Bending stress prediction model construction method and system and bending stress prediction method

Abstract

The invention discloses a bending stress prediction model construction method and system and a bending stress prediction method, and the method comprises the steps: arranging a displacement sensor at a first preset position of a wire clamp, and pasting a strain gauge at a second preset position of a power transmission line; a displacement sensor is used for measuring bending displacement generated by the power transmission conductor under the action of each parameter combination, and a strain gauge is used for measuring strain generated by the power transmission conductor under the action of each parameter combination; wherein the parameter combination comprises axial tension and vibration frequency of the transmission conductor; and carrying out Bayesian calibration on a pre-constructed transmission conductor bending stress calculation model through an MCMC algorithm in combination with bending displacement and strain generated by the transmission conductor under the action of each parameter combination, and taking the transmission conductor bending stress calculation model subjected to Bayesian calibration as a bending stress prediction model. According to the method, the parameter posterior distribution is efficiently explored based on the actually measured data, so that the fitting degree of the model prediction result and the actual performance of the transmission conductor is improved.

Description

Technical Field

[0001] The present invention relates to the field of transmission line bending stress prediction, and in particular to a bending stress prediction model construction method, system and bending stress prediction method. Background Art

[0002] Transmission wires are usually made of multiple metal twisted wires and have good electrical conductivity and mechanical strength. Under certain conditions, such as wind, ice and snow loads, transmission wires will bend, resulting in bending stress. When transmission wires are severely bent and deformed, insulation damage may occur, thus affecting the operational stability and safety of the power grid system.

[0003] The main method currently used to evaluate the bending stress of transmission lines is the Poffenberger-Swart (PS) formula. Although the above evaluation method can predict the bending stress of transmission lines to a certain extent, it still has the following shortcomings: (1) Key parameters such as bending stiffness EI and tension T in the PS formula are usually simplified to constants, and their changes with factors such as the stress state of the conductor and environmental conditions are not considered, resulting in limited accuracy and applicability of the calculation results; (2) Most existing methods are based on idealized conductor models, ignoring the influence of complex nonlinear behaviors such as friction and slip between twisted wires on the bending stiffness of the conductor, and cannot accurately describe the stress characteristics of the conductor under different working conditions; (3) Due to the lack of effective integration with measured data, the parameter selection and calibration of existing models often rely on experience or trial and error, which makes it difficult to objectively reflect the actual performance of the conductor, and the reliability of the prediction results is difficult to guarantee. Summary of the invention

[0004] The embodiments of the present invention provide a bending stress prediction model construction method, system and bending stress prediction method, which efficiently explore the posterior distribution of parameters based on measured data, realize the probability estimation and uncertainty quantification of model parameters, and improve the fit between the model prediction results and the actual performance of the transmission line.

[0005] In order to solve the above technical problems, an embodiment of the present invention provides a method for constructing a bending stress prediction model, comprising:

[0006] A displacement sensor is arranged at a first preset position of the wire clamp, and a strain gauge is pasted at a second preset position of the transmission wire;

[0007] The displacement sensor is used to measure the bending displacement of the transmission wire under the action of each parameter combination, and the strain gauge is used to measure the strain of the transmission wire under the action of each parameter combination; wherein the parameter combination includes the axial tension and vibration frequency of the transmission wire;

[0008] Through the MCMC algorithm, combined with the bending displacement and strain generated by the transmission line under each parameter combination, the pre-constructed transmission line bending stress calculation model is Bayesian calibrated, and the transmission line bending stress calculation model that has completed the Bayesian calibration is used as the bending stress prediction model.

[0009] In the implementation of the embodiment of the present invention, a displacement sensor is arranged at a first preset position of the wire clamp, and a strain gauge is pasted at a second preset position of the transmission line, so that the displacement sensor is used to measure the bending displacement of the transmission line under each parameter combination, and the strain gauge is used to measure the strain of the transmission line under each parameter combination. Through the joint measurement of the displacement sensor and the strain gauge, the mechanical behavior of the transmission line under different load conditions can be more comprehensively understood, thereby revealing its structural performance and reliability in practical applications. Then, through the Markov Chain Monte Carlo (MCMC) sampling algorithm, combined with the above-mentioned measured data - the bending displacement and strain generated by the transmission line under each parameter combination, the pre-constructed transmission line bending stress calculation model is Bayesian calibrated, which can efficiently explore the parameter posterior distribution based on the measured data, realize the probability estimation and uncertainty quantification of the model parameters, and then optimize the bending stress prediction model for predicting the bending stress of the transmission line, avoiding complex finite element modeling and calculation, while ensuring accuracy. Improve the transmission line bending stress calculation speed. In addition, considering the combination of parameters such as axial tension and vibration frequency can make the model adaptable in different environments and operating conditions, and enhance the operational stability of the transmission line under complex conditions.

[0010] As a preferred solution, the construction of the transmission line bending stress calculation model is specifically as follows:

[0011] Establish a mathematical model of bending stress of transmission lines;

[0012] Based on the mapping relationship between the axial tension of the transmission line, the friction force between the strands and the bending stiffness of the transmission line, the parameters of the mathematical model of the bending stress of the transmission line are optimized, and the mathematical model of the bending stress of the transmission line with optimized parameters is used as the calculation model of the bending stress of the transmission line.

[0013] The preferred scheme of implementing the embodiment of the present invention optimizes the parameters of the mathematical model of the bending stress of the transmission line based on the mapping relationship between the axial tension of the transmission line, the friction between the strands and the bending stiffness of the transmission line. This can fully consider the influence of complex nonlinear behaviors such as the axial tension of the transmission line and the friction between the strands on the bending resistance of the transmission line, and then accurately describe the force characteristics of the line under different working conditions, reduce the uncertainty brought by traditional empirical formulas, and improve the prediction accuracy of the bending stress of the transmission line.

[0014] As a preferred solution, the mathematical model of the bending stress of the transmission line is specifically:

[0015] σ b =KY b ;

[0016]

[0017] In the formula, σ b Represents the bending stress amplitude on the surface of the transmission line; Y b represents the bending displacement amplitude measured by the displacement sensor; K represents the Poffenberger coefficient; E a represents the elastic modulus of the aluminum stranded wire; d represents the diameter of the outer stranded wire; a represents the distance between the displacement sensor and the last contact point of the clamp; λ represents the parameters related to the axial tension T and bending stiffness EI of the transmission line; the bending stiffness EI of the transmission line is min0 To EI max0 The time is uniformly distributed; n a Indicates the number of aluminum strands; d a Indicates the diameter of the aluminum stranded wire; n s Indicates the number of steel strands; E s Indicates the elastic modulus of the steel strand; d s Indicates the diameter of the steel strand; r a It indicates the average radius of the aluminum strand layer in the steel core aluminum stranded wire.

[0018] The preferred scheme of the embodiment of the present invention comprehensively considers the physical properties, geometric properties and external loads of the transmission line. In the modeling process, multiple parameters such as the Poffenberger coefficient, the distance between the displacement sensor for measuring the bending displacement and the last contact point of the wire clamp, the elastic modulus of the aluminum stranded wire and the steel stranded wire, and the diameter of the aluminum stranded wire and the steel stranded wire are introduced into the mathematical model of the bending stress of the transmission line, thereby providing a comprehensive basis for the prediction of the bending stress of the transmission line.

[0019] As a preferred solution, the mapping relationship between the friction force between the strands and the bending stiffness of the transmission wire is specifically:

[0020] EI=EI min +(EI max -EI min )(1-e -βκ );

[0021] Where β is a parameter related to the friction coefficient μ between the strands, and β controls the bending stiffness EI of the transmission line from EI min To EI max The transition rate; κ represents the bending curvature of the transmission line.

[0022] A preferred scheme for implementing an embodiment of the present invention introduces a parameter β related to the friction coefficient between the strands to control the transition rate of the bending stiffness of the transmission line from the minimum value to the maximum value, reflecting the influence of the friction between the strands on the bending strain or bending stress of the transmission line, so as to improve the accuracy of describing the mechanical behavior of the transmission line under different working conditions, thereby improving the reliability of the bending stress prediction results.

[0023] As a preferred solution, the mapping relationship between the axial tension of the transmission wire and the bending stiffness of the transmission wire is specifically:

[0024]

[0025] Where, EI min Indicates the minimum bending stiffness of the transmission line; EI max Indicates the maximum value of the bending stiffness of the transmission line; EI min0 Indicates the minimum bending stiffness of the transmission line in the initial state; EI max0 It indicates the maximum value of the bending stiffness of the transmission line in the initial state; the bending stiffness EI of the transmission line is EI min0 To EI max0 The time interval obeys uniform distribution; T represents the axial tension of the transmission line; T0 represents the rated breaking force of the transmission line; α1, α2, n1, and n2 represent parameters related to the axial tension of the transmission line.

[0026] A preferred scheme for implementing the embodiment of the present invention introduces parameters α1, α2, n1 and n2 that describe the influence of axial tension, which are used to characterize the power-law relationship between the minimum bending stiffness and maximum bending stiffness of the transmission line and the axial tension, reflecting the regulating effect of axial tension on the bending deformation resistance of the transmission line, so as to further accurately describe the force characteristics of the transmission line under different working conditions.

[0027] As a preferred solution, the MCMC algorithm is used to combine the bending displacement and strain generated by the transmission line under each parameter combination to perform Bayesian calibration on the pre-constructed transmission line bending stress calculation model, and the transmission line bending stress calculation model that has completed the Bayesian calibration is used as the bending stress prediction model, specifically:

[0028] Based on the strain generated by the transmission line under each parameter combination, the stress generated by the transmission line under each parameter combination is analyzed and obtained;

[0029] By using the MCMC algorithm, based on the prior distribution of the parameters of the transmission line bending stress calculation model and the bending displacement and stress generated by the transmission line under each parameter combination, a sample set of the posterior distribution of the parameters of the transmission line bending stress calculation model is obtained by sampling;

[0030] The bending stress prediction model is constructed based on the sample set of the posterior distribution of the parameters and the transmission line bending stress calculation model.

[0031] The preferred solution of the embodiment of the present invention is to sample a sample set of the posterior distribution of the parameters of the transmission line bending stress calculation model based on the prior distribution of the parameters of the transmission line bending stress calculation model and the bending displacement and stress generated by the transmission line under each parameter combination through the MCMC algorithm, and then construct a bending stress prediction model based on the sample set of the posterior distribution of the parameters and the transmission line bending stress calculation model. That is, in the process of optimizing the model parameters, the transmission line bending stress calculation model is reasonably constrained and updated by introducing prior knowledge and combining measured data to improve the objectivity of parameter selection and the prediction accuracy of the bending stress prediction model, so that the prediction result of the bending stress prediction model is closer to the actual performance of the transmission line.

[0032] In order to solve the same technical problem, an embodiment of the present invention further provides a bending stress prediction method applied to a transmission line, comprising:

[0033] Obtaining the bending displacement of the transmission line to be predicted;

[0034] Using a bending stress prediction model, combined with the bending displacement of the transmission line to be predicted, a number of bending stress samples corresponding to the transmission line to be predicted are analyzed and obtained; wherein the bending stress prediction model is constructed using the bending stress prediction model construction method;

[0035] The probability distribution of the bending stress of the transmission line to be predicted is analyzed according to all the bending stress samples corresponding to the transmission line to be predicted.

[0036] In order to solve the same technical problem, an embodiment of the present invention further provides a bending stress prediction model construction system, comprising:

[0037] The data acquisition module is used to arrange a displacement sensor at a first preset position of the wire clamp, and to paste a strain gauge at a second preset position of the transmission wire; using the displacement sensor, the bending displacement of the transmission wire generated under the action of each parameter combination is measured, and using the strain gauge, the strain of the transmission wire generated under the action of each parameter combination is measured; wherein the parameter combination includes the axial tension and vibration frequency of the transmission wire;

[0038] The model calibration module is used to perform Bayesian calibration on the pre-built transmission line bending stress calculation model by combining the bending displacement and strain generated by the transmission line under each parameter combination through the MCMC algorithm, and use the transmission line bending stress calculation model that has completed the Bayesian calibration as the bending stress prediction model.

[0039] As a preferred solution, the bending stress prediction model construction system further includes:

[0040] The modeling and optimization module is used to establish a mathematical model of the bending stress of the transmission line; based on the mapping relationship between the axial tension of the transmission line, the friction force between the strands and the bending stiffness of the transmission line, the parameters of the mathematical model of the bending stress of the transmission line are optimized, and the mathematical model of the bending stress of the transmission line with the optimized parameters is used as the calculation model of the bending stress of the transmission line.

[0041] As a preferred solution, the model calibration module specifically includes:

[0042] An analysis unit is used for analyzing and obtaining the stress generated by the transmission wire under each parameter combination based on the strain generated by the transmission wire under each parameter combination;

[0043] The sampling unit is used to obtain a sample set of the posterior distribution of the parameters of the transmission line bending stress calculation model by sampling through an MCMC algorithm based on the prior distribution of the parameters of the transmission line bending stress calculation model and the bending displacement and stress generated by the transmission line under each parameter combination; and to construct the bending stress prediction model based on the sample set of the posterior distribution of the parameters and the transmission line bending stress calculation model. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 : A schematic diagram of a process for constructing a bending stress prediction model provided in Example 1 of the present invention;

[0045] Figure 2 : A schematic flow chart of a method for predicting bending stress of a transmission line provided in the second embodiment of the present invention;

[0046] Figure 3 : A structural schematic diagram of a bending stress prediction model construction system provided in Example 3 of the present invention. DETAILED DESCRIPTION

[0047] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] Embodiment one:

[0049] Please refer to Figure 1 , is a method for constructing a bending stress prediction model provided by an embodiment of the present invention, the method includes steps S1 to S3, each step is specifically as follows:

[0050] Step S1, arranging a displacement sensor at a first preset position of the wire clamp, and pasting a strain gauge at a second preset position of the transmission wire.

[0051] In this embodiment, the first preset position of the wire clamp is a position 89 mm away from the last contact point of the wire clamp. The second preset position of the transmission wire is a surface of the transmission wire close to the wire clamp.

[0052] Step S2: using a displacement sensor to measure the bending displacement Y of the transmission line under the action of each parameter combination. b , and use strain gauges to measure the strain generated by the transmission wire under the action of each parameter combination.

[0053] The parameter combination includes the axial tension T and the vibration frequency f of the transmission line.

[0054] Step S3, using the MCMC algorithm, combined with the bending displacement and strain generated by the transmission line under each parameter combination, the pre-constructed transmission line bending stress calculation model is Bayesian calibrated, and the transmission line bending stress calculation model that has completed the Bayesian calibration is used as the bending stress prediction model.

[0055] As a preferred solution, a bending stress prediction model construction method provided in an embodiment of the present invention further includes a model construction optimization process before executing step S3, and the process includes steps S4 to S5, and each step is specifically as follows:

[0056] Step S4, establishing a mathematical model of the bending stress of the transmission line.

[0057] As a preferred solution, the mathematical model of the bending stress of the transmission line is specifically described in equations (1)(2)(3)(4)(5).

[0058] σ b =KY b ; (1)

[0059]

[0060] In the formula, σ b Represents the bending stress amplitude on the surface of the transmission line; Y b represents the bending displacement amplitude measured by the displacement sensor; K represents the Poffenberger coefficient; E a represents the elastic modulus of the aluminum stranded wire; d represents the diameter of the outer stranded wire; a represents the distance between the displacement sensor and the last contact point of the clamp; λ represents the parameters related to the axial tension T and bending stiffness EI of the transmission line; the bending stiffness EI of the transmission line is min0 To EI max0 The time is uniformly distributed; n a Indicates the number of aluminum strands; d a Indicates the diameter of the aluminum stranded wire; n s Indicates the number of steel strands; E s Indicates the elastic modulus of the steel strand; d s Indicates the diameter of the steel strand; r a It indicates the average radius of the aluminum strand layer in the steel core aluminum stranded wire.

[0061] In this embodiment, formula (1) is the Poffenberger-Swart (PS) formula. For the PS formula, the main parameters to be calibrated are the bending stiffness EI and the axial tension T. Based on prior knowledge, it is assumed that EI is min0 To EI max0 The time interval is uniformly distributed, and T is also uniformly distributed within the experimental error range. min0 and EI max0 They are calculated by equations (4) and (5) respectively.

[0062] Step S5, based on the mapping relationship between the axial tension of the transmission line, the friction force between the strands and the bending stiffness of the transmission line, the parameters of the mathematical model of the bending stress of the transmission line are optimized, and the mathematical model of the bending stress of the transmission line with optimized parameters is used as the calculation model of the bending stress of the transmission line.

[0063] As a preferred solution, the mapping relationship between the friction force between the strands and the bending stiffness of the transmission line is specifically shown in formula (6).

[0064] EI=EI min +(EI max -EI min )(1-e -βκ ); (6)

[0065] Where β is a parameter related to the friction coefficient μ between the strands, and β controls the bending stiffness EI of the transmission line from EI min To EImax The transition rate, the larger the β value, the stronger the friction between the strands, and the bending stiffness of the wire quickly approaches EI as the curvature increases. max ; κ represents the bending curvature of the transmission line.

[0066] In this embodiment, the friction coefficient μ is introduced to describe the friction characteristics between the strands. Assuming that when the curvature of the wire is small, there is relative sliding between the outer strands and the inner strands, and the bending stiffness at this time is close to EI min When the bending curvature increases to a certain value, the friction between the strands overcomes the relative sliding, and the bending stiffness of the conductor gradually transitions to EI max The relationship between the bending stiffness EI and the curvature κ can be described by equation (6). β can be used as a parameter to be calibrated in the model and is obtained by inverting the experimental data.

[0067] As a preferred solution, considering that the bending stiffness of the transmission line is also affected by the axial tension T, a mapping relationship between the axial tension of the transmission line and the bending stiffness of the transmission line is proposed. For details, please refer to equations (7) and (8).

[0068]

[0069] Where, EI min Indicates the minimum bending stiffness of the transmission line; EI max Indicates the maximum value of the bending stiffness of the transmission line; EI min0 It indicates the minimum value of the bending stiffness of the transmission line in the initial state (for example, tension-free state), which is related to the material properties and geometric configuration of the wire and reflects the ability of the wire to resist bending deformation when it slides relative to the strands. max0 It indicates the maximum value of the bending stiffness of the transmission line in the initial state, which corresponds to the bending stiffness of the conductor when there is no relative sliding between the strands, and mainly depends on the material properties and cross-sectional dimensions of the conductor. The bending stiffness EI of the transmission line is min0 To EI max0 The time interval obeys uniform distribution; T represents the axial tension of the transmission line; T0 represents the rated breaking force of the transmission line; α1, α2, n1, and n2 represent dimensionless parameters related to the axial tension of the transmission line, which can be obtained through calibration of experimental data.

[0070] Among them, α1 reflects the minimum bending stiffness EI of the conductor. min The scale factor of the power law relationship with the axial tension T. The larger α1 is, the greater the tension on EI min The more significant the impact is. n1 represents EI min The exponent of the power law relationship with the axial tension T. The larger n1 is, the greater EI minThe faster the growth rate is, the faster the tension increases. α2 reflects the maximum bending stiffness EI of the wire. max The scale factor of the power law relationship with the axial tension T. Similar to α1, the larger α2 is, the greater the tension on EI max The more obvious the impact is. n2 represents EI max The exponent of the power law relationship with the axial tension T. Similar to n1, the larger n2 is, the greater EI max The growth rate increases with the increase of axial tension.

[0071] It should be noted that the greater the axial tension of the transmission line, the greater the contact force between the strands and the greater the bending stiffness.

[0072] In this embodiment, after considering the influence of the friction between the strands and the axial tension of the transmission line, the Poffenberger coefficient K in formula (1) also needs to be corrected. The corrected expression is shown in formula (9).

[0073]

[0074] Where, the expression of λ′ can be found in equation (10).

[0075]

[0076] Where EI is calculated by referring to the functions in equations (6), (7), and (8).

[0077] In summary, the mathematical model of transmission line bending stress with optimized parameters, i.e., the expression of transmission line bending stress calculation model, is completed. For details, please refer to equations (1)(6)(7)(8)(9)(10). Among them, 7 parameters to be calibrated are introduced in the transmission line bending stress calculation model - parameter β related to friction coefficient μ, parameters α1, n1, α2 and n2 related to axial tension T, and initial bending stiffness EI min0 and EI max0 In the subsequent step S3, the above 7 parameters to be calibrated are calibrated in a Bayesian manner through the experimental data such as the bending displacement and stress generated by the transmission line under each parameter combination, and the posterior distribution of the parameters can be obtained, which is used for the uncertainty propagation analysis of the bending stress.

[0078] It should be noted that although the refined mathematical model increases the computational complexity, it can more accurately describe the bending behavior of transmission lines and help improve the reliability of bending stress assessment.

[0079] As a preferred solution, step S3 includes step S31 to step S33, and each step is specifically as follows:

[0080] Step S31, based on the strain generated by the transmission line under each parameter combination, the stress σ generated by the transmission line under each parameter combination is analyzed and obtained. b .

[0081] Step S32, using the MCMC algorithm, based on the prior distribution of the parameters of the transmission line bending stress calculation model, and the bending displacement and stress generated by the transmission line under each parameter combination, a sample set of the posterior distribution of the parameters of the transmission line bending stress calculation model is sampled.

[0082] In this embodiment, step S32 includes step S321 to step S323, and each step is specifically as follows:

[0083] Step S321: based on the bending displacement Y of the transmission line generated by each parameter combination obtained in step S2, b , and the stress σ generated by the transmission line under each parameter combination obtained in step S31 b , construct M sets of experimental data, each set of data includes the bending displacement Y under a given axial tension T and frequency f b and stress σ b , that is, D = {(T i , f i , Y bi , σ bi ), i = 1, 2, ..., M}. The parameter to be calibrated of the model is θ = [EI min0 , EI max0 , β, α1, n1, α2, n2].

[0084] Step S322, define the likelihood function p(D|θ) and the prior distribution p(θ).

[0085] Specifically, according to Bayes' theorem, the posterior distribution p(θ|D) of the parameter is proportional to the product of the likelihood function p(D|θ) and the prior distribution p(θ), see formula (11) for details.

[0086] p(θ|D)∝p(D|θ)p(θ); (11)

[0087] The likelihood function p(D|θ) measures the probability of the observed data D occurring given the parameters θ.

[0088] Assuming that the observation errors follow an independent and identically distributed Gaussian distribution, the expression of the likelihood function can be found in equation (12).

[0089]

[0090] In the formula, σ bi(θ) is the stress prediction value corresponding to the i-th group of data calculated by parameter θ, and s is the standard deviation of the observation error.

[0091] The prior distribution of the parameter p(θ) is set according to prior knowledge. For example, for EI min0 and EI max0 , we can assume that they obey the log-normal distribution as shown in equations (13) and (14).

[0092]

[0093] Among them, μ min , σ min , μ max , σ max It is estimated based on the existing transmission line bending stiffness test results or experience.

[0094] For other parameters such as β, α1, n1, α2, n2, appropriate prior distributions can be selected according to their physical meanings, such as uniform distribution, Gamma distribution, etc.

[0095] Step S323, after defining the likelihood function and the prior distribution, use the MCMC algorithm to sample the posterior distribution of the parameter. Commonly used MCMC algorithms include the Metropolis-Hastings algorithm and the Gibbs sampling algorithm. Taking the Metropolis-Hastings algorithm as an example, its sampling steps are as follows:

[0096] Initialize parameter vector θ0 and set the number of iterations N;

[0097] For the t-th iteration (t=1, 2, ..., N):

[0098] a. According to the proposal distribution q(θ|θ t-1 ) Generate candidate parameters θ * ;

[0099] b. Refer to formula (15) to calculate the acceptance probability:

[0100] a t =min{1,(p(θ * |D)q(θ t-1 |θ * ) / (p(θ t-1 |D)q(θ * |θ t-1 ))}; (15)

[0101] c. Sample u from the uniform distribution U(0,1), if u t , then accept the candidate parameters and let θ t =θ​* , otherwise let θ t =θ t-1 .

[0102] Get the sample set {θ1, θ2, ..., θ N}.

[0103] To improve sampling efficiency, adaptive MCMC algorithms such as the Adaptive Metropolis algorithm or the Hamiltonian Monte Carlo algorithm can be used.

[0104] Step S33, constructing a bending stress prediction model based on the sample set of the posterior distribution of the parameter and the transmission line bending stress calculation model.

[0105] Embodiment two:

[0106] Please refer to Figure 2 , a bending stress prediction method provided by an embodiment of the present invention is applied to a transmission line. The method includes steps S6 to S8, and each step is specifically as follows:

[0107] Step S6, obtaining the bending displacement of the transmission line to be predicted.

[0108] Step S7, using the bending stress prediction model and combining the bending displacement of the transmission line to be predicted, analyzing and obtaining a plurality of bending stress samples corresponding to the transmission line to be predicted.

[0109] The bending stress prediction model is constructed using the bending stress prediction model construction method described in the first embodiment.

[0110] Step S8: analyzing the probability distribution of the bending stress of the transmission line to be predicted based on all bending stress samples corresponding to the transmission line to be predicted.

[0111] In this embodiment, after obtaining the posterior distribution samples of the parameters, the calibrated model can be used to propagate uncertainty to obtain the probability distribution of the bending stress of the wire. The specific steps are as follows:

[0112] Randomly sample S sets of parameter values ​​θ from the parameter posterior distribution sample s =[EI min0s , EI max0s , β s , α 1s , n 1s , α 2s , n 2s ], s = 1, 2, ..., S;

[0113] For each set of parameter values ​​θ s, please refer to formula (16) to calculate the corresponding Poffenberger coefficient K s .

[0114]

[0115] in, EI s By θ s Calculated.

[0116] For a given bending displacement Yb, refer to equation (17) to calculate S sets of bending stress samples.

[0117] σ bs =K s Y b ,s=1,2,...,S; (17)

[0118] According to the bending stress samples of group S, estimate the bending stress σ b The mean, variance, quantile and other statistics of are used to obtain its probability distribution.

[0119] Repeat the above steps to obtain different bending displacements Y b Probability distribution of bending stress in the lower conductor.

[0120] It should be noted that in order to evaluate the prediction performance of the calibrated model, the root mean square error (RMSE), log probability density (Log-likelihood) and confidence interval coverage (Coverage Ratio) and other indicators can be used to compare the bending stress probability distribution predicted by the model with the measured data. Among them, the expression of the root mean square error (RMSE) can be found in formula (18), the log probability density (Log-likelihood) can be found in formula (19), and the confidence interval coverage (Coverage Ratio) can be found in formula (20).

[0121]

[0122] In the formula, μ i is the predicted mean value of bending stress corresponding to the experimental data of the i-th group. RMSE reflects the average deviation between the predicted value and the measured value.

[0123]

[0124] In the formula, p(σ bi |Y bi ,D) is the bending stress prediction probability density function corresponding to the i-th group of experimental data. LL measures the overall explanatory power of the model for the measured data.

[0125]

[0126] In the formula, Q i (α) is the α quantile of the predicted bending stress distribution corresponding to the i-th group of experimental data, and I(·) is the indicator function. CR reflects the coverage of the confidence interval of the model prediction to the measured data.

[0127] In addition, a scatter plot of the predicted bending stress distribution and the measured data can be drawn to intuitively evaluate the prediction performance of the model.

[0128] Embodiment three:

[0129] Please refer to Figure 3 , is a structural schematic diagram of a bending stress prediction model construction system provided by an embodiment of the present invention, the system includes a data acquisition module M1 and a model calibration module M2, and the specific details of each module are as follows:

[0130] The data acquisition module M1 is used to arrange a displacement sensor at a first preset position of the wire clamp, and to paste a strain gauge at a second preset position of the transmission wire; the displacement sensor is used to measure the bending displacement of the transmission wire under the action of each parameter combination, and the strain gauge is used to measure the strain of the transmission wire under the action of each parameter combination; wherein the parameter combination includes the axial tension and vibration frequency of the transmission wire;

[0131] The model calibration module M2 is used to perform Bayesian calibration on the pre-constructed transmission line bending stress calculation model by combining the bending displacement and strain generated by the transmission line under each parameter combination through the MCMC algorithm, and use the transmission line bending stress calculation model that has completed the Bayesian calibration as the bending stress prediction model.

[0132] As a preferred option, please refer to Figure 3 The bending stress prediction model construction system provided by the embodiment of the present invention also includes a modeling optimization module M3, which is specifically as follows:

[0133] The modeling optimization module M3 is used to establish a mathematical model of the bending stress of the transmission line; based on the mapping relationship between the axial tension of the transmission line, the friction between the strands and the bending stiffness of the transmission line, the parameters of the mathematical model of the bending stress of the transmission line are optimized, and the mathematical model of the bending stress of the transmission line with optimized parameters is used as the calculation model of the bending stress of the transmission line.

[0134] As a preferred solution, the model calibration module M2 specifically includes an analysis unit 21 and a sampling unit 22, and the details of each unit are as follows:

[0135] An analysis unit 21 is used to analyze and obtain the stress generated by the transmission wire under each parameter combination based on the strain generated by the transmission wire under each parameter combination;

[0136] The sampling unit 22 is used to obtain a sample set of the posterior distribution of the parameters of the transmission line bending stress calculation model through the MCMC algorithm based on the prior distribution of the parameters of the transmission line bending stress calculation model and the bending displacement and strain generated by the transmission line under each parameter combination; and to form a bending stress prediction model based on the sample set of the posterior distribution of the parameters and the transmission line bending stress calculation model.

[0137] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the system described above can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0138] Compared with the prior art, the embodiments of the present invention have the following beneficial effects:

[0139] The present invention provides a bending stress prediction model construction method, system and bending stress prediction method. A displacement sensor is arranged at a first preset position of a line clamp, and a strain gauge is pasted at a second preset position of a transmission line, so that the displacement sensor is used to measure the bending displacement of the transmission line under the action of each parameter combination, and the strain gauge is used to measure the strain of the transmission line under the action of each parameter combination. Through the joint measurement of the displacement sensor and the strain gauge, the mechanical behavior of the transmission line under different load conditions can be more comprehensively understood, thereby revealing its structural performance and reliability in practical applications. Then, through a Markov chain Monte Carlo (MCMC) sampling algorithm, combined with the above-mentioned measured data - the bending displacement and strain generated by the transmission line under the action of each parameter combination, a pre-constructed transmission line bending stress calculation model is Bayesian calibrated, which can efficiently explore the parameter posterior distribution based on the measured data, realize the probability estimation and uncertainty quantification of the model parameters, and make the model prediction result more in line with the actual performance of the transmission line, thereby optimizing the bending stress prediction model for predicting the bending stress of the transmission line, avoiding complex finite element modeling and calculation, and improving the transmission line bending stress calculation speed while ensuring accuracy. In addition, considering the combination of parameters such as axial tension and vibration frequency can make the model adaptable in different environments and operating conditions, and enhance the operational stability of the transmission line under complex conditions.

[0140] The specific embodiments described above further illustrate the purpose, technical solutions and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. It is particularly pointed out that for those skilled in the art, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for constructing a bending stress prediction model, characterized in that: include: A displacement sensor is arranged at a first preset position of the wire clamp, and a strain gauge is pasted at a second preset position of the transmission wire; The displacement sensor is used to measure the bending displacement of the transmission wire under the action of each parameter combination, and the strain gauge is used to measure the strain of the transmission wire under the action of each parameter combination; wherein the parameter combination includes the axial tension and vibration frequency of the transmission wire; Through the MCMC algorithm, combined with the bending displacement and strain generated by the transmission line under each parameter combination, the pre-constructed transmission line bending stress calculation model is Bayesian calibrated, and the transmission line bending stress calculation model that has completed the Bayesian calibration is used as the bending stress prediction model.

2. A method for constructing a bending stress prediction model according to claim 1, characterized in that: The construction of the transmission line bending stress calculation model is specifically as follows: Establish a mathematical model of bending stress of transmission lines; Based on the mapping relationship between the axial tension of the transmission line, the friction force between the strands and the bending stiffness of the transmission line, the parameters of the mathematical model of the bending stress of the transmission line are optimized, and the mathematical model of the bending stress of the transmission line with optimized parameters is used as the calculation model of the bending stress of the transmission line.

3. A method for constructing a bending stress prediction model according to claim 2, characterized in that: The mathematical model of the bending stress of the transmission line is specifically: σ b =KY b ; In the formula, σ b Represents the bending stress amplitude on the surface of the transmission line; Y b represents the bending displacement amplitude measured by the displacement sensor; K represents the Poffenberger coefficient; E a represents the elastic modulus of the aluminum stranded wire; d represents the diameter of the outer stranded wire; a represents the distance between the displacement sensor and the last contact point of the clamp; λ represents the parameters related to the axial tension T and bending stiffness EI of the transmission line; the bending stiffness EI of the transmission line is min0 To EI max0 The time is uniformly distributed; n a Indicates the number of aluminum strands; d a Indicates the diameter of the aluminum stranded wire; n s Indicates the number of steel strands; E s Indicates the elastic modulus of the steel strand; d s Indicates the diameter of the steel strand; r a It indicates the average radius of the aluminum strand layer in the steel core aluminum stranded wire.

4. A method for constructing a bending stress prediction model according to claim 2, characterized in that: The mapping relationship between the friction force between the strands and the bending stiffness of the transmission line is specifically: NO=NO min +(NO max -NO min (1-e) -βκ ); Where β is a parameter related to the friction coefficient μ between the strands, and β controls the bending stiffness EI of the transmission line from EI min To EI max The transition rate; κ represents the bending curvature of the transmission line.

5. A method for constructing a bending stress prediction model according to claim 2, characterized in that: The mapping relationship between the axial tension of the transmission wire and the bending stiffness of the transmission wire is specifically: Where, EI min Indicates the minimum bending stiffness of the transmission line; EI max Indicates the maximum value of the bending stiffness of the transmission line; EI min0 Indicates the minimum value of the bending stiffness of the transmission line in the initial state; EI max0 It indicates the maximum value of the bending stiffness of the transmission line in the initial state; the bending stiffness EI of the transmission line is EI min0 To EI max0 The time interval obeys uniform distribution; T represents the axial tension of the transmission line; T0 represents the rated breaking force of the transmission line; α1, α2, n1, and n2 represent parameters related to the axial tension of the transmission line.

6. A method for constructing a bending stress prediction model according to claim 1, characterized in that: The MCMC algorithm is used to combine the bending displacement and strain of the transmission line under each parameter combination to perform Bayesian calibration on the pre-constructed transmission line bending stress calculation model, and the transmission line bending stress calculation model that has completed the Bayesian calibration is used as the bending stress prediction model, specifically: Based on the strain generated by the transmission line under each parameter combination, the stress generated by the transmission line under each parameter combination is analyzed and obtained; By using the MCMC algorithm, based on the prior distribution of the parameters of the transmission line bending stress calculation model and the bending displacement and stress generated by the transmission line under each parameter combination, a sample set of the posterior distribution of the parameters of the transmission line bending stress calculation model is obtained by sampling; The bending stress prediction model is constructed based on the sample set of the posterior distribution of the parameters and the transmission line bending stress calculation model.

7. A bending stress prediction method, characterized in that: Applied to transmission lines, including: Obtaining the bending displacement of the transmission line to be predicted; Using a bending stress prediction model, combined with the bending displacement of the transmission line to be predicted, a number of bending stress samples corresponding to the transmission line to be predicted are analyzed and obtained; wherein the bending stress prediction model is constructed using a bending stress prediction model construction method according to any one of claims 1 to 6; The probability distribution of the bending stress of the transmission line to be predicted is analyzed according to all the bending stress samples corresponding to the transmission line to be predicted.

8. A bending stress prediction model construction system, characterized in that: include: A data acquisition module is used to arrange a displacement sensor at a first preset position of the wire clamp and to paste a strain gauge at a second preset position of the transmission wire; The displacement sensor is used to measure the bending displacement of the transmission wire under the action of each parameter combination, and the strain gauge is used to measure the strain of the transmission wire under the action of each parameter combination; wherein the parameter combination includes the axial tension and vibration frequency of the transmission wire; The model calibration module is used to perform Bayesian calibration on the pre-built transmission line bending stress calculation model by combining the bending displacement and strain generated by the transmission line under each parameter combination through the MCMC algorithm, and use the transmission line bending stress calculation model that has completed the Bayesian calibration as the bending stress prediction model.

9. A bending stress prediction model construction system according to claim 8, characterized in that: Also includes: Modeling and optimization module, used to establish the mathematical model of bending stress of transmission lines; Based on the mapping relationship between the axial tension of the transmission line, the friction force between the strands and the bending stiffness of the transmission line, the parameters of the mathematical model of the bending stress of the transmission line are optimized, and the mathematical model of the bending stress of the transmission line with optimized parameters is used as the calculation model of the bending stress of the transmission line.

10. A bending stress prediction model construction system according to claim 8, characterized in that: The model calibration module specifically includes: An analysis unit is used for analyzing the stress generated by the transmission wire under each parameter combination based on the strain generated by the transmission wire under each parameter combination; The sampling unit is used to obtain a sample set of the posterior distribution of the parameters of the transmission line bending stress calculation model by sampling through an MCMC algorithm based on the prior distribution of the parameters of the transmission line bending stress calculation model and the bending displacement and stress generated by the transmission line under each parameter combination; and to construct the bending stress prediction model based on the sample set of the posterior distribution of the parameters and the transmission line bending stress calculation model.

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