Sensor additional mass elimination method and device suitable for lead modal vibration test

Abstract

The invention discloses a sensor additional mass elimination method and device suitable for a lead modal vibration test, and belongs to the technical field of modal tests.The method comprises the steps that a vibration test is conducted on an overhead lead based on a preset impact force signal, so that a sensor collects acceleration data, and a frequency response function matrix is constructed; rewriting the frequency response function matrix into a linear frequency response equation containing a polynomial coefficient to be solved; solving the polynomial coefficient to be solved by adopting a singular value decomposition method to obtain a test modal parameter; constructing a sensor additional mass matrix by measuring the mass of the sensor and the mounting position of the sensor; constructing a kinetic equation of sensorless additional mass; and adopting a Newton-Raphson iteration method to carry out iterative solution on the kinetic equation based on the test modal parameter and the sensor additional mass matrix to obtain a modal parameter without sensor additional mass. By implementing the invention, the problem that the additional quality influence of the sensor in the prior art is difficult to eliminate can be solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of modal testing, in particular to a sensor additional mass elimination method and device suitable for conductor modal vibration test. BACKGROUND

[0002] Test modal analysis is an important method for structural dynamic design and equipment fault diagnosis by identifying modal parameters through test of collected system input and output signals. In the process of modal vibration test of overhead conductor, acceleration sensors need to be arranged on the test conductor. The acceleration sensors installed on the conductor will introduce additional mass to the conductor vibration system. When the mass of the structure increases, the modal frequency of the structure will inevitably decrease, and the degree of influence will gradually increase with the increase of the modal order. Especially for the conductor structure with small diameter, the influence of additional mass caused by the sensor is more severe. Some scholars believe that when the total mass of the structure is much larger than the mass of the sensor, the additional mass introduced by the sensor will not have a significant impact on the structure. However, it is worth noting that the part of the structure that participates in the modal is not the total mass of the structure, but the effective mass that is active on the modal. The ratio of the mass of the sensor to the total mass of the structure may be very small, but the ratio of the mass of the sensor to the active part of the mass on the modal may be very large. At this time, the additional mass of the sensor will have a serious impact on the modal. Therefore, in order to accurately obtain the vibration modal parameters measured in the conductor vibration modal test, it is necessary to propose a method for removing the additional mass of the sensor.

[0003] At present, the methods for eliminating the influence of additional mass of the sensor include: 1. changing the mass of the sensor to eliminate the influence of additional mass of the sensor in the transfer function by repeated test, but this method needs to perform inverse operation on a matrix which is easily disturbed by measurement noise and is prone to ill-condition, and the numerical calculation stability is poor. 2. through the modification of variable stiffness acceleration sensor, the additional mass caused by the sensor is compensated by the change of stiffness, but this method needs to redesign the body of the acceleration sensor, which is time-consuming and laborious and does not have universality. SUMMARY

[0004] The present application provides a sensor additional mass elimination method and device suitable for conductor modal vibration test, which can solve the problem that the influence of additional mass of the sensor is difficult to eliminate in the prior art.

[0005] In order to solve the above technical problems, the present application provides a sensor additional mass elimination method suitable for conductor modal vibration test, comprising:

[0006] Based on the preset impact force signal, the vibration test is performed on the overhead conductor, so that the acceleration data of the plurality of sensors on the overhead conductor are collected;

[0007] constructing a frequency response function matrix based on the preset impact force signal and the acceleration data;

[0008] rewriting the frequency response function matrix into a linear frequency response equation; wherein the linear frequency response equation comprises polynomial coefficients to be solved;

[0009] solving the polynomial coefficients to be solved by using a singular value decomposition method to obtain the test modal parameters of the overhead conductor; wherein the test modal parameters comprise test modal frequencies and test modal shapes;

[0010] constructing a sensor additional mass matrix by measuring the sensor mass and the sensor installation position of the overhead conductor;

[0011] constructing a dynamics equation without sensor additional mass based on the principle of structural mechanics;

[0012] iteratively solving the dynamics equation based on the test modal parameters and the sensor additional mass matrix by using a Newton-Raphson iteration method, and determining the modal parameters without sensor additional mass when a preset convergence condition is met.

[0013] As a preferred solution, the rewriting of the frequency response function matrix into a linear frequency response equation comprises:

[0014] rewriting the frequency response function matrix into a frequency response function matrix rational fraction by using the following formula:

[0015]

[0016] Ω m (ω)=(jω) m

[0017] In the formula, [H(ω)] is the frequency response function matrix; A(ω) is the denominator polynomial; [B(ω)] is the numerator polynomial matrix; am m is the mth polynomial coefficient to be solved; Ω m (ω) is a matrix composed of the mth power of the Laplace operator; [B m ] is the coefficient matrix of the mth numerator polynomial; ω is the angular frequency of vibration; [LR] is the low-frequency residual term; [UR] is the high-frequency residual term; n is the expected modal order;

[0018] rewriting the frequency response function matrix rational fraction into a linear frequency response equation by discarding the low-frequency residual term and the high-frequency residual term of the frequency response function matrix rational fraction:

[0019] [H(ω k )]A(ω k )=[B(ω k )]

[0020] wherein [H(ω k )] is a linear frequency response function of the kth order; A(ω k ) is a denominator polynomial of the kth order; [B(ω k )] is a numerator polynomial matrix of the kth order;

[0021] wherein the linear frequency response equation is expanded as:

[0022]

[0023] wherein [H(ω k )] is a linear frequency response function of the kth order; [B(ω k )] is a numerator polynomial matrix of the kth order; Ω 2n (ω 2n ) = (jω) 2n is the 2nth power of Laplace operator; a 2n is a coefficient of the 2nth order denominator polynomial; is a linear frequency response product matrix; is a polynomial coefficient matrix to be solved; is a numerator polynomial matrix.

[0024] As a preferred solution, the singular value decomposition method is used to solve the polynomial coefficient to be solved, and the test modal parameters of the overhead conductor are obtained, comprising:

[0025] The linear frequency response product matrix is decomposed into a left singular matrix, a diagonal singular matrix and a right singular matrix;

[0026] Based on the left singular matrix, the diagonal singular matrix, the right singular matrix and the linear frequency response function, a polynomial coefficient expression to be solved is constructed;

[0027] The polynomial coefficient expression is solved to obtain the root of the denominator polynomial;

[0028] Based on the root of the denominator polynomial, the test modal frequency is calculated by using the following formula:

[0029]

[0030] wherein ω k is the kth test modal frequency; λ k is the root of the kth denominator polynomial;

[0031] Based on the right singular matrix, the test modal shape is calculated by using the following formula:

[0032] {φ k} = U(:,k)

[0033] wherein φ k is the kth order test modal shape; U(:,k) is the kth column vector of the right singular matrix;

[0034] wherein the to-be-solved polynomial coefficient expression is expressed by the following formula:

[0035]

[0036] wherein [V] is the left singular matrix; [S] is the diagonal singular matrix; and [U] is the right singular matrix.

[0037] As a preferred solution, the constructing the sensor additional mass matrix by measuring the sensor mass and the sensor installation position of the overhead conductor includes:

[0038] measuring the sensor mass of each sensor on the overhead conductor;

[0039] recording the sensor installation position of each sensor on the overhead conductor;

[0040] constructing the sensor additional mass matrix based on the sensor mass and the sensor installation position;

[0041] wherein the sensor additional mass matrix is:

[0042]

[0043] wherein ΔM is the sensor additional mass matrix; m sn is the sensor mass of the nth sensor.

[0044] As a preferred solution, the constructing the dynamics equation without sensor additional mass based on the structural mechanics principle includes:

[0045] the dynamics equation without sensor additional mass is constructed by the following formula:

[0046]

[0047] wherein ω0 is the conductor vibration natural frequency without sensor additional mass; φ0 is the conductor vibration mode shape without sensor additional mass; K is the stiffness matrix of the overhead conductor; and M0 is the conductor mass matrix without sensor additional mass.

[0048] As a preferred solution, the iterative solving of the dynamics equation based on the test modal parameter and the sensor additional mass matrix by using the Newton-Raphson iteration method, and determining the modal parameter without sensor additional mass when a preset convergence condition is met, includes:

[0049] constructing a dynamic equation with sensor additional mass based on the sensor additional mass matrix;

[0050] The dynamic equation with sensor additional mass is:

[0051]

[0052] ω0= ω - Δω m is the natural frequency of conductor vibration with sensor additional mass; φ0= φ - Δφ m is the mode shape of conductor vibration with sensor additional mass; K is the stiffness matrix of overhead conductor; M0is the conductor mass matrix without sensor additional mass; ΔM is the sensor additional mass matrix;

[0053] constructing a residual function according to the dynamic equation without sensor additional mass and the dynamic equation with sensor additional mass;

[0054] constructing a Jacobian matrix based on the residual function;

[0055] constructing a change amount calculation formula of the natural frequency change amount of conductor vibration and the mode shape change amount of conductor vibration based on the Jacobian matrix;

[0056] determining the initial value of the natural frequency of conductor vibration without sensor additional mass and the initial value of the mode shape of conductor vibration without sensor additional mass according to the test modal parameters;

[0057] iteratively updating the natural frequency of conductor vibration without sensor additional mass and the mode shape of conductor vibration without sensor additional mass based on the initial value of the natural frequency of conductor vibration, the initial value of the mode shape of conductor vibration and the change amount calculation formula;

[0058] stopping the iterative updating when a preset iteration requirement is reached, and determining the current natural frequency of conductor vibration without sensor additional mass and the mode shape of conductor vibration without sensor additional mass as the modal parameters without sensor additional mass.

[0059] As a preferred solution, the residual function is constructed according to the dynamic equation without sensor additional mass and the dynamic equation with sensor additional mass, comprising:

[0060] The residual function is:

[0061]

[0062] ω0= ω - Δω m is the natural frequency of conductor vibration with sensor additional mass; φ0= φ - Δφ mA sensor additional mass is added to a conductor vibration mode shape; M0 is a conductor mass matrix without a sensor additional mass; and ΔM is a sensor additional mass matrix.

[0063] As a preferred solution, the constructing the Jacobian matrix based on the residual function comprises:

[0064] The Jacobian matrix is:

[0065]

[0066] In the formula, J is the Jacobian matrix; R is the residual function; ω0 is the conductor vibration natural frequency without a sensor additional mass; φ0 is the conductor vibration mode shape without a sensor additional mass; M0 is the conductor mass matrix without a sensor additional mass; and ΔM is the sensor additional mass matrix.

[0067] As a preferred solution, the constructing the change amount calculation formula of the conductor vibration natural frequency change amount and the conductor vibration mode shape change amount based on the Jacobian matrix comprises:

[0068] The change amount calculation formula is:

[0069]

[0070] In the formula, Δω0 is the conductor vibration natural frequency change amount; Δφ0 is the conductor vibration mode shape change amount; J is the Jacobian matrix; and R is the residual function.

[0071] Correspondingly, the application provides a sensor additional mass elimination device suitable for conductor modal vibration test, comprising a data acquisition module, a frequency response function construction module, a frequency response function conversion module, a test parameter solving module, a mass matrix construction module, a dynamics equation construction module and a modal parameter determination module.

[0072] The data acquisition module is used for performing vibration test on the overhead conductor based on a preset impact force signal, so that a plurality of sensors on the overhead conductor collect acceleration data.

[0073] The frequency response function construction module is used for constructing a frequency response function matrix based on the preset impact force signal and the acceleration data.

[0074] The frequency response function conversion module is used for rewriting the frequency response function matrix into a linear frequency response equation; wherein the linear frequency response equation comprises polynomial coefficients to be solved.

[0075] The test parameter solving module is used for solving the polynomial coefficients to be solved by using a singular value decomposition method, to obtain test modal parameters of the overhead conductor; wherein the test modal parameters comprise test modal frequencies and test modal shapes.

[0076] The mass matrix construction module is configured to construct a sensor additional mass matrix by measuring sensor mass and sensor installation position of the overhead conductor;

[0077] The dynamic equation construction module is configured to construct a dynamic equation without sensor additional mass based on structural mechanics principle;

[0078] The modal parameter determination module is configured to solve the dynamic equation iteratively based on the test modal parameter and the sensor additional mass matrix by using Newton-Raphson iteration method, and determine the modal parameter without sensor additional mass when a preset convergence condition is met.

[0079] Compared with the prior art, the embodiment of the present application has the following beneficial effects:

[0080] The present application provides a sensor additional mass elimination method suitable for conductor modal vibration test, which is based on a preset impact force signal to perform vibration test on the overhead conductor so that the sensors on the overhead conductor collect acceleration data; a frequency response function matrix is constructed based on the preset impact force signal and the acceleration data; the frequency response function matrix is rewritten as a linear frequency response equation containing to-be-solved polynomial coefficients; the to-be-solved polynomial coefficients are solved by using singular value decomposition method to obtain the test modal parameter of the overhead conductor; a sensor additional mass matrix is constructed by measuring the sensor mass and the sensor installation position of the overhead conductor; a dynamic equation without sensor additional mass is constructed based on structural mechanics principle; the dynamic equation is solved iteratively based on the test modal parameter and the sensor additional mass matrix by using Newton-Raphson iteration method, and the modal parameter without sensor additional mass is determined when a preset convergence condition is met. The present application can extract the test modal parameter containing the acceleration sensor by performing the conductor modal vibration test without changing the sensor body structure and mass, and can effectively eliminate the influence of the acceleration sensor additional mass on the test result by using Newton-Raphson iteration algorithm based on the test modal parameter and the constructed sensor additional mass matrix, so as to accurately obtain the modal parameter without sensor additional mass. BRIEF DESCRIPTION OF DRAWINGS

[0081] In order to more clearly illustrate the technical solutions of the present application, the following will briefly introduce the drawings needed in the embodiments. Obviously, the drawings described in the following only constitute some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0082] Figure 1 A flowchart of an embodiment of the sensor additional mass elimination method suitable for conductor modal vibration test provided by the present application;

[0083] Figure 2 A flow chart of another embodiment of the sensor additional mass elimination method suitable for the wire modal vibration test provided by the present application;

[0084] Figure 3 A structure diagram of an embodiment of the sensor additional mass elimination device suitable for the wire modal vibration test provided by the present application. DETAILED DESCRIPTION

[0085] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without any creative work fall within the scope of protection of the present application.

[0086] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs; the terminology used in the specification herein is for describing the specific embodiments only and not intended to be limiting of the present application; the terms "include" and "have" and any variations thereof used in the specification and the claims and the above description of drawings are intended to cover the non-exclusive inclusion.

[0087] In the description of the embodiments of the present application, the technical terms "first", "second", etc. are only used to distinguish different objects, and cannot be understood as indicating or implying relative importance or implicitly indicating the number, specific order or primary and secondary relationship of the indicated technical features. In the description of the embodiments of the present application, the meaning of "a plurality of" is two or more, unless otherwise explicitly and specifically limited.

[0088] Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the present application. The appearance of the phrase in various places in the specification does not necessarily all refer to the same embodiment, nor is it necessarily independent or alternative embodiments to each other. Those skilled in the art explicitly and implicitly understand that the embodiments described herein can be combined with other embodiments.

[0089] In the description of the embodiments of the present application, the term "and / or" is only a description of the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B, which can represent the three cases of A alone, A and B together, and B alone. In addition, the character " / " in the present application generally represents an "or" relationship between the associated objects.

[0090] In the description of the embodiments of the present application, the term "a plurality of" refers to two or more (including two), and similarly, "a plurality of groups" refers to two or more groups (including two groups), and "a plurality of pieces" refers to two or more pieces (including two pieces).

[0091] In the description of the embodiments of the present application, unless otherwise explicitly specified and limited, the technical terms "mounting", "connecting", "connecting", "fixing" and the like should be understood in a broad sense, for example, can be fixedly connected, or can be detachably connected, or can be integrated; can be mechanically connected, or can be electrically connected; can be directly connected, or can be indirectly connected through an intermediate medium; can be the internal communication of two elements or the interaction relationship between two elements. For those skilled in the art, the specific meanings of the above terms in the embodiments of the present application can be understood according to the specific circumstances.

[0092] Reference Figure 1 To solve the problem that the additional mass of the sensor in the prior art is difficult to eliminate, an embodiment of the present application provides a sensor additional mass elimination method suitable for conductor modal vibration test, which comprises steps 101 to 107, and each step is specifically as follows:

[0093] Step 101: Based on a preset impact force signal, the overhead conductor is subjected to a vibration test, so that a plurality of sensors on the overhead conductor collect acceleration data.

[0094] In the embodiment of the present application, during the modal vibration test of the overhead conductor, sensors need to be arranged on the experimental conductor to collect acceleration data. The vibration antinode is the position with the maximum displacement in the vibration mode, and the inertia effect of the structure at this position is the most significant. The vibration signal captured by the sensor at this position has the highest intensity and the best signal-to-noise ratio. Since the disturbance of the additional mass to the dynamic characteristics of the structure is mainly concentrated in the local area, the high-energy vibration at the antinode makes the influence of the additional mass relatively easy to quantify. Therefore, in order to facilitate the subsequent construction of the sensor additional mass matrix, the sensors need to be arranged and installed at the antinode as much as possible.

[0095] In the embodiment of the present application, the positions of the vibration node and the vibration antinode can be determined according to the following method:

[0096] The overhead conductor is simplified as a homogeneous Euler-Bernoulli beam, and the undamped vibration differential equation of the overhead conductor can be established as:

[0097]

[0098] In the formula, y is the vertical displacement of the overhead conductor, ρ is the linear density of the overhead conductor, EI is the bending stiffness of the overhead conductor; t is the data acquisition time; and x is the data acquisition position.

[0099] Assuming that the solution of the simple harmonic vibration is y(x,t) = φ(x)ejωt wherein, φ(x) is a mode function. Substituting the solution of the simple harmonic vibration into the above undamped vibration differential equation, the following equation is obtained:

[0100]

[0101] wherein,

[0102] Solving the mode function, the following equation is obtained:

[0103] φ(x)=Asin(βx)+Bcos(βx)+Csinh(βx)+Dcosh(βx)

[0104] wherein, A, B, C and D are undetermined coefficients.

[0105] Since the overhead conductor can be equivalent to a simply supported beam with both ends fixed, the mechanical boundary condition of the overhead conductor is:

[0106] φ(0)=φ(L)=0

[0107]

[0108] Substituting the mechanical boundary condition into the mode function, the vibration equation of the conductor is obtained as follows:

[0109]

[0110] wherein, k is the modal order; and L is the length of the overhead conductor.

[0111] According to the vibration equation of the conductor, different modal orders correspond to different antinodes. For example, when k=1, the antinode is at L / 2 of the overhead conductor; when k=2, the antinodes are at L / 4 and 3L / 4 of the overhead conductor. Therefore, according to the test conditions, the modal order to be obtained can be determined, so that the acceleration sensor is installed at the corresponding antinode.

[0112] In the embodiment of the present application, the preset impact force signal is used to apply a knocking excitation to the overhead conductor, and the corresponding acceleration data can be collected. The position of the excitation should be selected at a position capable of exciting the target mode. Therefore, the position of the excitation should be located at the modal antinode of the conductor as much as possible. For example, for the first order mode (k=1), the antinode is at the middle L / 2 position, and the node is at the two end points. Therefore, when the first order mode is excited, the knocking position should be near L / 2 of the conductor, rather than the end points, so as to effectively excite the mode. The present application needs to obtain the modal information of each order as much as possible, and therefore the excitation position needs to avoid the node positions of each order mode as much as possible.

[0113] In the embodiment of the present application, for the simply supported beam model, the wave node position of the kth order is nL / k (n=1, 2, 3…k-1). In the test process, the range of the modal order number to be obtained (such as k=1 to k=5) needs to be determined, and the wave node position set to be avoided is established:

[0114]

[0115] Therefore, in order to determine the application position of the excitation on the overhead conductor, the wave node position needs to be avoided in the position not occupied on the overhead conductor, so as to select the candidate point for applying the excitation.

[0116] In the embodiment of the present application, the impact force hammer is used to apply the knocking excitation at the above-mentioned selected candidate point, and the impact force signal F(t) is recorded. The sampling frequency fs of the acquisition card needs to satisfy fs>2.56×fmax (fmax is the upper limit of the frequency of interest). At the same time of applying the knocking excitation, each sensor on the overhead conductor collects the acceleration data A i (t) of the conductor vibration in real time, wherein the accuracy of the acceleration sensor can be set to 10k.

[0117] Step 102: constructing a frequency response function matrix based on the preset impact force signal and the acceleration data.

[0118] In the embodiment of the present application, for each measuring point, the collected impact force signal F(t) and acceleration data A i (t) are respectively subjected to frequency domain conversion, such as FFT (fast Fourier transform), to form the frequency domain force spectrum of the impact force hammer and the frequency spectrum measured by the acceleration sensor:

[0119] F(ω)=FFT(F(t))

[0120] A i (ω)=FFT(A i (t))

[0121] In the formula, F(ω) is the frequency domain force spectrum; A i (ω) is the frequency spectrum measured by the i th acceleration sensor.

[0122] According to the above-mentioned frequency domain data, the frequency response function of the overhead conductor is calculated:

[0123]

[0124] In the formula, is the frequency response function calculated by the i th acceleration sensor.

[0125] Since the overall modal of the overhead conductor needs to be analyzed in the test, the frequency response functions of all measuring points need to be combined into a matrix form:

[0126]

[0127] In the formula, [H(ω)] is the frequency response function matrix.

[0128] Step 103: Rewrite the frequency response function matrix into a linear frequency response equation; wherein the linear frequency response equation includes the coefficients of the polynomial to be determined.

[0129] In this embodiment of the invention, PolyMAX (least squares complex frequency domain method) can be used to identify the conductor vibration modal parameters with acceleration-added mass from the frequency response function. First, the frequency response function matrix is ​​rewritten to include the coefficients of the polynomial to be determined. By solving for the coefficients of the polynomial to be determined, and combining the solution value, the conductor vibration modal parameters with acceleration-added mass in the vibration test can be identified.

[0130] In this embodiment of the invention, the frequency response function matrix is ​​rewritten as a linear frequency response equation. First, the frequency response function matrix is ​​expressed in rational fractional form:

[0131]

[0132] In the formula, [H(ω)] is the frequency response function matrix; A(ω) is the denominator polynomial (related to the poles); [B(ω)] is the numerator polynomial matrix (related to the mode shape); ω is the vibration angular frequency; [LR] is the low-frequency residual term; and [UR] is the high-frequency residual term.

[0133] A(ω) and [B(ω)] can be calculated using the following formula:

[0134]

[0135] Ω m (ω)=(jω) m

[0136] In the formula, a m Ω represents the coefficients of the polynomial in the m-th denominator polynomial. m (ω) is a matrix formed by raising the Laplace operator to the mth power; [B m ] is the coefficient matrix of the m-th numerator polynomial; n is the expected mode order.

[0137] The rational fractional form of the frequency response function matrix above can be rewritten as a linear equation:

[0138] [H(ω k )]A(ω k )=[B(ω k )]+residual terms

[0139] In the formula, [H(ω kis the linear frequency response function of the kth order; A(ω k ) is the denominator polynomial of the kth order; [B(ω k )] is the numerator polynomial matrix of the kth order; the residual term includes a high-frequency residual term [UR] and a low-frequency residual term [LR].

[0140] Neglecting the residual term of the linear equation above, the linear frequency response equation is obtained as follows:

[0141] [H(ω k )]A(ω k )=[B(ω k )]

[0142] The expansion form of the linear frequency response equation is as follows:

[0143]

[0144] wherein, [H(ω k )] is the linear frequency response function of the kth order; [B(ω k )] is the numerator polynomial matrix of the kth order; Ω 2n (ω 2n )=(jω) 2n is the 2nth power of the Laplace operator; a 2n is the coefficient of the 2nth order denominator polynomial; is the linear frequency response product matrix; is the polynomial coefficient matrix to be solved; is the numerator polynomial matrix.

[0145] Step 104: the polynomial coefficient to be solved is solved by using the singular value decomposition method, and the test modal parameters of the overhead conductor are obtained; wherein, the test modal parameters include test modal frequency and test modal vibration mode.

[0146] In the embodiment of the present application, the expansion form of the linear frequency response equation can be simplified as [Φ]a=B, wherein, [Φ] is the linear frequency response product matrix; a is the polynomial coefficient matrix to be solved; and B is the numerator polynomial matrix.

[0147] In order to avoid numerical problems, the singular value decomposition (SVD) is used to solve a, and specifically:

[0148] The linear frequency response product matrix is decomposed into a left singular matrix, a diagonal singular matrix and a right singular matrix, and is expressed as:

[0149] [Φ]=[U][S][V] H

[0150] Therefore, the polynomial coefficient a to be solved can be expressed as:

[0151] a = [V] [S] -1 [U] H B

[0152] In the formula, [V] is a left singular matrix; [S] is a diagonal singular matrix; and [U] is a right singular matrix.

[0153] The above to-be-solved polynomial coefficient expression is substituted into the denominator polynomial, and roots of the denominator polynomial are solved. The roots of the denominator polynomial are complex numbers, and are expressed as: λ k (k = 1,..., 2n).

[0154] According to the roots of the denominator polynomial, modal parameters of the overhead conductor are further solved, including a test modal frequency and a test modal shape. The test modal frequency is calculated by using the following formula:

[0155]

[0156] In the formula, ω k is the kth-order test modal frequency; and λ k is the root of the kth-order denominator polynomial.

[0157] The shape vector φ k (corresponding to the kth order) can be directly extracted by a right singular matrix U after singular value decomposition (SVD), for example, the kth-order shape is the kth column of the right singular matrix. The formula is expressed as:

[0158] {φ k} = U(:, k)

[0159] In the formula, φ k is the kth-order test modal shape; and U(:, k) is the kth column vector of the right singular matrix.

[0160] Step 105: constructing a sensor additional mass matrix by measuring sensor masses and sensor installation positions of the overhead conductor.

[0161] In the embodiment of the present application, accurate acquisition of the sensor additional mass matrix is a key to correcting modal parameters and obtaining modal parameters without sensor additional mass. The sensor additional mass matrix is constructed based on masses and installation positions of sensors on the overhead conductor.

[0162] As a preferred scheme of the embodiment, the sensor additional mass matrix is constructed by measuring sensor masses and sensor installation positions of the overhead conductor, including:

[0163] measuring sensor masses of the sensors on the overhead conductor;

[0164] recording sensor installation positions of the sensors on the overhead conductor;

[0165] constructing a sensor additional mass matrix based on the sensor mass and the sensor installation position;

[0166] wherein the sensor additional mass matrix is:

[0167]

[0168] wherein ΔM is the sensor additional mass matrix; m sn is the sensor mass of the nth sensor.

[0169] In the embodiment of the present application, the sensor additional mass matrix ΔM is constructed, first, the mass m s (unit: kg) of each acceleration sensor is measured by using a precision electronic balance. If the sensor has a cable, a mounting bracket, and an adhesive, the mass of the cable, the mounting bracket, and the adhesive needs to be included (total additional mass = sensor mass + adhesive + cable). The list of the mass of the acceleration sensors is [m s1, m s2 ,…,m sn ], wherein m sn is the sensor mass of the nth sensor. Then, the installation position of the acceleration sensor is recorded. Since the axial radius of the wire is negligible compared to its radial length, only a one-dimensional coordinate system is considered, and the installation position of each sensor on the overhead wire is recorded, thereby establishing the coordinate matrix P = [P1, P2, …, Pn] of each acceleration sensor, wherein Pn is the installation position of the nth sensor. After obtaining the sensor mass and the sensor installation position, the sensor additional mass matrix is constructed.

[0170] Step 106: constructing a dynamic equation without sensor additional mass based on the principle of structural mechanics.

[0171] In the embodiment of the present application, based on the Newton-Raphson iteration method, combined with the test modal parameters (ω m , φ m ) obtained through the test and the constructed sensor additional mass matrix, the true modal parameters (ω0, φ0) of the sensor additional mass can be deduced.

[0172] As a preferred scheme of the embodiment, the dynamic equation without sensor additional mass is constructed based on the principle of structural mechanics, including:

[0173] The dynamic equation without sensor additional mass is constructed by using the following formula:

[0174]

[0175] In the formula, ω0 is the inherent frequency of the conductor vibration without the sensor additional mass; φ0 is the vibration mode of the conductor vibration without the sensor additional mass; K is the stiffness matrix of the overhead conductor; and M0 is the conductor mass matrix without the sensor additional mass.

[0176] Step 107: iteratively solving the dynamic equation based on the test modal parameters and the sensor additional mass matrix by using the Newton-Raphson iteration method, and determining the modal parameters without the sensor additional mass when a preset convergence condition is met.

[0177] In the embodiment of the present application, the dynamic equation with the sensor additional mass is established based on the structural mechanics principle:

[0178]

[0179] In the formula, ω0 is the inherent frequency of the conductor vibration without the sensor additional mass; φ0 is the vibration mode of the conductor vibration without the sensor additional mass; K is the stiffness matrix of the overhead conductor; and M0 is the conductor mass matrix without the sensor additional mass. m In the formula, ω0 is the inherent frequency of the conductor vibration without the sensor additional mass; φ0 is the vibration mode of the conductor vibration without the sensor additional mass; K is the stiffness matrix of the overhead conductor; and M0 is the conductor mass matrix without the sensor additional mass. m

[0180] As a preferred scheme of the embodiment, the residual function is constructed according to the dynamic equation without the sensor additional mass and the dynamic equation with the sensor additional mass, and the residual function comprises:

[0181] The residual function is:

[0182]

[0183] In the formula, R is the residual function; ω0 is the inherent frequency of the conductor vibration without the sensor additional mass; φ0 is the vibration mode of the conductor vibration without the sensor additional mass; ω is the inherent frequency of the conductor vibration with the sensor additional mass; φ is the vibration mode of the conductor vibration with the sensor additional mass; M0 is the conductor mass matrix without the sensor additional mass; and ΔM is the sensor additional mass matrix. m In the formula, R is the residual function; ω0 is the inherent frequency of the conductor vibration without the sensor additional mass; φ0 is the vibration mode of the conductor vibration without the sensor additional mass; ω is the inherent frequency of the conductor vibration with the sensor additional mass; φ is the vibration mode of the conductor vibration with the sensor additional mass; M0 is the conductor mass matrix without the sensor additional mass; and ΔM is the sensor additional mass matrix. m

[0184] As a preferred scheme of the embodiment, the Jacobian matrix is constructed based on the residual function:

[0185]

[0186] In the formula, J is the Jacobian matrix; R is the residual function; ω0 is the inherent frequency of the conductor vibration without the sensor additional mass; φ0 is the vibration mode of the conductor vibration without the sensor additional mass; M0 is the conductor mass matrix without the sensor additional mass; and ΔM is the sensor additional mass matrix.

[0187] ​​As a preferred scheme of the embodiment, based on the Jacobian matrix, a variation calculation formula of the conductor vibration natural frequency variation and the conductor vibration mode shape variation is constructed:

[0188]

[0189] In the formula, Δω0 is the conductor vibration natural frequency variation; Δφ0 is the conductor vibration mode shape variation; J is the Jacobian matrix; and R is the residual function.

[0190] In the embodiment, the initial value of the conductor vibration natural frequency without the sensor additional mass and the initial value of the conductor vibration mode shape without the sensor additional mass are determined according to the test modal parameters. Specifically, the test modal frequency is determined as the initial value of the conductor vibration natural frequency without the sensor additional mass, and the test modal mode shape is determined as the initial value of the conductor vibration mode shape without the sensor additional mass, which can be expressed by the following formula:

[0191]

[0192] In the formula, ω0 is the initial value of the conductor vibration natural frequency without the sensor additional mass; φ0 is the initial value of the conductor vibration mode shape without the sensor additional mass; ω is the conductor vibration natural frequency with the sensor additional mass; and φ is the conductor vibration mode shape with the sensor additional mass. m m

[0193] In the embodiment, after the initial value of the conductor vibration natural frequency and the initial value of the conductor vibration mode shape are determined, and the variation calculation formula of the conductor vibration natural frequency variation and the conductor vibration mode shape variation is obtained, the conductor vibration natural frequency without the sensor additional mass and the conductor vibration mode shape without the sensor additional mass are iteratively updated. The iterative calculation equation of the conductor vibration natural frequency without the sensor additional mass and the conductor vibration mode shape without the sensor additional mass is as follows:

[0194]

[0195] In the formula, ωk+1 is the conductor vibration natural frequency without the sensor additional mass at the k+1 moment; ωk is the conductor vibration natural frequency without the sensor additional mass at the k moment; φk+1 is the conductor vibration mode shape without the sensor additional mass at the k+1 moment; and φk is the conductor vibration mode shape without the sensor additional mass at the k moment.

[0196] ​​​​​​​​In each iteration update, it is judged whether the current data reaches the preset iteration requirement, if the preset iteration requirement is reached, the iteration update is stopped, and the current wire vibration natural frequency without sensor additional mass and the wire vibration mode shape without sensor additional mass are determined as the modal parameters without sensor additional mass; if the preset iteration requirement is not reached, the iteration update is further performed.

[0197] As an example of the embodiment of the present application, the preset iteration requirement can be:

[0198]

[0199] ||R||<10 -6

[0200] In the formula, Δω0 is the wire vibration natural frequency variation; ω0 is the wire vibration natural frequency without sensor additional mass; and R is the residual function.

[0201] Referring to Figure 2 is a flowchart of another embodiment of the sensor additional mass elimination method for the wire modal vibration test provided by the present application. The present application firstly performs the wire modal vibration test, determines the acceleration sensor installation position and the impact force hammer knocking position by determining the position of each and the overhead conductor wave crest, applies the knocking excitation to the overhead conductor, records the impact force signal of the impact force hammer and the acceleration sensor data, thereby calculates the frequency response containing the sensor additional mass, and further extracts the vibration modal parameters containing the sensor additional mass; subsequently, the acceleration sensor additional mass matrix is constructed by accurately measuring the mass of the acceleration sensor and the installation position of the acceleration sensor on the wire; finally, the modal parameters after removing the additional mass effect are solved based on the Newton-Raphson iteration method, and the influence of the acceleration sensor additional mass on the test result is effectively eliminated.

[0202] The above embodiment has the following effects:

[0203] The application provides a sensor additional mass elimination method suitable for conductor modal vibration test, performs vibration test on overhead conductors based on a preset impact force signal, so that sensors on the overhead conductors collect acceleration data, constructs a frequency response function matrix based on the preset impact force signal and the acceleration data, rewrites the frequency response function matrix into a linear frequency response equation containing to-be-solved polynomial coefficients, solves the to-be-solved polynomial coefficients by using a singular value decomposition method, and obtains test modal parameters of the overhead conductors, constructs a sensor additional mass matrix by measuring the sensor mass and the sensor installation position of the overhead conductors, constructs a dynamics equation without sensor additional mass based on the principle of structural mechanics, iteratively solves the dynamics equation based on the test modal parameters and the sensor additional mass matrix by using a Newton-Raphson iteration method, and determines the modal parameters without sensor additional mass when the preset convergence condition is met.

[0204] As shown in the above method embodiment, corresponding device embodiments are provided; Figure 3

[0205] An embodiment of the application provides a sensor additional mass elimination device suitable for conductor modal vibration test, which comprises a data acquisition module, a frequency response function construction module, a frequency response function conversion module, a test parameter solving module, a mass matrix construction module, a dynamics equation construction module and a modal parameter determination module.

[0206] The data acquisition module is used for performing vibration test on overhead conductors based on a preset impact force signal, so that a plurality of sensors on the overhead conductors collect acceleration data.

[0207] The frequency response function construction module is used for constructing a frequency response function matrix based on the preset impact force signal and the acceleration data.

[0208] The frequency response function conversion module is used for rewriting the frequency response function matrix into a linear frequency response equation; wherein the linear frequency response equation comprises to-be-solved polynomial coefficients.

[0209] The test parameter solving module is used for solving the to-be-solved polynomial coefficients by using a singular value decomposition method, and obtaining test modal parameters of the overhead conductors; wherein the test modal parameters comprise test modal frequencies and test modal shapes.

[0210] ​The mass matrix construction module is configured to construct a sensor additional mass matrix by measuring sensor mass and sensor installation position of the overhead conductor;

[0211] The dynamic equation construction module is configured to construct a dynamic equation without sensor additional mass based on structural mechanics principles;

[0212] The modal parameter determination module is configured to iteratively solve the dynamic equation based on the test modal parameters and the sensor additional mass matrix by using a Newton-Raphson iteration method, and determine modal parameters without sensor additional mass when a preset convergence condition is met.

[0213] It can be understood that the above device item embodiments are corresponding to the method item embodiments of the present application, and can realize the sensor additional mass elimination method suitable for conductor modal vibration test provided by any one of the above method item embodiments of the present application.

[0214] It should be noted that the device embodiments described above are only schematic, and part or all of the modules can be selected to achieve the purpose of the present embodiment scheme according to actual needs. In addition, in the device embodiment provided by the present application, the connection relationship between the modules indicates that there is a communication connection between them, which can be realized as one or more communication buses or signal lines. Those skilled in the art can understand and implement it without creative labor.

[0215] The above specific embodiments further illustrate the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above description is only for specific embodiments of the present application and does not limit the protection scope of the present application. It is particularly pointed out that any modification, equivalent replacement, improvement, etc. made by those skilled in the art within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A sensor additional mass elimination method suitable for a wire modal vibration test, characterized by, The method comprises the following steps: performing a vibration test on the overhead conductor based on a preset impact force signal, so that a plurality of sensors on the overhead conductor collect acceleration data; constructing a frequency response function matrix based on the preset impact force signal and the acceleration data; rewriting the frequency response function matrix into a linear frequency response equation; wherein the linear frequency response equation comprises polynomial coefficients to be solved; solving the polynomial coefficients to be solved by using a singular value decomposition method to obtain test modal parameters of the overhead conductor; wherein the test modal parameters comprise test modal frequencies and test modal shapes; constructing a sensor additional mass matrix by measuring sensor masses and sensor installation positions of the overhead conductor; constructing a dynamics equation without sensor additional mass based on the principle of structural mechanics; iteratively solving the dynamics equation based on the test modal parameters and the sensor additional mass matrix by using a Newton-Raphson iteration method, and determining the modal parameters without sensor additional mass when a preset convergence condition is met.

2. The sensor additional mass elimination method suitable for a wire modal vibration test according to claim 1, characterized by, The rewriting of the frequency response function matrix into a linear frequency response equation comprises: rewriting the frequency response function matrix into a frequency response function matrix rational fraction by using the following formula: Ω m (ω) = (jω) m where [H(ω)] is the frequency response function matrix; A(ω) is the denominator polynomial; [B(ω)] is the numerator polynomial matrix; a m is the mth polynomial coefficient to be solved; Ω m (ω) is the matrix of the mth power of the Laplacian operator; [B m ] is the coefficient matrix of the mth numerator polynomial; ω is the angular frequency of vibration; [LR] is the low frequency residual; [UR] is the high frequency residual; n is the expected modal order; rewriting the frequency response function matrix rational fraction into a linear frequency response equation by removing low-frequency residual terms and high-frequency residual terms of the frequency response function matrix rational fraction: [H(ω k )]A(ω k ) = [B(ω k )] where [H(ω k )] is the linear frequency response function of order k; A(ω k ) is the denominator polynomial of order k; and [B(ω k )] is the numerator polynomial matrix of order k. wherein the linear frequency response equation has an expansion form of: where [H(ω k )] is the linear frequency response function of the kth order; [B(ω k )] is the numerator polynomial matrix of the kth order; Ω 2n (ω 2n ) = (jω) 2n is the 2n power of the Laplace operator; a 2n is the coefficient of the denominator polynomial of the 2n order; is the linear frequency response product matrix; is the polynomial coefficient matrix to be solved; is the numerator polynomial matrix.

3. The sensor additional mass elimination method for wire modal vibration test according to claim 2, characterized in that, The solving of the polynomial coefficients to be solved by using a singular value decomposition method to obtain test modal parameters of the overhead conductor comprises: decomposing the linear frequency response product matrix into a left singular matrix, a diagonal singular matrix, and a right singular matrix; constructing a polynomial coefficient expression to be solved based on the left singular matrix, the diagonal singular matrix, the right singular matrix, and the linear frequency response function; solving roots of the denominator polynomial from the polynomial coefficient expression; calculating test modal frequencies based on the roots of the denominator polynomial by using the following formula: where ωk k is the kth order trial modal frequency; λk k is the kth order root of the denominator polynomial; calculating test modal shapes based on the right singular matrix by using the following formula: {φ k} = U(:,k) where φ k is the kth order trial mode shape; U(:,k) is the kth column vector of the right singular matrix; wherein the polynomial coefficient expression to be solved is expressed by using the following formula: wherein [V] is the left singular matrix; [S] is the diagonal singular matrix; and [U] is the right singular matrix.

4. The sensor additional mass elimination method for a wire modal vibration test according to claim 3, characterized by, The construction of the sensor additional mass matrix by measuring the sensor masses and the sensor installation positions of the overhead conductor comprises: measuring sensor masses of each sensor on the overhead conductor; recording sensor installation positions of each sensor on the overhead conductor; constructing a sensor additional mass matrix based on the sensor masses and the sensor installation positions; wherein the sensor additional mass matrix is: where ΔM is the sensor added mass matrix; m sn is the mass of the nth sensor.

5. The sensor additional mass elimination method for wire modal vibration test according to claim 4, wherein, The construction of the dynamics equation without sensor additional mass based on the principle of structural mechanics comprises: constructing the dynamics equation without sensor additional mass by using the following formula: wherein ω0 is the inherent frequency of conductor vibration without sensor additional mass; φ0 is the vibration mode of conductor vibration without sensor additional mass; K is the stiffness matrix of the overhead conductor; and M0 is the mass matrix of the conductor without sensor additional mass.

6. The sensor additional mass elimination method for wire modal vibration test according to claim 5, wherein, The Newton-Raphson iteration method is used to iteratively solve the dynamic equation based on the test modal parameters and the sensor additional mass matrix, and when a preset convergence condition is met, the modal parameters without sensor additional mass are determined, including: A dynamic equation with sensor additional mass is constructed based on the sensor additional mass matrix; The dynamic equation with sensor additional mass is: where ω m is the natural frequency of the conductor vibration with the sensor added mass; φ m is the mode shape of the conductor vibration with the sensor added mass; K is the stiffness matrix of the overhead conductor; M0 is the mass matrix of the conductor without the sensor added mass; ΔM is the mass matrix of the sensor added mass; According to the dynamic equation without sensor additional mass and the dynamic equation with sensor additional mass, a residual function is constructed; A Jacobian matrix is constructed based on the residual function; Based on the Jacobian matrix, a change amount calculation formula of the conductor vibration natural frequency change amount and the conductor vibration mode shape change amount is constructed; According to the test modal parameters, the initial value of the conductor vibration natural frequency without sensor additional mass and the initial value of the conductor vibration mode shape without sensor additional mass are determined; Based on the initial value of the conductor vibration natural frequency, the initial value of the conductor vibration mode shape, and the change amount calculation formula, the conductor vibration natural frequency without sensor additional mass and the conductor vibration mode shape without sensor additional mass are iteratively updated; When the preset iteration requirement is reached, the iteration update is stopped, and the current conductor vibration natural frequency without sensor additional mass and the conductor vibration mode shape without sensor additional mass are determined as the modal parameters without sensor additional mass.

7. The sensor additional mass elimination method for wire modal vibration test according to claim 6, wherein, The residual function is constructed according to the dynamic equation without sensor additional mass and the dynamic equation with sensor additional mass, including: The residual function is: where R is the residual function; ω0is the natural frequency of the conductor vibration without the sensor added mass; φ0is the mode shape of the conductor vibration without the sensor added mass; ω m is the natural frequency of the conductor vibration with the sensor added mass; φ m is the mode shape of the conductor vibration with the sensor added mass; M0is the mass matrix of the conductor without the sensor added mass; and ΔM is the mass matrix of the sensor added mass.

8. The sensor additional mass elimination method for wire modal vibration test according to claim 7, characterized in that, The Jacobian matrix is constructed based on the residual function, including: The Jacobian matrix is: In the formula, J is the Jacobian matrix; R is the residual function; ω0 is the conductor vibration natural frequency without sensor additional mass; φ0 is the conductor vibration mode shape without sensor additional mass; M0 is the conductor mass matrix without sensor additional mass; ΔM is the sensor additional mass matrix.

9. The sensor additional mass elimination method for wire modal vibration test according to claim 8, wherein, Based on the Jacobian matrix, a change amount calculation formula of the conductor vibration natural frequency change amount and the conductor vibration mode shape change amount is constructed, including: The change amount calculation formula is: In the formula, Δω0 is the conductor vibration natural frequency change amount; Δφ0 is the conductor vibration mode shape change amount; J is the Jacobian matrix; R is the residual function.

10. A sensor additional mass canceling device for a wire modal vibration test, characterized by, Including: The data acquisition module, the frequency response function construction module, the frequency response function conversion module, the test parameter solving module, the mass matrix construction module, the dynamic equation construction module, and the modal parameter determination module; The data acquisition module is used to perform a vibration test on the overhead conductor based on a preset impact force signal, so that a plurality of sensors on the overhead conductor collect acceleration data; The frequency response function construction module is used to construct a frequency response function matrix based on the preset impact force signal and the acceleration data; The frequency response function conversion module is used to rewrite the frequency response function matrix into a linear frequency response equation; wherein the linear frequency response equation includes polynomial coefficients to be solved; The test parameter solving module is configured to solve the polynomial coefficients to be solved by using a singular value decomposition method, and obtain the test modal parameters of the overhead conductor; the test modal parameters include test modal frequencies and test modal shapes; The mass matrix construction module is configured to construct a sensor additional mass matrix by measuring sensor mass and sensor installation positions of the overhead conductor; The dynamic equation construction module is configured to construct a dynamic equation without sensor additional mass based on structural mechanics principles; The modal parameter determination module is configured to solve the dynamic equation based on the test modal parameters and the sensor additional mass matrix by using a Newton-Raphson iteration method, and determine modal parameters without sensor additional mass when a preset convergence condition is met.

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