Extreme value combination method of power transmission tower line system under non-Gaussian wind vibration response

Abstract

The invention relates to the technical field of power transmission tower lines, in particular to an extreme value combination method of a power transmission tower line system under non-Gaussian wind vibration response, which comprises a method for comparing and discussing a Gaussian peak factor calculated by a classical formula with a tower line system response peak factor determined by wind tunnel test data; based on Monte Carlo sample parameter analysis of a first override theory and a complete quadratic combination criterion, exporting a corrected complete quadratic combination criterion suitable for the tower line system and a corresponding peak factor formula; aeroelastic wind tunnel test data is adopted to verify and correct the precision of the complete quadratic combination criterion, and parameterization research is carried out to inspect the influence of a non-Gaussian response component on a combined extreme value, so that a correction CQC extreme value estimation criterion is established; quantitative analysis in combination with correlation coefficients and standard deviations shows that the MCQC criterion has excellent precision in estimation of the total wind vibration response of the tower line system. Effectiveness of the MCQC criterion is verified based on wind tunnel test data, and a predicted value is well matched with a test value.

Description

Technical Field

[0001] The present invention relates to the technical field of transmission towers and lines, and in particular to an extreme value combination method for a transmission tower and line system under non-Gaussian wind vibration response. Background Art

[0002] The dynamic response of tower-line systems under wind loads may exhibit significant non-Gaussian characteristics, which is mainly attributed to their complex operating environment (such as airflow disturbances in mountainous terrain and extreme climatic conditions) and the inherent nonlinear dynamic characteristics of the structure. Structural responses with non-Gaussian characteristics will accelerate fatigue damage. However, current international standards for wind-resistant design of high-rise buildings generally assume that the structural response is a stationary Gaussian random process when calculating extreme values. This traditional method may introduce potential safety risks under long-term wind loads. Accurately characterizing the probability distribution of structural responses and accurately estimating the extreme value response quantity are the basic prerequisites for structural reliability analysis and performance-based design. Therefore, it is urgent to establish an extreme value combination criterion that effectively incorporates the non-Gaussian wind-induced response of tower-line systems.

[0003] Current approaches to modeling non-Gaussian wind-induced responses include: high-order cumulants (using Volterra series to extract the third / fourth moments of the response to construct a non-Gaussian peak factor model); neural network models (using deep learning to map the target non-Gaussian power spectrum to a Gaussian spectrum to efficiently generate non-Gaussian time histories); and Bayesian extreme value theory (integrating the threshold exceedance method with the Poisson process to accurately estimate the tail distribution and quantifying uncertainty through prior-posterior updating). Methods based on extreme value statistics of random processes do not require a preset distribution form and are widely applicable to various types of non-Gaussian excitations.

[0004] Existing research indicates that ignoring non-Gaussian characteristics in the analysis of extreme responses of tension leg platform structures can lead to underestimated responses. Three-dimensional wind-induced responses often exhibit non-Gaussian properties, and applying traditional Gaussian combination criteria will result in significant extreme value estimation errors. The first transcendence theory of non-Gaussian processes provides a potential framework for improved combination strategies for high-rise buildings. Gong and Chen proposed a modified CQC criterion to address the bias in extreme value estimation of combinations containing non-Gaussian components, but its computational complexity limits its engineering application. Due to the presence of long-span flexible cables, the wind-induced response of tower-cable systems exhibits significant nonlinear characteristics. This means that Gaussian-based extreme value combination criteria may inaccurately predict wind-induced vibrations in tower-cable systems, compromising structural resilience under extreme wind loads. Liu et al. systematically reviewed research directions and future trends in the resilience of critical infrastructure systems, such as energy grids. To improve structural resilience, an assessment framework that considers the impact of structural degradation has been proposed. It is important to emphasize that, as a key component of power grid infrastructure, tower-cable systems require accurate consideration of the extreme values ​​of wind-induced vibration responses to enhance wind resilience.

[0005] However, the existing extreme value combination criteria ignore the impact of non-Gaussian wind vibration of the tower-line system on extreme value estimation. Summary of the Invention

[0006] The purpose of the present invention is to provide an extreme value combination method for a transmission tower-line system under non-Gaussian wind-induced vibration response, aiming to solve the problem that the existing extreme value combination criterion ignores the impact of non-Gaussian wind-induced vibration of the tower-line system on extreme value estimation.

[0007] To achieve the above object, the present invention provides an extreme value combination method for a transmission tower-line system under non-Gaussian wind-induced vibration response, comprising the following steps:

[0008] The Gaussian peak factor calculated by the classical formula and the peak factor method of the tower-line system response determined by wind tunnel test data are compared and discussed.

[0009] Based on the Monte Carlo sample parameter analysis of the first transcendence theory and the perfect quadratic combination criterion, a modified perfect quadratic combination criterion and the corresponding peak factor formula applicable to the tower-line system are derived.

[0010] The accuracy of the modified complete quadratic combination criterion is verified using aeroelastic wind tunnel test data.

[0011] Among them, the peak factor method requires: the wind tunnel test adopts a 1:5 scale ratio, the average wind speed at the top of the tower is 4m / s, the data acquisition system is set to a sampling frequency of 51.2Hz, the total duration is 30h, the extreme value samples are divided into 10-minute time intervals, and a total of 180 groups of valid data samples are obtained at each measuring point.

[0012] Among them, the wind-induced vibration response characteristics of the tower-line system were tested and analyzed at four key measuring points, including two T-type tower measuring points and two double-span conductor measuring points. The T-type tower measuring points included the downwind displacement measuring point T1 and the crosswind displacement measuring point T2, and the double-span conductor measuring points included the mid-span measuring point L1 and the 1 / 4 span measuring point L2.

[0013] Among them, the random vibration process of the lower transmission tower line system cannot be characterized by a deterministic function and needs to be quantitatively described using a probabilistic statistical method. It can be divided into a Gaussian process and a non-Gaussian process. The Gaussian vibration process can be determined by the mean, variance and power spectrum density function; while the non-Gaussian vibration process exhibits significant skewed probability density distribution characteristics. If the equivalent Gaussian method is used, it will lead to significant simulation errors. It is necessary to introduce higher-order statistics such as skewness and kurtosis to accurately characterize the probability distribution characteristics of the non-Gaussian process.

[0014] The trajectory of the non-Gaussian signal can be obtained by static transformation of a potential Gaussian process, and the Monte Carlo method is used to simulate a combination of a non-Gaussian process and a standard Gaussian process.

[0015] The present invention provides an extreme value combination method for transmission tower-line systems under non-Gaussian wind-induced vibration response. The method compares and discusses the Gaussian peak factor calculated by the classical formula and the peak factor method of the tower-line system response determined by wind tunnel test data. Based on the Monte Carlo sample parameter analysis of the first transcendence theory and the complete quadratic combination criterion, a modified complete quadratic combination criterion and the corresponding peak factor formula applicable to the tower-line system are derived. The accuracy of the modified complete quadratic combination criterion is verified using aeroelastic wind tunnel test data. This method uses wind tunnel test data to generate extreme value samples with specified first four statistical moments through Monte Carlo simulation. A parametric study is carried out to examine the influence of non-Gaussian response components on the combination extreme value, and then a modified CQC (MCQC) extreme value estimation criterion is established. Quantitative analysis of the correlation coefficient and standard deviation shows that, among the classical combination criteria, the proposed MCQC criterion has excellent accuracy in estimating the total wind-induced vibration response of the tower-line system. The effectiveness of the MCQC criterion is verified based on wind tunnel test data, and the predicted values ​​are in good agreement with the experimental values.

[0016] This method simultaneously considers the correlation between response components and their non-Gaussian characteristics, and verifies the effectiveness of the proposed criterion through comparative analysis of wind-induced vibration of tower-line systems using the classic combination criterion. The main conclusions are as follows:

[0017] If the wind-induced response of a tower-and-line system is assumed to follow a Gaussian distribution, the extreme response prediction will be underestimated, resulting in the peak factor based on the Gaussian assumption potentially failing to meet structural safety requirements. Therefore, the peak factor should be appropriately increased in the analysis of wind-induced extreme response of a tower-and-line system.

[0018] When there is a strong negative correlation between the non-Gaussian response component X1(t) and the Gaussian response component X2(t), the peak factor of the combined response P(t) increases with the standard deviation of X1(t). When the standard deviation of X1(t) reaches 1.5, the peak factor of P(t) exceeds that of X1(t), indicating that the combined extreme response may be amplified. In engineering practice, caution should be exercised regarding the combined effects of strongly correlated response components. The MCQC criterion exhibits a reduced root mean square error, a mean relative error approaching zero, and strong adaptability to varying correlation coefficients, demonstrating improved accuracy and robustness in both engineering reliability and statistical prediction.

[0019] For non-Gaussian extreme value combinations of tower-line systems, the SRSS and CQC criteria are less applicable than other criteria (especially for strongly negatively correlated components). The 40%, 75%, and TR criteria are more applicable to combinations of weakly correlated response components. The proposed MCQC criterion has a combined coefficient of 0.83 for tower-line systems. The SRSS and CQC criteria are less applicable for calculating extreme wind-induced displacement responses of tower-line systems. Compared with other criteria, the MCQC criterion reduces the average error of extreme value estimation by 53%, and the minimum relative error between its calculated and experimental values ​​is 5.27%, meeting engineering design requirements.

[0020] The method of estimating the total response of the tower-line system using wind-induced vibration response components effectively incorporates the non-Gaussian characteristics of wind-induced vibration. The MCQC criterion achieves optimal applicability when the standard deviation ratio is greater than 1.5 or the absolute value of the correlation coefficient is less than 0.4. For more complex transmission tower-line systems, future research needs to further explore the impact of lattice tower configurations and multi-split conductor arrangements on wind-induced vibration to improve the wind resilience of transmission lines. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0022] Figure 1 This is a flow chart of an extreme value combination method for a transmission tower line system under non-Gaussian wind vibration response provided by the present invention.

[0023] Figure 2 This is a schematic diagram of the distribution of displacement measurement points in the wind tunnel test.

[0024] Figure 3 are the probability distribution histograms of the response components and the total response, including (a) the probability distribution histogram of the response component X1(t), (b) the probability distribution histogram of the response component X2(t), and (c) the probability distribution histogram of the total response P(t).

[0025] Figure 4 Schematic diagram of the key statistical parameters and target values ​​of the Monte Carlo simulation results, including (a) mean, (b) standard deviation, (c) skewness, and (d) kurtosis.

[0026] Figure 5 This is a schematic diagram of the verification of the sample correlation coefficient and the target correlation coefficient, where (a) is the scatter plot of X1(t) and X2(t), and (b) is the relative error between the sample correlation coefficient and the target correlation coefficient.

[0027] Figure 6 It is g x1 Change curves under different standard deviations.

[0028] Figure 7 is the peak factor g of X1(t) x1 The changing curves under different skewness and kurtosis conditions, where (a) g x1 Change curve under different skewness conditions (b)g x1 Change curves under different kurtosis conditions.

[0029] Figure 8is the peak factor g of P(t) p Changes under different parameters, (a) g under different standard deviations and correlation coefficients p Changes in (b)g p Follow g x1 The changing relationship.

[0030] Figure 9 Comparison between the extreme values ​​calculated under different extreme value combination rules and the true values, including: (a) the relative error between the extreme values ​​calculated by the SRSS combination rule and the true value, (b) the relative error between the extreme values ​​calculated by the CQC combination rule and the true value, (c) the relative error between the extreme values ​​calculated by the 40% combination rule and the true value, (d) the relative error between the extreme values ​​calculated by the 75% combination rule and the true value, (e) the relative error between the extreme values ​​calculated by the TR combination rule and the true value, and (f) the relative error between the extreme values ​​calculated by the MCQC combination rule and the true value.

[0031] Figure 10 It is an aeroelastic model used for wind tunnel tests, including: a) Case 1: aeroelastic model of the tower without wires, Case 2: aeroelastic model of the tower-wire system with the tower covered, and Case 3: aeroelastic model of the tower-wire system.

[0032] Figure 11 is the probability density distribution of wind-induced vibration displacement response, where (a) measuring point T1 under working condition 1, (b) measuring point T2 under working condition 1, (c) measuring point T1 under working condition 2, (d) measuring point T2 under working condition 2, (e) measuring point T1 under working condition 3, and (f) measuring point T2 under working condition 3.

[0033] Figure 12 These are the correlation coefficient and standard deviation of measuring point T1 under working conditions 1 and 2, (a) correlation coefficient, (b) standard deviation.

[0034] Figure 13 is the relative error between the extreme displacement calculated by formula (26) and the test value. DETAILED DESCRIPTION

[0035] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0036] See also Figures 1 to 13 ,The present invention provides an extreme value combination method for a transmission tower-line system under non-Gaussian wind-induced vibration response, comprising the following steps;

[0037] S1 compares and discusses the Gaussian peak factor calculated by the classical formula and the peak factor method of the tower-line system response determined by wind tunnel test data;

[0038] In the embodiment of the present invention, it is assumed that n groups of random variables X1, X2, ..., X n Satisfies independent and identical distribution, the distribution function is F X (x), then relative to its extreme value The distribution of F X (x) is the parent distribution, the data set {x i}(i=1,2,…,n) is the population data. To obtain the extreme values ​​of the corresponding variables, there are three main data sample processing methods: using extreme value samples, using super-threshold samples, and using population samples. According to classical extreme value theory, when n→∞, its extreme value distribution form is one of the Gumbel distribution, Frechet distribution, and Weibull distribution, regardless of its original distribution form. Moreover, these three distributions can be expressed in a unified form, namely:

[0039]

[0040] in, and are the position, scale and shape parameters respectively.

[0041] The above formula is called the generalized extreme value distribution (GEVD). Formula (1) is the Gumbel distribution, which is as follows:

[0042]

[0043] Based on the extreme value data, the extreme value distribution of the data can be obtained by fitting using formula (1). The analysis of extreme wind speed based on long-term meteorological records can directly apply the classical extreme value theory, while the wind load and wind-induced vibration response data are subject to the sample limitations of wind tunnel tests. Therefore, in engineering practice, the extreme values ​​of wind load and wind-induced vibration response are usually analyzed and estimated based on the parent data. This paper mainly studies the non-Gaussian wind-induced vibration extreme value response characteristics of the tower-line system, and here the focus is on the solution method for the extreme value of non-Gaussian random wind-induced vibration response based on the parent sample.

[0044] For the non-Gaussian random wind-induced vibration response time history X(t), establish the relationship between X(t) and X s (t) is the conversion process of the mapping relationship between them, namely:

[0045]

[0046] where F Xand Φ represent X(t) and X s Cumulative distribution function of (t); Indicates F X The inverse function of Denotes X(t) and X S (t) is the mapping transformation relationship. When X(t) is the general Gaussian random wind vibration response time history, g(X s )=μ x +σ x X s (t). According to the literature

[30] , the extreme value distribution of the non-Gaussian random wind-induced vibration response time history is obtained as follows:

[0047]

[0048] Where T is the time interval; v 0x is the response X(t) in μ x The average penetration rate under horizontal conditions can be calculated by the following formula:

[0049]

[0050] where σ x and are the standard deviations of X(t) and the derivative of X(t); f is the frequency; S X (f) is the power spectral density function of X(t). The mapping relationship described by formula (1) is implicit. For non-Gaussian time history X(t) and standard Gaussian time history X S The explicit mapping relationship between (t) is explained in the Hermitepolynomialmodel (HPM) method. In addition, the non-Gaussian wind vibration response is divided into a hardening process and a softening process based on the kurtosis of the sample data with 3 as the boundary, where the softening is the sample with a kurtosis greater than 3, and the corresponding HPM form is also different. For the non-Gaussian wind vibration response, it is divided into a hardening process and a softening process based on the kurtosis less than 3 and greater than 3, and the corresponding HPM form is also different. Under normal circumstances, the peak factor of the hardening time history is smaller than that of the Gaussian time history, and it can be estimated more conservatively by the Gaussian peak factor. For the softened non-Gaussian wind vibration response time history X(t), assume that X s (t) is a normalized non-Gaussian time history, then the HPM form of the first N Hermite sequence time history is as follows:

[0051]

[0052] Where H(z) represents Hermitepolynomial; κ and h i is the polynomial parameter, which can be obtained by X s The first four statistical moments of (t) are determined. Hermitepolynomial function Hi (z) can be calculated by the following formula:

[0053]

[0054] Considering that the estimation error of higher-order moments of order 4 and above is too large, the first four orders are usually used, that is, when N=4:

[0055] X s (t)=κ[H1(z)+h3H2(z)+h4H3(z)], (8)

[0056] where, According to formula (7), we can know that H1(z)=z, H2(z)=z 2 -1, H3(z)=z 3 -3z. In order to accurately calculate the parameters h3 and h4 in the above formula, the following approximate calculation formula is proposed:

[0057]

[0058] where α3 and α4 represent X s The third and fourth moments of (t), namely skewness and kurtosis, are defined as follows:

[0059]

[0060] However, the above formula is limited by the number of samples in practical application. When the number of samples is insufficient, the calculation accuracy is not high. To solve this problem, a nonlinear analytical equation system with higher accuracy is proposed:

[0061]

[0062] By iteratively solving formula (11) and formula (12), the parameters h3 and h4 can be obtained. Based on formula (8), Z(t) can be expressed as X s (t), which is of the form:

[0063]

[0064] where, a=h3 / 3h4, b=1 / 3h4, d=(b-1-a 2 ) 3 However, the existence of formula (13) requires that the original function, formula (8), is monotonic, so it must satisfy the following formula:

[0065]

[0066] In order to improve the application efficiency of the above formula, the function area it represents is approximated as the inequality function area that the skewness and kurtosis need to satisfy, which is as follows:

[0067] 3+(1.25α3) 2 ≤α4. (15)

[0068] According to the extreme value distribution function of formula (4), The mean It can be calculated as follows:

[0069]

[0070] If X(t) obeys Gaussian distribution, then h3=h4=0 and κ=0. In this case, the calculated value of formula (16) is β+γ / β, which is the peak factor calculation formula. The peak factor calculated by this formula is defined as g D This shows that when the HPM method is used to calculate the extreme value response, the extreme value calculation of samples that satisfy the Gaussian distribution can be regarded as a special case of a non-Gaussian process. Subsequently, the non-Gaussian peak factor is expressed by the first four statistical moments of the Hermite polynomial as follows. The peak factor calculated by this formula is defined as g k :

[0071]

[0072] In the study of weakly softened non-Gaussian processes, a simplified empirical formula for the peak factor related only to the skewness parameter was established. This formula effectively incorporates the influence of the weak softening effect through empirical calibration, as shown below:

[0073]

[0074] Based on the measured extreme value data from wind tunnel tests, a verification study on the extreme values ​​of wind-induced vibration responses on T-type towers and double-span conductors was conducted to evaluate the applicability of Gaussian and non-Gaussian extreme value calculation methods.

[0075] The wind tunnel test used a 1:5 scale ratio, with an average wind speed of 4 m / s at the top of the tower (corresponding to a prototype wind speed of 20 m / s). The data acquisition system was set to a sampling frequency of 51.2 Hz and a total duration of 30 h. Extreme value samples were divided into 10-minute intervals, and a total of 180 groups of valid data samples were obtained at each measurement point, meeting the statistical requirements of the classical peak factor method. Given that the Hermite polynomial (Formula (17)) has both computational efficiency and theoretical completeness, this method was selected to evaluate the applicability of the HPM. Based on the wind-induced vibration response characteristics of the tower-line system, four key measurement points were selected for testing and analysis. Among them, the T-type tower measurement points include the downwind displacement measurement point T1 and the crosswind displacement measurement point T2; the double-span conductor measurement points include the mid-span measurement point L1 and the 1 / 4 span measurement point L2. Figure 2The schematic diagram of the measurement point arrangement is shown in Table 1. The skewness, kurtosis and calculated peak value results of the displacement response of each measurement point are systematically listed.

[0076] Table 1

[0077]

[0078] The peak factor developed by the Hermite polynomial model can reasonably model situations where the tower-line system response exhibits Gaussian characteristics, but it still results in significant errors when the tower-line system response exhibits a non-Gaussian distribution. It is particularly noteworthy that analyzing conductor response based on the Gaussian assumption leads to conservative designs for low-speed conditions (wasting materials) and dangerous designs for high-speed conditions (inadequate safety margins). Therefore, when analyzing conductor responses at extreme wind speeds, the peak factor should be appropriately increased.

[0079] S2 is based on the Monte Carlo sample parameter analysis of the first transcendence theory and the complete quadratic combination criterion, and the modified complete quadratic combination criterion and the corresponding peak factor formula applicable to the tower line system are derived;

[0080] In an embodiment of the present invention, the MCQC criterion is derived by integrating the first transcendence theory and the CQC criterion. Using the wind tunnel test data of the tower-line system, a large number of Gaussian and non-Gaussian samples are generated through Monte Carlo simulation to support extreme value analysis. Then, based on the statistical moments of the non-Gaussian response components, a parametric study of the standard deviation, correlation coefficient and peak factor of the combined response of the tower-line system is conducted. An empirical formula for the peak factor of the combined response is established, and finally an MCQC criterion specifically for the tower-line system is proposed. Finally, from the perspective of the correlation coefficient and standard deviation ratio, the applicability of the MCQC criterion is systematically compared with the SRSS, CQC and TR criteria.

[0081] Taking the wind-induced vibration response of a tower in a tower-line system under wind load as an example, a combination rule for estimating the extreme value of the total response P(t) is proposed. The tower response components caused by only the conductor support reaction and only the tower dynamic wind load are expressed as X1(t) and X2(t), respectively. Assume that their extreme values ​​are and In wind tunnel testing, when obtaining the non-Gaussian component X1(t), the entire tower is shielded, ensuring that there is no displacement response under the shielding. The tower displacement measured after the line is installed on the tower is then X1(t). When obtaining the Gaussian component X2(t), only the tower displacement response measured after the tower is installed is retained as X2(t). Consider the scalar (linear) composite response P(t) expressed in the two random response processes X1(t) and X2(t) as:

[0082] P(t)=X1(t)+X2(t) (19)

[0083] Without loss of generality, we will discuss the zero mean case below. According to Formula 5, we can get the extreme value of P:

[0084]

[0085] where,g p and σ p are the peak factor and standard deviation of P(t) respectively. p It can be calculated as follows:

[0086]

[0087] where, is the correlation coefficient of response components.

[0088] Assume that the peak factors of the response components X1(t) and X2(t) are approximately equal, that is, According to the CQC combination rule, we can get:

[0089]

[0090] In this case, the simplified CQC combination rule form can be obtained:

[0091]

[0092] where, and are the extreme values ​​of the response components X1(t) and X2(t), respectively; and are the peak factors of X1(t) and X2(t), respectively; and are the standard deviations of X1(t) and X2(t), respectively; is the correction coefficient. Combining formulas (20) and (24), Can be rewritten as:

[0093]

[0094] Here A is defined as the combination coefficient, is the ratio of the standard deviations of the response components X1(t) and X2(t).

[0095] Substituting formula (26) into formula (25) yields a simplified CQC combination rule, which is named MCQC:

[0096]

[0097] Random vibration processes cannot be characterized by deterministic functions and require a quantitative description using probabilistic statistical methods. In engineering practice, random vibration is selected as a stationary process whose statistical characteristic parameters do not change over time. Random processes can be divided into Gaussian and non-Gaussian processes. Based on their probability distribution characteristics, random processes can be divided into two categories: Gaussian and non-Gaussian. Gaussian vibration processes can be characterized by their mean, variance, and power spectral density (PSD). Non-Gaussian vibration processes, on the other hand, exhibit significant skewness in their probability density distribution. Using an equivalent Gaussianization method will result in significant simulation errors. To this end, it is necessary to introduce higher-order statistics such as skewness α3 and kurtosis α4 to accurately characterize the probability distribution characteristics of non-Gaussian processes.

[0098] The trajectory of the non-Gaussian signal can be represented by the latent Gaussian process X S (t) is obtained by static conversion. For specific conversion, refer to formula (3). At this time, z(t)=X S (t). Monte Carlo methods are used to simulate the combination of a non-Gaussian process X1(t) and a standard Gaussian process X2(t). The HPM of the non-Gaussian process is developed based on its first four statistical moments.

[0099] Generates time history samples at a given combination of mean, standard deviation, correlation coefficient, skewness, and kurtosis. Figure 3 (a)-(b) shows that the probability distribution histogram of the non-Gaussian process is steeper than that of the Gaussian process. This is because its kurtosis is greater than that of the Gaussian distribution. This also shows that the generated non-Gaussian distribution process initially meets the requirements. The probability distribution histogram of the scalar combination of the result response is as follows Figure 3 (c) In order to determine the optimal sample size to reduce computational cost and verify the accuracy of the generated Gaussian and non-Gaussian time history samples, the key statistical parameters of the actual history samples obtained based on Monte Carlo simulation, such as mean, standard deviation, skewness, and kurtosis, were compared with the target parameters. Figure 4 As shown in the figure, the sample statistical parameters gradually approach the target values ​​as the sample size increases, and the approach speed gradually slows down. After the sample size reaches 2×105, the sample statistical parameters become flat, and there is no significant change in the sample statistical parameters. Therefore, 2×105 is selected as the optimal sample size. This also shows that the Monte Carlo method used in this paper to generate the target time history samples is reasonable.

[0100] Since the correlation coefficient of the response component was selected as the key variable parameter, the correlation coefficient under the optimal sample size was compared with the target coefficient, e.g. Figure 5 shown. Figure 5 (a) shows the The following scatter plot shows a clear positive correlation with no obvious outliers. The slope of the linear regression line obtained by the least squares method is 0.802, which basically meets the target correlation coefficient. Depend on Figure 5 (b) It can be seen that The relative error between the sample correlation coefficient and the target correlation coefficient has been kept within 5%, meeting the accuracy requirement. In summary, the Monte Carlo simulation method can be used to generate the target time history.

[0101] Monte Carlo simulation is used to conduct a more in-depth study of the above-mentioned related variables in order to p According to the optimal sample size, 200 sets of time history samples with duration T = 2000s and time interval dt = 0.01s are generated for each working condition to ensure sufficient sample size to estimate the extreme value. The change curves under different standard deviations are as follows Figure 6 As shown in the figure, the superscripts "+" and "-" represent ±5% of the mean value of the corresponding target parameter. For non-Gaussian responses, when the skewness and kurtosis are constant, the change in the crest factor is small with the change in the standard deviation, showing repeated fluctuations. Figure 7 is the peak factor of the non-Gaussian response X1(t) The change curve under different skewness and kurtosis. For non-Gaussian response, its peak factor As the skewness and kurtosis increase, they increase and show a significant logarithmic relationship, so the logarithmic function can be used to describe their correlation.

[0102] Discussion on the effect of standard deviation and correlation coefficient on the peak factor g of scalar (linear) composite response P(t) p According to formula (19), the non-Gaussian response X1(t) and Gaussian response X2(t) under the working condition in Section 3.2 are combined to obtain P(t). Figure 8 (a) shows g p In different and The following curve, when When the peak factor g changes between 0 and 0.8, p along with The increase of increases with the increase of, and the rate of increase gradually becomes slow. and When the peak factor g p With the standard deviation of the non-Gaussian component The increase of Gradually slow down when it reaches about 1000 km / h, until it remains basically stable. In the range of 0.8, the peak factor and Remains essentially unchanged. Figure 8 As shown in (b), in a certain and Next, g p and It is an approximately linear relationship. From the previous analysis, we can see that It is mainly controlled by the skewness and kurtosis of X1(t), so it can be It can be viewed as a function of skewness α3 and kurtosis α4.

[0103] In summary, the peak factor g of the combined response P(t) p Related parameters In, g p and the standard deviation of the response component X1(t) and correlation coefficient They affect each other and are mainly controlled by the skewness and kurtosis of X1(t). Since this paper mainly studies the extreme value combination of non-Gaussian time history and Gaussian time history, the standard deviation of the Gaussian response component X2(t) Let's take 1, It can be calculated by Davenport's peak factor formula. p It changes with the standard deviation and correlation coefficient of X1(t). Therefore, combined with the above analysis, formula (26) can be redefined as follows:

[0104]

[0105] where, is the ratio of the peak factors of the response components; Ψ(·) is the ratio of the peak factors of the response components with respect to λ σ and function, let Based on Monte Carlo simulation data, the least squares method is used to Figure 8 The combined peak factor g in p The fitting is performed as follows:

[0106]

[0107] Where a i , i=1,2,3,4,5,6 are formula parameters.

[0108] Table 2.Parametervalues ​​for formula (29)

[0109]

[0110] The extreme value combination of non-Gaussian time history and Gaussian time history is studied, where the mean, variance, skewness and kurtosis of the non-Gaussian wind load response component X1(t) are set to and The mean, variance, skewness and kurtosis of the Gaussian distribution wind load response component X2(t) are set as and Correlation coefficient of the response component, Monte Carlo simulation was used to generate random component values ​​for the aforementioned specific conditions. For each operating condition, 200 time history samples were generated with a duration of T = 2000 s and a time interval of dt = 0.01 s to ensure a sufficient sample size for estimating extreme values. The maximum value of each response group was extracted, and the average of the 200 groups was calculated as the true value for each operating condition. Figure 9 The relative errors between the extreme values ​​of the tower-line system combinations calculated using different combination rules and the true values ​​under different correlation coefficients and standard deviations are shown, where the red dotted line represents the ±5% error range.

[0111] like Figure 9 As shown in the figure, the relative error between the extreme value and the true value of the SRSS and CQC rule combinations increases with the increase of the standard deviation ratio, and both deviate from the relative error range of e = ± 5%. This shows that the applicability of the SRSS and CQC rules is lower than that of other combination rules when used for non-Gaussian extreme value combinations. In particular, when the response components X1(t) and X2(t) show a strong negative correlation, the extreme value of the CQC rule combination is nearly 55% lower than the true value, which is difficult to ensure its safety for engineering design. When When , the extreme values ​​of 40%, 75% and TR combinations are closer to the true values, and as the standard deviation ratio increases, the relative error becomes smaller. When , both the 40% and 75% rules overestimate the combined extreme value, and the relative error with the true value reaches a maximum when the standard deviation ratio is around 1. It is worth noting that when the standard deviation ratio is less than 1, the TR rule combined extreme value will produce unacceptable errors. For the MCQC rule proposed in this paper, when When , no matter how the standard deviation ratio changes, the relative error is less than 5%; when When the standard deviation ratio is less than 1.5, the relative error between the extreme value and the true value is partially greater than 5%; but when the standard deviation ratio is greater than 1.5, the relative error is basically less than 5%. This shows that the MCQC rule is effective when the standard deviation ratio is greater than 1.5 or The results show that the average extreme value of the combined response calculated according to formula (25) is in better agreement with the Monte Carlo simulation results than other combination rules.

[0112] S3 uses aeroelastic wind tunnel test data to verify the accuracy of the modified complete quadratic combination criterion.

[0113] In the embodiment of the present invention, the wind vibration response data of the T-type tower-line system structure is used to perform extreme value analysis, and the MCQC rules proposed in this paper are verified based on the data. A wind tunnel test of the aeroelastic model of the tower-line system is carried out in the wind tunnel laboratory of Tianjin Institute of Water Science and Technology. The simulated landform category is Class B landform in the Chinese standard, and the ground roughness length is 0.23m. This section sets up three test conditions to determine the extreme values ​​of the total wind vibration response of the tower in the tower-line system using direct measurement and indirect measurement, such as Figure 10 (a)-(c) are shown. Condition 1 is used to measure the displacement response of the tower under wind load when there is no conductor acting. Condition 2 uses an aeroelastic model of the tower line with the tower body shielded to measure the tower displacement response caused by the conductor through the dynamic support reaction under wind load. Condition 3 is used to measure the tower displacement response caused by wind load acting on the actual tower line system. In addition, two measuring points are arranged on each model crossbar, and none of the measuring points are loose during the test. For each measuring point, the wind-induced displacement data can be divided into 180 segments of 10-minute data. In the following discussion, the influence of the mean and standard deviation of the time history X(t) will not be considered.

[0114] Figure 11 The comparison between the probability density distribution and Gaussian distribution of the longitudinal displacement response of the tower T1 and T2 measuring points under three working conditions is given. Figure 11 As can be seen from (a)-(b), under working condition 1, the actual distribution of the response is consistent with the Gaussian distribution. This shows that when calculating the extreme response of the wind-induced displacement of the T-type tower (without conductors), it is reasonable to assume that the response probability density function satisfies the Gaussian distribution, and the Davenport formula can be used to estimate the peak factor. Under working conditions 2 and 3, the actual probability distribution of the longitudinal displacement response of the T1 and T2 measuring points is partially different from the Gaussian distribution, and overall it exhibits a wider distribution characteristic. At high wind speeds, although the actual distribution form of the response is similar to the Gaussian distribution, it exhibits a "sharp and narrow" single-peak distribution form.

[0115] The mean skewness and kurtosis values ​​of the data at different measuring points for Conditions 1-3 are shown in Table 3. It can be seen that for the wind-induced displacement response of the tower top of the T-type tower-line system model, the kurtosis values ​​of the data are generally greater than 3 due to the tower-line model displacement caused by the conductor support reaction force due to non-Gaussian loads. In particular, under Condition 2, when the tower-line system model is only subjected to the conductor wind load, the peak factor at measuring point T1 is 15.5% and 7.8% larger than those under Conditions 1 and 3, respectively.

[0116] Table 3

[0117]

[0118]

[0119] This paper mainly focuses on the extreme value of wind-induced displacement in the downwind direction. Therefore, the correlation coefficient and standard deviation of the 10 sets of wind-induced displacement data at the T1 measuring point under the above working conditions 1 and 2 are obtained as follows: Figure 12 The correlation coefficient and standard deviation are both within the applicable range of the MCQC rule (standard deviation ratio greater than 1.5 or correlation coefficient < 0.4).

[0120] According to formula (26), the extreme value combination coefficient A is 0.83, and the relative error between the extreme value displacement response and the extreme value response under working condition 3 is as follows: Figure 13 As shown in Table 4, only one set of data has an error exceeding 10%. The relative error between the extreme values ​​calculated using the remaining formulas and the experimental extreme values ​​is within 5%, demonstrating good overall consistency. This verifies the accuracy of the extreme value combination coefficient for the T-type tower system. Furthermore, other combination rules were applied to calculate the extreme value response of wind-induced displacement at the T1 measuring point of the T-type tower system. The relative errors of different combination rules were obtained, as shown in Table 4. This indicates that applying the MCQC combination rule to calculate the extreme value response of wind-induced displacement for the T-type tower system is more accurate.

[0121] Table 4

[0122]

[0123] The above disclosure is only a preferred embodiment of the extreme value combination method of the transmission tower line system under non-Gaussian wind vibration response of the present invention. Of course, this cannot be used to limit the scope of rights of the present invention. Ordinary technicians in this field can understand that implementing all or part of the processes of the above embodiment and making equivalent changes in accordance with the claims of the present invention still fall within the scope of the invention.

Claims

1. An extreme value combination method for a transmission tower-line system under non-Gaussian wind-induced vibration response, characterized in that: The following steps are included: The Gaussian peak factor calculated by the classical formula and the peak factor method of the tower-line system response determined by wind tunnel test data are compared and discussed. Based on the Monte Carlo sample parameter analysis of the first transcendence theory and the perfect quadratic combination criterion, a modified perfect quadratic combination criterion and the corresponding peak factor formula applicable to the tower-line system are derived. The accuracy of the modified complete quadratic combination criterion is verified using aeroelastic wind tunnel test data.

2. The extreme value combination method of the transmission tower-line system under non-Gaussian wind-induced vibration response according to claim 1 is characterized in that ； The peak factor method requires that the wind tunnel test adopts a scale ratio of 1:5, the average wind speed at the top of the tower is 4m / s, the data acquisition system is set to a sampling frequency of 51.2Hz, the total duration is 30h, the extreme value samples are divided into 10-minute time intervals, and a total of 180 groups of valid data samples are obtained at each measuring point.

3. The extreme value combination method of the transmission tower-line system under non-Gaussian wind-induced vibration response according to claim 1 is characterized in that ； Four key measuring points were selected for testing and analysis of the wind-induced vibration response characteristics of the tower-line system, including two T-shaped tower measuring points and two double-span conductor measuring points. The T-shaped tower measuring points included the downwind displacement measuring point T1 and the crosswind displacement measuring point T2, and the double-span conductor measuring points included the mid-span measuring point L1 and the 1 / 4 span measuring point L2.

4. The extreme value combination method for a transmission tower-line system under non-Gaussian wind-induced vibration response according to claim 1, It is characterized by: The random vibration process of the lower transmission tower line system cannot be characterized by a deterministic function and needs to be quantitatively described using a probabilistic statistical method. It can be divided into a Gaussian process and a non-Gaussian process. The Gaussian vibration process can be determined by the mean, variance and power spectrum density function; while the non-Gaussian vibration process exhibits significant skewed probability density distribution characteristics. If the equivalent Gaussian method is used, it will lead to significant simulation errors. It is necessary to introduce higher-order statistics such as skewness and kurtosis to accurately characterize the probability distribution characteristics of the non-Gaussian process.

5. The extreme value combination method for a transmission tower-line system under non-Gaussian wind-induced vibration response according to claim 4, characterized in that: The trajectory of the non-Gaussian signal can be obtained by static transformation of the potential Gaussian process, and the Monte Carlo method is used to simulate the combination of a non-Gaussian process and a standard Gaussian process.

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