Flange bolt loosening positioning monitoring method based on ultrasonic guided wave probability imaging

Abstract

The invention provides a flange bolt loosening positioning monitoring method based on ultrasonic guided wave probability imaging, belongs to the technical field of structural health monitoring and nondestructive testing, and can perform loosening positioning and monitoring on a flange bolt by fully utilizing the advantage of large-range detection of ultrasonic guided waves. The system has the characteristics of strong visual positioning capability, high monitoring efficiency and less sensor consumption. According to the method, different ultrasonic guided wave signals of the bolts in a healthy state and a damaged state are utilized to calculate damage indexes, guided wave signal changes are converted into a visual damage probability cloud picture through a probability imaging technology, the looseness index of each bolt is obtained, visual accurate positioning of the loosened bolts is achieved, and the reliability of the bolts is improved. Therefore, the looseness indexes of all bolts in the monitoring range are judged and compared. According to the invention, the synchronous monitoring of all bolt states of the whole flange ring can be realized only by using a small number of sensors by utilizing the space coverage capability of'one-point excitation and multi-point receiving 'of guided waves and probability imaging.

Description

Technical Field

[0001] This invention belongs to the field of structural health monitoring and non-destructive testing technology, specifically relating to a flange bolt loosening location monitoring method based on ultrasonic guided wave probability imaging, which is particularly suitable for online monitoring and damage visualization location of multi-bolt connection status of flanges in key structures such as aerospace engines and pressure pipelines. Background Technology

[0002] Flange bolt connections are one of the most critical connection methods in industrial equipment, widely used in aerospace engine casing connections, chemical piping systems, wind turbine generators, and other major equipment. These structures often operate under conditions of strong vibration, alternating loads, and extreme temperatures. Bolts are prone to loosening due to stress relaxation and fatigue, leading to sealing failure at the connection interface, reduced structural stiffness, and even catastrophic accidents. Therefore, real-time and accurate monitoring of the flange bolt connection status is of paramount engineering importance.

[0003] Existing bolt loosening detection technologies mainly include: direct physical quantity measurement methods, vibration-based analysis methods, piezoresistive impedance methods, and ultrasonic guided wave methods. Direct physical quantity measurement methods, such as using torque wrenches for re-tightening and ultrasonic bolt axial force meters, offer high accuracy but are offline methods, unable to achieve real-time online monitoring, and inefficient when dealing with numerous bolts. Vibration-based analysis methods indirectly determine bolt condition by analyzing changes in the overall or local vibration response (such as natural frequencies and mode shapes). However, this method lacks sensitivity to localized loosening and is easily affected by environmental noise. Piezoresistive impedance methods utilize the coupling relationship between the impedance of a lead zirconate titanium plate (PZT) adhered to the bolt or structural surface and the structural mechanical impedance. This method is sensitive to near-field damage, but its monitoring range is limited; a single PZT can only effectively monitor 1-2 bolts nearby. Ultrasonic guided wave methods utilize the changes in energy, amplitude, or phase of ultrasonic guided waves as they propagate through a structure and pass through the bolt connection interface as damage indicators for monitoring. While ultrasonic guided waves offer a wide monitoring range, current guided wave-based bolt location methods can only locate single or a few bolts, and for multiple loose bolts, they rely on machine learning techniques. However, machine learning models are typically black boxes, exhibiting poor interpretability and poor generalization ability.

[0004] Currently, ultrasonic guided wave technology offers various damage imaging and localization methods for cracks, corrosion, and impact damage in structures such as flat plates, including elliptical localization, phased array guided wave damage imaging, and probabilistic imaging. However, its application in flange bolt structures still faces significant challenges. This is mainly due to the complex structure of bolted connections, which easily leads to complex scattering and mode conversion of guided waves. Furthermore, multipath effects such as helical guided waves in thin-walled cylindrical structures increase the difficulty of signal analysis, resulting in a lack of effective imaging and localization methods for bolt loosening. The probabilistic imaging method (Reconstruction Algorithm for Probabilistic Inspection of Damage, RAPID algorithm) is an ultrasonic guided wave damage localization imaging technique. It reconstructs the probability distribution of damage at various points on the structure by acquiring signal changes through a sensor array, thus visually presenting the damage location in image form. This technique is suitable for complex guided wave signals and holds promise for imaging and localizing bolt loosening. The literature (Lü Bowang. Research on Monitoring Technology for Loosening Key Flange Bolts in Reactors Based on Guided Waves [D]. Harbin Institute of Technology, 2024. DOI:10.27061 / d.cnki.ghgdu.2024.001866.) uses ultrasonic guided wave technology combined with probabilistic imaging to locate loose flange bolts. Because its detection method is closer to the detection method of flat bolt lap structure, it does not consider the flange curved thin-wall structure, but only considers the local area in the flange with high similarity to the flat bolt lap structure. Under the condition of low sensor density, in order to improve the monitoring accuracy, it only considers the monitoring of local bolts. Moreover, the excitation receiving interface produced by its sensor arrangement is the connection interface through the flange bolts, which theoretically has low parameter sensitivity of signal energy loss. Therefore, the proposed method is limited to the monitoring of some bolts in the flange.

[0005] Therefore, existing technologies lack a method for large-scale monitoring and location of bolts in flanges using ultrasonic guided wave technology, as well as corresponding damage indicators and imaging algorithms. Summary of the Invention

[0006] The purpose of this invention is to address the technical problems of existing technologies using ultrasonic guided wave technology for monitoring bolt loosening in flanges, which struggle to cover all bolts and lack suitable damage indicators and effective imaging algorithms. This invention provides a flange bolt loosening location monitoring method based on ultrasonic guided wave probabilistic imaging. This method aims to: utilize a sparsely arranged sensor array, combined with probabilistic imaging techniques from ultrasonic guided wave technology, to construct a damage indicator sensitive to changes in preload, thereby achieving simultaneous monitoring and location imaging of the loosening state of all bolts on the flange bolt structure.

[0007] To achieve the above objectives, the technical solution provided by this invention is:

[0008] This invention provides a method for monitoring and locating loose flange bolts based on ultrasonic guided wave probabilistic imaging, comprising the following steps:

[0009] Step 1, Structural Parameter Measurement: Obtain the key geometric parameters and material acoustic properties of the flange, calculate the guided wave velocity of the S0 mode in the thin-walled cylinder of the flange, and initially select the excitation frequency band within the frequency range where the S0 mode is the dominant mode.

[0010] Step 2, Sensor Optimization Arrangement: Multiple sensor pairs are arranged on the thin-walled cylindrical surfaces on both sides of the flange connection interface. Each sensor pair consists of an excitation sensor on one side of the connection interface and a receiving sensor on the other side. The guided waves from the excitation and reception of the sensor pairs cover the monitoring area where all bolts are located. The arrangement position and number of sensors are determined based on the geometric parameters of the flange and the number of bolts.

[0011] Step 3, Excitation Signal Optimization: Within the excitation frequency band, different excitation signals are used to excite the excitation sensor and acquire ultrasonic guided wave signals; based on preset signal criteria, the optimal excitation signal is selected from the different excitation signals; if ultrasonic guided wave signals of the bolt in both healthy and damaged states can be acquired, the first criterion of maximizing the difference between ultrasonic guided wave signals is followed; if only ultrasonic guided wave signals of the bolt in healthy states can be acquired, the second criterion of optimizing the signal-to-noise ratio of ultrasonic guided wave signals is followed.

[0012] Step 4, Helical waveguide path selection: Based on the key geometric parameters of the flange and the arrangement of the sensors, calculate the length of each order of helical waveguide path from each excitation sensor to all receiving sensors; based on the waveguide velocity of the S0 mode and the length of each order of helical waveguide path, calculate the theoretical arrival time of the signal propagating from the excitation sensor to the receiving sensor along each helical waveguide path.

[0013] Step 5: Acquire reference signal and damage signal: In the healthy state and the damaged state, each excitation sensor is excited sequentially using the optimal excitation signal, and the ultrasonic guided wave signals received by all receiving sensors are collected; taking the theoretical arrival time as the starting point, the ultrasonic guided wave signals in the healthy state and the damaged state are intercepted respectively in the interval of a complete direct wave packet in the healthy state, to obtain the reference signal and damage signal of each pair of sensors.

[0014] Step 6: Calculate and correct damage indices; If the amplitude of the damage signal in a certain segment exceeds the reference signal, it is considered abnormal data and is removed using a characteristic function. A segment length balancing function is introduced to standardize all signals. Based on the processed reference and damage signals of each sensor pair, damage indices are calculated. A weighting factor is introduced to correct the damage indices, resulting in corrected damage indices. The weighting factor is related to the order and length of the helical waveguide path.

[0015] Step 7: Probabilistic imaging based on the RAPID algorithm: Divide the monitoring area into a pixel grid, calculate the total damage probability of each pixel based on the corrected damage index, and obtain the damage probability cloud map of the entire monitoring area.

[0016] Step 8: Calculate bolt loosening index and locate loose bolts: Define a circular region of interest (ROI) with the theoretical center position of each bolt as the circle. Calculate the loosening index of each bolt based on the total damage probability of all pixels within the ROI of each bolt. Compare the loosening indices of all bolts, and identify bolts with indices higher than those at other positions as loose bolts.

[0017] Furthermore, in step 2, the sensor placement follows the principle of maximizing the placement of multiple bolts on the shortest propagation path of different sensor pairs.

[0018] Furthermore, in step 3, the healthy state refers to the state after the flange is installed or after the bolt preload is recalibrated; the damaged state refers to the unknown state to be tested; and the data from each test can be used as the data for the healthy state during the next positioning monitoring.

[0019] Furthermore, in step 3, the first criterion is to select the excitation signal that maximizes the difference between the ultrasonic guided wave signal in the healthy state and the damaged state as the optimal excitation signal; the second criterion is to select the signal that maximizes the signal-to-noise ratio of the ultrasonic guided wave signal in the healthy state as the optimal excitation signal.

[0020] Furthermore, in step 5, under healthy conditions, each excitation sensor is sequentially excited, and the ultrasonic guided wave signals received by all receiving sensors are collected multiple times. The average value is taken as the baseline healthy condition data. Based on the baseline healthy condition data, the direct wave packet is intercepted using the theoretical arrival time and used as the baseline signal. Under damaged conditions, each excitation sensor is sequentially excited, and the ultrasonic guided wave signals received by all receiving sensors are collected multiple times. The average value is taken as the damaged condition data. Based on the damaged condition data, the direct wave packet is intercepted using the theoretical arrival time and used as the damaged signal.

[0021] Furthermore, in step 6, define Characteristic function:

[0022]

[0023] The truncation length balancing function is then expressed as:

[0024]

[0025] The damage index is then expressed as:

[0026]

[0027] in Indicates damage index, , This indicates the start and end times of the intercepted direct wave packet. Indicates damage signal, Indicates the reference signal. Indicates the excitation sensor number. Indicates the receiving sensor number, Indicates the order of the helical waveguide path. This represents the truncation length balancing function.

[0028] Furthermore, the revised damage index is shown in the following formula:

[0029]

[0030]

[0031] in This indicates the corrected damage index. Indicates the weighting factor. This indicates the path length of each order of helical waveguide.

[0032] Furthermore, in step 7, the total damage probability of each pixel is as follows:

[0033]

[0034] in Represents pixels The total probability of damage, Indicates the number of sensors. This represents the weights of the linear probability distribution.

[0035] Furthermore, the linear probability distribution weights As shown in the following formula:

[0036]

[0037] in This represents the preset proportional distribution parameter. Indicates the path length of each order of helical waveguide. Represents pixels The sum of the distances to excitation sensor i and receiving sensor j.

[0038] Furthermore, in step 8, the loosening index is shown in the following formula:

[0039]

[0040] in Indicates a loosening indicator. Represents the circular region of interest, with the theoretical center of the bolt at the center. The center is [the point of the circle].

[0041] The advantages of this invention are:

[0042] 1. This invention provides a flange bolt loosening location monitoring method based on ultrasonic guided wave probabilistic imaging. It fully utilizes the wide-range detection advantage of ultrasonic guided waves to locate and monitor flange bolt loosening. Compared with existing technologies, it features strong visualization and positioning capabilities, high monitoring efficiency, and a small number of sensors. By utilizing the different ultrasonic guided wave signals of bolts in healthy and damaged states, damage indices are calculated. Through probabilistic imaging technology, the changes in guided wave signals are transformed into an intuitive damage probability cloud map, obtaining the loosening index of each bolt. This achieves visualized and precise location of loose bolts, thereby determining and comparing the loosening indices of all bolts within the monitoring range. This application utilizes the "one-point excitation, multi-point reception" of guided waves and the spatial coverage capability of probabilistic imaging, requiring only a small number of sensors to achieve synchronous monitoring of the state of all bolts in the entire flange ring.

[0043] 2. The present invention provides a flange bolt loosening location monitoring method based on ultrasonic guided wave probability imaging. In the selection of guided wave path, it makes full use of the characteristics of multi-path spiral guided waves in thin-walled cylindrical structures to comprehensively extract and utilize received information. Under the condition that the number of sensors remains unchanged, a larger detection range is obtained by using "multi-path".

[0044] 3. This invention provides a method for monitoring and locating loose flange bolts based on ultrasonic guided wave probabilistic imaging. This method can eliminate abnormal signals in the reference signal and damage signal, and uses a length balance function to standardize the signals involved in the damage index calculation, thereby improving data consistency and comparability. Addressing the problem that signal attenuation due to path length reduction during propagation lowers the feasibility of containing ideal damage information, a weighting factor related to path order and length is introduced to correct this, thus improving the recognition reliability of long-path signals. Furthermore, the collected damage state data can serve as a new benchmark for subsequent comparisons, enabling bolt loosening detection even when standard healthy state signals are unavailable, and allowing further status assessment of bolts other than those already identified as loose. Therefore, this invention has a wider detection range and stronger engineering applicability. Attached Figure Description

[0045] The features and advantages of the invention will become more readily apparent from the following description with reference to the accompanying drawings, which are not drawn to scale and some features are enlarged or reduced to show details of specific parts.

[0046] Figure 1This is a schematic diagram of sensor arrangement and bolt type in an embodiment of the present invention;

[0047] Figure 2 This is a schematic diagram showing the positional relationship between the bolt and the sensor pair in an embodiment of the present invention;

[0048] Figure 3 This is a schematic diagram showing the positional relationship between the excitation sensor and the receiving sensor in an embodiment of the present invention;

[0049] Figure 4 This is a schematic diagram of multi-path helical propagation of thin-walled cylindrical waveguides in an embodiment of the present invention;

[0050] Figure 5 A schematic diagram of the flange structure dimensions in an embodiment of the present invention;

[0051] Figure 6 This is an example of a probabilistic imaging cloud map for bolt loosening location in an embodiment of the present invention;

[0052] Figure 7 In this embodiment of the invention, when the first bolt loosens, each bolt Q... M value;

[0053] Figure 8 This is a comparative cloud map of the final damage indicators of each bolt under different degrees of loosening in the embodiments of the present invention;

[0054] Figure 9 This is the result of the loosening and positioning of the bolt with a remaining torque of 0 Nm (fully loose) in the embodiment of the present invention.

[0055] In the diagram, 1-sensor pair; 2-connection interface; 3-first bolt; 4-path one; 5-path two; 6-detecting loose position; 7-excitation sensor; 8-receiving sensor. Detailed Implementation

[0056] The present invention will now be described in detail with reference to the accompanying drawings and exemplary embodiments thereof. It should be noted that the following detailed description of the present invention is for illustrative purposes only and is not intended to limit the scope of the invention.

[0057] This invention provides a method for monitoring and locating loose flange bolts based on ultrasonic guided wave probabilistic imaging, comprising the following steps:

[0058] Step 1, Structural Parameter Measurement: Obtain the key geometric parameters and material acoustic properties of the flange, calculate the guided wave velocity of the S0 mode in the thin-walled cylinder of the flange, and initially select the excitation frequency band within the frequency range where the S0 mode is the dominant mode.

[0059] Step 2, Sensor Optimization Arrangement: Multiple sensor pairs 1 are arranged on the thin-walled cylindrical surfaces on both sides of the flange connection interface 2. Each sensor pair 1 consists of an excitation sensor 7 on one side of the connection interface 2 and a receiving sensor 8 on the other side. The guided waves excited and received by the sensor pair 1 cover the monitoring area where all bolts 3 are located. The arrangement position and number of sensors are determined based on the geometric parameters of the flange and the number of bolts 3.

[0060] Step 3, Excitation Signal Optimization: Within the excitation frequency band, different excitation signals are used to excite the excitation sensor 7 and ultrasonic guided wave signals are acquired; based on preset signal criteria, the optimal excitation signal is selected from the different excitation signals; if ultrasonic guided wave signals of bolt 3 in both healthy and damaged states can be acquired, then the first criterion of maximizing the difference between ultrasonic guided wave signals is followed; if only ultrasonic guided wave signals of bolt 3 in healthy state can be acquired, then the second criterion of optimal ultrasonic guided wave signal-to-noise ratio is followed.

[0061] Step 4, Helical waveguide path selection: Based on the key geometric parameters of the flange and the arrangement of the sensors, calculate the length of each order of helical waveguide path from each excitation sensor 7 to all receiving sensors 8; based on the waveguide velocity of the S0 mode and the length of each order of helical waveguide path, calculate the theoretical arrival time of the signal propagating from the excitation sensor to the receiving sensor along each helical waveguide path.

[0062] Step 5: Acquire reference signal and damage signal: In the healthy state and the damaged state, each excitation sensor 7 is excited in sequence using the excitation signal, and the ultrasonic guided wave signals received by all receiving sensors 8 are collected; taking the theoretical arrival time as the starting point, the ultrasonic guided wave signals in the healthy state and the damaged state are respectively intercepted in the interval of a complete direct wave packet in the healthy state, to obtain the reference signal and damage signal of each pair of sensors 1.

[0063] Step 6: Calculate and correct damage indices; If the amplitude of the damage signal in a certain segment exceeds the reference signal, it is considered abnormal data and is removed using a characteristic function. A segment length balancing function is introduced to standardize all signals. Based on the reference signal and damage signal of each sensor pair after processing, damage indices are calculated. A weighting factor is introduced to correct the path damage indices, resulting in corrected damage indices. The weighting factor is related to the order and length of the helical waveguide path.

[0064] Step 7: Probabilistic imaging based on the RAPID algorithm: Divide the monitoring area into a pixel grid, calculate the total damage probability of each pixel based on the corrected damage index, and obtain the damage probability cloud map of the entire monitoring area.

[0065] Step 8: Calculate bolt loosening index and locate loose bolts: Define a circular region of interest with the theoretical center position of each bolt 3 as a circle. Calculate the loosening index of each bolt 3 based on the total damage probability of all pixels within the circular region of interest of each bolt 3. Compare the loosening indices of all bolts 3. Bolts 3 with significantly higher loosening indices than those at other positions are considered loose bolts 3.

[0066] This invention provides a method for monitoring and locating loose flange bolts 3 based on ultrasonic guided wave probabilistic imaging. This method fully utilizes the wide-range detection advantage of ultrasonic guided waves to locate and monitor the loosening of flange bolts 3. Compared with existing technologies, it features strong visualization and positioning capabilities, high monitoring efficiency, and a small number of sensors. By applying probabilistic imaging technology to the loosening of flange bolts 3, changes in guided wave signals are transformed into an intuitive damage probability cloud map, achieving visualized and precise positioning of the loose bolts 3. Utilizing the "one-point excitation, multi-point reception" principle of guided waves and the spatial coverage capability of probabilistic imaging, only a small number of sensors are needed to achieve synchronous monitoring of the status of all bolts 3 on the entire flange ring.

[0067] The following is a detailed explanation of each step:

[0068] Before step 1, the monitoring system needs to be set up:

[0069] The hardware acquisition subsystem includes an excitation module and a receiving module. The excitation module generates an excitation signal using an arbitrary waveform generator, amplifies it using a power amplifier, and then applies it to the excitation sensor 7. The receiving module synchronously acquires the signal from the receiving sensor 8 using a high-precision data acquisition module. A sampling frequency is set to ensure complete capture of signal details. Software processing utilizes MATLAB to write control and processing programs, data storage, and subsequent signal processing and probabilistic imaging algorithms.

[0070] Step 1: Structural parameter measurement

[0071] Key geometric parameters include the outer diameter and wall thickness of the thin-walled cylinder in the flange, as well as the diameter of the flange and the diameter of the bolt distribution circle; the guided wave velocity of the S0 mode in the thin-walled cylinder is calculated, and the group velocity is obtained. In other embodiments, the cylinder structure can also use a medium wall thickness (30mm). For signal excitation processing, if excitation is performed in a higher frequency band, various modal signals such as A0, S0, A1, and S1 will be generated simultaneously, which will greatly increase the complexity of processing. Therefore, in the frequency range with a relatively pure S0 mode, the excitation frequency band is initially selected, and excitation is performed in a lower frequency range. Ideally, only single modal signals of A0 and S0 will be generated, reducing the complexity of subsequent processing.

[0072] Step 2: Optimize sensor placement

[0073] Piezoelectric ceramic sheets are used as excitation sensor 7 and receiving sensor 8, such as Figure 1 , 3 As shown, an equal number of excitation sensors 7 and receiving sensors 8 are arranged on both sides of the flange connection interface 2, forming an excitation-receiving channel. The sensors should be firmly bonded using high-strength epoxy resin adhesive to ensure good acoustic coupling. The excitation sensor 7 can be paired with multiple receiving sensors 8 to form multiple sensor pairs 1.

[0074] The guided wave coverage area of ​​a sensor refers to the sum of the elliptical distribution areas of all sensor path probabilities. The sensor arrangement principle is to place multiple bolts 3 on the shortest propagation path (0th order path) of different sensor pairs 1 as much as possible to maximize monitoring coverage and sensitivity. Figure 2 , 3 As shown, the excitation sensor 7 and the receiving sensor 8 are arranged symmetrically along the uniform axis, and each bolt 3 and each sensor is numbered.

[0075] Step 3: Optimization of excitation signal

[0076] In the laboratory, tightening bolt 3 to the rated torque value is defined as a healthy state, and the state in which bolt 3 is loose is defined as a damaged state.

[0077] In practical applications, the state after the flange is first installed or after the preload of bolt 3 is recalibrated is defined as the healthy state, and the unknown state to be tested is defined as the damaged state. At this time, bolt 3 may be loose or it may not be loose.

[0078] Ultrasonic guided wave signals acquired in both healthy and damaged states must be stored in a database for subsequent location monitoring.

[0079] If the above-mentioned standard health status signal data cannot be obtained in practical applications, health status data from the laboratory or data detected under damaged conditions can be used as substitutes. Data from each test can be used as health status data for comparison in the next test, and the loosened condition can be further loosened using existing loosening detection.

[0080] Within the excitation frequency band, different excitation signals are used to excite the excitation sensor 7. The optimal excitation signal is determined based on preset signal criteria, which can narrow the selection range of the optimal excitation signal and reduce the workload.

[0081] If the ultrasonic guided wave signals of bolt 3 in both healthy and damaged states can be obtained, the optimal excitation signal is determined by the first criterion. The first criterion is: select the excitation signal that maximizes the difference between the ultrasonic guided wave signals in the healthy and damaged states as the optimal excitation signal.

[0082] If the ultrasonic guided wave signal of bolt 3 in the damaged state cannot be obtained, the excitation signal is determined by the second criterion. The second criterion is: compare the amplitude of the ultrasonic guided wave signal of the sensor in the healthy state, and select the signal that makes the ultrasonic guided wave signal in the healthy state with the highest signal-to-noise ratio as the optimal excitation signal.

[0083] Step 4: Helical waveguide path selection

[0084] Based on the propagation characteristics of helical guided waves in thin-walled cylindrical structures within flange structures, the path length of the signal from any excitation sensor 7 to each receiving sensor 8 is calculated sequentially. The shortest path between each excitation-receiver pair is designated as the 0th-order path, the second shortest helical path as the 1st-order path, the third shortest helical path as the 2nd-order path, and so on. Let the length of each path be d. ijk Where i is the excitation sensor number 7, j is the receiving sensor number 8, and k is the order. Usually, only the first two orders of paths are used. If the excitation and receiving sensors are symmetrically arranged, there may be two paths of the same order with the same length. The orders of the two paths can be denoted as ±k, and + and - are uniformly defined to represent clockwise and counterclockwise directions, respectively. Based on the group velocity of the S0 mode in the thin-walled cylindrical structure and the path length d of each order... ijk Calculate the arrival time t of the S0 wave packet along each path. ijk The time of arrival is the theoretical arrival time.

[0085] Step 5: Baseline Health Status Data Collection

[0086] In a healthy state, each excitation sensor 7 is sequentially activated, and the ultrasonic guided wave signals received by all receiving sensors 8 are collected multiple times. The collected healthy state signal V is then taken. 0ij The average value of (t) is used as the baseline health status data; based on the baseline health status data, taking the theoretical arrival time of the signal in each helical waveguide path as the starting point, a complete direct wave packet under the health status is extracted as the reference signal V. 0ijk (t); To improve robustness, baseline health status data can be repeatedly collected, and the average value of the extracted health status data can be used as the baseline signal V. 0ijk (t). This step effectively separates the contributions of different pathways, improving the signal-to-noise ratio of subsequent damage indicators. It allows for repeated measurements, expanding the baseline health status data.

[0087] In the damaged state, the processing method is the same as that in the healthy state. Each excitation sensor 7 is sequentially excited, and the ultrasonic guided wave signals received by all receiving sensors 8 are collected multiple times. The average value is taken as the damaged state data. Starting from the theoretical arrival time, the damaged state data is truncated within an interval of one complete direct-arrival wave packet selected in the healthy state, and this is taken as the damaged signal V. ijk (t).

[0088] Step 6: Calculate and correct damage indices

[0089] Calculate the signal difference for each excitation-receiver path in the damaged state and the healthy state.

[0090] Preferably, define Characteristic function:

[0091]

[0092] If the amplitude of the damage signal in the selected segment is less than the reference signal, the calculation result is the ratio of the reduction in energy of the normal damage state to the energy of the healthy state; if the amplitude of the damage signal in a certain selected segment exceeds the reference signal, it is judged as abnormal and removed using the characteristic function.

[0093] If due to the characteristic function To remove outlier signals, the length of the signals involved in the calculation changes. Therefore, a truncation length balancing function needs to be introduced to standardize all signals. express:

[0094]

[0095] The damage index is then expressed as:

[0096]

[0097] in Indicates damage index, , These represent the start and end times of the intercepted direct wave packet, respectively. Indicates the reference signal. Indicates damage signal, Indicates the excitation sensor number. Indicates the receiving sensor number, This indicates the order of the helical waveguide path.

[0098] The longer the time span from excitation to reception of the signal, the lower the feasibility of it containing ideal state impairment information. Therefore, a weighting factor s related to the path order k is introduced. k As shown in the following formula:

[0099]

[0100] The path damage index (DI) is corrected based on weighting factors. ij As shown in the following formula:

[0101]

[0102] in This represents the corrected impairment index. The path impairment index has been corrected by reducing the weight of higher-order paths with longer propagation paths and less stable signals, thus highlighting the contribution of the most sensitive and reliable 0th-order path.

[0103] Step 7: Probabilistic Imaging Based on the RAPID Algorithm

[0104] The monitoring area is divided into a pixel grid, that is, the entire connection area of ​​the flange bolt structure (especially the bolt distribution circumference) is discretized into a pixel grid. For each pixel p in the grid, the following operations are performed:

[0105] Calculate the relative distance from point p to each path's excitation-receiving sensor (i,j), which is defined as the sum of the distances l from point p to excitation sensor 7 and receiving sensor 8. ijk The path length d between excitation sensor 7 and receiving sensor 8 ijk The ratio. Substitute the ratio into the elliptic distribution function. Calculate the linear probability distribution weight W of pixel p for the k-th order path in sensor pair 1. ijk(p) The preset proportional distribution parameter β is used to control the size of the effective region of the ellipse.

[0106]

[0107] Among them W ijk(p) Represents the weights of a linear probability distribution. This represents the preset proportional distribution parameter. Represents pixels The sum of the distances to excitation sensor 7 and receiving sensor 8. Wherein Common settings are slightly greater than 1. Experience shows that this value is related to the number of bolts 3 and the sensor distribution density. Adjust it flexibly according to the actual situation.

[0108] After traversing all paths, sum the probability values ​​contributed by each sensor to pixel 1 to obtain the total damage probability P of that point. (p) As shown in the following formula, after calculating the damage probability cloud map of the entire monitoring area, a damage probability cloud map is generated after all pixels are calculated.

[0109]

[0110] in Represents pixels The total probability of damage, Indicates the number of sensors.

[0111] Step 8: Calculate bolt loosening index and locate loosening.

[0112] To focus the imaging results on determining the looseness of bolt 3, the theoretical center position of each bolt 3 was further analyzed. Define a circular region of interest (ROI) with radius γ centered at the center. Calculate all pixels within the 3ROI for each bolt. The sum of the total damage probabilities is used as the loosening index Q of bolt 3. M This indicator comprehensively reflects the degree of abnormality in the contact state of the area near bolt 3. The diffuse cloud map information is concentrated on the specific location of bolt 3, which facilitates automated judgment.

[0113]

[0114] Compare the final loosening index Q of all bolts 3 M Q M Bolt 3 with a value significantly higher than other positions is identified as loose bolt 3, thereby achieving synchronous positioning and identification of the loose state of multiple bolts 3.

[0115] This example uses a typical 12-bolt flange connection as the monitoring object, with a thin-walled cylindrical pipe made of aluminum alloy. It details the entire process from system setup to result analysis.

[0116] Step 1: Setting up the monitoring system

[0117] The hardware acquisition subsystem employs the following methods: At the excitation end, an arbitrary waveform generator (AWG) module from the NI PXIe-1088 platform generates an excitation signal. This signal is amplified by a TEGAM power amplifier (voltage gain 50x) and then applied to the excitation piezoelectric ceramic sheet. At the receiving end, a high-precision digital oscilloscope module from the NI PXIe-1088 platform synchronously acquires and receives the signal from the piezoelectric ceramic sheet. The sampling frequency is set to 20MHz.

[0118] Step 2: Structural Parameter Measurement

[0119] The geometric parameters of the flange and pipe were measured: pipe outer diameter 172mm, wall thickness 4mm, flange diameter 200mm, bolt distribution circle diameter 180mm, and 12 M6 bolts arranged uniformly and symmetrically in the circumferential direction. The wave group velocity c = 2300m / s of the aluminum alloy material at the expected frequency was obtained through literature review or experimental measurements.

[0120] Step 3: Sensor Placement

[0121] The sensor uses eight PZT-5A type piezoelectric ceramic sheets (size: Φ8mm×0.5mm) as the excitation and receiving sensors. Figure 1As shown, four sensors are arranged on each side of the thin-walled pipe surface at flange connection interface 2, forming four pairs of excitation-receiver channels. Finally, the piezoelectric sensors are positioned 56.5 mm above and below the flange outer wall at connection interface 2, and are evenly and symmetrically arranged circumferentially. Figure 3 and Figure 5 As shown in (a); the distribution of bolts 3 on the flange is as follows Figure 2 and Figure 5 As shown in (b), the bolt 3 directly above is the first bolt 3 and the sensor pair 1 is the first sensor pair. The bolt 3 and the sensor pair 1 are numbered sequentially in a clockwise direction. Figure 5 The pipe dimensions are indicated in (a). Figure 5 (b) The flange dimensions are indicated.

[0122] Step 4: Optimization of Excitation Signal

[0123] Tightening bolt 3 to its rated torque value is defined as the healthy state, while the state where bolt 3 is loose is defined as the damaged state. The preferred excitation signal is a 3.5-cycle sine wave modulated with a Hanning window. Through frequency sweep experiments (within the excitation frequency range of 50kHz-700kHz), the significance of the signal difference between the healthy state and a state where bolt 3 is completely loose is compared. Ultimately, the center frequency most sensitive to the interface contact state is determined to be 300kHz, and this is set as the excitation signal.

[0124] Step 5: Path Calculation and Signal Interception Strategy Determination

[0125] Based on the geometric parameters measured in step one and the sensor positions determined in step three, calculate the length d of each helical path between each pair of sensor pairs 1. ijk , where k is the path order. For example... Figure 3 , 4 As shown, considering only paths of order k=0, ±1, calculate the path length d of path 4 (path 1) and path 5 (path 2). ijk And detection is carried out at the loosening location 6. Based on the waveguide group velocity c and path length d... ijk Calculate the theoretical arrival time t of the signal along each path. k With t k Starting from the healthy state, the signal interval of the next complete wave packet is truncated.

[0126] Step Six: Establishing a Health Status Database

[0127] Using a calibrated torque wrench, tighten all 12 bolts 3 to the rated torque (8 Nm in this example); this state is defined as the "healthy state". Sequentially activate each activation sensor 7 (activation sensors one through four), simultaneously acquiring signals from all receiving sensors 8 (receiving sensors one through four) during each activation. Repeat this process 5 times, and take the average value as the health state signal. For each set of health state signals V... 0ij (t) and based on the path order k and arrival time t k Extract the signal segments corresponding to each path. Repeat the sampling 5 times and take the average value as the final reference signal V. 0ijk (t).

[0128] Step 7: Signal Detection

[0129] To verify the method under damaged conditions, a single bolt 3 (such as the first bolt) was sequentially loosened to different torque states as simulated loosening states: 0 Nm (fully loose), 2 Nm, and 4 Nm. After each loosening, the remaining 11 bolts 3 were held at 8 Nm. The signal V of the current state was obtained. ij (t), and finally the reference signal V ijk (t).

[0130] Step 8: Calculation of Path-Weighted Damage Indicators

[0131] For each path k of each sensor pair 1, an abnormal signal is removed using a characteristic function, and the energy after balancing the truncated length is used as the damage index R. ijk Introduce a weighting factor related to the path order k. The damage index is corrected to obtain the corrected path damage index DI. ij .

[0132] Step Nine: Probabilistic Imaging and Bolt 3-Area Focusing Analysis

[0133] The annular region containing the flange bolt distribution circle is discretized into a dense pixel grid of 0.5mm × 0.5mm. Based on the elliptic distribution function W... ijk (p) For each pixel p, normalize all pixels p and calculate its contribution probability to all sensor pairs 1 and each path k. The preset proportional distribution parameter β=1.15 is used to control the size of the effective region of the ellipse.

[0134] The total damage probability P(p) of a pixel is obtained by summing the contribution probabilities of all sensors to point 1 and the path. After calculating the damage probability of all pixels, a two-dimensional damage probability cloud map of the entire monitoring area is generated, as shown below. Figure 6 As shown.

[0135] With the theoretical center position of each bolt 3 Define a circular region of interest (ROI) with radius γ = 5 mm centered at the center. Calculate the sum of the damage probabilities of all pixels within the ROI of each bolt 3, which will be used as the final loosening index Q for that bolt 3. M .

[0136] Step 10: Loosen and Position

[0137] like Figure 7 Q is the value of each bolt 3 when the first bolt 3 is loose. M Value. Directly set the maximum Q. M The value corresponding to bolt 3 was determined to be loose bolt 3. The experiment was repeated a large number of times under three conditions: the remaining torque of bolt 3 was 0 Nm (fully loose), 2 Nm (25% loose), and 4 Nm (50% loose). The number of experiments were repeated 156 times, 78 times, and 78 times respectively. The results of the positioning judgment accuracy are shown in Table 1.

[0138] Table 1. Bolt positioning accuracy under different degrees of looseness

[0139] Remaining torque 0Nm (fully relaxed) 2Nm(25%) 4Nm (50%) Positioning accuracy (148 / 156)94.87% (60 / 78)76.92% (44 / 78)56.41%

[0140] like Figure 8 As shown, the positioning accuracy gradually increases as the remaining torque decreases (6Nm→4Nm→2Nm→0Nm). Figure 9 The specific positioning results of 12 different bolts 3 on the flange were obtained by sequentially and completely loosening them. Each bolt 3 was tested 13 times. The positioning accuracy of this method can reach more than 94.87% when the bolts are completely loosened.

[0141] Finally, it should be noted that the features mentioned and / or shown in the above description of exemplary embodiments of the present invention can be combined in the same or similar manner with one or more other embodiments, combined with features in other embodiments, or substituted for corresponding features in other embodiments. These combined or substituted technical solutions should also be considered to be included within the scope of protection of the present invention.

Claims

1. A method for monitoring and locating loose flange bolts based on ultrasonic guided wave probabilistic imaging, characterized in that, Includes the following steps: Step 1, Structural Parameter Measurement: Obtain the key geometric parameters and material acoustic properties of the flange, calculate the guided wave velocity of the S0 mode in the thin-walled cylinder of the flange, and initially select the excitation frequency band within the frequency range where the S0 mode is the dominant mode. Step 2, Sensor Optimization Arrangement: Multiple sensor pairs are arranged on the thin-walled cylindrical surfaces on both sides of the flange connection interface. Each sensor pair consists of an excitation sensor on one side of the connection interface and a receiving sensor on the other side. The guided waves from the excitation and reception of the sensor pairs cover the monitoring area where all bolts are located. The arrangement position and number of sensors are determined based on the geometric parameters of the flange and the number of bolts. Step 3, Excitation Signal Optimization: Within the excitation frequency band, different excitation signals are used to excite the excitation sensor and acquire ultrasonic guided wave signals; based on preset criteria, the optimal excitation signal is selected from the different excitation signals; if ultrasonic guided wave signals of the bolt in both healthy and damaged states can be acquired, the first criterion of maximizing the difference between ultrasonic guided wave signals is followed; if only ultrasonic guided wave signals of the bolt in healthy states can be acquired, the second criterion of optimizing the signal-to-noise ratio of ultrasonic guided wave signals is followed. Step 4, Helical waveguide path selection: Based on the key geometric parameters of the flange and the arrangement of the sensors, calculate the length of each order of helical waveguide path from each excitation sensor to all receiving sensors; based on the waveguide velocity of the S0 mode and the length of each order of helical waveguide path, calculate the theoretical arrival time of the signal propagating from the excitation sensor to the receiving sensor along each helical waveguide path. Step 5: Acquire reference signal and damage signal: In the healthy state and the damaged state, each excitation sensor is excited sequentially using the optimal excitation signal, and the ultrasonic guided wave signals received by all receiving sensors are collected; taking the theoretical arrival time as the starting point, the ultrasonic guided wave signals in the healthy state and the damaged state are intercepted respectively in the interval of a complete direct wave packet in the healthy state, to obtain the reference signal and damage signal of each pair of sensors. Step 6: Calculate and correct damage indices; If the amplitude of the damage signal in a certain segment exceeds the reference signal, it is considered abnormal data and is removed using a characteristic function. A segment length balancing function is introduced to standardize all signals. Based on the processed reference and damage signals of each sensor pair, damage indices are calculated. A weighting factor is introduced to correct the damage indices, resulting in corrected damage indices. The weighting factor is related to the order and length of the helical waveguide path. Step 7: Probabilistic imaging based on the RAPID algorithm: Divide the monitoring area into a pixel grid, calculate the total damage probability of each pixel based on the corrected damage index, and obtain the damage probability cloud map of the entire monitoring area. Step 8: Calculate bolt loosening index and locate loose bolts: Define a circular region of interest (ROI) with the theoretical center position of each bolt as the circle. Calculate the loosening index of each bolt based on the total damage probability of all pixels within the ROI of each bolt. Compare the loosening indices of all bolts, and identify bolts with indices higher than those at other positions as loose bolts.

2. The flange bolt loosening location monitoring method according to claim 1, characterized in that, In step 2, the sensor placement follows the principle of maximizing the placement of multiple bolts on the shortest propagation path of different sensor pairs.

3. The flange bolt loosening location monitoring method according to claim 1, characterized in that, In step 3, The healthy state refers to the state after the flange is installed or after the bolt preload is recalibrated; the damaged state refers to the unknown state to be tested; the data from each test can be used as the data for the healthy state at the next positioning monitoring.

4. The flange bolt loosening location monitoring method according to claim 1, characterized in that, In step 3, the first criterion is: select the excitation signal that maximizes the difference between the ultrasonic guided wave signals in the healthy state and the damaged state as the optimal excitation signal; The second criterion is to select the signal that gives the highest signal-to-noise ratio to the ultrasonic guided wave signal in a healthy state as the optimal excitation signal.

5. The flange bolt loosening location monitoring method according to claim 1, characterized in that, In step 5, under healthy conditions, each excitation sensor is excited sequentially, and the ultrasonic guided wave signals received by all receiving sensors are collected multiple times. The average value is taken as the baseline healthy state data. Based on the baseline healthy state data, the direct wave packet is intercepted using the theoretical arrival time and used as the reference signal. Under the damaged state, each excitation sensor is excited sequentially, and the ultrasonic guided wave signals received by all receiving sensors are collected multiple times. The average value is taken as the damaged state data. Based on the damage state data, the direct wave packet is extracted using the theoretical arrival time and used as the damage signal.

6. The flange bolt loosening location monitoring method according to claim 5, characterized in that, In step 6, define Characteristic function: The truncation length balancing function is then expressed as: The damage index is then expressed as: in Indicates damage index, , This indicates the start and end times of the intercepted direct wave packet. Indicates damage signal, Indicates the reference signal. Indicates the excitation sensor number. Indicates the receiving sensor number, Indicates the order of the helical waveguide path. This represents the truncation length balancing function.

7. The flange bolt loosening location monitoring method according to claim 6, characterized in that, The corrected damage index is shown in the following formula: in This indicates the corrected damage index. Indicates the weighting factor. This indicates the path length of each order of helical waveguide.

8. The flange bolt loosening location monitoring method according to claim 7, characterized in that, In step 7, the total damage probability of each pixel is shown in the following formula: in Represents pixels The total probability of damage, Indicates the number of sensors. This represents the weights of the linear probability distribution.

9. The flange bolt loosening location monitoring method according to claim 8, characterized in that, Linear probability distribution weights As shown in the following formula: in This represents the preset proportional distribution parameter. Indicates the path length of each order of helical waveguide. Represents pixels The sum of the distances to excitation sensor i and receiving sensor j.

10. The flange bolt loosening location monitoring method according to claim 9, characterized in that, In step 8, the loosening index is shown in the following formula: in Indicates a loosening indicator. Represents the circular region of interest, with the theoretical center of the bolt at the center. The center is [the point of the circle].

Images