Rotation sampling spectrum-based fan response peak factor calculation method during variable pitch

Abstract

The invention discloses a fan response peak factor calculation method based on a rotation sampling spectrum during variable pitch, and the method comprises the steps: building a high-order moment and probability distribution theory calculation model of the aerodynamic load and tower structure response of a fan under a variable pitch condition through considering the nonlinear characteristics of a time-varying pitch angle and based on a rotation sampling wind speed spectrum frequency domain analysis framework; and then, according to a CDF-Mapping method and a Hermite model, theoretical evaluation of a tower structure response short-term peak factor is realized. According to the method, the accurate calculation of the response peak factor of the tower structure is realized, and the design efficiency of the fan structure is improved.

Description

Technical Field

[0001] This invention belongs to the field of wind power generation technology, and in particular relates to a method for calculating the peak factor of wind turbine response during pitch control based on a rotating sampling spectrum. Background Technology

[0002] To improve wind energy utilization efficiency, wind turbines are continuously becoming larger, with support structures becoming more flexible, their natural frequencies and damping reduced, making them more sensitive to wind-induced dynamic responses. Modern wind turbine blades have complex aerodynamic shapes, and during operation, the turbine adjusts its speed and pitch angle in real time according to changes in the wind field. This dynamic characteristic further increases the complexity of aerodynamic loads. Numerous studies have shown that the response of wind turbine support structures in operation exhibits significant non-Gaussian characteristics, with a marked increase in extreme responses, and this non-Gaussian characteristic is even more pronounced under complex terrain and non-Gaussian wind field conditions. Evaluating the peak factor of the dynamic response of the wind turbine support structure according to a Gaussian process would severely underestimate the extreme responses. While time-domain simulation tools such as FAST and BLADED can directly simulate the time history of the wind turbine structure's dynamic response and statistically obtain the peak factor, the large sample size in time-domain calculations severely restricts the efficiency of scheme comparison in the early stages of wind turbine design.

[0003] Scholars have developed empirical formulas (including response mean, variance, and peak factor) for calculating the 10-minute short-term extreme response of wind turbine towers by fitting simulation results. However, these empirical formulas are only simplified data-driven models and have not yet deeply analyzed the physical mechanism of pitch control on aerodynamic loads, thus failing to establish a universal mathematical connection between time-varying pitch angle and the probability distribution of extreme response of the support structure. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for calculating the peak factor of wind turbine response during pitch control based on a rotating sampling spectrum.

[0005] This invention provides a method for calculating the peak factor of wind turbine response under pitch control based on a rotating sampling spectrum. By considering the nonlinear characteristics of the time-varying pitch angle, and establishing a high-order moment and probability distribution theoretical calculation model of the wind turbine aerodynamic load and tower structural response under pitch control based on a rotating sampling wind speed spectrum frequency domain analysis framework, the method then evaluates the short-term peak factor of the tower structural response using the CDF-Mapping method and the Hermite model. Specifically, the method includes the following steps:

[0006] Step 1: Wind field transformation.

[0007] In turbulent wind fields, the wind speed experienced by the rotating blades of a wind turbine differs from that at a fixed point in space. To facilitate frequency domain analysis of the load on the wind turbine blades during operation, it is necessary to convert the conventional fixed-point wind spectrum into a rotating sampled wind speed spectrum to account for the blade rotation effect. Assuming the rotational speed is... The rotation frequency is blade radius and Interval between two points The wind speed is and Its related functions Using fixed-point correlation functions express:

[0008] (1)

[0009] (2)

[0010] (3)

[0011] In the formula, Indicates the sign of the expectation; This represents the bilateral wind speed spectrum at a fixed point. Represents natural frequency; For wind speed spatial coherence function; This represents the initial phase angle. For a three-bladed fan, when two points are located on the same blade, When the two points are located on different blades, ; .

[0012] For related functions The theoretical expression for the rotating sampled wind speed spectrum is obtained by performing a Fourier transform:

[0013] (4)

[0014] (5)

[0015] Step 2: Simplified representation of time-varying pitch angle.

[0016] Based on the steady-state wind speed-pitch angle relationship, the time-varying pitch angle can be approximately represented linearly by the fluctuating wind speed:

[0017] (6)

[0018] (7)

[0019] (8)

[0020] In the formula, The pitch coefficient is linear and is determined by the slope of the steady-state wind speed-pitch angle curve. This represents the effective wind speed after filtering and time-delay shifting, which represents the fluctuating wind speed. The impeller represents the pulsating wind speed, which is considered to be the average of the wind speeds sampled at various points along the entire impeller. This is the pitch delay time; Let be the impulse response function of the low-pass filter. Represents a time variable; Number of leaves; This refers to the blade length.

[0021] Based on the steady-state wind speed-pitch angle relationship curve, the pitch angle is expressed as a nonlinear function of wind speed:

[0022] (9)

[0023] In the formula, Represents a polynomial function; The average wind speed at the wheel hub; The initial pitch speed is generally close to the rated speed.

[0024] The steady-state wind speed-pitch angle relationship is an ideal pitch curve. In practical applications, such as commonly used gain PI control strategies, it cannot perfectly follow this curve in turbulent wind fields and often exhibits stronger nonlinear characteristics. Therefore, it is necessary to make certain empirical corrections to the wind speed-pitch angle relationship curve to cut off the wind speed. Define the corrected pitch angle as a reference:

[0025] (10)

[0026] (11)

[0027] In the formula, Represents a polynomial function; This represents the pitch angle correction amplitude coefficient; and These represent the rated wind speed and the cut-out wind speed, respectively.

[0028] The modified simplified nonlinear pitch model is expressed as follows:

[0029] (12)

[0030] In the formula, This represents the initial pitch wind speed of the corrected pitch model.

[0031] Step 3: Frequency domain calculation of aerodynamic load and tower structure response.

[0032] Establish the first-order modal motion equations of the tower:

[0033] (13)

[0034] (14)

[0035] in, The first-order modal generalized displacement at the top of the tower; The generalized velocity of the first-order mode at the top of the tower; The first-order modal generalized acceleration at the top of the tower; For first-order modal generalized mass; Indicates the mass of the blades and nacelle; Indicates the distributed mass of the tower; The first-order modal angular frequency, The natural frequency of the first-order mode; and These represent the first-order structural damping ratio and the aerodynamic damping ratio, respectively. It is a first-order modal shape function; The load is a first-order modal generalized load, and the tower load is ignored. , This indicates the impeller thrust.

[0036] The power spectrum of the bending moment at the base of the tower is expressed as:

[0037] (15)

[0038] (16)

[0039] (17)

[0040] In the formula, The impeller thrust power spectrum, For tower-order modal generalized stiffness, This refers to the tower height.

[0041] The tower response is decomposed into background response and resonant response. The background response is estimated using a quasi-static analysis method, while the resonant response is considered as white noise excitation.

[0042] (18)

[0043] ; (19)

[0044] (20)

[0045] In the formula, Indicates impeller thrust; This represents the standard deviation of impeller thrust.

[0046] The background response of the tower structure maintains the same probability distribution as the load. According to the central limit theorem, the output of any distributed white noise after passing through a finite bandwidth linear system is approximately a Gaussian process; therefore, the resonant response can be considered as a Gaussian distribution. Finally, the probability distribution of the total response of the tower structure is obtained by convolving the probability distributions of the background response and the resonant response:

[0047] (twenty one)

[0048] In the formula, (z), and Let represent the probability distribution functions of the total response, background response, and resonance response, respectively.

[0049] blade radius The outward thrust pulsating load per unit length in a plane is expressed as:

[0050] (twenty two)

[0051] (twenty three)

[0052] In the formula, Indicates the combined wind speed of the blades; This is the chord length of the blade; This refers to the blade rotation speed; This represents the derivative of the lift coefficient with respect to the angle of attack; For pulsating angle of attack; The pulsating inflow angle; This is the pulsating propeller pitch angle.

[0053] Integrating the distributed load over the blades yields the total impeller pulsating thrust:

[0054] (twenty four)

[0055] (25)

[0056] (26)

[0057] Nonlinear pitch control significantly affects the higher-order moments and non-Gaussian probability distribution of aerodynamic loads, but has a relatively small impact on their power spectrum and standard deviation. Therefore, when calculating the power spectrum of aerodynamic loads, if the nonlinear effect of pitch control is ignored and a linear pitch model is used, the impeller thrust power spectrum can be calculated using the following formula:

[0058] (27)

[0059] (28)

[0060] (29)

[0061] (30)

[0062] (31)

[0063] (32)

[0064] (33)

[0065] (34)

[0066] (35)

[0067] In the formula, This represents the thrust power spectrum caused by the inflow angle; This represents the thrust power spectrum caused by the pitch angle; This represents the cross-power spectrum of thrust caused by the inflow angle and thrust caused by the pitch angle. Indicates blade and Cross-power spectrum of two-point inflow angle; This indicates that the impeller represents the power spectrum of pulsating wind speed; Indicates blade The sampling wind speed at the location and the cross-power spectrum representing the pulsating wind speed.

[0068] According to equations (12) and (26), the pulsating thrust caused by the time-varying pitch angle From latent Gaussian processes Through nonlinear functions Indicate, respectively using and express and For two Gaussian processes, the moment of the thrust load is calculated using the following formula:

[0069] (36)

[0070] (37)

[0071] In the formula, Indicates pulsating thrust Specific values.

[0072] in Let be the joint probability density function of two Gaussian processes. The correlation coefficient is expressed by the following formula:

[0073] (38)

[0074] In the formula express The standard deviation is calculated using the power spectrum according to equation (28); express Standard deviation, through its power spectrum calculate.

[0075] The impeller thrust probability density function PDF and cumulative probability density function CDF are calculated using the following formula:

[0076] (39)

[0077] (40)

[0078] In the formula, This indicates the specific value of the thrust in the pitch control state.

[0079] After obtaining the probability density function of the load, the probability density function of the dynamic response of the tower structure is calculated by equations (19)-(21), and the statistical moments of the response are calculated by the probability density function.

[0080] Step 4: Theory of the transfer process and estimation of the peak factor.

[0081] Non-Gaussian processes with zero mean and unit variance Through memoryless monotonic translation functions and latent standard Gaussian processes Related:

[0082] (41)

[0083] in and These represent the specific values ​​for the standard non-Gaussian and Gaussian processes, respectively. It is a translation function; and They are respectively and The cumulative probability function CDF; express The inverse function of .

[0084] The extremum distribution of a non-Gaussian process is determined by the extremum distribution of the underlying Gaussian process (the number of crossovers follows a Poisson distribution) and the translation function:

[0085] (42)

[0086] in, For random processes At the threshold The average upcrossing rate at a given point, due to the monotonically increasing property of the translation function, is related to the Gaussian process. At the threshold The average upcrossing rate is equal at each location; Duration; For transfer function The inverse function; For a random process at the mean The upcrossing rate at a given point is estimated using the power spectrum of a stochastic process:

[0087] (43)

[0088] According to the theory of transport processes, the extremum distribution of any standard non-Gaussian process... quantile The transfer function is obtained by standard Gaussian process calculation; the transfer function is obtained by direct curve fitting of the numerical translation function generated by CDF-Mapping of cumulative distribution function, or by Hermite polynomial, whose coefficients are determined based on the statistical moments of non-Gaussian process.

[0089] The beneficial technical effects of this invention are as follows:

[0090] This invention considers the nonlinear characteristics of time-varying pitch angles and establishes a high-order moment and probability distribution theoretical calculation model for the aerodynamic loads and tower structural response of wind turbines under variable pitch conditions based on a rotating sampling wind speed spectrum frequency domain analysis framework. Then, it uses transfer process methods such as the CDF-Mapping method and the Hermite model to theoretically evaluate the short-term peak factor of the tower structural response, thereby improving the efficiency of wind turbine structural design. Attached Figure Description

[0091] Figure 1 The spatial geometric relationship of wind speed for blade rotation sampling.

[0092] Figure 2 , Figure 3 The pitch angle versus wind speed curve is shown below. Figure 2 This is the steady-state pitch angle (basic). Figure 3 To correct the pitch angle.

[0093] Figure 4 A simplified model of an onshore wind turbine.

[0094] Figure 5 This is a schematic diagram of the formation mechanism of non-Gaussian aerodynamic loads in pitch control mode.

[0095] Figure 6 , Figure 7 The probability distribution of the bending moment response at the base of the tower ( (15 and 21 m / s respectively).

[0096] Figure 8 , Figure 9 The probability of exceeding the bending moment response at the base of the tower ( (15 and 21 m / s respectively).

[0097] Figure 10 This is the peak factor of the bending moment response at the base of the tower. Detailed Implementation

[0098] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0099] This invention provides a method for calculating the peak factor of wind turbine response during pitch control based on a rotating sampling spectrum, which mainly unfolds along two paths. The first path approximates a linear pitch assumption, calculating the impeller aerodynamic load and tower dynamic response in the frequency domain. The response is decomposed into a background response and a resonant response, and their standard deviations are determined. The uppass rate of the total response is then obtained using spectral methods. The second path needs to consider the nonlinear pitch effect. First, the non-Gaussian probability distribution of the impeller aerodynamic load is derived. Based on this, the background response is considered a quasi-static response, assumed to be distributed in the same way as the load; the resonant response is considered a Gaussian process under white noise excitation. Subsequently, the probability distribution after the superposition of the two is synthesized using a convolution method. Finally, the peak factor of the tower response is solved by combining the response distribution, uppass rate, and transmission process theory. Taking the NREL-5MW wind turbine as an example, the steps are as follows:

[0100] Step 1: Wind Field Transformation

[0101] When the wind turbine is in pitch control mode, the speed is maintained near the rated speed, and the speed is The rotation frequency is The fixed-point wind speed spectrum is converted into a rotating sampled wind speed spectrum according to the following formula:

[0102] (44)

[0103] (45)

[0104] (46)

[0105] In the formula, Represents the bilateral wind speed spectrum at a fixed point; For wind speed spatial coherence function; This represents the initial phase angle. For a three-bladed fan, when two points are located on the same blade, When the two points are located on different blades, ; The spatial geometric relationship of the blade sampling wind speed is as follows: Figure 1 As shown.

[0106] Step 2: Establish the relationship between wind speed and propeller pitch angle

[0107] Establish an approximately linear relationship between wind speed and blade pitch angle:

[0108] (47)

[0109] (48)

[0110] (49)

[0111] In the formula, The linear pitch coefficient can be determined by the slope of the steady-state wind speed-pitch angle curve. This represents the effective wind speed after filtering and time-delay shifting, which represents the fluctuating wind speed. The impeller represents the pulsating wind speed, which can be considered as the average of the wind speed sampled at various points on the entire impeller. For the pitch delay time, for the NREL-5MW wind turbine, it can be taken as... = 46 m; This is the impulse response function of the low-pass filter.

[0112] In practical applications, the frequency range of pitch angle variation is generally low. When using wind speed to represent the pitch angle, it is necessary to filter out its high-frequency components. Here, a center-point moving average filter is used, and its transfer function (i.e., the Fourier transform of the impulse response function) is:

[0113] (50)

[0114] In the formula For time step, The number of points in the moving average and the moving average time. With wind speed Increase and grow, for the NREL-5MW wind turbine, take = 0.22 m.

[0115] Establish a nonlinear relationship between wind speed and blade pitch angle:

[0116] (51)

[0117] The basic pitch model polynomial function The coefficients are as follows: , , , , Corrected pitch model polynomial function The coefficients are as follows: , , , , The pitch curve is as follows: Figure 2 , Figure 3 As shown.

[0118] Step 3: Calculation of aerodynamic loads and tower structure response

[0119] The total aerodynamic load on the impeller can be expressed as: , This represents the pulsating thrust caused by the inflow angle. The thrust pulsating due to the pitch angle is represented by the linear pitch model. Ignoring the nonlinear effects of pitch control, the impeller thrust power spectrum can be approximated using a linear pitch control model.

[0120] (52)

[0121] (53)

[0122] (54)

[0123] (55)

[0124] (56)

[0125] (57)

[0126] (58)

[0127] (59)

[0128] (60)

[0129] In the formula This represents the rotating sampled wind speed spectrum.

[0130] according to Figure 4 Calculate the power spectrum of bending moment at the base of an onshore wind turbine using a single-degree-of-freedom dynamic model:

[0131] (61)

[0132] (62)

[0133] (63)

[0134] In the formula, For tower-order modal generalized stiffness; The first-order modal generalized displacement at the top of the tower; Indicates the mass of the blades and nacelle; Indicates the distributed mass of the tower; The first-order modal frequency; and These represent the first-order structural damping ratio and the aerodynamic damping ratio, respectively. It is a first-order modal shape function; This indicates the impeller thrust.

[0135] The tower response can be decomposed into background response and resonant response:

[0136] ; (64)

[0137] (65)

[0138] The aerodynamic load caused by the inflow angle is a Gaussian process, and the nonlinear pitch control causes the aerodynamic load. As being non-Gaussian, the final synthesized aerodynamic load exhibits a non-Gaussian behavior, such as... Figure 5 According to equations (51) and (54), the pulsating thrust caused by the time-varying pitch angle It can be derived from a latent Gaussian process Through nonlinear functions Indicated. Respectively using and express and For two Gaussian processes, the moment of the thrust load can be calculated using the following formula:

[0139] (66)

[0140] (67)

[0141] in Let be the joint probability density function of two Gaussian processes. The correlation coefficient is expressed by the following formula:

[0142] (68)

[0143] In the formula express The standard deviation is calculated using the power spectrum according to equation (28); express Standard deviation, through its power spectrum calculate.

[0144] The impeller thrust probability density function (PDF) and cumulative probability density function (CDF) can be calculated using the following formula:

[0145] (69)

[0146] (70)

[0147] The background response of the tower structure maintains the same probability distribution as that of the load. According to the central limit theorem, the output of any distributed white noise after passing through a finite bandwidth linear system is approximately a Gaussian process. Therefore, the resonance response can be regarded as a Gaussian distribution, and the standard deviations of the two are calculated using equations (64) and (65). Finally, the probability distribution of the total response of the tower structure can be obtained by convolution operation of the probability distributions of the background response and the resonance response:

[0148] (71)

[0149] In the formula, (z), and Let represent the probability distribution functions of the total response, background response, and resonance response, respectively.

[0150] 4. Transport process theory and peak factor estimation

[0151] The extremum distribution of a non-Gaussian process can be determined by the extremum distribution of the underlying Gaussian process (the number of crossovers follows a Poisson distribution) and the translation function:

[0152] (72)

[0153] in, For random processes At the threshold The average upcrossing rate at a given point, due to the monotonically increasing property of the translation function, is related to the Gaussian process. At the threshold The average upcrossing rate is equal at each location; Duration; For transfer function The inverse function; For a random process at the mean The upcrossing rate at a given point is estimated using the power spectrum of a stochastic process:

[0154] (73)

[0155] According to the theory of transport processes, the extremum distribution of any standard non-Gaussian process... quantile It is calculated by a standard Gaussian process; the transfer function is obtained by direct curve fitting of the numerical translation function generated by the cumulative distribution function mapping (CDF-Mapping), or by Hermite polynomials, whose coefficients are determined based on the statistical moments of the non-Gaussian process.

[0156] Due to the pitch angle limiting device, the pitch angle will not decrease further when it reaches 0 degrees. At lower wind speeds, the tower response probability distribution exhibits strong asymmetry. Since the Hermite model often lacks sufficient fitting accuracy for the tail of the distribution when dealing with strongly asymmetric non-Gaussian processes, the CDF-Mapping method is more suitable in this case. Under high wind speed conditions, the tail estimation of the response probability distribution is easily affected by extreme values, resulting in poor stability. However, the probability distribution exhibits good symmetry, making the Hermite model's prediction results more reliable. It is recommended to use both methods simultaneously, taking the smaller value to estimate the peak factor.

[0157] (74)

[0158] Figure 6 , Figure 7 The probability distribution of the theoretically calculated bending moment response at the bottom of the tower is compared with the results of FAST simulation. Figure 8 , Figure 9 The theoretical calculation of the exceedance probability of the bending moment response at the bottom of the tower is compared with the FAST simulation results. Figure 10 The paper presents a comparison between the estimated peak moment factor at the tower base and the FAST simulation results. The method of this invention can effectively reflect the non-Gaussian probability distribution characteristics of the tower structure response, revealing the physical mechanism of the formation of non-Gaussian characteristics in the tower response under wind turbine pitch control and achieving efficient estimation of the short-term non-Gaussian peak moment factor of the tower response.

Claims

1. A method for calculating the peak factor of wind turbine response during pitch control based on a rotating sampling spectrum, characterized in that, By considering the nonlinear characteristics of time-varying pitch angles and establishing a high-order moment and probability distribution theoretical calculation model for the aerodynamic loads and tower structural response under variable pitch conditions based on the rotating sampling wind speed spectrum frequency domain analysis framework, the short-term peak factor of the tower structural response is evaluated using the CDF-Mapping method and the Hermite model. Specifically, the following steps are included: Step 1: Wind field transformation; The conventional fixed-point wind spectrum was converted into a rotating sampled wind speed spectrum to account for the blade rotation effect, assuming the rotational speed was... The rotation frequency is blade radius and Interval between two points The wind speed is and The correlation function of its wind speed Using fixed-point correlation functions express: （1） （2） （3） In the formula, Indicates the sign of the expectation. This represents the bilateral wind speed spectrum at a fixed point. Represents natural frequency; For wind speed spatial coherence function; This represents the initial phase angle. For a three-bladed fan, when two points are located on the same blade, When the two points are located on different blades, ; ; For related functions The theoretical expression for the rotating sampled wind speed spectrum is obtained by performing a Fourier transform: （4） （5） Step 2: Simplified representation of time-varying pitch angle; Based on the steady-state wind speed-pitch angle relationship, the time-varying pitch angle can be approximately represented linearly by the fluctuating wind speed: （6） （7） （8） In the formula, The pitch coefficient is linear and is determined by the slope of the steady-state wind speed-pitch angle curve. This represents the effective wind speed after filtering and time-delay shifting, which represents the fluctuating wind speed. The impeller represents the pulsating wind speed, which is considered to be the average of the wind speeds sampled at various points along the entire impeller. This is the pitch delay time; This is the impulse response function of a low-pass filter; Represents a time variable; Number of leaves; The blade length; Based on the steady-state wind speed-pitch angle relationship curve, the pitch angle is expressed as a nonlinear function of wind speed: （9） In the formula, Represents a polynomial function. The average wind speed at the wheel hub; The initial pitch speed is generally close to the rated wind speed. The wind speed-pitch angle relationship curve is empirically corrected to cut off the wind speed. Define the corrected pitch angle as a reference: （10） （11） In the formula, Represents a polynomial function; This represents the pitch angle correction amplitude coefficient; and These represent the rated wind speed and the cut-out wind speed, respectively. The modified simplified nonlinear pitch model is expressed as follows: （12） In the formula, This represents the initial pitch wind speed of the corrected pitch model; Step 3: Frequency domain calculation of aerodynamic loads and tower structure response; Establish the first-order modal motion equations of the tower: （13） （14） in, The first-order modal generalized displacement at the top of the tower; The generalized velocity of the first-order mode at the top of the tower; The first-order modal generalized acceleration at the top of the tower; For first-order modal generalized mass; Indicates the mass of the blades and nacelle; Indicates the distributed mass of the tower; The first-order modal frequency, The natural frequency of the first-order mode; and These represent the first-order structural damping ratio and the aerodynamic damping ratio, respectively. It is a first-order modal shape function; The load is a first-order modal generalized load, and the tower load is ignored. , Indicates impeller thrust; The power spectrum of the bending moment at the base of the tower is expressed as: （15） （16） （17） In the formula, The impeller thrust power spectrum, For tower-order modal generalized stiffness; The tower height; The tower response is decomposed into background response and resonant response. The background response is estimated using a quasi-static analysis method, while the resonant response is considered as white noise excitation. （18） ; （19） （20） In the formula, Indicates impeller thrust; The standard deviation of impeller thrust; The background response of the tower structure maintains the same probability distribution as the load. The probability distribution of the total response of the tower structure is obtained by convolution of the probability distributions of the background response and the resonant response. （21） In the formula, (z), and Let represent the probability distribution functions of the total response, background response, and resonance response, respectively; blade radius The outward thrust pulsating load per unit length in a plane is expressed as: （22） （23） In the formula, Indicates the combined wind speed of the blades; This is the chord length of the blade; This refers to the blade rotation speed; This represents the derivative of the lift coefficient with respect to the angle of attack; For pulsating angle of attack; The pulsating inflow angle; This refers to the pulsating propeller pitch angle; Integrating the distributed load over the blades yields the total impeller pulsating thrust: （24） （25） （26） When calculating the power spectrum of aerodynamic loads, if the nonlinear effect of pitch control is ignored and a linear pitch control model is used, the impeller thrust power spectrum is calculated using the following formula: （27） （28） （29） （30） （31） （32） （33） （34） （35） in, This represents the thrust power spectrum caused by the inflow angle; This represents the thrust power spectrum caused by the pitch angle; This represents the cross-power spectrum of thrust caused by the inflow angle and thrust caused by the pitch angle. Indicates blade and Cross-power spectrum of two-point inflow angle; This indicates that the impeller represents the power spectrum of pulsating wind speed; Indicates blade The sampling wind speed at the location and the cross-power spectrum representing the fluctuating wind speed; According to equations (12) and (26), the pulsating thrust caused by the time-varying pitch angle From latent Gaussian processes Through nonlinear functions Indicate, respectively using and express and For two Gaussian processes, the moment of the thrust load is calculated using the following formula: （36） （37） In the formula, Indicates pulsating thrust Specific values; in Let be the joint probability density function of two Gaussian processes. The correlation coefficient is expressed by the following formula: （38） In the formula express The standard deviation is calculated using the power spectrum according to equation (28); express Standard deviation, through its power spectrum calculate; The impeller thrust probability density function PDF and cumulative probability density function CDF are calculated using the following formula: （39） （40） In the formula, Indicates the specific value of thrust in pitch control mode; After obtaining the probability density function of the load, the probability density function of the dynamic response of the tower structure is calculated by equations (19)-(21), and the statistical moments of the response are calculated by the probability density function. Step 4: Transmission process theory and peak factor estimation; Non-Gaussian processes with zero mean and unit variance Through memoryless monotonic translation functions and latent standard Gaussian processes Related: （41） in and These represent the specific values ​​for the standard non-Gaussian and Gaussian processes, respectively. It is a translation function; and They are respectively and The cumulative probability function CDF; express The inverse function; The extremum distribution of a non-Gaussian process is determined by the extremum distribution and translation function of the underlying Gaussian process: （42） in, For random processes At the threshold The average upcrossing rate at a given point, due to the monotonically increasing property of the translation function, is related to the Gaussian process. At the threshold The average upcrossing rate is equal at each location; Duration; For transfer function The inverse function; For a random process at the mean The upcrossing rate at a given point is estimated using the power spectrum of a stochastic process: （43） According to the theory of transport processes, the extremum distribution of any standard non-Gaussian process... quantile The transfer function is obtained by standard Gaussian process calculation; the transfer function is obtained by direct curve fitting of the numerical translation function generated by CDF-Mapping of cumulative distribution function, or by Hermite polynomial, whose coefficients are determined based on the statistical moments of non-Gaussian process.

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