0082] Figure 9 Schematic diagram for preparation of example 2 in embodiment three;

[0083] Figure 10 Schematic diagram for example 3 in embodiment three;

[0084] Figure 11 Schematic diagram for example 4 in embodiment three. DETAILED DESCRIPTION

[0085] The following is further described in detail through specific embodiments:

[0086] Embodiment one

[0087] As shown in Figure 1 , Figure 2 , a structural dynamic tomography and damage monitoring method using self-excited waves is disclosed in the embodiment, which comprises the following steps:

[0088] S1, spatial discretization processing is performed on the monitoring object, which is divided into a plurality of three-dimensional discrete units, and a three-dimensional discrete model is established; a plurality of sensors are arranged on the monitoring object and the spatial coordinates of each sensor are recorded to form a sensor array for collecting self-excited waves of the monitoring object from different directions, wherein the self-excited waves are elastic waves generated spontaneously during the damage or damage propagation process of the structure inside the monitoring object, and the energy carried by the self-excited waves is converted from the strain energy inside the structure.

[0089] In specific implementation, the sensors arranged at each position of the monitoring object include piezoelectric ceramics, fiber Bragg gratings, and MEMS accelerometers.

[0090] S2, elastic wave propagation data is collected by applying external excitation at a known position, and the initial wave velocity field inside the monitoring object is inverted in combination with the wave travel time information;

[0091] S3, the data obtained by the sensor array under the service condition of the monitoring object is preprocessed, and the self-excited waves of the monitoring object received by each sensor are extracted, wherein the preprocessing includes filtering, denoising, and background interference suppression; wherein the filtering can use an adaptive Kalman filtering algorithm; the self-excited wave signals caused by the internal damage of the structure are screened out through threshold detection, energy mutation identification, or pattern classification method. In specific implementation, the phenomenon of self-excited waves (i.e. acoustic emission in the figure) and the signal collection process are as shown in Figure 3 .

[0092] In this way, the filtering, denoising and background interference suppression in the preprocessing step can effectively remove irrelevant components in the original signal, such as environmental noise, equipment electrical noise, etc. This not only improves the signal-to-noise ratio, making the subsequent analysis more accurate and reliable, but also reduces the influence of non-target information on the analysis results, ensuring the authenticity and purity of the signal. Further screening of the preprocessed signal using threshold detection, energy mutation identification or pattern classification methods can accurately capture the weak changes caused by internal structural damage. These methods can be customized to set parameters based on different types of damage characteristics, effectively separating the damage signal from the complex background and significantly improving the recognition and positioning accuracy of the damage signal.

[0093] S4, identifying the arrival time of each self-excited wave signal on each sensor; determining whether it is the first time to perform damage analysis; if so, combining the spatial coordinates of the sensors and the initial wave velocity field to inversely calculate the spatial coordinates of the wave source of each excited wave; if not, combining the spatial coordinates of the sensors and the wave velocity field calculated last time to inversely calculate the spatial coordinates of the wave source of each excited wave;

[0094] Wherein, for a self-excited wave received by a sensor, the arrival time is calculated as follows:

[0095] 1) Signal preprocessing; the time when the amplitude of the self-excited wave first exceeds the preset threshold is taken as the threshold point, and a preset number of data points (such as 99 points) are selected before and after the threshold point as the data of the signal window to be analyzed;

[0096] 2) Autoregressive (AR) model modeling; noise segment and signal segment separation: selecting the middle point as the noise data and signal data, respectively calculating the order M1, M2 and coefficient of the AR model; determining the AR model coefficient through Yule-Walker equation, minimizing the prediction error variance;

[0097] 3) AIC calculation and segmentation point determination; selecting each data point in the signal window as a segmentation point in turn, dividing the data sequence in the window into two segments - noise segment and signal segment; for each segmentation point K, calculating the AIC value of the noise segment and the signal segment, taking the K with the minimum AIC(K) value as the arrival time; wherein, the calculation formula of AIC(K) value is:

[0098] AIC(K) = (K-M1)log(σ12) + (N-K-M2)log(σ22) + 2(M1+M2);

[0099] Wherein, σ12, σ22 are the prediction error variances of the noise segment and the signal segment; N is the signal length.

[0100] The first step of the method determines the initial "candidate arrival time region" by setting an amplitude threshold, and then uses this region as the center to extract an analysis window containing data points before and after the arrival of the signal, effectively narrowing the computational scope for subsequent modeling. Compared to modeling the entire signal segment, this strategy significantly reduces the computational burden while avoiding interference from far-field noise or irrelevant signal segments on model parameter estimation. This preprocessing mechanism enables rapid focusing from the global to the local level, providing a high-quality data foundation for subsequent high-precision segmentation. Furthermore, this scheme divides the windowed signal into two parts: "noise in the front segment and signal in the back segment," and establishes autoregressive (AR) models for each. This effectively captures the stationary random characteristics of the noise segment and the structured dynamic changes of the signal segment. By solving the AR coefficients using the Yule-Walker equation and minimizing the prediction error variance, the model ensures optimal fitting of the statistical characteristics of each segment. This segmented modeling strategy fully considers the essential differences in the system response before and after signal arrival, improving the model's ability to approximate the real physical process.

[0101] In addition, the essence of arrival time is the boundary between the noise segment and the signal segment. This scheme introduces AIC (Akaike Information Criterion) as an evaluation index for the segmentation point K, comprehensively considering both model fit goodness (reflected by error variance) and model complexity (reflected by the order penalty term). By traversing all possible K values ​​and selecting the segmentation point that minimizes the total AIC, data-driven optimal breakpoint detection is achieved. This method does not rely on empirical thresholds or graphical interpretation, significantly improving the objectivity and repeatability of arrival time identification, and is particularly suitable for automated monitoring systems. Furthermore, the AIC formula includes penalty terms for M1 and M2 (2(M1+M2)), achieving a balance between model fitting accuracy and complexity. If a segmentation point leads to an excessively high model order or an insignificant decrease in error variance, its AIC value will increase due to the increased penalty term, thus being excluded. This mechanism effectively prevents misjudgment of arrival time due to overfitting noise, enhancing the robustness and anti-interference capability of the algorithm under low signal-to-noise ratio conditions. In specific implementation, the process of calculating the position coordinates of a wave source includes, but is not limited to, the following methods:

[0102] Based on sensor S i coordinates (x) i ,y i ,z i The elastic wave from the wave source reaches the sensor S. i Time t i Based on the relationship between distance, time, and wave speed, a system of n positioning equations is established:

[0103]

[0104] In the formula, t0 is the moment when the elastic wave originates from the wave source; i = 1, 2, 3, ..., n, where n is the number of sensors receiving the signal; (x, y, z) are the coordinates of the wave source; V AE The average wave velocity of an elastic wave propagating in a medium;

[0105] Based on the positioning equations, a system of equations is derived through identity transformation, which is based on... A cubic equation with unknowns:

[0106]

[0107] The coefficients a, b, c, and d are obtained by combining the coefficients of the original system of equations.

[0108] Solving this cubic equation, we get V. AE The value, and denoted as old V. AE ; the old V AE Substituting into the positioning equations, the coordinates of the wave source are obtained; based on the coordinates of the wave source and the sensor S... i The relative positions of the waves are determined by using ray tracing to search for the propagation path of the waves in the initial wave velocity field or the most recently calculated wave velocity field, and to identify all the elements that the self-excited waves pass through on the propagation path.

[0109] Using the ratio of the propagation path's length through a cell to the total length of the entire path as weights, a new V is obtained by weighted summation of the wave velocity values ​​passing through these cells in the wave velocity field. AE ;

[0110] If the old and new V AE If the difference is greater than a preset threshold (i.e., error limit), then the new V will be... AE As a new round of old V AE Substitute the solutions into the positioning equations and solve for the new source coordinates. Repeat the above process to update the source coordinate solutions and wave velocity solutions. If the old and new V... AE If the difference is less than or equal to a preset threshold, then the currently obtained wave source coordinates will be used as the actual wave source coordinates.

[0111] The technical scheme firstly establishes a positioning equation set containing n equations based on the wave signal time received by the sensor and the known position coordinates of the sensor, in combination with the propagation speed of elastic waves in the medium. This method can more accurately reflect the spatial relationship between the wave source and the sensor, thereby improving the positioning accuracy. An average wave speed is derived as an unknown quantity by means of an identity transformation, and the old average wave speed value is obtained by solving. This process avoids the difficulty of directly solving complex nonlinear equations, simplifies the calculation steps, and improves the calculation efficiency. In addition, the technical scheme introduces an iterative optimization process, and gradually approaches the real wave source position and wave speed value through multiple iterations. Compared with the one-time solving method, this iterative optimization strategy can significantly improve the accuracy of the positioning result, especially in the case of uneven wave speed field.

[0112] According to the relative position of the wave source coordinates and the sensor, the ray tracing method is used to track the wave propagation path in the wave speed field, and all the cells crossed by the wave propagation path are determined. This method can more accurately simulate the wave propagation process, further improving the positioning accuracy. In addition, the ratio of the length of the propagation path in the cell to the total length of the entire path is used as the weight, and the wave speed values of these cells in the wave speed field are weighted and summed to obtain a new average wave speed value. This weighted summation method considers the influence of different cells on the wave speed, making the calculation result more reasonable and accurate.

[0113] S5, based on the spatial coordinates of the wave source of each excited wave, synchronously solving and updating the wave speed field inside the monitoring object, processing to obtain the damage result of the monitoring object, the damage structure including the damage range;

[0114] The process of processing to obtain the damage result of the monitoring object includes:

[0115] The arrival time of each sensor receiving the excited wave is composed into a time vector T.

[0116] A distance matrix A is constructed. In the structure discretized regular grid, a cell corresponds to a column of the matrix A. The grid index needs to strictly correspond to the physical space coordinates to ensure the accuracy of the path calculation. According to the wave speed distribution of the medium, the actual wave propagation path is calculated by the ray tracing algorithm (such as Vidale finite difference method or cross-scan method) to reflect the influence of the non-uniform medium. For each path i, all grid cells j are traversed, and the physical contribution of path i in cell j is calculated, that is, the length a ij of path i in the cell, as the value of the i-th row and j-th column element in the A matrix.

[0117] Solving the imaging equation AS=T using the time vector T and the distance matrix A to obtain a slowness vector S; the slowness vector S is composed of the slowness values of elastic wave propagation in each discrete unit of the monitoring object, and each matrix element corresponds to the slowness value of a discrete unit; the slowness value is the reciprocal of wave velocity;

[0118] Based on the slowness vector S, the damage range of the monitoring object and the damage degree of each discrete unit in the damage range are determined. And the wave velocity field inside the monitoring object is updated based on the slowness matrix.

[0119] As the damage develops, the local wave velocity continues to decrease. If the initial high wave velocity model is still used, it will lead to early prediction of arrival time, and then cause systematic outward shift or diffusion of the wave source positioning system. This method updates the wave velocity field in real time, so that the positioning model always keeps consistent with the current state of the structure, can more sensitively capture the small medium changes, and timely identify the new appearing or expanding damage area, and improve the early warning ability of the monitoring system. Such a setting feeds back the inversion result (current wave velocity field) to the front-end positioning module, forming a closed-loop processing flow of "perception → modeling → re-perception". This mechanism enables the system to have "memory" and "learning" ability: each imaging result provides more accurate prior information for the next analysis, avoiding model drift and error accumulation caused by independent event processing, enhancing the spatio-temporal consistency of multi-source event fusion analysis, and promoting the development of the monitoring system towards intelligence and autonomy.

[0120] Figure 2 In the formula, the relationship between the elastic modulus and the damage is:

[0121]

[0122] In the formula, D is the damage degree; E is the elastic modulus of the undamaged material; E' is the elastic modulus of the damaged material.

[0123] In specific implementation, for each discrete unit in the damage range, the damage degree can be calculated by the following formula:

[0124]

[0125] In the formula, v p is the wave velocity, is the reciprocal of the slowness value of the discrete unit; p is the material density; and μ is the material Poisson's ratio.

[0126] In this way, by obtaining the wave velocity (slowness) distribution of each discrete unit of the structure, the damage state of the entire region can be intuitively understood.

[0127] In specific implementation, an algebraic reconstruction algorithm or the like is used to solve the imaging equation AS=T; the calculation process of the algebraic reconstruction algorithm includes:

[0128] Step 1, Initialization: Assign an initial slowness value to all discrete elements;

[0129] Step 2, Iterative Update: Using the current slowness value, iterate for the i-th propagation path to obtain an updated solution S; apply this solution to the (i+1)-th path and continue iterating to obtain a new modified solution; repeat the above process until all paths have completed one iteration;

[0130] Step 3, Convergence Check: Evaluate whether the new solution S obtained by iteration meets the preset convergence criteria; if the new solution does not meet the convergence criteria, return to Step 2 for further iteration until the convergence condition is met, obtaining the final slowness vector S.

[0131] In this way, by introducing the algebraic reconstruction algorithm to solve the imaging equation, not only does it overcome the defects of traditional imaging methods such as high data completeness requirements, weak noise resistance, and difficulty in adapting to complex monitoring environments, but it also fully utilizes the advantages of iterative reconstruction in terms of local sensitivity, prior information fusion, and dynamic updating.

[0132] Traditional tomography is mostly based on uniform grids and simplified propagation models, making it difficult to accurately reflect the true path and velocity changes of wave propagation in complex structures. This method constructs a distance matrix A by calculating the actual line segment length between each wave source and sensor, and combines it with the measured arrival time to form a to-time vector T, establishing an accurate AS=T imaging equation. This approach fully considers the geometric relationship of wave propagation in heterogeneous media, improving the spatial resolution during inversion and enabling the imaging results to more accurately reflect the internal physical state of the structure. In addition, the slowness (the inverse of wave speed) is used as a core parameter to represent the degree of damage, which has clear physical meaning: material damage usually leads to a decrease in elastic modulus and an increase in internal micro-cracks, resulting in a decrease in wave speed and an increase in slowness. Therefore, the value of each discrete element in the slowness vector S directly corresponds to the degree of medium degradation, with a larger value indicating more severe damage. This quantitative indicator based on physical mechanisms is more scientific and interpretable than traditional empirical judgments relying solely on signal energy or event density, and it helps to achieve hierarchical assessment and risk warning of damage. Furthermore, in actual engineering structures, damage often presents characteristics of multiple points, dispersion, or local aggregation. By constructing a global imaging equation and solving the slowness distribution in the entire region, this method can simultaneously process data from multiple wave sources and comprehensively invert the slowness field within the entire monitoring object, avoiding the information fragmentation problem caused by point-by-point positioning. Even in the presence of multiple damage regions, it can clearly distinguish the degree of slowness anomaly in different regions and effectively identify the main damage areas and potential weak areas.

[0133] S6, Based on the damage results of the monitoring object, perform corresponding processing.

[0134] In specific implementation, based on the damage result of the monitoring object, a corresponding three-dimensional damage display image is generated in combination with the three-dimensional discrete model thereof. In the three-dimensional damage display image, different colors are used to represent the severity of the damage. Traditional structural monitoring results are mostly output in the form of numerical values, graphs or two-dimensional slices, which are difficult to fully reflect the distribution characteristics of the damage in three-dimensional space. In the present scheme, the damage range and degree information is superimposed on the three-dimensional discrete model or digital twin model of the structure to generate a three-dimensional visual image, so that the user can observe the spatial position, geometric shape and expansion trend of the damage from any angle, greatly enhancing the intuitive cognitive ability of the internal state of the complex structure. By setting a color gradient (such as blue to yellow to red) corresponding to low to medium to high damage degree, the high sensitivity of the human eye to color differences is utilized to achieve rapid identification of the severity of the damage. Compared with traditional imaging methods that rely only on numerical values or gray scale changes, the color three-dimensional display image can more clearly distinguish the degradation levels of different regions, making it easier for engineers to quickly lock in the key damage areas and make priority judgments.

[0135] In specific implementation, in S6, the corresponding processing includes adjusting the positions of the sensors in the sensor array, increasing the number of sensors around the damage range area, to improve the local spatial sampling density and the collection sensitivity of the self-excited wave signal in the damage range area, and enhance the monitoring capability of the damage evolution behavior, according to the damage range of the monitoring object determined in S5.

[0136] Traditional structural monitoring results are mostly output in the form of numerical values, graphs or two-dimensional slices, which are difficult to fully reflect the distribution characteristics of the damage in three-dimensional space. In the present scheme, the damage range and degree information is superimposed on the three-dimensional discrete model of the structure to generate a three-dimensional visual image, so that the user can observe the spatial position, geometric shape and expansion trend of the damage from any angle, greatly enhancing the intuitive cognitive ability of the internal state of the complex structure. In addition, by setting a color gradient (such as blue to yellow to red) corresponding to low to medium to high damage degree, the high sensitivity of the human eye to color differences is utilized to achieve rapid identification of the severity of the damage. Compared with traditional imaging methods that rely only on numerical values or gray scale changes, the color three-dimensional display image can more clearly distinguish the degradation levels of different regions, making it easier for engineers to quickly lock in the key damage areas and make priority judgments. In addition, the present method dynamically increases the number of sensors around the damage range area according to the identified damage range, effectively improving the local spatial sampling density, making the wave field information collection of the damage area more intensive and detailed, thereby significantly improving the spatial resolution of damage positioning and imaging. Moreover, increasing the sensor arrangement near the damage area can more closely capture weak self-excited wave signals (such as acoustic emission signals generated by crack propagation, local loosening, etc.), improve the amplitude and signal-to-noise ratio of the signals, and facilitate the detection of early or minor damage.

[0137] In particular implementation, the structure can be detected and damage predicted for the whole life based on the damage result and the historical data of the wave velocity field evolution, so as to formulate a targeted maintenance and reinforcement auxiliary scheme.

[0138] Compared with the traditional active ultrasonic wave or impact echo technology which relies on manual excitation source, the method fully utilizes the elastic wave signal spontaneously generated by the micro-damage evolution (such as crack initiation and expansion) of the structure during service as the information source, and gets rid of the dependence on frequent external excitation device. This not only significantly reduces the system operation cost and operation complexity, but also makes continuous and long-term online monitoring possible, especially suitable for large infrastructure which is difficult to be frequently manually intervened or needs to be monitored all day round. In addition, in S2, the wave velocity field inside the structure is obtained by inversion of the initial external excitation or the self-excited wave signal collected during the service of the structure, which provides an accurate propagation medium model for the positioning of the subsequent self-excited wave source. Compared with the uniform or simplified wave velocity assumption commonly used in traditional tomography, the wave velocity field more truly reflects the heterogeneity of the material inside the structure, thereby significantly improving the inversion accuracy of the spatial coordinates of the wave source in S4. Combined with the three-dimensional discrete model and the spatial coverage of the multi-sensor array, high-resolution positioning and spatial distribution reconstruction of multiple damage sources can be realized.

[0139] In view of the problem that the self-excited wave signal is weak and easy to be submerged by noise, the data preprocessing mechanism is introduced in S3 to effectively extract the real self-excited event signal. Through multi-sensor collaborative analysis and accurate identification of arrival time, combined with the known sensor layout and the wave velocity field model, the reliability of signal feature extraction in a low signal-to-noise ratio environment is improved, and the defect of large positioning deviation caused by misjudgment of arrival time in the traditional acoustic emission technology is overcome. In addition, unlike the modal analysis method or static imaging technology which can only reflect the overall state change of the structure, the method can dynamically reconstruct the expansion path and range change of the damage area based on the spatial aggregation characteristics (S5) of a large number of self-excited wave sources, and realize the construction of the damage evolution map from point to plane. This dynamic tomography capability based on physical mechanism makes the development process of local damage visualized, which makes up for the deficiency of the existing technology that cannot capture the dynamic behavior of damage. Moreover, through three-dimensional discrete modeling and multi-source signal parallel processing, the method can identify multiple damage events at the same time and distinguish their spatial positions and activity levels, and is especially suitable for health monitoring of heterogeneous and multiphase composite structures such as reinforced concrete and composite materials. Compared with the traditional means which can only identify a single defect or overall stiffness degradation, the method has stronger adaptability and comprehensive diagnosis.

[0140] Embodiment two

[0141] Different from the embodiment one, in S5 of the present embodiment, the process of obtaining the damage result of the monitoring object comprises: clustering the points where the spatial coordinates of the wave sources of the respective excitation waves are located into a three-dimensional point set, and calculating a minimum convex envelope containing all position coordinate points in the three-dimensional point set as the damage range of the monitoring object.

[0142] Adaptive meshing of the excitation wave sources (red nodes) and their minimum convex envelope in the discrete model as shown in Figure 4 The determination of the damage range based on the excitation wave sources and their (minimum convex) envelope as shown in Figure 5 .

[0143] In this way, the minimum convex envelope containing all position coordinates of the three-dimensional point set is calculated as the damage range, which can effectively define the spatial region involved in the actual damage. This not only helps to understand the actual impact range of the damage, but also provides an important basis for subsequent maintenance decisions. Compared with the traditional tomographic imaging technology based on a single physical quantity (such as wave speed, attenuation coefficient) for inversion reconstruction, this method can more clearly and accurately define the damage boundary. And for structures with complex geometric shapes or material compositions, such as reinforced concrete, composite materials, etc., using the minimum convex envelope algorithm to process the spatial distribution of excitation wave sources can better adapt to the influence of internal heterogeneity. Even in the case of multiple small-scale damages coexisting, the spatial coordinates of multiple weak signal sources can be integrated to achieve comprehensive coverage and accurate assessment of the damage range, improving the ability to identify complex structural damage

[0144] For better understanding, the construction method of the minimum convex envelope (referred to as "convex hull") is explained as follows.

[0145] I. Principle

[0146] Definition of convex hull: The convex hull in three-dimensional space is the smallest convex polyhedron that contains all given points. Its mathematical definition is as follows:

[0147] • The convex hull is the intersection of all convex sets containing these points.

[0148] • The boundary of the convex hull consists of a set of triangular or quadrilateral facets whose normal vectors point outward.

[0149] Key properties

[0150] • Convexity: All points on the line segment connecting any two points are inside or on the boundary of the convex hull.

[0151] • Uniqueness: For a given point set, the convex hull is unique.

[0152] • Extreme points: The vertices of the convex hull must be a subset of the original point set.

[0153] Geometric meaning

[0154] · Convex hull is the "tightest" convex enclosure of a point set, commonly used in collision detection, shape analysis, point cloud processing, etc.

[0155] II. Mathematical formulas

[0156] 1. Plane equation

[0157] Each face of the convex hull can be represented as a plane equation:

[0158] ax+by+cz+d=0;

[0159] Where (a, b, c) is the normal vector of the plane, and d is the distance from the origin to the plane.

[0160] 2. Relationship between point and plane

[0161] For any point P(x0, y0, z0), substitute the plane equation:

[0162] · If ax0+by0+cz0+d>0: the point is in the positive half-space of the plane (outside).

[0163] · If ax0+by0+cz0+d=0: the point is on the plane.

[0164] · If ax0+by0+cz0+d<0: the point is in the negative half-space of the plane (inside).

[0165] 3. Boundary conditions of convex hull

[0166] · Each face of the convex hull must satisfy: all points are located in the non-positive half-space of the plane (i.e. ≤0).

[0167] · There must be at least one point on the plane (support face).

[0168] III. Common algorithms

[0169] 1. Gift Wrapping (Gift Wrapping Algorithm)

[0170] · Principle: Starting from the initial face, gradually expand the adjacent face until all points are included.

[0171] · Steps:

[0172] · Find a vertex of the convex hull (such as the point with the smallest coordinates).

[0173] · From this point, find two adjacent points that form the convex hull edge, forming an initial triangular face.

[0174] · For each edge of each face, find the next point (so that all other points are located in the non-positive half-space of the face) to generate a new face.

[0175] • Repeat until all faces are closed.

[0176] • Time complexity: O(n2), suitable for small-scale point sets.

[0177] 2. QuickHull (Quick Convex Hull Algorithm)

[0178] • Principle: Recursively divide the point set and build the convex hull.

[0179] • Steps:

[0180] • Find the two points farthest apart and form an initial line segment.

[0181] • Find the point farthest from this line segment and form an initial triangular face.

[0182] • Assign the remaining points to the visible regions of each face (points in the positive half-space of the face).

[0183] • Recursively process the visible points for each face until all points are included.

[0184] • Time complexity: Average O(n log n), suitable for large-scale point sets.

[0185] 3. Divide and Conquer (Divide and Conquer)

[0186] • Principle: Divide the point set into subsets, calculate the convex hull of each subset, and then merge the results.

[0187] • Steps:

[0188] • Recursively divide the point set into two subsets.

[0189] • Calculate the convex hull of each subset.

[0190] • Merge the two convex hulls by finding "bridge edges" to connect the two sub-convex hulls.

[0191] • Time complexity: O(n log n), suitable for large-scale point sets.

[0192] 4. Incremental Convex Hull (Incremental Algorithm)

[0193] • Principle: Add points one by one and dynamically update the convex hull.

[0194] • Steps:

[0195] • Start with an initial convex hull (such as a tetrahedron).

[0196] • For each new point, determine whether it is outside the current convex hull.

[0197] • If outside, remove all faces that are "seen" by the point and generate new faces connecting the point.

[0198] • Time complexity: O(n2), suitable for dynamic update scenarios.

[0199] Through the above principles and algorithms, the minimum convex envelope of a three-dimensional point set composed of self-excited wave sources can be efficiently calculated, and applied to online monitoring and damage identification of civil engineering structures and other scenarios.

[0200] Example Three

[0201] In order to better understand the method, the following example is given.

[0202] Example 1: Concrete column monitoring

[0203] 1. Preparation: As shown in the figure, multiple sensors are arranged on the four exposed surfaces of the concrete column, the sensor configuration is determined according to the basic requirements of source positioning, and the column structure is discretized into a set of elements; Figure 6

[0204] 2. Self-excited signal acquisition: Using a sensor network, receive self-excited signals from the structure interior induced by external loads;

[0205] 3. Self-excited wave source identification: Use adaptive methods to screen active sensors and the signals they receive to locate self-excited wave sources;

[0206] 4. Damage range determination: According to the geometric shape of the segment and the spatial distribution of the wave source, construct the minimum convex envelope of the wave source as the damage distribution range; as shown in the figure. Figure 7 5. Real-time wave speed field inversion: Use the signals generated by the self-excited wave sources to invert the real-time wave speed field in the segment; identify the low-speed region or region with significant changes in wave speed in the wave speed field, which can also be used as the damage range; as shown in the figure.

[0207] Figure 8

[0208] 6. Damage degree quantification: Convert the wave speed value of the discrete element in the structure to the material elastic parameter, and then estimate the damage degree of the element according to the change of the element elastic parameter in the time domain and combined with the damage mechanics model;

[0209] 7. Damage type inference: According to the signal parameters and characteristics and the change characteristics of the local wave speed field, use machine learning algorithms to establish the mapping relationship between signal parameters / characteristics and damage type / property, and realize the judgment of damage type. In specific implementation, the neural network model trained can be used to realize this.

[0210] Example 2: Monitoring and detection of prestressed concrete beam bridge box girder segment

[0211] ​​​1. Preparation: As shown in Figure 9 , sensors are arranged on the inner and outer surfaces of the box girder segment, the bottom plate and the web, respectively. The sensor configuration is determined according to the basic requirements of source positioning, and the effective signal acquisition is confirmed on site. The box girder segment is discretized into a unit set;

[0212] 2. Initial wave velocity field inversion: Use lead breaking or ultrasonic equipment to generate simulation sources and simulation signals; use this signal to invert the initial wave velocity field of the segment according to the method described in this patent;

[0213] 3. Reference state determination: Based on the initial wave velocity field, detect and evaluate the initial damage and state of the segment, and use it as the reference point and starting point for subsequent monitoring, analysis and evaluation;

[0214] 4. Self-excited signal acquisition: Use the sensor network to receive self-excited signals generated from the inside of the segment by environmental factors and service loads;

[0215] 5. Self-excited wave source positioning: Use adaptive methods to screen active sensors and the signals they receive to locate the self-excited wave source;

[0216] 6. Damage range determination: According to the geometric shape of the spatial distribution of the segment and the wave source, construct the (minimum / maximum) envelope of the wave source as the damage distribution range;

[0217] 7. Real-time wave velocity field inversion: Use the signals generated by the wave source to invert the real-time wave velocity field in the segment; identify the low-speed area or area with significant changes in velocity value in the wave velocity field, which can also be used as the damage range;

[0218] 8. Damage degree quantification: Convert the wave velocity value of the discrete unit in the structure into material elastic parameters, and then estimate the damage degree of the unit according to the changes in the elastic parameters of the unit in the time domain and combined with the damage mechanics model;

[0219] 9. Damage type inference: According to the signal parameters and characteristics and the change characteristics of the local wave velocity field, use machine learning algorithms to establish the mapping relationship between signal parameters / characteristics and damage type / property, and realize the judgment of damage type.

[0220] Example 3: Internal state monitoring of column structure

[0221] The column of a certain brick-concrete frame structure is made of C30 concrete. Self-excited wave tomography is used to monitor the concrete column (sensor arrangement see Figure 10 ), and the tomography result is shown in Figure 10 . From the imaging result, it can be seen that the average wave velocity of the column is about 4400 m / s; there is a low-speed area in the upper left corner of the column, with a wave velocity of about 3600 m / s, which is speculated to be a concrete defect.

[0222] Example 4: Monitoring of concrete frame structure

[0223] A certain multi-story concrete frame, consisting of beams, columns and their joints. To monitor this structure, the method described in the present invention was used to carry out real-time data acquisition and monitoring in-situ. A-A profile, located on a beam connected to a joint in the structure, as shown in Figure 11 . After the sensors were arranged, real-time tomography by self-excited wave was carried out, and the results are shown in Figure 11 . From this figure, it can be seen that the wave velocity is lower in the upper part of the A-A profile, while the inverted wave velocity is higher in the lower part; thus, it can be inferred that the concrete quality in the lower part of the beam segment where the A-A profile is located is higher, while there is obvious deterioration or damage in the upper part.

[0224] At the same time, the method described in the present invention was used to arrange sensors on the column connected to the joint, to detect the quality of the column and its concrete. After the sensors were arranged, real-time tomography by self-excited wave was carried out, and the results are shown in Figure 11 . From this figure, it can be seen that the wave velocity is higher in most of the B-B profile, while the inverted wave velocity is lower in the right lower part; thus, it can be inferred that the concrete quality in the segment where this profile is located is higher, and the mechanical state is better, but there is obvious cracking in the right lower part.

[0225] Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present invention, and are not intended to limit the technical solutions. Those of ordinary skill in the art should understand that modifications or equivalent replacements to the technical solutions of the present invention, without departing from the spirit and scope of the technical solutions, should be covered in the scope of the claims of the present invention.

Claims

1. A method for structural dynamic tomography and damage monitoring using self-excited waves, characterized by, The method comprises the following steps: S1, spatially discretizing the monitoring object to divide it into a plurality of three-dimensional discrete units, establishing a three-dimensional discrete model; arranging a plurality of sensors on the monitoring object and recording the spatial coordinates of each sensor to form a sensor array for collecting self-excited waves of the monitoring object from different directions, wherein the self-excited waves are elastic waves generated spontaneously during the damage or damage propagation process of the structure inside the monitoring object, and the energy carried by the self-excited waves is converted from the strain energy inside the structure; S2, collecting elastic wave propagation data by applying external excitation at a known position, combining wave travel time information, and inverting the initial wave velocity field inside the monitoring object; S3, pre-processing the data obtained by the sensor array under the service condition of the monitoring object, and extracting the self-excited waves generated by the monitoring object received by each sensor; S4, identifying the arrival time of each self-excited wave signal on each sensor; determining whether it is the first damage analysis; if yes, combining the spatial coordinates of the sensors and the initial wave velocity field to calculate the spatial coordinates of the self-excited wave source; if not, combining the spatial coordinates of the sensors and the wave velocity field calculated in the last time to calculate the spatial coordinates of the wave source of each excited wave; S5, based on the spatial coordinates of the wave source of each self-excited wave, synchronously solving and updating the wave velocity field inside the monitoring object to obtain the damage result of the monitoring object, wherein the damage result includes the damage range; S6, based on the damage result of the monitoring object, performing corresponding processing.

2. The method of structural dynamic tomography and damage monitoring using self-excited waves of claim 1, wherein: In S3, the pre-processing includes filtering, denoising and background interference suppression; the self-excited wave signal caused by the internal damage of the structure is screened out by threshold detection, energy mutation identification or pattern classification method.

3. The method of structural dynamic tomography and damage monitoring using self-excited waves of claim 2, wherein: In S4, the calculation method of the arrival time of a self-excited wave received by a sensor is as follows: 1) signal preprocessing; the time when the amplitude of the self-excited wave exceeds the preset threshold for the first time is taken as the threshold point, and a preset number of data points are selected before and after the threshold point as the data of the signal window to be analyzed; 2) autoregressive (AR) model building; Noise segment and signal segment separation: selecting the middle point as noise data and signal data, respectively calculating the order M1, M2 and coefficient of the AR model; determining the AR model coefficient by Yule-Walker equation, minimizing the prediction error variance; 3) AIC calculation and segmentation point determination; selecting each data point in the signal window as the segmentation point in turn, dividing the data sequence in the window into two segments: noise segment and signal segment; for each segmentation point K, calculate the AIC value of the noise segment and the signal segment, and take the K with the minimum AIC(K) value as the arrival time; wherein the calculation formula of AIC(K) value is: AIC(K) = (K-M1)log(σ12) + (N-K-M2)log(σ22) + 2(M1+M2); In the formula, σ12 and σ22 are the prediction error variances of the noise segment and the signal segment; N is the signal length.

4. The method of structural dynamic tomography and damage monitoring using self-excited waves of claim 1, wherein: In S4, the process of calculating the position coordinates of a wave source comprises: Based on the coordinates (x i ,y i ,z i ) of the sensor S i and the time t i of the elastic wave from the wave source reaching the sensor S i , according to the relationship between distance, time and wave speed, a positioning equation group containing n equations is established: In the formula, t0 is the time when the elastic wave is generated by the wave source; i = 1, 2, 3, …, n, n is the number of sensors receiving signals; (x, y, z) is the coordinate of the wave source; V AE is the average wave velocity of the elastic wave propagating in the medium; Based on the positioning equation set, a monomial cubic equation with unknown quantity is derived by means of identity deformation wherein the coefficients a, b, c and d are combined from the original equation set; Solving the cubic equation, we get the value of V AE , and call it old V AE ; substituting old V AE into the positioning equation set, we get the wave source coordinates; according to the relative position of the wave source coordinates and the sensor S i , we search the wave propagation path in the initial wave velocity field or the wave velocity field obtained in the last calculation by using the ray tracing method, and determine all the elements crossed by the self-excited wave propagation path. The wave velocity values of the wave velocity field passing through the unit are weighted and summed to obtain a new V AE ; If the difference between the new and old V AE is greater than a preset threshold, the new V AE is taken as the old V AE of a new round, substituted into the positioning equation set and solved to obtain new source coordinates, and the above process is repeated to update the source coordinate solution and wave velocity solution; if the difference between the new and old V AE is less than or equal to the preset threshold, the current obtained wave source coordinates are taken as the actual wave source coordinates.

5. The method of structural dynamic tomography and damage monitoring using self-excited waves of claim 1, wherein: In S5, the process of obtaining the damage result of the monitoring object comprises: collecting the points where the spatial coordinates of the wave sources of the respective excitation waves are located into a three-dimensional point set, and calculating a minimum convex envelope containing all position coordinate points in the three-dimensional point set as the damage range of the monitoring object.

6. The method of structural dynamic tomography and damage monitoring using self-excited waves of claim 1, wherein: In S5, the process of synchronously solving and updating the wave velocity field inside the monitoring object and obtaining the damage result of the monitoring object comprises: composing a time-of-arrival vector T from the arrival times of the excitation waves received by the respective sensors; calculating the elastic wave propagation path lengths from the wave sources to the respective sensors and the segment lengths of the paths in the discrete units they penetrate, to obtain a distance matrix A; solving the imaging equation AS=T using the time-of-arrival vector T and the distance matrix A to obtain a slowness vector S; the slowness vector S is composed of the slowness values of the elastic wave propagation in the respective discrete units of the monitoring object, and each element of the vector S corresponds to a slowness value of a discrete unit; the slowness value is the reciprocal of the wave velocity v; based on the slowness vector S, determining the damage range of the monitoring object and the damage degree of each discrete unit in the damage range; and updating the wave velocity field inside the monitoring object based on the slowness matrix.

7. The method of structural dynamic tomography and damage monitoring using self-excited waves of claim 6, wherein: For each discrete unit in the damage range, the damage degree is calculated by the following formula: where v p is the wave speed, D is the damage level, E is the elastic modulus of the undamaged material, p is the material density, and m is the material Poisson's ratio.

8. The method of structural dynamic tomography and damage monitoring using self-excited waves as claimed in claim 6, wherein: solving the imaging equation AS=T using an algebraic reconstruction algorithm; the calculation process of the algebraic reconstruction algorithm comprises: Step 1, initialization: assigning an initial slowness value to all discrete units; Step 2, iterative update: using the current slowness value, iterating for the i-th ray to obtain an updated solution S; applying this solution to the i+1-th ray, continuing iteration and obtaining a new corrected solution; repeating the above process until all rays have completed one iteration; Step 3, convergence check: evaluating whether the new solution S obtained by iteration meets the preset convergence criteria; if the new solution does not meet the convergence criteria, returning to Step 2 for iteration again until the convergence condition is met, and obtaining the final slowness vector S.

9. The method for structural dynamic tomography and damage monitoring using self-excited waves as claimed in claim 6, wherein: In S6, a corresponding three-dimensional damage display diagram is also generated based on the damage result of the monitoring object and in combination with its three-dimensional discrete model; in the three-dimensional damage display diagram, different colors are used to represent the severity of the damage.

10. The structural dynamic tomography and damage monitoring method using self-excited waves as described in claim 1, characterized in that: In S6, the corresponding processing comprises: adjusting the positions of the sensors in the sensor array based on the damage range of the monitoring object determined in S5, increasing the number of sensors around the damage range area, to improve the spatial sampling density and the collection sensitivity of the excitation wave signals in the local area of the damage range, and enhance the monitoring capability of the damage evolution behavior.

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