Bolt looseness full-period acoustic emission monitoring method based on variational mode decomposition

Abstract

The invention discloses a bolt looseness full-period acoustic emission monitoring method based on variational mode decomposition, and relates to the technical field of nondestructive testing, and the method comprises the steps: collecting acoustic emission signals of a bolt connection interface under a plurality of grades of pre-tightening forces; variational mode pre-decomposition is carried out on the acoustic emission signals, and the optimal decomposition layer number is determined through the decomposition mode energy difference rate; on the basis of the determined optimal decomposition layer number, performing variational mode decomposition on all the acoustic emission signals to obtain a plurality of intrinsic mode functions; calculating an energy value of each intrinsic mode function, establishing a change relationship between the energy value of each intrinsic mode function and different levels of pre-tightening forces, and screening out a characteristic mode most sensitive to the change of the pre-tightening forces; and establishing a mapping relation between the screened characteristic modal energy and the pre-tightening force, obtaining a loosening change curve, dividing the bolt loosening process into different stages according to the loosening change curve, and realizing quantitative monitoring of the whole period of bolt loosening. The safety and reliability of the bolt connection structure are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of nondestructive testing, and in particular relates to a full-cycle acoustic emission monitoring method for bolt loosening based on variational mode decomposition. Background Art

[0002] Bolt connection is a widely used fastening method in mechanical structures, and is widely used in aerospace, machinery manufacturing, bridge construction and other fields. The loosening of bolts will not only lead to a decrease in the strength of the connection structure, but may also cause serious safety hazards and even catastrophic accidents. Therefore, it is particularly important to effectively monitor and warn of bolt loosening. Traditional bolt loosening detection methods mainly include torque detection, ultrasonic detection and stress wave detection. However, these methods have certain limitations in practical applications, such as low detection sensitivity, complex operation, and difficulty in online monitoring. In recent years, acoustic emission (AE) technology has become an important means of bolt loosening detection due to its high sensitivity and real-time monitoring. AE technology can timely reflect the state of bolt loosening by capturing the AE signals generated during the process of microcrack expansion, friction and slip inside the material. However, AE signals usually have nonlinear and non-stationary characteristics, and are greatly affected by noise and other external interferences. Traditional signal processing methods are difficult to accurately extract feature information related to bolt loosening. Therefore, it is urgent to propose a full-cycle AE monitoring method for bolt loosening based on variational mode decomposition. Summary of the invention

[0003] In order to solve the above technical problems, the present invention proposes a full-cycle acoustic emission monitoring method for bolt loosening based on variational modal decomposition. By performing variational modal decomposition on the acoustic emission signal, the characteristic mode reflecting the loose state of the bolt is extracted, and real-time monitoring and early warning of the entire process of bolt loosening are achieved, thereby improving the safety and reliability of the bolt connection structure.

[0004] To achieve the above object, the present invention provides a full-cycle acoustic emission monitoring method for bolt loosening based on variational mode decomposition, comprising:

[0005] Collect acoustic emission signals of bolt connection interfaces under several levels of preload;

[0006] Performing variational modal pre-decomposition on the acoustic emission signal, performing variational modal pre-decomposition according to different decomposition levels, calculating decomposition modal energies corresponding to different decomposition levels, calculating decomposition modal energy difference rates according to the decomposition modal energies corresponding to different decomposition levels, and determining an optimal decomposition level using the decomposition modal energy difference rates;

[0007] Based on the optimal decomposition layer number, performing variational modal decomposition on all collected acoustic emission signals to obtain a number of intrinsic mode functions;

[0008] By calculating the energy value of each eigenmode function, the relationship between the energy value of each eigenmode function and the change of preload force at different levels is established, and the characteristic mode that is most sensitive to the change of preload force is screened out;

[0009] A mapping relationship between the selected characteristic modal energy and the preload force is established to obtain a loosening change curve. The bolt loosening process is divided into different stages according to the loosening change curve to achieve quantitative monitoring of the entire bolt loosening cycle.

[0010] Optionally, the plurality of levels of preload force satisfy a number greater than or equal to 8.

[0011] Optionally, the energy in the decomposed modal energy difference rate is expressed as:

[0012]

[0013] Where E represents the energy of the signal, x(i) represents the acquired signal sequence, n represents the number of sampling points, and i is the i-th sampling point in the signal sequence.

[0014] Optionally, the decomposed modal energy difference rate is expressed as:

[0015]

[0016] Among them, η represents the energy difference rate of the decomposed mode, E K represents the sum of the energies of all K components obtained by decomposing the Kth level, E K-1 Represents the sum of the energies of all K-1 components obtained by decomposition level K-1.

[0017] Optionally, determining the optimal number of decomposition layers by using the decomposition modal energy difference rate includes:

[0018] Step S1, initialize the number of decomposition layers, set the decomposition layer value, determine the search range of the decomposition layer number, set the step size, perform variational mode decomposition on the acoustic emission signal, calculate the energy of each decomposed intrinsic mode function for the set decomposition layer value, and calculate the sum of the energies of all intrinsic mode functions;

[0019] Step S2, increase the number of decomposition levels by 1, and continue step S1 until the maximum value of the search range is reached, and then proceed to step S3;

[0020] Step S3, comparing the decomposition modal energy difference rate corresponding to the decomposition layer value and the decomposition layer value corresponding to the maximum value of the decomposition modal energy difference rate, and determining the optimal decomposition layer number.

[0021] Optionally, variational mode decomposition is performed on all collected acoustic emission signals to obtain several eigenmode functions including:

[0022] Step 1: Parameter initialization: Before performing variational mode decomposition, set the required parameters, including the optimal decomposition layer number K, penalty parameter α, and convergence condition ε;

[0023] Step 2: Initialize the intrinsic mode function u k (t) and frequency center ω k ;

[0024] Step 3: Iterative optimization: construct the objective function using the Lagrange multiplier method, and calculate each eigenmode function u by performing bandpass filtering on each eigenmode function. k (t); Update the corresponding frequency center ω for each eigenmode function k , ensuring that each mode is concentrated in its specific frequency band; updating the Lagrange multiplier to ensure the reconstruction accuracy of the signal and reduce the decomposition error;

[0025] Step 4: Convergence determination: repeat the iterative process in step 3 until the convergence condition is reached. Optionally, the method for calculating the energy value of each eigenmode function includes:

[0026] For each intrinsic mode function IMF k (t), square it and calculate the instantaneous energy E k (t) = IMF k (t) 2 , the instantaneous energy E of each eigenmode function k (t) Perform time integration to obtain the total energy value E of the modal function in the entire time period k , the formula is:

[0027]

[0028] Where T is the total duration of the signal.

[0029] Optionally, the relationship between the energy value of each eigenmode function and the change of preload at different levels is established, and the eigenmodes most sensitive to the change of preload are selected, including:

[0030] For each eigenmode function, establish its energy value E k The relationship curve with the change of preload force F is as follows:

[0031] E k =f(F)

[0032] The energy of each intrinsic mode function is plotted as a function of preload. The energy curves of different intrinsic mode functions are compared, the amplitude of the energy value changing with preload is analyzed, and the intrinsic mode function with a large amplitude of energy changing with preload and which can monotonically indicate the change of preload is selected as the characteristic mode.

[0033] Optionally, a mapping relationship between the selected characteristic modal energy and the preload force is established to obtain a looseness change curve including:

[0034] Fit the eigenmode energy E using polynomial fitting or exponential, logarithmic or linear regression curve fitting methods 特征 The relationship between and preload force F.

[0035] Optionally, dividing the bolt loosening process into different stages according to the loosening change curve includes:

[0036] The bolt loosening process is divided into different stages according to the slope characteristics of the loosening change curve.

[0037] Technical effect of the invention: The invention discloses a full-cycle acoustic emission monitoring method for bolt loosening based on variational modal decomposition. By combining acoustic emission technology with variational modal decomposition method, real-time monitoring of the full cycle of bolt loosening is achieved. The complex acoustic emission signal is decomposed and feature extracted using variational modal decomposition, which effectively reduces the influence of noise and external interference, thereby improving the accuracy and stability of signal processing. The method can monitor the state of bolts in different loosening stages, provides comprehensive health monitoring for bolted connection structures, greatly improves the safety and reliability of bolted connections, reduces the risk of equipment failures and accidents, and has important application value for ensuring the stable operation of machinery and structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0039] Figure 1 A schematic flow chart of a method for monitoring full-cycle acoustic emission of bolt loosening based on variational mode decomposition according to an embodiment of the present invention;

[0040] Figure 2 This is a schematic diagram of a bolt loosening acoustic emission monitoring test bench according to an embodiment of the present invention;

[0041] Figure 3 Schematic diagram of the relationship between the number of decomposition layers K and the decomposition modal energy difference rate η according to an embodiment of the present invention;

[0042] Figure 4 This is a schematic diagram of energy variation trend of IMF1 according to an embodiment of the present invention;

[0043] Figure 5 This is a schematic diagram of energy variation trend of IMF2 according to an embodiment of the present invention;

[0044] Figure 6This is a schematic diagram of energy variation trend of IMF3 according to an embodiment of the present invention;

[0045] Figure 7 This is a schematic diagram of energy variation trend of IMF4 according to an embodiment of the present invention;

[0046] Figure 8 It is a schematic diagram of classification monitoring of the full cycle stage of bolt loosening according to an embodiment of the present invention;

[0047] Among them, 1 is a signal generator, 2 is a power amplifier, 3 is an exciter, 4 is a push rod, 5 is a 5 mm steel plate, 6 is a digital display, 7 is an M8 bolt, 8 is a pressure sensor, 9 is an acoustic emission sensor, 10 is a preamplifier, 11 is an acoustic emission collector, 12 is a PC, 13 is a bench vise, 14 is a foundation, and 15 is a 5 mm steel plate. DETAILED DESCRIPTION

[0048] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0049] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0050] Related terms introduction:

[0051] Variational mode decomposition (VMD): The VMD method decomposes complex signals into several intrinsic mode functions (IMFs), each of which represents a different characteristic component of the signal. As an emerging signal processing method, variational mode decomposition (VMD) has gradually attracted the attention of researchers. Compared with traditional signal decomposition methods, VMD has better adaptability and resolution, can effectively retain the local characteristics of the signal, and significantly improve the accuracy of signal processing. Therefore, VMD has broad application prospects in acoustic emission signal analysis, especially in bolt loosening monitoring under complex working conditions, and can provide more accurate feature extraction and analysis methods.

[0052] like Figure 1 As shown, this embodiment provides a full-cycle acoustic emission monitoring method for bolt loosening based on variational mode decomposition, including:

[0053] Collect acoustic emission signals of bolt connection interfaces under several levels of preload;

[0054] Performing variational modal pre-decomposition on the acoustic emission signal according to different decomposition levels, calculating the decomposition modal energies corresponding to different decomposition levels, and then calculating the decomposition modal energy difference rate according to the decomposition modal energies corresponding to different decomposition levels, and determining the optimal decomposition level by using the decomposition modal energy difference rate;

[0055] Based on the determined optimal decomposition layer number, all collected acoustic emission signals are subjected to variational mode decomposition to obtain several intrinsic mode functions;

[0056] By calculating the energy value of each eigenmode function, the relationship between the energy value of each eigenmode function and the change of preload at different levels is established, and the characteristic mode that is most sensitive to the change of preload is screened out;

[0057] The mapping relationship between the screened characteristic modal energy and the preload force is established to obtain the loosening change curve. The bolt loosening process is divided into different stages according to the loosening change curve to achieve quantitative monitoring of the entire bolt loosening cycle.

[0058] Furthermore, the plurality of levels of preload force satisfy a number that is greater than or equal to 8.

[0059] By increasing the number of preload levels, the effect of preload changes on the acoustic emission signal can be captured in more detail. Collecting data at 8 or more different preload levels can ensure that the relationship between energy change and preload is clearer and form a more accurate mapping model. This helps to more accurately assess the state of the bolt at different loosening stages and improve the accuracy of monitoring.

[0060] Furthermore, the energy in the decomposed modal energy difference rate is expressed as:

[0061]

[0062] Where E represents the energy of the signal, x(i) represents the acquired signal sequence, n represents the number of sampling points, and i is the i-th sampling point in the signal sequence.

[0063] By calculating the total energy of the signal through this formula, the intensity of the acoustic emission signal can be effectively quantified, which is convenient for evaluating the energy contribution of each decomposed mode during the bolt loosening process.

[0064] Furthermore, the decomposed modal energy difference rate is expressed as:

[0065]

[0066] Among them, η represents the energy difference rate of the decomposed mode, E Krepresents the sum of the energies of all K components obtained by decomposing the Kth level, E K-1 Represents the sum of the energies of all K-1 components obtained by decomposition level K-1.

[0067] The energy difference rate of the decomposed modes calculated by this formula can reflect the change trend between the energy of modes at different decomposition levels, providing a basis for the subsequent screening of characteristic modes.

[0068] Furthermore, the number of decomposition layers is determined by using the decomposition modal energy difference rate, including:

[0069] Step S1, initialize the number of decomposition layers, set the decomposition layer value, determine the search range of the decomposition layer number, set the step size, perform variational mode decomposition on the acoustic emission signal, calculate the energy of each decomposed intrinsic mode function for the set decomposition layer value, and calculate the sum of the energies of all intrinsic mode functions;

[0070] Step S2, increase the number of decomposition levels by 1, and continue step S1 until the maximum value of the search range is reached, and then proceed to step S3;

[0071] Step S3, comparing the decomposition modal energy difference rate corresponding to the decomposition layer value and the decomposition layer value corresponding to the maximum value of the decomposition modal energy difference rate, and determining the number of decomposition layers.

[0072] By presetting the search range and step size of the decomposition layer, we can effectively avoid excessive redundant decomposition, reduce unnecessary computing work, and improve the efficiency of signal processing. The final number of decomposition layers is determined by the principle of maximizing the energy difference rate, which means that the system will not over-decompose the signal, nor will it lose key information due to insufficient decomposition, thus achieving a balance between computing efficiency and accuracy.

[0073] Furthermore, all collected acoustic emission signals are subjected to variational mode decomposition to obtain several intrinsic mode functions including:

[0074] Step 1: Parameter initialization: Before performing variational mode decomposition, set the required parameters, including the optimal decomposition layer number K, penalty parameter α, and convergence condition ε.

[0075] Step 2: Initialize the intrinsic mode function u k (t) and frequency center ω k .

[0076] Step 3: Iterative optimization: construct the objective function using the Lagrange multiplier method, and calculate each eigenmode function u by performing bandpass filtering on each eigenmode function. k (t); Update the corresponding frequency center ω for each eigenmode function k, ensuring that each mode is concentrated in its specific frequency band; updating the Lagrange multiplier to ensure the reconstruction accuracy of the signal and reduce the decomposition error.

[0077] Step 4: Convergence determination: repeat the iterative process in step 3 until the convergence condition is reached.

[0078] Through variational mode decomposition, complex acoustic emission signals can be decomposed into several eigenmode functions of different frequency bands. Since each eigenmode function is concentrated in a specific frequency band, this precise decomposition ensures the independence of different modal signals, and can better capture the characteristic frequencies of different stages in the bolt loosening process, greatly improving the analysis and monitoring accuracy of the loosening process.

[0079] Furthermore, the method for calculating the energy value of each eigenmode function includes:

[0080] For each intrinsic mode function IMF k (t), square it and calculate the instantaneous energy E k (t) = IMF k (t) 2 ; The instantaneous energy E of each eigenmode function k (t) Perform time integration to obtain the total energy value E of the modal function in the entire time period k , the formula is:

[0081]

[0082] Where T is the total duration of the signal.

[0083] By squaring and integrating each eigenmode function, the modal energy can be accurately calculated, which can clearly reflect the energy distribution of each eigenmode in the entire signal time period, making the energy characteristics of the signal clearer.

[0084] Furthermore, the relationship between the energy value of each eigenmode function and the change of preload at different levels is established, and the characteristic modes most sensitive to the change of preload are screened out, including:

[0085] For each eigenmode function, establish its energy value E k The relationship curve with the change of preload force F is as follows:

[0086] E k =f(F)

[0087] Draw a graph of the energy of each eigenmode function versus preload. Compare the energy curves of different eigenmode functions, analyze the magnitude of the energy value changing with preload, and select the eigenmode function with a large energy change with preload and the one that can monotonically indicate the change of preload as the characteristic mode.

[0088] By establishing a relationship curve between the energy value of the intrinsic mode function and the change in preload, the effect of the change in preload on the energy of each mode can be intuitively reflected. This relationship diagram can reveal the degree of response of different modes to the change in preload, and help to screen out the characteristic mode that is most sensitive to the change in preload, thereby improving the accurate monitoring of the loosening state of the bolt.

[0089] Furthermore, a mapping relationship between the selected characteristic modal energy and the preload force is established, and the looseness change curve is obtained, including:

[0090] Use polynomial fitting or other suitable curve fitting methods (such as exponential, logarithmic or linear regression) to fit the characteristic mode energy E 特征 The relationship between and preload force F.

[0091] By using appropriate curve fitting methods such as polynomial fitting, exponential, logarithmic or linear regression, an accurate mapping relationship between characteristic modal energy and preload can be established. This mapping relationship not only provides a quantitative evaluation basis for the bolt loosening process, but also enables visualization of preload changes, providing solid data support for accurate monitoring and early warning of bolt loosening.

[0092] Furthermore, the bolt loosening process is divided into different stages according to the loosening change curve, including:

[0093] The bolt loosening process is divided into different stages according to the slope characteristics of the loosening change curve.

[0094] Through the analysis of the loosening change curve, the bolt loosening stage can be effectively divided. The loosening characteristics of different stages are significantly different, and the stage division can provide support for the system to formulate differentiated early warning strategies. In the early loosening stage, a more sensitive early warning signal can be triggered, while in the late loosening stage, stronger alarm measures can be taken to reduce the impact of bolt loosening on structural safety.

[0095] The implementation process of a specific application example of the present invention includes:

[0096] Step 1: If Figure 2As shown, a bolt loosening acoustic emission monitoring test bench is built to collect acoustic emission signals at the bolt connection interface. The signal generator 1 outputs a 5Hz sinusoidal signal and transmits it to the power amplifier 2. The power amplifier 2 has an output voltage of 1V, which amplifies the signal and provides sufficient power for the exciter 3. The exciter 3 converts the amplified electrical signal into mechanical vibration and transmits it to the steel plate 5 through the push rod 4. The steel plates 5 and 15 are used as the medium for vibration propagation. In the experiment, they are fixed by the bench vise 13 to ensure stability. The digital display 6 displays the preload applied to the bolt 7 in real time. The M8 bolt 7 monitors the applied preload through the pressure sensor 8, and the pressure sensor transmits the measurement data to the digital display 6. The acoustic emission sensor 9 is used to detect the acoustic emission signal generated by the bolt during the loosening process. The sensor is attached to the steel plate 15 to capture the acoustic emission signal. The preamplifier 10 amplifies the weak signal from the acoustic emission sensor for processing by the acoustic emission collector 11. The acoustic emission collector converts the amplified signal into digital data and transmits it to the PC 12 for real-time monitoring, analysis and storage. The bench vise 13 fixes the steel plate, and the foundation 14 provides stable support for the entire device to ensure that the components will not be displaced or interfered during the experiment. Among them, the strength grade of the M8 bolt used is 8.8. According to the German Engineers Association standard VDI 2230: Part 1, its allowable preload is 16.5kN. In the experiment, the preload changes from 2kN to 16kN in increments of 2kN. The sampling frequency is set to 10MHz. Six sets of data are collected for each preload level.

[0097] Step 2: Use VMD to process the original AE signal. First, use the decomposition modal energy difference rate to select the parameter K so that the VMD algorithm can perform modal decomposition with the optimal decomposition layer. A group of AE signals are randomly selected for analysis, and the signal length is 0.2 seconds, which is a vibration cycle. Figure 3 The relationship between the number of decomposition layers and the decomposition modal energy difference rate is given. It can be seen that the decomposition modal energy difference rate of the AE signal after VMD decomposition reaches the maximum value when K = 4. Therefore, the optimal K value for VMD decomposition is 4.

[0098] Step 3: According to the determined optimal decomposition layer number of 4 layers, all the collected acoustic emission signals of 8 levels of preload are decomposed by VMD, and each acoustic emission signal is decomposed into 4 IMFs, namely IMF1, IMF2, IMF3, and IMF4.

[0099] Step 4: If Figures 4 to 7 As shown, the energy value of each IMF is calculated, and the relationship between the energy value of IMF1 to IMF4 and the 8 levels of preload is established. Figure 5 The energy of IMF2 is most sensitive to the change of preload and can monotonically indicate the change of preload, so the IMF2 component is selected as the characteristic mode.

[0100] Step 5: If Figure 8 As shown in the figure, the mapping relationship between the characteristic modal energy and the preload is established to obtain the loosening change curve. According to the different slopes of the loosening change curve, the loosening process is divided into three stages, namely early loosening, mid-term loosening and late loosening. Using the fitting equations of each stage, quantitative monitoring of the entire bolt loosening cycle can be achieved.

[0101] The present invention discloses a full-cycle acoustic emission monitoring method for bolt loosening based on variational modal decomposition. By combining acoustic emission technology with variational modal decomposition method, real-time monitoring of the full cycle of bolt loosening is achieved. The complex acoustic emission signal is decomposed and feature extracted using variational modal decomposition, which effectively reduces the influence of noise and external interference, thereby improving the accuracy and stability of signal processing. The method can monitor the state of bolts in different loosening stages, provides comprehensive health monitoring for bolted structures, greatly improves the safety and reliability of bolted connections, reduces the risk of equipment failures and accidents, and has important application value for ensuring the stable operation of machinery and structures.

[0102] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A full-cycle acoustic emission monitoring method for bolt loosening based on variational mode decomposition, characterized in that: include: Collect acoustic emission signals of bolt connection interfaces under several levels of preload; Performing variational modal pre-decomposition on the acoustic emission signal, performing variational modal pre-decomposition according to different decomposition levels, calculating decomposition modal energies corresponding to different decomposition levels, calculating decomposition modal energy difference rates according to the decomposition modal energies corresponding to different decomposition levels, and determining an optimal decomposition level using the decomposition modal energy difference rates; Based on the optimal decomposition layer number, performing variational modal decomposition on all collected acoustic emission signals to obtain a number of intrinsic mode functions; By calculating the energy value of each eigenmode function, the relationship between the energy value of each eigenmode function and the change of preload force at different levels is established, and the characteristic mode that is most sensitive to the change of preload force is screened out; A mapping relationship between the selected characteristic modal energy and the preload force is established to obtain a loosening change curve. The bolt loosening process is divided into different stages according to the loosening change curve to achieve quantitative monitoring of the entire bolt loosening cycle.

2. The full-cycle acoustic emission monitoring method for bolt loosening based on variational modal decomposition according to claim 1 is characterized in that: The plurality of levels of preload force satisfy a number that is greater than or equal to 8.

3. The full-cycle acoustic emission monitoring method for bolt loosening based on variational modal decomposition according to claim 1 is characterized in that: The energy in the decomposed modal energy difference rate is expressed as: Where E represents the energy of the signal, x(i) represents the acquired signal sequence, n represents the number of sampling points, and i is the i-th sampling point in the signal sequence.

4. The method for monitoring bolt loosening full-cycle acoustic emission based on variational modal decomposition according to claim 1 is characterized in that: The decomposed modal energy difference rate is expressed as: Among them, η represents the energy difference rate of the decomposed mode, E K represents the sum of the energies of all K components obtained by decomposing the Kth level, E K-1 Represents the sum of the energies of all K-1 components obtained by decomposition level K-1.

5. The method for monitoring bolt loosening in full cycle based on variational modal decomposition according to claim 1 is characterized in that: Determining the optimal number of decomposition layers using the decomposition modal energy difference rate includes: Step S1, initialize the number of decomposition layers, set the decomposition layer value, determine the search range of the decomposition layer number, set the step size, perform variational mode decomposition on the acoustic emission signal, calculate the energy of each decomposed intrinsic mode function for the set decomposition layer value, and calculate the sum of the energies of all intrinsic mode functions; Step S2, increase the number of decomposition levels by 1, and continue step S1 until the maximum value of the search range is reached, and then proceed to step S3; Step S3, comparing the decomposition modal energy difference rate corresponding to the decomposition layer value and the decomposition layer value corresponding to the maximum value of the decomposition modal energy difference rate, and determining the optimal decomposition layer number.

6. The full-cycle acoustic emission monitoring method for bolt loosening based on variational modal decomposition according to claim 1 is characterized in that: All collected acoustic emission signals are subjected to variational mode decomposition to obtain several eigenmode functions including: Step 1: Parameter initialization: Before performing variational mode decomposition, set the required parameters, including the optimal decomposition layer number K, penalty parameter α, and convergence condition ε; Step 2: Initialize the intrinsic mode function u k (t) and frequency center ω k ; Step 3: Iterative optimization: construct the objective function using the Lagrange multiplier method, and calculate each eigenmode function u by performing bandpass filtering on each eigenmode function. k (t); Update the corresponding frequency center ω for each eigenmode function k , ensuring that each mode is concentrated in its specific frequency band; updating the Lagrange multiplier to ensure the reconstruction accuracy of the signal and reduce the decomposition error; Step 4: Convergence determination: repeat the iterative process in step 3 until the convergence condition is reached.

7. The method for monitoring bolt loosening in full cycle based on variational modal decomposition according to claim 1, characterized in that: The method for calculating the energy value of each eigenmode function includes: For each intrinsic mode function IMF k (t), square it and calculate the instantaneous energy E k (t) = IMF k (t) 2 , the instantaneous energy E of each eigenmode function k (t) Perform time integration to obtain the total energy value E of the modal function in the entire time period k , the formula is: Where T is the total duration of the signal.

8. The full-cycle acoustic emission monitoring method for bolt loosening based on variational modal decomposition according to claim 1 is characterized in that: The relationship between the energy value of each eigenmode function and the change of preload at different levels is established, and the eigenmodes most sensitive to the change of preload are screened out, including: For each eigenmode function, establish its energy value E k The relationship curve with the change of preload force F is as follows: E k =f(F) The energy of each intrinsic mode function is plotted as a function of preload. The energy curves of different intrinsic mode functions are compared, the amplitude of the energy value changing with preload is analyzed, and the intrinsic mode function with a large amplitude of energy changing with preload and which can monotonically indicate the change of preload is selected as the characteristic mode.

9. The full-cycle acoustic emission monitoring method for bolt loosening based on variational modal decomposition according to claim 1 is characterized in that: The mapping relationship between the selected characteristic modal energy and the preload force is established, and the looseness change curve is obtained, including: Fit the eigenmode energy E using polynomial fitting or exponential, logarithmic or linear regression curve fitting methods 特征 The relationship between and preload force F.

10. The full-cycle acoustic emission monitoring method for bolt loosening based on variational modal decomposition according to claim 1 is characterized in that: According to the loosening change curve, the bolt loosening process is divided into different stages including: The bolt loosening process is divided into different stages according to the slope characteristics of the loosening change curve.

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