A method and system for locating nonlinear damage of super large equipment based on high-order bispectrum tensor and generalized transmissivity

Abstract

The application provides a large equipment nonlinear damage positioning method and system based on high-order bispectrum tensor and generalized transmissivity. The method discards the high-order operational modal analysis architecture of the traditional linear modal framework, discretely arranges extremely sparse vibration sensors in the key area of the large equipment, and constructs a spatial cross bispectrum tensor. By using the characteristics that the bispectrum is naturally immune to Gaussian noise and highly sensitive to nonlinear phase coupling, the linear temperature drift is accurately stripped. Then, the generalized bispectrum transmissivity tensor is extracted, and the high-order bispectrum modal confidence analysis is introduced. Combined with the adaptive intelligent threshold diagnosis engine and the multi-level virtual physical anchor boundary constraint mapping, not only the zero false alarm intelligent primary diagnosis of the equipment is realized, but also the sub-grid level high-precision spatial targeted positioning is realized under the extremely sparse array where the traditional method fails.

Description

Technical Field

[0001] This invention relates to the field of structural health monitoring, and in particular to a method and system for locating nonlinear damage in large-scale equipment based on high-order bispectral tensors and generalized transmittance. Background Technology

[0002] Major pieces of equipment, such as bridges, wind turbine towers and blades, power transmission towers, offshore platform jackets, and main shafts of large rotating machinery, are highly susceptible to early microcracks in critical load-bearing areas due to the cumulative effects of cyclic loads, material fatigue, and environmental corrosion during long-term service. If these cracks are not detected in time before they reach critical dimensions, they can lead to structural failure within a short period, causing significant casualties and property damage. Therefore, establishing a real-time and reliable online structural health monitoring system for these major pieces of equipment is a core technological requirement for ensuring the safe operation of major engineering facilities.

[0003] Currently, the mainstream technical approach in structural health monitoring is Operational Modal Analysis (OMA) based on vibration response. This method does not require the application of known excitations; it extracts structural modal parameters solely using environmental vibration response signals from the equipment under normal service conditions, offering advantages such as high ease of engineering implementation and minimal disruption to production operations. However, in practical engineering monitoring, existing technologies still face the following fundamental shortcomings:

[0004] A. Large-scale equipment is exposed to the natural environment for extended periods. Diurnal and seasonal temperature variations cause thermal expansion and contraction of structural materials, leading to periodic changes in the structure's equivalent stiffness and ultimately resulting in a significant drift in the structure's natural frequency. Traditional linear power spectrum monitoring systems cannot distinguish between temperature-induced frequency drift and frequency drops caused by structural damage. Once the dominant frequency shifts significantly, the system triggers an alarm, misinterpreting normal thermodynamic responses as major structural damage, resulting in numerous invalid false alarms and severely interfering with normal operation and maintenance decisions.

[0005] B. The impact of breathing cracks on the overall structural stiffness during the initiation stage is extremely weak, and the resulting change in natural frequency is often drowned out by environmental noise and measurement errors. Traditional linear power spectra are unable to identify such weak nonlinear signals. The spectral curves of the healthy state and the state containing microcracks almost completely overlap, causing the system to misjudge the dangerous state with hidden damage as the healthy state, resulting in serious underreporting and creating a major safety hazard.

[0006] C. The physical scale of ultra-large equipment dictates that, within acceptable engineering costs and construction conditions, sensors can only be deployed at extremely low density and sparsely, with the spacing between adjacent measuring points often far exceeding the Nyquist space sampling limit. Under these conditions, traditional damage spatial localization algorithms based on modal curvature suffer from severe spatial aliasing when calculating the second-order spatial derivative of structural vibration modes, resulting in completely distorted numerical calculations. The reconstructed damage curve exhibits violent, physically meaningless oscillations and forms numerous spurious peaks in regions far from the actual damage location, leading to localization errors of up to tens of meters. This renders the algorithm completely ineffective in practical engineering.

[0007] D. Some existing positioning algorithms still force extreme value searches on the damage index curve even when the device is in a completely healthy state, causing the system to output false damage coordinates when there is no real damage. This significantly reduces the reliability of the monitoring results and severely restricts the engineering promotion and application of related technologies.

[0008] Therefore, it is of great significance to develop a nonlinear damage localization method and system for ultra-large equipment based on high-order bispectral tensors and generalized transmittance. Summary of the Invention

[0009] The purpose of this invention is to provide a nonlinear damage localization method and system for ultra-large equipment based on high-order bispectral tensors and generalized transmittance, so as to solve the problems existing in the prior art.

[0010] The technical solution adopted to achieve the purpose of this invention is as follows: a nonlinear damage localization method for ultra-large equipment based on high-order bispectral tensor and generalized transmittance, wherein N measuring points are arranged on the surface of the ultra-large equipment to form a sparse accelerometer array, where N≥3. The localization method includes the following steps:

[0011] S1) Under normal service conditions, the time-domain vibration acceleration signals of each measuring point are synchronously collected, and after being segmented by a time sliding window, a fast Fourier transform is performed to obtain the frequency domain complex response signals of each measuring point.

[0012] S2) Based on the frequency domain signal obtained in step S1), calculate the spatial cross bispectral tensor between any two measurement points, and construct the cross bispectral tensor matrix characterizing the nonlinear phase coupling characteristics of the breathing crack.

[0013] S3) Based on the cross-bispectral tensor matrix obtained in step S2), a generalized bispectral transmittance tensor is constructed using the bispectral data of each measurement point as the normalization benchmark, thereby eliminating the influence of external unknown broadband excitation on the monitoring results.

[0014] S4) Based on the generalized bispectral transmittance tensor obtained in step S3), calculate the higher-order bispectral modal confidence index, perform intelligent threshold initial diagnosis, and determine the current status of the equipment. If it is determined to be in a healthy state, directly output the health diagnosis conclusion and terminate the process. If it is determined to be in a damaged state, calculate the spatial nonlinear damage index and proceed to step S5).

[0015] S5) Apply multi-level virtual zero-energy anchor point constraints to the spatial nonlinear damage index curve obtained in step S4), and perform spatial reconstruction by combining cubic spline interpolation to output the spatial coordinates of the damage location on the super-large equipment.

[0016] Furthermore, in step S1), the frequency domain mapping expression of the fast Fourier transform is:

[0017]

[0018] In the formula, Let f be the complex frequency domain response signal of measurement point i at frequency f. Let be the time-domain vibration acceleration signal collected at measurement point i at time t, where j is the imaginary unit, f is the frequency variable, and t is the time variable.

[0019] Furthermore, in step S2), the spatial cross-spectral tensor The calculation expression is:

[0020]

[0021] in, The expected value is calculated by averaging multiple time-sliding window slices. These are two independent reference frequency variables. , For measurement point i at frequency and The complex spectrum at that location. For measurement point j at frequency The complex conjugate spectrum at the given location. For any linear process following a Gaussian distribution, the cross-bispectral tensor is always equal to zero, thus filtering temperature drift and linear noise interference at a mathematical level.

[0022] Furthermore, in step S3), the generalized bispectral transmittance tensor The calculation expression is:

[0023]

[0024] In the formula, Let i be the self-bispectrum of measurement point i. Through complex ratio operations of the numerator and denominator, the self-power spectral term of the external unknown broadband excitation is mathematically canceled out, making... It becomes a system-inherent parameter that only contains the characteristics of the nonlinear transmission path within the ultra-large equipment.

[0025] Further, in step S4), the calculation expression for the higher-order bispectral mode confidence index is:

[0026]

[0027] In the formula, The current bispectral transmittance tensor is calculated from real-time monitoring data. This is the baseline bispectral transmittance tensor obtained when the device is in a healthy and undamaged state. The intelligent threshold initial diagnosis is achieved by extracting the maximum coupling extremum of the current generalized bispectral matrix and comparing it with the healthy baseline noise level. When the extremum does not reach the safe multiple threshold of the healthy noise level, the system automatically blocks the extremum search and directly outputs the health diagnosis conclusion.

[0028] Furthermore, in step S4), the spatial nonlinear damage index The calculation expression is:

[0029]

[0030] In the formula, This represents the comprehensive nonlinear damage probability index for the spatial coordinates of a large-scale device corresponding to the region near measuring point j. N is the total number of sensor nodes. (Conditions) Ensure the computational space cross-transmission relationship. The double integral modulates the frequency variable within the effective two-dimensional dual-frequency plane. and implement.

[0031] Furthermore, in step S5), the multi-level virtual zero-energy anchor point constraint mechanism is implemented by automatically injecting multi-level gradient decay virtual zero-energy points into the mathematical space outside the physical sensor array. Combined with cubic spline interpolation, while allowing the curve to naturally overshoot and find peaks inside the sensor, the divergence and drift trend of the boundary blind zone is constrained, thereby breaking through the Nyquist space sampling limit and realizing high-precision damage spatial positioning under extremely sparse array conditions.

[0032] This invention also discloses a nonlinear damage localization system for ultra-large equipment based on high-order bispectral tensors and generalized transmittance for implementing the method described in any one of claims 1 to 7, comprising:

[0033] The signal acquisition module is used to synchronously acquire the time-domain vibration acceleration signals of each measuring point through a sparse accelerometer array deployed on the surface of the extra-large equipment, and perform a fast Fourier transform to obtain the frequency domain complex response signal.

[0034] The bispectral tensor construction module is used to calculate the spatial cross bispectral tensor between each measurement point based on the frequency domain complex response signal, and to construct the cross bispectral tensor matrix.

[0035] The generalized transmittance extraction module is used to construct a generalized bispectral transmittance tensor based on the cross bispectral tensor matrix and using the bispectral data of each measurement point as a normalization reference.

[0036] The intelligent diagnostic module is used to calculate the higher-order bispectral modal confidence index based on the generalized bispectral transmittance tensor, perform intelligent threshold initial diagnosis, determine the health status or damage status of the equipment, and calculate the spatial nonlinear damage index when the equipment is determined to be in a damaged state.

[0037] The spatial positioning module is used to apply multi-level virtual zero-energy anchor point constraints to the spatial nonlinear damage index curve and perform cubic spline interpolation spatial reconstruction to output the spatial coordinates of the damage location.

[0038] Furthermore, the signal acquisition module includes a sparse broadband accelerometer array deployed on the surface of the extra-large equipment and an edge data acquisition card. The bispectral tensor construction module, generalized transmittance extraction module, intelligent diagnostic module, and spatial positioning module are deployed in a cloud server or edge server containing a high-order tensor parallel computing unit.

[0039] The present invention also discloses an application of the above method in structural health monitoring and early damage location of bridges, wind turbine towers and blades, power transmission towers, offshore platform jackets or main shafts of large rotating machinery.

[0040] The technical effects of this invention are beyond doubt:

[0041] A. Linear environmental interferences such as temperature changes and wind loads are completely filtered out from the signal, making the monitoring system completely insensitive to temperature drift. Regardless of diurnal temperature differences or seasonal temperature variations, the system maintains extremely low background noise and does not generate false alarms;

[0042] B. By constructing a spatially cross bispectral tensor, the nonlinear frequency coupling energy induced by breathing cracks is specifically captured, and the weak early damage signal is highly focused and amplified in the dual frequency domain, so that a significant and distinguishable feature difference is formed between the healthy state and the state containing microcracks, which greatly improves the sensitivity and reliability of damage detection.

[0043] C. The multi-level virtual zero-energy anchor point constraint mechanism effectively suppresses the divergence and drift of the interpolation curve in the boundary blind zone under the condition of extremely sparse sensor array. Combined with the high-order bispectral mode confidence integral index, the relative error of crack spatial positioning can still be controlled at a low level under the condition of extremely low sensor density, which significantly reduces the engineering implementation cost of health monitoring of large equipment structures.

[0044] D. An intelligent threshold initial diagnosis mechanism is introduced. Before entering the spatial positioning process, the maximum coupling extremum of the current bispectral matrix is ​​compared with the noise floor of the healthy baseline. When the device is in a purely healthy state, the system mathematically blocks the extremum search and peak finding process and directly outputs a health diagnosis conclusion. Attached Figure Description

[0045] Figure 1 The overall architecture and signal flow diagram of a nonlinear damage monitoring system for ultra-large equipment based on high-order bispectral tensor and generalized transmittance;

[0046] Figure 2 A comparison diagram of the sensitivity discrimination logic of traditional linear cross power spectrum (CPS) and higher-order bispectrum for temperature drift and breathing cracks;

[0047] Figure 3 This is a comparison of the resistance to temperature drift between the conventional linear power spectrum and the high-order bispectral spectrum of this invention under conditions containing hidden microcracks.

[0048] Figure 4 This is a comparison of the detection and identification capabilities of the traditional linear power spectrum and the high-order bispectral spectrum of this invention for breathing cracks under conditions containing hidden microcracks.

[0049] Figure 5 A comparison of the spatial positioning accuracy of the traditional modal curvature localization algorithm and the HO-OMA integrated nonlinear damage index of the present invention under an extremely sparse sensor array.

[0050] Figure 6 This is a graph verifying the anti-interference capability of the traditional linear power spectrum and the high-order bispectrum of this invention against temperature drift under pure healthy conditions.

[0051] Figure 7 This diagram shows the performance verification of the high-order dual-spectrum intelligent diagnosis with zero false alarms under pure healthy conditions.

[0052] Figure 8 This is a zero-false-report verification diagram of the spatial nonlinear damage probability curve of a large-scale device based on generalized bispectral transmittance under pure healthy conditions. Detailed Implementation

[0053] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0054] Example 1:

[0055] See Figure 1This embodiment provides a nonlinear damage localization method for ultra-large equipment based on high-order bispectral tensors and generalized transmittance. N measuring points are deployed on the surface of the ultra-large equipment to form a sparse accelerometer array, where N ≥ 3. The localization method includes the following steps:

[0056] S1) Under normal service conditions, the time-domain vibration acceleration signals of each measuring point are synchronously collected, and after being segmented by a time sliding window, a fast Fourier transform is performed to obtain the frequency domain complex response signals of each measuring point.

[0057] S2) Based on the frequency domain signal obtained in step S1), calculate the spatial cross bispectral tensor between any two measurement points, and construct the cross bispectral tensor matrix characterizing the nonlinear phase coupling characteristics of the breathing crack.

[0058] S3) Based on the cross-bispectral tensor matrix obtained in step S2), a generalized bispectral transmittance tensor is constructed using the bispectral data of each measurement point as the normalization benchmark, thereby eliminating the influence of external unknown broadband excitation on the monitoring results.

[0059] S4) Based on the generalized bispectral transmittance tensor obtained in step S3), calculate the higher-order bispectral modal confidence index, perform intelligent threshold initial diagnosis, and determine the current status of the equipment. If it is determined to be in a healthy state, directly output the health diagnosis conclusion and terminate the process. If it is determined to be in a damaged state, calculate the spatial nonlinear damage index and proceed to step S5).

[0060] S5) Apply multi-level virtual zero-energy anchor point constraints to the spatial nonlinear damage index curve obtained in step S4), and perform spatial reconstruction by combining cubic spline interpolation to output the spatial coordinates of the damage location on the super-large equipment.

[0061] Figures 3-5 A comparison of the traditional cross-power spectrum and the simulation positioning results of this invention under the condition of microcrack initiation (damage state) in large equipment; Figure 3 In the traditional linear power spectrum results, the dominant frequency shifts significantly when the temperature decreases (orange dashed line). In traditional online monitoring systems, such a large shift in the dominant frequency would immediately trigger an alarm, assuming a decrease in equipment stiffness and a major fracture—a classic false alarm. However, the dual spectrum of this invention on the right maintains extremely low noise even with temperature drift and does not trigger an alarm. Figure 4 In the traditional linear power spectrum results on the left, when a device develops a hidden microcrack, the crack signal is completely submerged, and the red line (crack) and the blue line (healthy) almost completely overlap. The system may misidentify the system as being in normal condition, resulting in missed detections. In contrast, the invention on the right accurately identifies 100% of the giant peaks and successfully captures them. Figure 5As shown in the figure, the traditional modal curvature method, represented by the gray dashed line, suffers from severe spatial aliasing in mathematical calculations due to the limitation of the large-spacing sampling limit of the Nyquist space. The reconstructed damage curve not only produces violent and physically meaningless numerical oscillations but also forms a huge false peak misjudgment source in the region far from the actual microcrack on the left, causing its calculated coordinates to deviate from the actual damage by tens of meters, resulting in extremely high relative errors and rendering it completely ineffective in practical engineering. In stark contrast, the HO-OMA comprehensive nonlinear damage index of this invention, represented by the purple solid line, effectively suppresses boundary divergence through a multi-level virtual anchor point mechanism, exhibiting an extremely smooth and concentrated targeted envelope along the entire physical path of the large-scale equipment. The crack coordinates ultimately locked by the algorithm, with a poor data source of only 6 channels, have an absolute error of 1.894m and a relative error controlled at an extremely low level of 3.16%.

[0062] Figures 6-7 This is a simulation result verification diagram of the intelligent diagnosis and false alarm prevention of this system under the condition of fault-free (pure healthy state) of a large-scale equipment. Figure 6 The system's response characteristics were demonstrated when the device was in a completely healthy and undamaged state. This is thanks to the physical filtering characteristics of bispectral analysis and the intelligent threshold diagnostic mechanism of this invention. Figure 7 No nonlinear mutation artifacts were found, and the system accurately diagnosed the patient as healthy. Figure 8 The spatial damage probability curve in the figure is flush with the zero-value baseline (green line), indicating that the system mathematically terminates the false alarm at extreme values. This figure strongly demonstrates the system's excellent industrial performance with strong resistance to background noise interference and zero false alarms.

[0063] This invention proposes a High-Order Operating Modal Analysis (HO-OMA) architecture that abandons the traditional linear modal framework. The system discretely deploys extremely sparse vibration sensors in critical areas of large-scale equipment to construct a spatially cross-spectral tensor. Utilizing the inherent immunity of bispectral data to Gaussian noise and its high sensitivity to nonlinear phase coupling, linear temperature drift is accurately stripped away. Subsequently, a generalized bispectral transmittance tensor is extracted, and a high-order bispectral modal confidence level (HO-OMA) is introduced. Analysis. By combining an adaptive intelligent threshold diagnostic engine with multi-level virtual physical anchor point boundary constraint mapping, not only is zero-false alarm intelligent initial diagnosis of the device achieved, but also sub-grid-level high-precision spatial targeting positioning is achieved in extremely sparse arrays where traditional methods fail.

[0064] Example 2:

[0065] The main content of this embodiment is the same as that of Embodiment 1, except that, in step S1), the frequency domain mapping expression of the fast Fourier transform is:

[0066]

[0067] In the formula, Let f be the complex frequency domain response signal of measurement point i at frequency f. Let be the time-domain vibration acceleration signal collected at measurement point i at time t, where j is the imaginary unit, f is the frequency variable, and t is the time variable.

[0068] Example 3:

[0069] The main content of this embodiment is the same as that of embodiment 1 or 2, wherein, in step S2), the spatial cross-bispectral tensor The calculation expression is:

[0070]

[0071] in, The expected value is calculated by averaging multiple time-sliding window slices. These are two independent reference frequency variables. , For measurement point i at frequency and The complex spectrum at that location. For measurement point j at frequency The complex conjugate spectrum at the given location. For any linear process following a Gaussian distribution, the cross-bispectral tensor is always equal to zero, thus filtering temperature drift and linear noise interference at a mathematical level.

[0072] Example 4:

[0073] The main content of this embodiment is the same as any one of embodiments 1 to 3, wherein, in step S3), the generalized bispectral transmittance tensor... The calculation expression is:

[0074]

[0075] In the formula, Let i be the self-bispectrum of measurement point i. Through complex ratio operations of the numerator and denominator, the self-power spectral term of the external unknown broadband excitation is mathematically canceled out, making... It becomes a system-inherent parameter that only contains the characteristics of the nonlinear transmission path within the ultra-large equipment.

[0076] Further, in step S4), the calculation expression for the higher-order bispectral mode confidence index is:

[0077]

[0078] In the formula, The current bispectral transmittance tensor is calculated from real-time monitoring data. This is the baseline bispectral transmittance tensor obtained when the device is in a healthy and undamaged state. The intelligent threshold initial diagnosis is achieved by extracting the maximum coupling extremum of the current generalized bispectral matrix and comparing it with the healthy baseline noise level. When the extremum does not reach the safe multiple threshold of the healthy noise level, the system automatically blocks the extremum search and directly outputs the health diagnosis conclusion.

[0079] Furthermore, in step S4), the spatial nonlinear damage index The calculation expression is:

[0080]

[0081] In the formula, This represents the comprehensive nonlinear damage probability index for the spatial coordinates of a large-scale device corresponding to the region near measuring point j. N is the total number of sensor nodes. (Conditions) Ensure the computational space cross-transmission relationship. The double integral modulates the frequency variable within the effective two-dimensional dual-frequency plane. and implement.

[0082] Example 5:

[0083] The main content of this embodiment is the same as any one of embodiments 1 to 4. In step S5), the multi-level virtual zero-energy anchor point constraint mechanism is implemented by automatically injecting multi-level gradient decay virtual zero-energy points into the mathematical space outside the physical sensor array. Combined with cubic spline interpolation, while allowing the curve to naturally overshoot and find peaks inside the sensor, the divergence and drift trend of the boundary blind zone is constrained, thereby breaking through the Nyquist space sampling limit and realizing high-precision damage spatial positioning under extremely sparse array conditions.

[0084] Example 6:

[0085] The main content of this embodiment is the same as that of Embodiment 1, except that the specific implementation steps are as follows:

[0086] Step S1: Multi-channel non-stationary vibration response acquisition and Fourier mapping

[0087] Layout on the surface of extra-large equipment Each measuring point (e.g.) (Sparse array). Under normal operating conditions (purely unknown environmental excitation), the time-series response signals of each measuring point are synchronously acquired. The signal is segmented using a time sliding window, and a Fast Fourier Transform (FFT) is performed to obtain the frequency domain mapping. :

[0088]

[0089] The characters in the above formula have the following meanings:

[0090] Measurement point In frequency The complex response signal in the frequency domain at that point;

[0091] Measurement point In time The acquired time-domain vibration acceleration signal;

[0092] Time variable;

[0093] Frequency variable;

[0094] Imaginary unit (satisfying) );

[0095] Pi (π) is a constant representing the ratio of π to π.

[0096] Step S2: Construct a spatially cross-bispectral tensor matrix characterizing the coherent coupling of the breathing crack.

[0097] Because breathing cracks can cause nonlinear modulation of the local stiffness of a structure, the originally independent frequency components... and This generates second-order nonlinear coupling, producing new sum / difference frequency components (such as...). This invention introduces a frequency domain representation of the third-order cumulant—bispectrum—to capture this nonlinear eigenvalue.

[0098] Calculate measuring points With measuring points Cross-bispectral tensors :

[0099]

[0100] The characters in the above formula have the following meanings:

[0101] Measurement point and measuring points Cross-bispectral values ​​between;

[0102] Statistical mathematical expectation (achieved by averaging multiple time-sliding window slices);

[0103] Two independent reference frequency variables (together forming a two-dimensional dual-frequency analysis plane);

[0104] , Measurement point In frequency and The complex spectrum at the location;

[0105] Measurement point In frequency The complex conjugate spectrum at the location.

[0106] Physical prior constraints (decoupling of noise resistance and temperature drift resistance): According to higher-order statistical theory, for any linear process that follows a Gaussian distribution (such as thermal expansion and contraction caused by a uniform temperature field, or Gaussian white noise wind load), its bispectral density is always equal to zero (i.e., Therefore, this formula thoroughly filters out temperature drift and linear mechanical noise from a mathematical level. The sensitivity discrimination logic of traditional linear cross-power spectrum and the high-order dual spectrum of this invention for temperature and breathing cracks is as follows: Figure 2 As shown. After removing linear interference, only the nonlinear phase coupling energy generated by the evolution of internal cracks in the structure is retained in the matrix. This step achieves simulation effects that resist temperature drift and linear noise interference and demonstrate a truly minimal computational noise floor. Figure 3 As shown.

[0107] Step S3: Extract the generalized bispectral transmittance tensor to eliminate excitation source interference.

[0108] In actual operating conditions, the spectrum of the external environmental excitation force is unknown and time-varying. To eliminate the reliance on prior knowledge of the excitation force, this invention constructs a spatially dimensional generalized bispectral transmittance tensor. :

[0109]

[0110] The characters in the above formula have the following meanings:

[0111] From the measuring point to the measuring point The higher-order nonlinear transmittance function;

[0112] Measurement point and measuring points The cross-bispectral tensor between them;

[0113] Measurement point The auto-bispectrum, whose expansion form is the fraction in the denominator. .

[0114] By performing complex ratio calculations at spatial measurement points in the frequency domain, the self-power spectral term of the external unknown broadband excitation is mathematically canceled out in the numerator and denominator, thus... It becomes a system-inherent parameter that only contains the characteristics of the nonlinear transmission path within the ultra-large equipment.

[0115] Step S4: Nonlinear damage index calculation and target topology mapping localization

[0116] In traditional OMA, MAC is used to evaluate the correlation of linear spatial mode shapes. This invention innovatively proposes a higher-order bispectral mode confidence level (MAC). This is used to evaluate the geometrical consistency of the nonlinear topological vectors between the reference state and the current monitoring state in a two-dimensional dual-frequency domain plane.

[0117]

[0118] [Intelligent Diagnostic and Judgment Mechanism]: The system performs an intelligent threshold initial diagnosis before entering spatial positioning. It extracts the maximum coupling extremum of the current generalized bispectral matrix and compares it with the noise floor of the healthy baseline.

[0119] State A (Equipment in Pure Health): If the extreme value is extremely low (not reaching the safety multiple threshold for health noise, such as 3 times), the system mathematically blocks the extreme value search for peaks in the positioning map and directly outputs that the large equipment is currently in a safe and healthy state (see...). Figure 8 (The curve is flat against the bottom). This mechanism completely eliminates the ghost false alarm vulnerability in traditional systems that forcibly fit maximum values ​​in a disease-free state.

[0120] State B (Initiation of latent microcracks): If the high-frequency coupling effect is amplified sharply, an extreme value jump occurs (see...). Figure 4 ), If the deviation from 1 is significant (topological distortion), proceed to step S5 to extract the spatial nonlinear damage index. And perform targeted mapping:

[0121] To capture subtle early phase coupling distortion, an integral spatial nonlinear damage exponent is defined. :

[0122]

[0123] The characters in the above formula have the following meanings:

[0124] Spatial coordinates on extra-large equipment correspond to measuring points The comprehensive nonlinear damage probability index of the surrounding area;

[0125] The total number of sensor nodes deployed on large-scale equipment;

[0126] Sensor node spatial index number, condition Ensure the cross-transmission relationship in the computational space;

[0127] : Frequency variables within an effective two-dimensional dual-frequency plane (specific bandwidth) and The double integral operator is performed;

[0128] Corresponding frequency and Differential and integral elements;

[0129] | |: Absolute value operator;

[0130] Bispectral modal confidence criterion (used to calculate the cosine of the geometric angle between two complex tensors in the bispectral domain, removing amplitude fluctuations and retaining only nonlinear phase abrupt changes).

[0131] The current bispectral transmittance tensor is dynamically calculated from real-time monitoring data of the system.

[0132] : The reference bispectral transmittance tensor obtained when the device is in a healthy and undamaged state.

[0133] Step S5: Multi-level virtual anchor point mapping and high-precision positioning with extremely sparse array

[0134] Overcoming Spatial Extrapolation Divergence: To address the problem that extremely sparse sensor arrays cannot fully cover the entire length of the device, causing traditional interpolation curves to diverge severely in the boundary blind zone (i.e., Runge phenomenon), this invention proposes a multi-level virtual zero-energy anchor point constraint mechanism.

[0135] Even if the sensor's first and last nodes are far from the device boundary, the system will automatically inject virtual zero-energy points with multi-level gradient decay into the mathematical space outside the physical array. Combined with Cubic cubic spline interpolation, this mechanism allows the curve to naturally overshoot and find peaks inside the sensor (precisely locking the damage area), while firmly pinpointing the divergence and drift trend of the boundary blind zone.

[0136] Breakthrough compared to traditional positioning algorithms: For example, when only 6 sensors are deployed on a 60-meter-long device (with a physical spacing of up to 10 meters), traditional positioning algorithms based on OMA modal curvature will completely collapse due to severe spatial aliasing, causing complete distortion in the calculation of the second spatial derivative and making it impossible to generate a map; while this invention relies on... The integral and virtual anchor point constraint mapping successfully broke through the Nyquist space sampling limit, and the measured relative positioning error was controlled within 10% (see...). Figure 5 This enables low-cost, high-precision positioning on extremely large equipment.

[0137] Example 7:

[0138] This embodiment discloses a nonlinear damage localization system for ultra-large equipment based on high-order bispectral tensors and generalized transmittance, used to implement the method described in any one of embodiments 1 to 6, comprising:

[0139] The signal acquisition module is used to synchronously acquire time-domain vibration acceleration signals at various measurement points using a sparse accelerometer array deployed on the surface of the large equipment, and to perform a fast Fourier transform to obtain the frequency-domain complex response signal. The signal acquisition module includes a sparse broadband accelerometer array deployed on the surface of the large equipment and an edge data acquisition card. The bispectral tensor construction module, generalized transmittance extraction module, intelligent diagnostic module, and spatial positioning module are deployed on a cloud server or edge server containing a high-order tensor parallel computing unit.

[0140] The bispectral tensor construction module is used to calculate the spatial cross bispectral tensor between each measurement point based on the frequency domain complex response signal, and to construct the cross bispectral tensor matrix.

[0141] The generalized transmittance extraction module is used to construct a generalized bispectral transmittance tensor based on the cross bispectral tensor matrix and using the bispectral data of each measurement point as a normalization reference.

[0142] The intelligent diagnostic module is used to calculate the higher-order bispectral modal confidence index based on the generalized bispectral transmittance tensor, perform intelligent threshold initial diagnosis, determine the health status or damage status of the equipment, and calculate the spatial nonlinear damage index when the equipment is determined to be in a damaged state.

[0143] The spatial positioning module is used to apply multi-level virtual zero-energy anchor point constraints to the spatial nonlinear damage index curve and perform cubic spline interpolation spatial reconstruction to output the spatial coordinates of the damage location.

[0144] This embodiment innovatively establishes a high-order bispectral modal confidence index system, completely eliminating false alarms even when there is no problem: breaking through the bottleneck of traditional OMA, which can only analyze linear mode shapes (MACs). Utilizing an intelligent threshold diagnostic mechanism, the diagnostic curve will present an absolute zero-energy dead state when the equipment is in a purely healthy state, fundamentally avoiding false positives caused by traditional methods forcibly fitting extreme values ​​under pure environmental noise. Completely immune to temperature and environmental interference, capturing early latent degradation: breaking through the constraint of relying on frequency decrease to determine damage. Utilizing the mathematical law that the third-order cumulant of a Gaussian process is always zero, it automatically filters out large-range frequency drifts caused by gradual temperature changes and linear wind loads. Bispectral coherence acts like a mathematical microscope, specifically amplifying the secondary phase coupling characteristics in the frequency band, significantly improving the sensitivity to early latent microcracks. Overcoming spatial aliasing and boundary divergence, achieving precise sub-grid positioning under extremely sparse arrays: addressing the defect of traditional modal curvature methods collapsing under sparse arrays (large spacing), this system does not require sensors to be placed at the physical edge of the equipment. By introducing a multi-level virtual physical anchor point constraint mapping mechanism, the spatial extrapolation divergence phenomenon was successfully suppressed. The measured relative error is far below the international industry standard of 10%, which greatly reduces the hardware deployment and life-cycle maintenance costs of a single large-scale device.

[0145] Example 8:

[0146] This embodiment discloses a method for implementing any one of embodiments 1 to 6. The present invention also discloses an application of the above method in structural health monitoring and early damage location of bridges, wind turbine towers and blades, transmission towers, offshore platform jackets or main shafts of large rotating machinery.

Claims

1. A nonlinear damage localization method for ultra-large equipment based on high-order bispectral tensors and generalized transmittance, characterized in that, A sparse acceleration sensor array is formed by deploying N measuring points on the surface of the large equipment; where N≥3; the positioning method includes the following steps: S1) Under normal service conditions, the time-domain vibration acceleration signals of each measuring point are collected synchronously, and after being segmented by a time sliding window, a fast Fourier transform is performed to obtain the frequency domain complex response signals of each measuring point. S2) Based on the frequency domain signal obtained in step S1), calculate the spatial cross bispectral tensor between any two measurement points, and construct the cross bispectral tensor matrix characterizing the nonlinear phase coupling characteristics of the breathing crack. S3) Based on the cross-bispectral tensor matrix obtained in step S2), a generalized bispectral transmittance tensor is constructed using the bispectral data of each measurement point as the normalization benchmark to eliminate the influence of external unknown broadband excitation on the monitoring results. S4) Based on the generalized bispectral transmittance tensor obtained in step S3), calculate the higher-order bispectral modal confidence index, perform intelligent threshold initial diagnosis, and determine the current status of the device; if it is determined to be in a healthy state, directly output the health diagnosis conclusion and terminate the process; if it is determined to be in a damaged state, calculate the spatial nonlinear damage index and proceed to step S5). S5) Apply multi-level virtual zero-energy anchor point constraints to the spatial nonlinear damage index curve obtained in step S4), and perform spatial reconstruction by combining cubic spline interpolation to output the spatial coordinates of the damage location on the super-large equipment.

2. The nonlinear damage localization method for ultra-large equipment based on high-order bispectral tensor and generalized transmittance according to claim 1, characterized in that, In step S1), the frequency domain mapping expression of the fast Fourier transform is: In the formula, Let f be the complex frequency domain response signal of measurement point i at frequency f. Let be the time-domain vibration acceleration signal collected at measurement point i at time t, where j is the imaginary unit, f is the frequency variable, and t is the time variable.

3. The nonlinear damage localization method for ultra-large equipment based on high-order bispectral tensor and generalized transmittance according to claim 1, characterized in that, In step S2), the spatial cross-spectral tensor The calculation expression is: in, The expected value is calculated by averaging multiple time-sliding window slices. These are two independent reference frequency variables; , For measurement point i at frequency and The complex spectrum at that location; For measurement point j at frequency The complex conjugate spectrum at the point; for any linear process that follows a Gaussian distribution, the cross bispectral tensor is always equal to zero, thus filtering temperature drift and linear noise interference at the mathematical level.

4. The nonlinear damage localization method for ultra-large equipment based on high-order bispectral tensor and generalized transmittance according to claim 1, characterized in that, In step S3), the generalized bispectral transmittance tensor The calculation expression is: In the formula, The self-bispectrum of measurement point i; through complex ratio operations of the numerator and denominator, the self-power spectral term of the external unknown broadband excitation is mathematically canceled out, making... It becomes a system-inherent parameter that only contains the characteristics of the nonlinear transmission path within the ultra-large equipment.

5. The nonlinear damage localization method for ultra-large equipment based on high-order bispectral tensor and generalized transmittance according to claim 1, characterized in that, In step S4), the calculation expression for the higher-order bispectral mode confidence index is: In the formula, The current bispectral transmittance tensor is calculated from real-time monitoring data. The reference bispectral transmittance tensor is obtained when the equipment is in a healthy and undamaged state; The intelligent threshold initial diagnosis is achieved by extracting the maximum coupling extremum of the current generalized bispectral matrix and comparing it with the healthy baseline noise. When the extremum does not reach the safe multiple threshold of the healthy noise, the system automatically blocks the extremum search and directly outputs the health diagnosis conclusion.

6. The nonlinear damage localization method for ultra-large equipment based on high-order bispectral tensor and generalized transmittance according to claim 1, characterized in that, In step S4), the spatial nonlinear damage index The calculation expression is: In the formula, The spatial coordinates of the equipment correspond to the comprehensive nonlinear damage probability index of the region near the measuring point j; N is the total number of sensor nodes; conditions Ensure the computational space cross-transmission relationship; the double integral applies frequency variables within the effective two-dimensional dual-frequency plane. and implement.

7. The nonlinear damage localization method for ultra-large equipment based on high-order bispectral tensor and generalized transmittance according to claim 1, characterized in that: In step S5), the multi-level virtual zero-energy anchor point constraint mechanism is implemented by automatically injecting virtual zero-energy points with multi-level gradient decay into the mathematical space outside the physical sensor array. Combined with cubic spline interpolation, while allowing the curve to naturally overshoot and find peaks inside the sensor, the divergence and drift trend of the boundary blind zone is constrained, thereby breaking through the Nyquist space sampling limit and realizing high-precision damage spatial positioning under extremely sparse array conditions.

8. A nonlinear damage localization system for ultra-large equipment based on high-order bispectral tensor and generalized transmittance for implementing the method described in any one of claims 1 to 7, characterized in that, include: The signal acquisition module is used to synchronously acquire the time-domain vibration acceleration signals of each measuring point through a sparse accelerometer array deployed on the surface of the extra-large equipment, and perform a fast Fourier transform to obtain the frequency domain complex response signal. The bispectral tensor construction module is used to calculate the spatial cross bispectral tensor between each measurement point based on the frequency domain complex response signal, and to construct the cross bispectral tensor matrix. The generalized transmittance extraction module is used to construct a generalized bispectral transmittance tensor based on the cross bispectral tensor matrix and with each measurement point’s bispectral spectrum as a normalization benchmark. The intelligent diagnostic module is used to calculate the higher-order bispectral modal confidence index based on the generalized bispectral transmittance tensor, perform intelligent threshold initial diagnosis, determine the health status or damage status of the equipment, and calculate the spatial nonlinear damage index when the equipment is determined to be in a damaged state. The spatial positioning module is used to apply multi-level virtual zero-energy anchor point constraints to the spatial nonlinear damage index curve and perform cubic spline interpolation spatial reconstruction to output the spatial coordinates of the damage location.

9. The system according to claim 8, characterized in that: The signal acquisition module includes a sparse broadband accelerometer array and an edge data acquisition card deployed on the surface of the extra-large equipment; the dual-spectrum tensor construction module, generalized transmittance extraction module, intelligent diagnostic module and spatial positioning module are deployed in a cloud server or edge server containing a high-order tensor parallel computing unit.

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