A method and system for identifying the type of narrow-band spectral vibration-induced load in a current-carrying pipeline

Abstract

The present invention belongs to the technical field of load identification, and discloses a method and system for identifying the type of narrow-band spectral vibration-induced load in a current-carrying pipeline. The present invention uses variational mode decomposition technology to decompose the autocorrelation function of the measured vibration response to obtain an ensemble of intrinsic mode functions. On this basis, statistical methods are used to obtain the probability density function of each intrinsic mode function, and the correlation coefficient between it and the probability density function of the autocorrelation function of the vibration response under the excitation of a standard discrete-spectrum load is calculated. Finally, the calculated correlation coefficient is compared with a set threshold to identify whether the narrow-band spectral vibration-induced load type in the current-carrying pipeline is induced by a discrete-spectrum load or a continuous-spectrum load. The present invention can distinguish what type of load induces the narrow-band spectrum of the vibration of the current-carrying pipeline, and can lay a foundation for improving the governance efficiency of the narrow-band spectrum of vibration.

Description

Technical Field

[0001] The present invention belongs to the technical field of load identification, and more specifically, relates to a method and system for identifying the types of vibration-induced loads in a current-carrying pipeline with narrow-band spectra. Background Art

[0002] As the "blood vessels" of the power system, current-carrying pipelines are widely used in fields such as ships. During operation, the fluid medium inside the pipeline flows rapidly under the drive of power sources such as pumps. As the main sound source, on the one hand, the unbalanced force generated by its operation will cause mechanical vibration of the pipeline; on the other hand, the rotation of its impeller drives the fluid medium to flow, generating pressure waves in the fluid and inducing vibration of the pipeline; in addition, when the driven fluid flows in the pipeline, it will excite the turbulent pressure pulsation of the fluid inside the pipeline, which will also cause vibration of the structure. Due to the influence of many excitation sources such as mechanical unbalanced forces, sound source pressure waves, and fluid turbulent pulsation pressures, the pipeline vibration presents multi-narrow-band spectral characteristics. The vibration narrow-band spectra may induce fatigue damage to the pipeline structure and also reduce the acoustic stealth performance of military ships, increasing the risk of detection.

[0003] Generally speaking, the types of excitations received by current-carrying pipelines are mainly divided into two categories, namely continuous-spectrum loads and discrete-spectrum loads. Correspondingly, the vibration narrow-band spectra of current-carrying pipelines can also be divided into modal narrow-band spectra at the natural frequencies induced by continuous-spectrum loads and harmonic narrow-band spectra at the excitation frequencies induced by discrete-spectrum loads. The modal narrow-band spectra are often suppressed by increasing the pipeline damping and optimizing the pipeline structure mode, and the harmonic narrow-band spectra are often controlled by optimizing the pump source structure or reducing the connection stiffness between the pump source and the pipeline connection parts. Given that there are huge differences in the vibration control ideas for the narrow-band spectra induced by the two excitation loads, therefore, in order to ensure the effectiveness of vibration control measures in practice and improve the efficiency of narrow-band spectrum control, it is necessary to be able to identify the types of induced loads corresponding to each vibration narrow-band spectrum.

[0004] However, since the time-frequency signal characteristics of the vibration response of current-carrying pipelines under continuous-spectrum and discrete-spectrum excitations are not yet mastered, it is very difficult to directly distinguish from the perspective of measured data processing which type of load induces the vibration narrow-band spectrum of the current-carrying pipeline. Summary of the Invention

[0005] The present invention provides a method and system for identifying the types of vibration-induced loads in a current-carrying pipeline with narrow-band spectra, solving the problem that it is difficult to identify the types of vibration-induced loads in a current-carrying pipeline with narrow-band spectra based on measured data in the prior art.

[0006] The present invention provides a method for identifying the types of vibration-induced loads in a current-carrying pipeline with narrow-band spectra, including the following steps:

[0007] Test a number of measuring points on the current-carrying pipeline to obtain the vibration responses of each measuring point;

[0008] Perform autocorrelation analysis on the vibration responses of each measuring point to obtain the autocorrelation functions of the vibration responses of each measuring point;

[0009] Perform variational mode decomposition on the autocorrelation functions of the vibration responses of each measuring point to obtain a set of intrinsic mode functions;

[0010] Use statistical methods to obtain the probability density functions of each intrinsic mode function;

[0011] Calculate the correlation coefficients between the probability density functions of each intrinsic mode function and the probability density function of the autocorrelation function of the vibration response under the excitation of the standard discrete spectrum load;

[0012] Compare the calculated correlation coefficients with a set threshold; if the correlation coefficient is greater than or equal to the set threshold, the narrowband spectrum vibration-induced load type corresponding to the intrinsic mode function is identified as induced by the discrete spectrum load; otherwise, it is identified as induced by the continuous spectrum load.

[0013] Preferably, the vibration responses of each measuring point are measured by using velocity sensors or acceleration sensors arranged on the current-carrying pipeline.

[0014] Preferably, the vibration responses of each measuring point obtained by measurement are multi-narrowband spectrum vibration responses.

[0015] Preferably, the intrinsic mode functions obtained by the variational mode decomposition are single-narrowband spectrum intrinsic mode functions.

[0016] Preferably, if the intrinsic mode functions obtained by the variational mode decomposition are multi-narrowband spectrum intrinsic mode functions, then perform secondary data processing based on the blind source separation method of virtual multi-channels to obtain intrinsic mode functions that meet the orthogonality requirements.

[0017] Preferably, the variational mode decomposition decomposes the autocorrelation function of the vibration response into a superposition of a series of amplitude-modulated and frequency-modulated signals, and the autocorrelation function of the vibration response is expressed as:

[0018]

[0019] In the formula, represents the autocorrelation function of the vibration response, represents the k th intrinsic mode function, K represents the number of intrinsic mode functions, represents instantaneous amplitude, represents instantaneous phase, represents instantaneous center frequency.

[0020] Preferably, the variational mode decomposition establishes a constrained variational problem, transforms the constrained variational problem into an unconstrained variational problem through an augmented Lagrangian function, and uses the alternating direction method of multipliers to solve for the optimal solution, obtaining a set of intrinsic mode functions.

[0021] Preferably, the obtaining of the probability density function of each intrinsic mode function by using a statistical method includes:

[0022] Dividing the value range of the intrinsic mode function into L equally spaced intervals, and obtaining the probability density function value of the intrinsic mode function in each interval by counting the number of data points falling within the interval;

[0023]

[0024] In the formula, represents the probability density function value of the k th intrinsic mode function in the i th interval, represents the k th intrinsic mode function, represents the lower limit value of the i th interval, represents the width of the i th interval, N represents the total number of measured data points, represents the number of data points falling within the interval ;

[0025] Among them,

[0026]

[0027] In the formula, and respectively represent the maximum and minimum values corresponding to the value range of the k th intrinsic mode function, L represents the total number of intervals, i = 1, 2,..., L ;

[0028] After obtaining the probability density function values of the intrinsic mode function in each interval, represent the probability density function of the intrinsic mode function as a function of the interval center value; among them, the probability density function of the k th intrinsic mode function is denoted as , , represents the center value of the i th interval.

[0029] Preferably, the probability density function of the autocorrelation function of the vibration response under the standard discrete spectrum load excitation is expressed as:

[0030]

[0031] wherein, represents the probability density function of the autocorrelation function of the vibration response under the standard discrete spectrum load excitation corresponding to the k th intrinsic mode function.

[0032] On the other hand, the present invention provides a system for identifying the type of narrowband spectrum vibration-induced load in a current-carrying pipeline, including:

[0033] A vibration response acquisition module, configured to test and obtain the vibration responses of a plurality of measuring points on the current-carrying pipeline;

[0034] An autocorrelation analysis module, configured to perform autocorrelation analysis on the vibration responses of each measuring point to obtain the autocorrelation function of the vibration response of each measuring point;

[0035] A variational mode decomposition module, configured to perform variational mode decomposition on the autocorrelation function of the vibration response of each measuring point to obtain a set of intrinsic mode functions;

[0036] A probability density function acquisition module, configured to obtain the probability density function of each intrinsic mode function by using a statistical method;

[0037] A correlation coefficient calculation module, configured to calculate the correlation coefficient between the probability density function of each intrinsic mode function and the probability density function of the autocorrelation function of the vibration response under the standard discrete spectrum load excitation;

[0038] A type identification module, configured to compare the calculated correlation coefficient with a set threshold; if the correlation coefficient is greater than or equal to the set threshold, the type of narrowband spectrum vibration-induced load corresponding to the intrinsic mode function is identified as being induced by a discrete spectrum load; otherwise, it is identified as being induced by a continuous spectrum load;

[0039] The system for identifying the type of narrowband spectrum vibration-induced load in the current-carrying pipeline is used to execute the steps in the above-mentioned method for identifying the type of narrowband spectrum vibration-induced load in the current-carrying pipeline.

[0040] One or more technical solutions provided in the present invention have at least the following technical effects or advantages:

[0041] The present invention decomposes the autocorrelation function of the measured vibration response by using variational mode decomposition technology to obtain a set of intrinsic mode functions. On this basis, statistical methods are used to obtain the probability density functions of each intrinsic mode function, and the correlation coefficient between its probability density function and the probability density function of the autocorrelation function of the vibration response under the excitation of the standard discrete spectrum load is calculated. Finally, the calculated correlation coefficient is compared with a set threshold value to identify whether the narrowband spectrum vibration-induced load type of the current-carrying pipeline is induced by discrete spectrum load or continuous spectrum load. That is, the present invention can distinguish from the measured data what type of load induces the narrowband spectrum of the vibration of the current-carrying pipeline, which can lay a foundation for improving the treatment efficiency of the narrowband spectrum of vibration. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 FIG. is a flowchart of a method for identifying the type of narrowband spectrum vibration-induced load of a current-carrying pipeline provided in Embodiment 1 of the present invention.

[0043] Figure 2 is the theoretical probability density curve; wherein, Figure 2 in (a) is the probability density curve of the autocorrelation function of the pipeline vibration response under the action of continuous spectrum load, Figure 2 in (b) is the probability density curve of the autocorrelation function of the vibration response of the current-carrying pipeline under the action of discrete spectrum load. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0044] In order to better understand the above technical solutions, the following will describe the above technical solutions in detail in conjunction with the accompanying drawings of the specification and specific embodiments.

[0045] Embodiment 1:

[0046] Embodiment 1 provides a method for identifying the type of narrowband spectrum vibration-induced load of a current-carrying pipeline. Refer to Figure 1 , which includes the following steps:

[0047] Step 1: Test a number of measuring points on the current-carrying pipeline to obtain the vibration responses of each measuring point.

[0048] For any operating current-carrying pipeline system in actual engineering, a series of velocity or acceleration sensors can be arranged to test the vibration responses of multiple narrowband spectra at each measuring point on the pipeline.

[0049] Step 2: Perform autocorrelation analysis on the vibration responses of each measuring point to obtain the autocorrelation function of the vibration response of each measuring point.

[0050] Perform autocorrelation analysis on the vibration responses of multiple narrowband spectra of each measuring point (denoted as p point), and the autocorrelation function of the vibration response of p point can be obtained .

[0051] Step 3: Perform variational mode decomposition on the autocorrelation function of the vibration response at each measurement point to obtain a set of intrinsic mode functions.

[0052] Generally, the intrinsic mode functions obtained through the variational mode decomposition are intrinsic mode functions with single narrow-band spectra. In special cases, such as when the test noise is relatively high and the orthogonality of the decomposed intrinsic mode functions is insufficient, the intrinsic mode functions are still a type of multi-narrow-band spectral mode functions. In this case, secondary data processing can be performed through a blind source separation method based on virtual multi-channels to make the orthogonality of the obtained intrinsic mode functions meet the requirements. That is, if the intrinsic mode functions obtained through the variational mode decomposition are multi-narrow-band spectral intrinsic mode functions, then secondary data processing is performed through a blind source separation method based on virtual multi-channels to obtain intrinsic mode functions that meet the orthogonality requirements.

[0053] That is, this step mainly decomposes the autocorrelation function of the vibration response with multi-narrow-band spectra into a series of independent intrinsic mode functions with single narrow-band spectra.

[0054] Specifically, use the variational mode decomposition method to p the autocorrelation function of the vibration response at the point for variational mode decomposition to obtain a series of independent intrinsic mode functions . The specific steps of the variational mode decomposition are as follows:

[0055] Use the variational mode decomposition method to decompose the autocorrelation function of the vibration response into a superposition of a series of amplitude-modulated and frequency-modulated signals. The autocorrelation function of the vibration response is expressed as:

[0056]

[0057] In the formula, represents the autocorrelation function of the vibration response, represents the k th intrinsic mode function, K represents the number of intrinsic mode functions, represents 's instantaneous amplitude, represents 's instantaneous phase, represents 's instantaneous center frequency. and are slowly varying compared to .

[0058] In the variational mode decomposition method, the intrinsic mode functions and their center frequencies can be obtained by solving the following variational problem:

[0059]

[0060] In the formula, is a set of K eigenmode functions to be solved, is the set of central frequencies corresponding to the set of eigenmode functions, is the partial derivative with respect to the time delay T, is the Dirichlet function, j is the imaginary number, T is the time delay, is the convolution symbol.

[0061] To find the optimal solution of the constrained variational problem in the above equation, the Lagrange multiplier operator and the quadratic penalty factor υ are introduced to transform it into an unconstrained variational problem. The extended Lagrangian expression is as follows:

[0062]

[0063] In the formula, represents the extended Lagrangian expression, represents the inner product of two vectors.

[0064] Use the alternating direction method of multipliers to solve the optimal solution of the above expression, and obtain the set of eigenmode functions of the autocorrelation function of the vibration response .

[0065] Based on the above description, it can be seen that the present invention uses the variational mode decomposition to establish a constrained variational problem, transforms the constrained variational problem into an unconstrained variational problem through the augmented Lagrangian function, and uses the alternating direction method of multipliers to solve the optimal solution to obtain the set of eigenmode functions.

[0066] Step 4: Use statistical methods to obtain the probability density function of each eigenmode function.

[0067] Specifically, the use of statistical methods to obtain the probability density function of each eigenmode function includes: dividing the value range of the eigenmode function into L equally spaced intervals, and by counting the number of data points falling within the intervals, obtaining the probability density function values of the eigenmode function in each interval;

[0068]

[0069] In the formula, represents the probability density function value of the k th eigenmode function in the i th interval; represents the k th eigenmode function, that is, the above-mentioned ; represents the lower limit value of the i th interval, represents the width of the i th interval, N represents the total number of measured data points, represents the number of data points falling within the interval .

[0070] Among them,

[0071]

[0072] In the formula, and respectively represent the maximum and minimum values corresponding to the value range of the k th intrinsic mode function, L represents the total number of intervals, i = 1, 2, …, L .

[0073] After obtaining the probability density function values of the intrinsic mode functions in each interval, the probability density function of the intrinsic mode function is characterized as a function of the interval central value; among them, the probability density function of the k th intrinsic mode function is denoted as , , represents the central value of the i th interval.

[0074] Step 5: Calculate the correlation coefficient between the probability density function of each intrinsic mode function and the probability density function of the autocorrelation function of the vibration response under the standard discrete spectrum load excitation.

[0075] Among them, the probability density function of the autocorrelation function of the vibration response under the standard discrete spectrum load excitation is expressed as:

[0076]

[0077] In the formula, represents the probability density function of the autocorrelation function of the vibration response under the standard discrete spectrum load excitation corresponding to the k th intrinsic mode function, simply referred to as the standard function.

[0078] The calculation formula of the correlation coefficient is as follows:

[0079]

[0080] In the formula, represents the correlation coefficient; represents the probability density function of the k th intrinsic mode function, that is, the appearing in the above text; Indicates a standard function, i.e., the one that appeared in the above text ; Indicates covariance calculation; Indicates variance calculation.

[0081] Step 6: Compare the calculated correlation coefficient with the set threshold; if the correlation coefficient is greater than or equal to the set threshold, the narrowband spectral vibration induced load type corresponding to the intrinsic mode function is identified as being induced by discrete spectral load; otherwise, it is identified as being induced by continuous spectral load.

[0082] There are differences in the probability density of the autocorrelation function of the pipeline narrowband spectral vibration under discrete spectral and continuous spectral excitations, as can be seen in Figure 2 , where Figure 2 (a) in is the probability density curve of the autocorrelation function of the pipeline vibration response under continuous spectral load, Figure 2 (b) in is the probability density curve of the autocorrelation function of the vibration response of the current-carrying pipeline under discrete spectral load. It can be seen that the probability distribution of the autocorrelation function of the vibration response under continuous spectral load shows a unimodal characteristic, and the probability distribution of the autocorrelation function of the vibration response under discrete spectral load shows a bimodal characteristic. The present invention utilizes the differences in the probability distributions of the pipeline vibration autocorrelation functions under the two excitation types, establishes the probability density function of the autocorrelation function of the vibration response under standard discrete spectral load excitation, calculates the correlation coefficient, and identifies the induced load type of each vibration narrowband spectrum through the calculated correlation coefficient.

[0083] The value range of the correlation coefficient is , The larger the value, the higher the correlation between the probability density function of the k th intrinsic mode function obtained by variational mode decomposition and the standard function, indicating that the probability that the k th narrowband spectrum of the measured vibration response is induced by discrete spectral load is higher; on the contrary, The smaller the value, the lower the correlation between the approximate probability density function of the k th intrinsic mode function obtained by variational mode decomposition and the standard function, indicating that the probability that the k th narrowband spectrum of the measured vibration response is induced by continuous spectral load is higher.

[0084] Considering that the length of the measured vibration response data sequence is limited and the amplitude attenuation degree of the intrinsic mode function of the vibration response under continuous spectral load excitation is small, the present invention divides the intrinsic mode functions into two categories by judging whether the correlation coefficient between the probability density function of the intrinsic mode function and the standard function meets the strong correlation requirement (for example, judging whether it meets ): The intrinsic mode functions corresponding to the narrowband spectrum are identified as being induced by discrete spectral load, while The narrowband spectrum corresponding to the intrinsic mode function is identified as being induced by continuous spectrum load.

[0085] In summary, the method for identifying the type of vibration-induced load of the narrowband spectrum of the current-carrying pipeline provided in Embodiment 1 uses the variational mode decomposition technique to decompose the autocorrelation function of the measured vibration response, and obtains a series of orthogonal intrinsic mode functions. On this basis, the probability density function of each intrinsic mode function is obtained by using statistical methods, and the correlation coefficient between it and the probability density function of the autocorrelation function of the vibration response under the excitation of the standard discrete spectrum load is calculated. By analyzing the correlation between the two probability density functions, the type of induced load (discrete spectrum load or continuous spectrum load) of the vibration narrowband spectrum is identified.

[0086] In addition, when identifying the type of vibration-induced load of the narrowband spectrum of the current-carrying pipeline in Embodiment 1, only the measured vibration response data of the current-carrying pipeline is used, and it is not necessary to establish a numerical model of the actual current-carrying pipeline. It has the advantages of high efficiency and good reliability, and provides a new idea for identifying the type of vibration-induced load of the narrowband spectrum of the pipeline.

[0087] Embodiment 2:

[0088] Embodiment 2 provides a system for identifying the type of vibration-induced load of the narrowband spectrum of a current-carrying pipeline, including:

[0089] A vibration response acquisition module for testing and obtaining the vibration responses of several measuring points on the current-carrying pipeline;

[0090] An autocorrelation analysis module for performing autocorrelation analysis on the vibration responses of each measuring point to obtain the autocorrelation function of the vibration response of each measuring point;

[0091] A variational mode decomposition module for performing variational mode decomposition on the autocorrelation function of the vibration response of each measuring point to obtain a set of intrinsic mode functions;

[0092] A probability density function acquisition module for obtaining the probability density function of each intrinsic mode function by using statistical methods;

[0093] A correlation coefficient calculation module for calculating the correlation coefficient between the probability density function of each intrinsic mode function and the probability density function of the autocorrelation function of the vibration response under the excitation of the standard discrete spectrum load;

[0094] A type identification module for comparing the calculated correlation coefficient with a set threshold; if the correlation coefficient is greater than or equal to the set threshold, the narrowband spectrum vibration-induced load type corresponding to the intrinsic mode function is identified as being induced by a discrete spectrum load; otherwise, it is identified as being induced by a continuous spectrum load.

[0095] The system for identifying the type of narrowband spectral vibration induced load of the current-carrying pipeline provided in Embodiment 2 is used to execute the steps in the method for identifying the type of narrowband spectral vibration induced load of the current-carrying pipeline as described in Embodiment 1.

[0096] Since the functions of the modules in the system for identifying the type of narrowband spectral vibration induced load of the current-carrying pipeline provided in Embodiment 2 correspond to the steps in the method for identifying the type of narrowband spectral vibration induced load of the current-carrying pipeline provided in Embodiment 1, reference can be made to the description of Embodiment 1 for understanding Embodiment 2, and details are not repeated here.

[0097] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the examples, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for identifying the type of narrow-band spectral vibration-induced load in a current-carrying pipeline, characterized in that, It includes the following steps: Test several measuring points on the current-carrying pipeline to obtain the vibration responses of each measuring point; Perform autocorrelation analysis on the vibration responses of each measuring point to obtain the autocorrelation function of the vibration response of each measuring point; Perform variational mode decomposition on the autocorrelation function of the vibration response of each measuring point to obtain a set of intrinsic mode functions; Use statistical methods to obtain the probability density function of each intrinsic mode function; Calculate the correlation coefficient between the probability density function of each intrinsic mode function and the probability density function of the autocorrelation function of the vibration response under the excitation of the standard discrete spectrum load; Compare the calculated correlation coefficient with a set threshold; if the correlation coefficient is greater than or equal to the set threshold, the narrowband spectrum vibration-induced load type corresponding to the intrinsic mode function is identified as induced by the discrete spectrum load; Otherwise, it is identified as induced by the continuous spectrum load.

2. The method for identifying the type of narrowband spectral vibration-induced load of a current-carrying pipeline according to claim 1, wherein Use velocity sensors or acceleration sensors arranged on the current-carrying pipeline to test and obtain the vibration responses of each measuring point.

3. The method for identifying the type of narrow-band spectral vibration-induced load of a current-carrying pipeline according to claim 1, wherein The vibration responses of each measuring point obtained by testing are multi-narrowband spectrum vibration responses.

4. The method for identifying the type of narrow-band spectral vibration-induced load of a current-carrying pipeline according to claim 1, wherein The intrinsic mode functions obtained by the variational mode decomposition are single-narrowband spectrum intrinsic mode functions.

5. The method for identifying the type of narrow-band spectral vibration-induced load of a current-carrying pipeline according to claim 1, wherein If the intrinsic mode functions obtained by the variational mode decomposition are multi-narrowband spectrum intrinsic mode functions, perform secondary data processing based on the blind source separation method of virtual multi-channels to obtain intrinsic mode functions that meet the orthogonality requirements.

6. The method for identifying the type of narrow-band spectral vibration-induced load of a current-carrying pipeline according to claim 1, wherein The variational mode decomposition decomposes the autocorrelation function of the vibration response into a superposition of a series of amplitude-modulated and frequency-modulated signals, and the autocorrelation function of the vibration response is expressed as: In the formula, represents the autocorrelation function of the vibration response, represents the k th intrinsic mode function, K represents the number of intrinsic mode functions, represents the instantaneous amplitude of represents the instantaneous phase of represents the instantaneous center frequency of 7. The method for identifying the type of narrow-band spectral vibration-induced load of a current-carrying pipeline according to claim 6, wherein The variational mode decomposition establishes a constrained variational problem, transforms the constrained variational problem into an unconstrained variational problem through the augmented Lagrangian function, and uses the alternating direction method of multipliers to solve for the optimal solution to obtain a set of intrinsic mode functions.

8. The method for identifying the type of vibration-induced load in a current-carrying pipeline narrowband spectrum according to claim 1, characterized in that, The use of statistical methods to obtain the probability density function of each intrinsic mode function includes: Divide the value range of the intrinsic mode function into L equally spaced intervals, and obtain the probability density function values of the intrinsic mode function in each interval by counting the number of data points falling within the intervals; In the formula, represents k the probability density function value of the i th intrinsic mode function in the th interval, k represents the th intrinsic mode function, i represents the lower limit value of the th interval, i represents the width of the N th interval, represents the total number of measured data points, represents the number of data points falling within the interval Wherein, Wherein, and respectively represent the maximum value and the minimum value corresponding to the value range of the k th intrinsic mode function, L represents the total number of intervals, i = 1, 2, …, L ; After obtaining the probability density function values of the intrinsic mode functions in each interval, the probability density function of the intrinsic mode function is characterized as a function of the interval center value; where the probability density function of the k th intrinsic mode function is denoted as , , represents the center value of the i th interval.

9. The method for identifying the type of narrow-band spectral vibration-induced load of a current-carrying pipeline according to claim 8, wherein The probability density function of the autocorrelation function of the vibration response under the excitation of the standard discrete spectrum load is expressed as: In the formula, represents the probability density function of the autocorrelation function of the vibration response under the excitation of the standard discrete spectrum load corresponding to the k th intrinsic mode function.

10. A narrow-band spectral vibration-induced load type identification system for current-carrying pipelines, characterized in that, It includes: A vibration response acquisition module for testing and obtaining the vibration responses of several measuring points on the current-carrying pipeline; An autocorrelation analysis module for performing autocorrelation analysis on the vibration responses of each measuring point to obtain the autocorrelation function of the vibration response of each measuring point; A variational mode decomposition module for performing variational mode decomposition on the autocorrelation function of the vibration response of each measuring point to obtain a set of intrinsic mode functions; A probability density function acquisition module for using statistical methods to obtain the probability density function of each intrinsic mode function; A correlation coefficient calculation module for calculating the correlation coefficient between the probability density function of each intrinsic mode function and the probability density function of the autocorrelation function of the vibration response under the excitation of the standard discrete spectrum load; A type identification module for comparing the calculated correlation coefficient with a set threshold; if the correlation coefficient is greater than or equal to the set threshold, the narrowband spectrum vibration-induced load type corresponding to the intrinsic mode function is identified as induced by the discrete spectrum load; Otherwise, it is identified as induced by the continuous spectrum load; The narrowband spectrum vibration-induced load type identification system for the current-carrying pipeline is used to execute the steps in the narrowband spectrum vibration-induced load type identification method for the current-carrying pipeline as described in any one of claims 1-9.

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