Current-carrying pipeline complex modal parameter identification method and system

Abstract

The invention belongs to the technical field of working modal analysis, and discloses a current-carrying pipeline complex modal parameter identification method and system. The method comprises the following steps: acquiring vibration responses of a plurality of measuring points on a current-carrying pipeline under load excitation; calculating a vibration response correlation function of each measuring point and the reference point; decomposing the vibration response correlation function into a series of independent intrinsic mode functions by using variational mode decomposition; dividing the intrinsic mode functions into two types: intrinsic mode functions with variable amplitude and constant amplitude; eliminating an intrinsic mode function with a constant amplitude, and establishing an intrinsic mode function matrix; performing Hilbert transformation on the intrinsic mode function matrix, and combining the intrinsic mode function matrix with a Hilbert transformation matrix thereof to obtain a signal analysis matrix; and identifying the amplitude and the phase of the complex modal shape of the current-carrying pipeline and the inherent frequency and the damping ratio of the current-carrying pipeline based on the signal analysis matrix. According to the invention, the complex mode parameters of the current-carrying pipeline in the operation state can be identified.

Description

Technical Field

[0001] The present invention belongs to the technical field of working modal analysis, and more specifically, relates to a method and system for identifying complex modal parameters of a current-carrying pipeline. Background Art

[0002] As the energy density of power equipment gradually increases, various fields have put forward higher requirements for the dynamic performance of current-carrying pipelines. In actual operation, the current-carrying pipelines may have problems of excessive local or overall vibration, which may induce fatigue damage of the pipelines, increase their leakage risk, and affect the overall safety and stability of the system. In order to ensure the safety of current-carrying pipelines, it is necessary to adopt scientific and reasonable testing and signal processing methods to establish a long-term health monitoring system for in-service pipelines, and analyze and evaluate the dynamic performance of pipelines in real time under operating conditions. Generally speaking, the dynamic characteristics of industrial structures can be described as three key modal parameters, namely, natural frequency, damping ratio and modal vibration shape. These modal parameters can usually be obtained through two methods: experimental modal analysis and operating modal analysis. Experimental modal analysis is to apply excitation force to the test structure through a hammer or exciter, and identify the modal parameters from the frequency response function of the structure. This method usually requires the size and position of the pure external force excitation applied to the structure to be known. The working modal analysis directly uses the vibration response generated by internal or external excitation of the structure under operation to identify the vibration response of the structure. The advantage of this method is that it does not require the known load form and size of the structure, so it is widely used in fields such as structural health monitoring, state assessment and intelligent control. For engineering current-carrying pipelines, since the power equipment will cause the static pressure deformation of the pipeline and the flow of the internal fluid during operation, the geometric shape and system parameters of the same current-carrying pipeline in the operating state and non-operating state may be very different. Therefore, it is difficult to invert or characterize the dynamic performance of the current-carrying pipeline in the operating state through the experimental modal analysis results in the non-operating state. In addition, due to the operating excitation interference of the power equipment connected to the pipeline in the operating state, it is difficult to conduct experimental modal analysis methods on the pipeline in the operating stage to obtain its modal parameters. Therefore, the working vibration mode analysis method has become a key method for analyzing and evaluating the dynamic performance of current-carrying pipelines with operating excitation interference.

[0003] Due to the influence of Coriolis force and centrifugal force caused by the flow of fluid in the pipe, the modal vibration shape of the running pipeline is generally a complex modal vibration shape. The existing methods are inefficient in the identification and calculation of the working vibration shape of the current-carrying pipeline, and it is even difficult to obtain the accurate complex modal vibration shape of the current-carrying pipeline. For the problem of structural complex modal parameter identification, the most commonly used method is the time-frequency analysis method based on Hilbert transform. This method extracts the instantaneous amplitude and phase from the vibration response data obtained from the test through Hilbert transform, and then uses polynomial fitting technology to identify the modal frequency, damping ratio, response amplitude and initial phase of the structure. This method is effective for single-degree-of-freedom systems or multi-degree-of-freedom systems with low degree of coupling between modes, but it is difficult to work for complex systems with dense modes or high degree of coupling between modes. Therefore, it is necessary to establish a complex modal parameter identification method for current-carrying pipelines with working load excitation (random excitation and harmonic excitation). Summary of the invention

[0004] The present invention solves the problem in the prior art that complex modal parameters of a current-carrying pipeline are difficult to identify in an operating state by providing a method and a system for identifying complex modal parameters of a current-carrying pipeline.

[0005] The present invention provides a method for identifying complex modal parameters of a current-carrying pipeline, comprising the following steps: Obtain the vibration response of several measuring points on the current-carrying pipeline under load excitation; Select a reference point and calculate the vibration response correlation function of each measuring point and the reference point; By using variational mode decomposition, the vibration response related functions under the combined excitation of harmonic load and random load are decomposed into a series of independent eigenmode functions. The intrinsic mode functions are divided into two categories: the intrinsic mode functions with variable amplitude corresponding to random load excitation and the intrinsic mode functions with constant amplitude corresponding to harmonic load excitation. Eliminate the intrinsic mode function with constant amplitude and establish the intrinsic mode function matrix; perform Hilbert transform on the intrinsic mode function matrix, and combine the intrinsic mode function matrix with its Hilbert transform matrix to obtain the signal analysis matrix; Based on the signal analysis matrix, the amplitude and phase of the complex mode vibration shape of the current-carrying pipeline, as well as the natural frequency and damping ratio of the current-carrying pipeline are identified.

[0006] Preferably, a velocity sensor or an acceleration sensor is arranged on the current-carrying pipeline to test and obtain the vibration response of the measuring point under load excitation.

[0007] Preferably, a measuring point on the current-carrying pipeline whose vibration response is greater than a first threshold and whose number of modal peaks is greater than a second threshold is selected as a reference point.

[0008] Preferably, the variational modal decomposition decomposes the vibration response related function into a superposition of a series of amplitude-frequency modulated signals, the variational modal decomposition establishes a constrained variational problem, transforms the constrained variational problem into an unconstrained variational problem through an augmented Lagrangian function, and uses the multiplication operator alternating direction method to solve the optimal solution to obtain the eigenmode function and its corresponding center frequency.

[0009] Preferably, after each iterative update of the intrinsic mode function and the center frequency, the Lagrange multiplication operator is updated first, and then the iteration is continued until the convergence condition is met.

[0010] Preferably, the set of intrinsic mode functions with varying amplitudes is expressed as: ; in, ; In the formula, For the i an intrinsic mode function with varying amplitude, For the i The amplitude of an intrinsic mode function with varying amplitude, For the i The amplitude constant of an eigenmode function with varying amplitude, For the i Damping ratio of order, For the i The natural frequency, T For delay, For the i The phase of an eigenmode function with varying amplitude, p Indicates the measuring point, q Indicates the reference point, i =1、2、……、 , is the number of eigenmode functions with varying amplitudes; The set of eigenmode functions with constant amplitude is expressed as: : in, ; In the formula, For the h An eigenmode function with constant amplitude, For the h The amplitude of an eigenmode function with constant amplitude, For the h The phase of an eigenmode function with constant amplitude, h =1, 2, ..., , is the number of eigenmode functions with constant amplitude, ,K is the total number of eigenmode functions.

[0011] Preferably, the first p Line i The elements of a column are represented as:

[0012] In the formula, is the first in the eigenmode function matrix p Line i The elements of the column, p =1, 2, ..., , is the total number of measurement points, i =1, 2, ..., , is the number of eigenmode functions with varying amplitudes; q Indicates a reference point; The signal analysis matrix p Line i The elements of a column are represented as:

[0013] in, ; In the formula, is the first p Line i Elements of a column; In the expressions of the intrinsic mode function matrix and the signal analysis matrix, is the first p Line i The magnitude of the elements of the column, is the first p Line i The magnitude constant of the elements of the column, For the i Damping ratio of order, For the i The natural frequency, is the first p Line i the phase of the elements of the column; in, , For the i The first modal frequency; Degree of freedom p and q Vibration response correlation function at frequency The phase difference at .

[0014] Preferably, the complex mode vibration shape of the current-carrying pipeline is expressed as:

[0015] In the formula, is the complex mode shape of the current-carrying pipeline, is the amplitude matrix of the complex mode shape of the current-carrying pipeline, is the phase matrix of the complex mode vibration shape of the current-carrying pipeline; by q The degrees of freedom are taken as the reference point, and we get Middle p Line i The elements of a column are represented as: ,and The q The elements of the row are all 1; by q The degrees of freedom are taken as the reference point, and we get Middle p Line i The elements of a column are represented as: ,and Middle q The elements of the row are all 0; In the formula, for Middle p Line i The elements of the column represent the first p The degree of freedom i The amplitude of the first mode shape; is the first q Line i The magnitude constant of the elements of the column; for Middle p Line i The elements of the column, Indicates the first p The degree of freedom i The phase of the first mode shape; As reference point q The frequency of the autocorrelation function of the vibration response The phase difference at .

[0016] Preferably, if the amplitude and phase of the complex modal vibration shape of the current-carrying pipeline identified based on the signal analysis matrix are time-varying, they are processed by a linear regression method to obtain the amplitude and phase of the complex modal vibration shape that are time-invariant.

[0017] In another aspect, the present invention provides a complex modal parameter identification system for a current-carrying pipeline, comprising: A vibration response acquisition module is used to acquire the vibration responses of several measuring points on the current-carrying pipeline under load excitation; A correlation function calculation module is used to select a reference point and calculate the vibration response correlation function of each measuring point and the reference point; The variational mode decomposition module is used to decompose the vibration response related functions under the joint excitation of harmonic loads and random loads into a series of independent eigenmode functions by using variational mode decomposition; A classification module is used to classify the intrinsic mode functions into two categories: the intrinsic mode functions with variable amplitudes corresponding to random load excitations and the intrinsic mode functions with constant amplitudes corresponding to harmonic load excitations; A matrix construction module, for eliminating the intrinsic mode function with a constant amplitude and establishing an intrinsic mode function matrix; and for performing a Hilbert transform on the intrinsic mode function matrix and combining the intrinsic mode function matrix with its Hilbert transform matrix to obtain a signal analysis matrix; An identification module, used for identifying the amplitude and phase of the complex modal vibration shape of the current-carrying pipeline, as well as the natural frequency and damping ratio of the current-carrying pipeline based on the signal analysis matrix; The current-carrying pipeline complex modal parameter identification system is used to execute the steps in the above-mentioned current-carrying pipeline complex modal parameter identification method.

[0018] One or more technical solutions provided in the present invention have at least the following technical effects or advantages: In order to solve the random noise and harmonic modal interference problems in the complex modal analysis of the operation of a current-carrying pipeline and realize the identification of complex modal parameters under the operation state of the current-carrying pipeline, the complex modal parameter identification scheme of the current-carrying pipeline proposed in the present invention first obtains the vibration response of several measuring points on the current-carrying pipeline under load excitation, calculates the vibration response correlation function of each measuring point and the reference point, and then uses variational mode decomposition to decompose the vibration response correlation function under the common excitation of harmonic load and random load into a series of independent intrinsic mode functions; then the intrinsic mode functions are divided into two categories: eigenmode functions with variable amplitudes corresponding to random load excitation and eigenmode functions with constant amplitudes corresponding to harmonic load excitation; then the eigenmode functions with constant amplitudes are eliminated to establish an eigenmode function matrix; the eigenmode function matrix is ​​Hilbert transformed, and the eigenmode function matrix is ​​combined with its Hilbert transform matrix to obtain a signal analysis matrix; finally, the amplitude and phase of the complex modal vibration shape of the current-carrying pipeline, as well as the natural frequency and damping ratio of the current-carrying pipeline are identified based on the signal analysis matrix.

[0019] The present invention transforms the problem of identifying the operating modal parameters of a current-carrying pipeline into the problem of decomposing and analyzing the related functions of the pipeline vibration response. The vibration response related functions are decomposed into a series of independent eigenmodal components consisting of structural modal components and harmonic components using variational modal decomposition technology. Based on the characteristics and differences of the vibration response related functions under the two load excitations derived through theoretical derivation, the harmonic components are eliminated from the decomposed eigenmodal components. On this basis, the Hilbert transform method is introduced to obtain the instantaneous amplitude and phase of each structural modal component, and the frequency, damping ratio, response amplitude and phase corresponding to each mode are extracted therefrom. The complex modal vibration shape of the current-carrying pipeline under the working state can be obtained through the transfer function analysis method.

[0020] The method proposed in the present invention is the first complex modal parameter identification method for running current-carrying pipelines. On the one hand, it can effectively eliminate the influence of harmonic excitation of pipeline operation without increasing the matrix dimension of the calculation process, avoid false modes caused by harmonic response in modal parameter identification, and enhance the reliability of the identification result; on the other hand, it parses the vibration response correlation function into independent amplitude function and phase function through Hilbert transform, and identifies the amplitude and phase of the complex modal vibration shape of the current-carrying pipeline respectively, avoiding the accumulation of real part identification errors of larger magnitude on the imaginary part identification result of smaller magnitude when the real and imaginary parts of traditional complex modal vibration shapes are simultaneously identified, thereby increasing the accuracy of the complex modal vibration shape identification result; in addition, by introducing correlation functions and variational mode decomposition, the test error of the pipeline vibration response and the vibration response phase noise induced by random excitation can be greatly suppressed, and the stability and robustness of the identification result are also enhanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 A flow chart of a method for identifying complex modal parameters of a current-carrying pipeline provided for one example of implementation of the present invention. DETAILED DESCRIPTION

[0022] In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0023] Embodiment 1: Example 1 provides a method for identifying complex modal parameters of a current-carrying pipeline, see Figure 1 , including the following steps: Obtain the vibration response of several measuring points on the current-carrying pipeline under load excitation; Select a reference point and calculate the vibration response correlation function of each measuring point and the reference point; By using variational mode decomposition, the vibration response related functions under the combined excitation of harmonic load and random load are decomposed into a series of independent eigenmode functions. The intrinsic mode functions are divided into two categories: the intrinsic mode functions with variable amplitude corresponding to random load excitation and the intrinsic mode functions with constant amplitude corresponding to harmonic load excitation. Eliminate the intrinsic mode function with constant amplitude and establish the intrinsic mode function matrix; perform Hilbert transform on the intrinsic mode function matrix, and combine the intrinsic mode function matrix with its Hilbert transform matrix to obtain the signal analysis matrix; Based on the signal analysis matrix, the amplitude and phase of the complex mode vibration shape of the current-carrying pipeline, as well as the natural frequency and damping ratio of the current-carrying pipeline are identified.

[0024] Among them, a velocity sensor or an acceleration sensor can be arranged on the current-carrying pipeline to test and obtain the vibration response of the measuring point under load excitation.

[0025] A measuring point on the current-carrying pipeline whose vibration response is greater than a first threshold and whose number of modal peaks is greater than a second threshold may be selected as a reference point.

[0026] The variational modal decomposition decomposes the vibration response related function into a superposition of a series of amplitude-frequency modulated signals. The variational modal decomposition establishes a constrained variational problem, transforms the constrained variational problem into an unconstrained variational problem by augmenting the Lagrangian function, and uses the multiplication operator alternating direction method to solve the optimal solution to obtain the eigenmode function and its corresponding center frequency. After each iterative update of the eigenmode function and the center frequency, the Lagrangian multiplication operator is updated first, and then the iteration is continued until the convergence condition is met.

[0027] Specifically, the set of intrinsic mode functions with varying amplitudes is expressed as: ; in, ; In the formula, For the i an intrinsic mode function with varying amplitude, For the i The amplitude of an intrinsic mode function with varying amplitude, For the i The amplitude constant of an eigenmode function with varying amplitude, For the i Damping ratio of order, For the i The natural frequency, T For delay, For the i The phase of an eigenmode function with varying amplitude, p Indicates the measuring point, q Indicates the reference point, i =1, 2, ..., , is the number of eigenmode functions with varying amplitudes.

[0028] The set of eigenmode functions with constant amplitude is expressed as: : in, ; In the formula, For the h An eigenmode function with constant amplitude, For the h The amplitude of an eigenmode function with constant amplitude, For the h The phase of an eigenmode function with constant amplitude, h =1, 2, ..., , is the number of eigenmode functions with constant amplitude, , K is the total number of eigenmode functions.

[0029] Specifically, the first p Line i The elements of a column are represented as:

[0030] In the formula, is the first in the eigenmode function matrix p Line i The elements of the column, p =1, 2, ..., , is the total number of measurement points, i =1, 2, ..., , is the number of eigenmode functions with varying amplitudes; q Indicates a reference point.

[0031] The signal analysis matrix p Line i The elements of a column are represented as:

[0032] in, ; In the formula, is the first p Line i Elements of a column.

[0033] In the expressions of the intrinsic mode function matrix and the signal analysis matrix, is the first p Linei The magnitude of the elements of the column, is the first p Line i The magnitude constant of the elements of the column, For the i Damping ratio of order, For the i The natural frequency, is the first p Line i The phase of the elements of the column.

[0034] in, , For the i The modal frequency, Degree of freedom p and q Vibration response correlation function at frequency The phase difference at .

[0035] Specifically, the complex mode vibration shape of the current-carrying pipeline is expressed as:

[0036] In the formula, is the complex mode shape of the current-carrying pipeline, is the amplitude matrix of the complex mode shape of the current-carrying pipeline, is the phase matrix of the complex mode shape of the current-carrying pipeline.

[0037] by q The degrees of freedom are taken as the reference point, and we get Middle p Line i The elements of a column are represented as: ,and The q The elements of a row are all 1.

[0038] by q The degrees of freedom are taken as the reference point, and we get Middle p Line i The elements of a column are represented as: ,and Middle q The elements of the row are all 0.

[0039] In the formula, for Middle p Line i The elements of the column represent the first p The degree of freedom i The amplitude of the first mode shape; is the firstq Line i The magnitude constant of the elements of the column; for Middle p Line i The elements of the column, Indicates the first p The degree of freedom i The phase of the first mode shape; As reference point q The frequency of the autocorrelation function of the vibration response The phase difference at .

[0040] In addition, if the amplitude and phase of the complex modal vibration shape of the current-carrying pipeline identified based on the signal analysis matrix are time-varying, they are processed by a linear regression method to obtain the amplitude and phase of the complex modal vibration shape that are time-invariant.

[0041] The present invention is further described below in its entirety.

[0042] Step 1: Obtain the vibration response of several measuring points on the current-carrying pipeline under load excitation.

[0043] In actual engineering, for any given operating current-carrying pipeline system, a series of velocity or acceleration sensors can be arranged to test the vibration response of each measuring point on the pipeline under the excitation of the operating load.

[0044] Step 2: Select a reference point and calculate the vibration response correlation function between each measuring point and the reference point.

[0045] Solve for each measuring point (i.e. each position, denoted as p ) and the reference point (denoted as q )'s vibration response .

[0046] In particular, the reference point can be selected based on the characteristics of the vibration response spectrum of each position, and the position with a large vibration response and a large number of modal peaks can be selected.

[0047] Step 3: Using variational mode decomposition, the vibration response related functions under the joint excitation of harmonic loads and random loads are decomposed into a series of independent eigenmode functions.

[0048] The vibration response correlation function of each measuring point is calculated using the variational mode decomposition method (VMD). Perform variational modal decomposition to separate the harmonic components and system modal components in the vibration response correlation function of the current-carrying pipeline to obtain a series of independent eigenmode functions. The specific steps of variational mode decomposition are as follows: For the calculated vibration response correlation function, the variational mode decomposition method can be used to decompose it into a superposition of a series of amplitude-frequency modulated signals, that is, It can be approximately expressed as:

[0049] In the formula, is the eigenmode function to be solved; K is the total number of eigenmode functions, for The instantaneous amplitude of for The instantaneous phase of for The instantaneous center frequency. and Compared to It changes slowly.

[0050] 1) In the VMD method, the eigenmode function and its center frequency can be obtained by solving the following variational problem:

[0051] In the formula, for K A set of eigenmode functions to be solved, is the center frequency set corresponding to this set; For delay T The partial derivative of is the Dirichlet function, is the convolution symbol.

[0052] 2) To find the optimal solution to the constrained variational problem in equation (2), the Lagrange multiplication operator is introduced: With the quadratic penalty factor υ, it is transformed into an unconstrained variational problem. The expanded Lagrangian expression is as follows: (3) In the formula, is the extended Lagrangian expression, Represents the inner product of two vectors.

[0053] 3) Use the Alternate Direction Method of Multipliers (ADMM) to find the optimal solution of equation (3). The number of eigenmodes is preset, and each modal component and its center frequency can be obtained through iterative calculation. Taking a modal component as an example, its intrinsic mode function and its corresponding center frequency can be obtained by the following equations (4) and (5).

[0054]

[0055] in, , and Respectively , and The Fourier transform of n is the number of iterations.

[0056] Based on the above description, it can be known 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 multiplication operator alternating direction method to solve the optimal solution to obtain a set of intrinsic mode functions.

[0057] 4) After each iteration of the mode and center frequency update, the Lagrange multiplication operator can be updated according to the following formula:

[0058] in, is the noise tolerance. To achieve a better noise reduction effect, the present invention sets =10 -8 .

[0059] 5) Continue the above iteration until the convergence condition is met, that is:

[0060] In the formula, ε As the convergence criterion, the present invention takes ε=1×10 -7 .

[0061] After variational mode decomposition, the vibration response related functions under the joint excitation of harmonic loads and random loads can be approximately expressed as the linear superposition of a series of orthogonal eigenmode functions.

[0062] That is, step three is mainly used to decompose the measured pipeline vibration response correlation function, and decompose the pipeline multi-line spectrum vibration response correlation function into a series of independent eigenmode functions.

[0063] Step 4: Divide the intrinsic mode functions into two categories: the intrinsic mode functions with variable amplitude corresponding to random load excitation and the intrinsic mode functions with constant amplitude corresponding to harmonic load excitation.

[0064] According to formula (8), the amplitude of the vibration response correlation function under harmonic excitation is not affected by the damping of the pipeline system, and the vibration amplitude of the correlation function is almost constant with the increase of time delay and does not change; on the contrary, the amplitude of the vibration response correlation function under random load excitation will be affected by the damping of the pipeline system, and will show a trend of attenuation or amplification with the increase of time delay. Therefore, according to the different distribution of the probability density function of the amplitude of the vibration response correlation function under the two excitations with time delay, the intrinsic mode function can be divided into two categories, namely:

[0065] It can be understood that the set of intrinsic mode functions with varying amplitudes in equation (8) is and the set of intrinsic mode functions with constant amplitude .

[0066] , .

[0067] In the formula, and denote the intrinsic mode functions with varying amplitude and constant amplitude, respectively, and are the amplitudes corresponding to the two eigenmode functions respectively; and are the phases corresponding to the two eigenmode functions; i =1, 2, ..., , h =1, 2, ..., ; and denote the number of two eigenmode functions, and .

[0068] It should be emphasized that among all the intrinsic mode functions obtained, only the modal peak with attenuation characteristics is a direct reflection of the dynamic characteristics of the pipeline system itself. Therefore, the present invention eliminates the intrinsic mode functions with constant amplitudes caused by harmonic loads and only retains the intrinsic mode functions with free attenuation characteristics to participate in the modal parameter identification calculations later. The corresponding modal function set can be expressed as:

[0069] In the formula, and Respectively i order natural frequency and damping ratio, is a constant amplitude.

[0070] Step 4: According to the changing trend of the amplitude of the intrinsic modal function of the vibration response related function, the harmonic modal response caused by harmonic excitation and the structural modal response caused by broadband random excitation are distinguished, and then the harmonic modal response is accurately filtered out to avoid the harmonic false mode affecting the identification result of the complex modal parameters of the pipeline.

[0071] Step 5: Eliminate the intrinsic mode functions with constant amplitude and establish the intrinsic mode function matrix; perform Hilbert transform on the intrinsic mode function matrix, and combine the intrinsic mode function matrix with its Hilbert transform matrix to obtain the signal analysis matrix.

[0072] After eliminating the eigenmode functions with constant amplitude, the eigenmode components with variable amplitude at all measuring points of the pipeline are substituted into equation (10) to establish the eigenmode matrix of pipeline vibration response.

[0073] (10) In the formula, represents the intrinsic mode function matrix.

[0074] Perform Hilbert transform on Y(T), and combine the original signal matrix Y(T) with its Hilbert transform matrix X(T) to obtain the signal analysis matrix Z(T).

[0075] (11) Where Z(T) is the signal analysis matrix, Y(T) is the intrinsic mode function matrix, and X(T) is the matrix obtained after Hilbert transform of the intrinsic mode function matrix.

[0076] Step 6: Based on the signal analysis matrix, the amplitude and phase of the complex modal vibration shape of the current-carrying pipeline, as well as the natural frequency and damping ratio of the current-carrying pipeline are identified.

[0077] The amplitude matrix of the signal analysis matrix is ​​expressed as follows:

[0078] The phase matrix of the signal analysis matrix is ​​expressed as follows:

[0079] If the pipeline q The degree of freedom is the reference point, and the amplitude matrix of the complex mode vibration shape of the pipeline can be obtained by the following formula:

[0080] In the formula, represents the amplitude matrix of the complex mode shape of the current-carrying pipeline, whose q All row elements are 1; Indicates the first p The degree of freedomi The amplitude of the first mode shape; The amplitude modulation matrix constructed is expressed as:

[0081] Accordingly, on the pipeline q The degree of freedom is taken as the reference point, and the phase matrix of the complex modal vibration shape of the current-carrying pipeline is obtained as follows:

[0082] In the formula, The phase matrix of the complex mode shape of the current-carrying pipeline is represented by its first q All row elements are 0; Indicates the first p The degree of freedom i The phase angle of the first mode shape; The phase modulation matrix constructed is expressed as:

[0083] The complex mode shape of the current-carrying pipeline can be expressed as:

[0084] Reference Points q The logarithmic amplitude and phase of the eigenmode component of the vibration response autocorrelation function are both linear functions of time and can be expressed as:

[0085] In the formula, is the first value in the amplitude modulation matrix Λ i Line i The elements of the column, For the i Damping ratio of order, For the i The natural frequency, T For delay, is the first q Line i The magnitude constant of the elements of the column, For the i The instantaneous phase of the first mode, For the i The modal frequency, As reference point q The vibration response autocorrelation function is at the frequency The phase difference at and Respectively represent i The logarithmic amplitude-time curve and phase-time curve slope of each eigenmode component; and are constants, and they can be solved by linear least squares method. and About delay T The linear function fitting is obtained.

[0086] The current-carrying pipeline i The natural frequency and i The order damping ratio can be expressed as:

[0087] Obviously, the complex modal parameters of the current-carrying pipeline in the operating state can be identified through equations (14), (16) and (20).

[0088] That is, step six can effectively identify the amplitude and phase of the complex modal vibration shape of the current-carrying pipeline, can solve the problem of inaccurate identification results of the complex modal vibration shape of the pipeline caused by the accumulation of numerical errors, and can accurately identify the natural frequency and damping ratio of the current-carrying pipeline.

[0089] In particular, due to the interference of test noise and error, the amplitude and phase of the identified complex mode vibration shape may be time-varying. In this case, the noise interference can be removed by linear regression method to obtain the time-invariant complex mode amplitude and phase.

[0090] In summary, Example 1 provides a method for identifying complex modal parameters of a current-carrying pipeline under harmonic excitation and broadband random excitation. By introducing variational modal decomposition, the pipeline vibration response related function is decomposed into a series of independent eigenmodal components, and then according to the constant amplitude characteristics of the eigenmodal components of the vibration response related function under harmonic excitation and the variable amplitude characteristics of the eigenmodal components of the vibration response related function under broadband random excitation given by the following formula (8), the structural modal response of the pipeline and the false modal response caused by the harmonic load are distinguished, and the eigenmodal components of the vibration response related function under harmonic excitation are eliminated, and only the eigenmodal components of the vibration response related function under broadband random excitation are retained, thereby solving the false mode problem in the identification of complex modal parameters of the current-carrying pipeline under the operating state. By using the Hilbert transform to analyze the eigenmode matrix under random excitation, the amplitude and phase of the complex modal vibration mode of the current-carrying pipeline are separately identified according to equations (14) and (16). This avoids the accumulation of real part identification errors of larger magnitude on the imaginary part identification results of smaller magnitude when the real and imaginary parts of the traditional complex modal vibration mode are simultaneously identified, thereby improving the accuracy of the complex modal vibration mode identification results.

[0091] Embodiment 2: Embodiment 2 provides a current-carrying pipeline complex modal parameter identification system, including: A vibration response acquisition module is used to acquire the vibration responses of several measuring points on the current-carrying pipeline under load excitation; A correlation function calculation module is used to select a reference point and calculate the vibration response correlation function of each measuring point and the reference point; The variational mode decomposition module is used to decompose the vibration response related functions under the joint excitation of harmonic loads and random loads into a series of independent eigenmode functions by using variational mode decomposition; A classification module is used to classify the intrinsic mode functions into two categories: the intrinsic mode functions with variable amplitudes corresponding to random load excitations and the intrinsic mode functions with constant amplitudes corresponding to harmonic load excitations; A matrix construction module, for eliminating the intrinsic mode function with a constant amplitude and establishing an intrinsic mode function matrix; and for performing a Hilbert transform on the intrinsic mode function matrix and combining the intrinsic mode function matrix with its Hilbert transform matrix to obtain a signal analysis matrix; The identification module is used to identify the amplitude and phase of the complex modal vibration shape of the current-carrying pipeline, as well as the natural frequency and damping ratio of the current-carrying pipeline based on the signal analysis matrix.

[0092] The current-carrying pipeline complex modal parameter identification system provided in Example 2 is used to execute the steps in the current-carrying pipeline complex modal parameter identification method described in Example 1.

[0093] Since the functions of each module in the current-carrying pipeline complex modal parameter identification system provided in Example 2 correspond to the steps in the current-carrying pipeline complex modal parameter identification method provided in Example 1, they can be understood by referring to the description of Example 1 and will not be repeated here.

[0094] Finally, it should be noted that the above specific implementation methods are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A method for identifying complex modal parameters of a current-carrying pipeline, characterized in that: The following steps are involved: Obtain the vibration response of several measuring points on the current-carrying pipeline under load excitation; Select a reference point and calculate the vibration response correlation function of each measuring point and the reference point; By using variational mode decomposition, the vibration response related functions under the combined excitation of harmonic load and random load are decomposed into a series of independent eigenmode functions; The intrinsic mode functions are divided into two categories: the intrinsic mode functions with variable amplitude corresponding to random load excitation and the intrinsic mode functions with constant amplitude corresponding to harmonic load excitation. Eliminate the intrinsic mode function with constant amplitude and establish the intrinsic mode function matrix; perform Hilbert transform on the intrinsic mode function matrix, and combine the intrinsic mode function matrix with its Hilbert transform matrix to obtain the signal analysis matrix; Based on the signal analysis matrix, the amplitude and phase of the complex mode vibration shape of the current-carrying pipeline, as well as the natural frequency and damping ratio of the current-carrying pipeline are identified.

2. The method for identifying complex modal parameters of a current-carrying pipeline according to claim 1, characterized in that: By arranging a velocity sensor or an acceleration sensor on the current-carrying pipeline, the vibration response of the measuring point under load excitation is tested.

3. The method for identifying complex modal parameters of a current-carrying pipeline according to claim 1, characterized in that: A measuring point on the current-carrying pipeline whose vibration response is greater than a first threshold and whose number of modal peaks is greater than a second threshold is selected as a reference point.

4. The method for identifying complex modal parameters of a current-carrying pipeline according to claim 1, characterized in that: The variational modal decomposition decomposes the vibration response related function into a superposition of a series of amplitude-frequency modulated signals. The variational modal decomposition establishes a constrained variational problem, transforms the constrained variational problem into an unconstrained variational problem through an augmented Lagrangian function, and uses the multiplication operator alternating direction method to solve the optimal solution to obtain the eigenmode function and its corresponding center frequency.

5. The method for identifying complex modal parameters of a current-carrying pipeline according to claim 4, characterized in that: After each iteration of the intrinsic mode function and the center frequency, the Lagrange multiplication operator is updated first, and then the iteration is continued until the convergence condition is met.

6. The method for identifying complex modal parameters of a current-carrying pipeline according to claim 1, characterized in that: The set of intrinsic mode functions with varying amplitudes is expressed as: ; in, ; In the formula, For the i an intrinsic mode function with varying amplitude, For the i The amplitude of an intrinsic mode function with varying amplitude, For the i The amplitude constant of an eigenmode function with varying amplitude, For the i Damping ratio of order, For the i The natural frequency, T For delay, For the i The phase of an eigenmode function with varying amplitude, p Indicates the measuring point, q Indicates the reference point, i =1、2、……、 , is the number of eigenmode functions with varying amplitudes; The set of eigenmode functions with constant amplitude is expressed as: : in, ; In the formula, For the h An eigenmode function with constant amplitude, For the h The amplitude of an eigenmode function with constant amplitude, For the h The phase of an eigenmode function with constant amplitude, h =1、2、……、 , is the number of eigenmode functions with constant amplitude, , K is the total number of eigenmode functions.

7. The method for identifying complex modal parameters of a current-carrying pipeline according to claim 1, characterized in that: The eigenmode function matrix p Line i The elements of a column are represented as: In the formula, is the first in the eigenmode function matrix p Line i The elements of the column, p =1、2、……、 , is the total number of measurement points, i =1、2、……、 , is the number of eigenmode functions with varying amplitudes; q Indicates a reference point; The signal analysis matrix p Line i The elements of a column are represented as: in, ; In the formula, is the first p Line i Elements of a column; In the expressions of the intrinsic mode function matrix and the signal analysis matrix, is the first p Line i The magnitude of the elements of the column, is the first p Line i The magnitude constant of the elements of the column, For the i Damping ratio of order, For the i The natural frequency, is the first p Line i the phase of the elements of the column; in, , For the i The first modal frequency; Degree of freedom p and q Vibration response correlation function at frequency The phase difference at .

8. The method for identifying complex modal parameters of a current-carrying pipeline according to claim 7, characterized in that: The complex mode vibration shape of the current-carrying pipeline is expressed as: In the formula, is the complex mode shape of the current-carrying pipeline, is the amplitude matrix of the complex mode shape of the current-carrying pipeline, is the phase matrix of the complex mode shape of the current-carrying pipeline; by q The degrees of freedom are taken as the reference point, and we get Middle p Line i The elements of a column are represented as: ,and The q The elements of the row are all 1; by q The degrees of freedom are taken as the reference point, and we get Middle p Line i The elements of a column are represented as: ,and Middle q The elements of the row are all 0; In the formula, for Middle p Line i The elements of the column represent the first p The degree of freedom i The amplitude of the first mode shape; is the first q Line i The magnitude constant of the elements of the column; for Middle p Line i The elements of the column, Indicates the first p The degree of freedom i The phase of the first mode shape; As reference point q The vibration response autocorrelation function at frequency The phase difference at .

9. The method for identifying complex modal parameters of a current-carrying pipeline according to claim 1, characterized in that: If the amplitude and phase of the complex modal vibration shape of the current-carrying pipeline identified based on the signal analysis matrix are time-varying, they are processed by a linear regression method to obtain the amplitude and phase of the complex modal vibration shape that are time-invariant.

10. A complex modal parameter identification system for a current-carrying pipeline, characterized in that: include: A vibration response acquisition module is used to acquire the vibration responses of several measuring points on the current-carrying pipeline under load excitation; A correlation function calculation module is used to select a reference point and calculate the vibration response correlation function of each measuring point and the reference point; The variational mode decomposition module is used to decompose the vibration response related functions under the joint excitation of harmonic loads and random loads into a series of independent eigenmode functions by using variational mode decomposition; A classification module is used to classify the intrinsic mode functions into two categories: the intrinsic mode functions with variable amplitudes corresponding to random load excitations and the intrinsic mode functions with constant amplitudes corresponding to harmonic load excitations; A matrix construction module, for eliminating the intrinsic mode function with a constant amplitude and establishing an intrinsic mode function matrix; and for performing a Hilbert transform on the intrinsic mode function matrix and combining the intrinsic mode function matrix with its Hilbert transform matrix to obtain a signal analysis matrix; An identification module, used for identifying the amplitude and phase of the complex modal vibration shape of the current-carrying pipeline, as well as the natural frequency and damping ratio of the current-carrying pipeline based on the signal analysis matrix; The current-carrying pipeline complex modal parameter identification system is used to execute the steps in the current-carrying pipeline complex modal parameter identification method as described in any one of claims 1-9.

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