Wind power blade life extension evaluation method based on inverse Gaussian process

Abstract

The invention discloses a wind power blade life extension evaluation method based on an inverse Gaussian process, and the method employs the inverse Gaussian process to describe a blade rigidity degradation process, builds an inverse Gaussian process model of the blade rigidity degradation process, carries out the life evaluation of a blade through the built inverse Gaussian process model, and guarantees that the life meets the safety limit life of reliability. An optimal evaluation time period is also determined by optimizing the life extension evaluation time period to determine when to perform a next evaluation. According to the method, the nonlinear degradation process of the blade rigidity along with time can be simulated, the remaining service life and reliability of the blade are predicted, and important data support and analysis tools are provided for optimal service life extension decision making of the blade.

Description

Technical Field

[0001] The invention relates to the technical field of life extension assessment of in-service wind turbine blades, and in particular to a wind turbine blade life extension assessment method based on an inverse Gaussian process. Background Art

[0002] As the core component of wind turbine generators, the performance and quality of wind turbine blades directly affect the overall operating efficiency and safety of the unit. With the continuous development of wind power technology, the size of wind turbine blades has gradually increased, and the working environment has become increasingly complex, so it is particularly important to evaluate their lifespan.

[0003] The life of wind turbine blades is affected by many factors, including dynamic loads caused by changes in wind speed and direction, microscopic defects in the blade manufacturing process, and harsh natural environments (such as strong winds, low temperatures, etc.). These factors will accelerate fatigue damage to the blades and shorten their service life.

[0004] The life assessment of wind turbine blades is a complex and important process that requires the comprehensive use of multiple methods and technologies for assessment and analysis. Through scientific assessment processes and accurate assessment results, it can provide strong support for the maintenance, replacement and optimization design of wind turbine blades. Summary of the invention

[0005] The purpose of the present invention is to provide a wind turbine blade life extension assessment method based on an inverse Gaussian process, which can simulate the nonlinear degradation process of blade stiffness over time and predict the remaining service life and reliability of the blade, providing important data support and analysis tools for the optimal blade life extension decision.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] The present invention provides a wind turbine blade life extension assessment method based on an inverse Gaussian process, comprising:

[0008] (1) Define the degradation variable of wind turbine blades as the degree of blade stiffness degradation, use the inverse Gaussian process to describe the blade stiffness degradation process, and establish the inverse Gaussian process model of the blade stiffness degradation process;

[0009] (2) Use the established inverse Gaussian process model to evaluate the blade life to ensure that it meets the safety limit life of reliability;

[0010] (3) Optimize the life extension assessment time period to determine the optimal assessment time period to determine when to conduct the next assessment.

[0011] Furthermore, the specific method of establishing the inverse Gaussian process model of the blade stiffness degradation process includes:

[0012] S1, inverse Gaussian process modeling of blade stiffness degradation;

[0013] The inverse Gaussian process with strict monotonicity is used to describe the blade stiffness performance degradation process. Let Y(t) be the degradation characteristic of the blade at time t. The blade stiffness degradation Y(t) obeys the IG process and has the following properties:

[0014] ①, Y(t) = 0;

[0015] ②, Y(t) has independent increments, that is, for any 0<t1<t2<t3<t4, Y(t4)-Y(t3) and Y(t2)-Y(t1) are independent random variables;

[0016] ③ The degenerate increment Y(t)-Y(s) obeys the IG distribution, that is, Y(t)-Y(s)~IG(μΔΛ,λ(ΔΛ) 2 )(0≤s<t), where ΔΛ=Λ(t)-Λ(s), Λ(t) is a monotonically increasing function, and Λ(0)=0; when the random variable Y(t)~IG(μΛ(t),λΛ 2 (t)), where the shape parameter μ is a function of the load level; the scale parameter λ is a constant independent of the load level; Λ(t) is a monotonically increasing function related to time, in the form of a linear or power function; according to the properties of the IG process, the probability density function expression of Y(t) is:

[0017]

[0018] The cumulative distribution function expression of Y(t) is:

[0019]

[0020] Where: Φ(·)—standard normal distribution function;

[0021] S2. Determine the expression of the cumulative distribution function of blade life;

[0022] If the failure threshold of blade stiffness is E rc , then the blade life T D The performance degradation reaches E for the first time rc Time:

[0023] T D = inf{t|Y(t)≥E rc ,t>0} (11)

[0024] According to formula (11), T D The cumulative distribution function expression is:

[0025]

[0026] Furthermore, the specific method of blade life assessment includes:

[0027] S1. Determine the cumulative distribution function and probability density function of the remaining useful life of the blade and the expression of the blade reliability function based on the established inverse Gaussian process model;

[0028] The expression of the cumulative distribution function of the remaining service life of the blade is determined by: assuming that the blade has not failed at time ta, and the stiffness Y degenerates to E a , then the cumulative distribution function of the remaining service life Tr of the blade is expressed as:

[0029]

[0030] The probability density function of the remaining service life of the blade is expressed as:

[0031]

[0032] The blade life T D The reliability function is expressed as:

[0033] R(t)=Pr(T D >t)=Pr(Y<E rc )=1-F(t) (15)

[0034] Therefore, the blade reliability function is expressed as:

[0035]

[0036] S2. The maximum likelihood estimation method is used to estimate the parameters μ and λ in the inverse Gaussian process model. The estimated parameter values ​​μ and λ are substituted into equations (9), (10), (12), (13) and (16) respectively to obtain the probability density function of blade stiffness degradation, the cumulative distribution function of blade stiffness degradation, the cumulative distribution function of blade life, the cumulative distribution function of blade remaining service life and the blade reliability function based on the inverse Gaussian process. The life extension assessment is carried out based on the cumulative distribution function of blade remaining service life.

[0037] Furthermore, the step of estimating the parameters μ, λ in the inverse Gaussian process model using the maximum likelihood estimation method is:

[0038] (1) The blade is subjected to fatigue test. During the test, m measurements are performed. Then t1, t2, L t m The measured values ​​at the time are Y1, Y2, LY m , record ΔY j =Y j -Y j-1 , is the leaf at time t j-1 and t jThe stiffness degradation between j =t j -t j-1 , j = 1, 2, ... m, the likelihood function of blade stiffness degradation can be obtained as:

[0039]

[0040] The log-likelihood function is:

[0041]

[0042] Where: μ, λ—are the parameters to be estimated;

[0043] The blade stiffness degradation follows the IG process, E(t)~IG(μΛ(t),λΛ 2 (t)), Λ(t) is in the form of a linear or power function, assuming Λ(t) = t, ΔΛ(t) = Λ(t j )-Λ(t j-1 ) = t j -t j-1 , the degradation of blade stiffness ΔE(t j ) obeys the IG distribution, that is, ΔE(t j )~IG(μΛ(t j ),λΛ 2 (t j )), then the blade stiffness degradation ΔE(t j ) is:

[0044]

[0045] (2) Apply concentrated loads to the cross-section in the span direction of the blade so that each cross-section of the blade is subjected to a bending moment load in a specific direction, and measure the stiffness value under the action of these fatigue vibration times. The stiffness value is the performance degradation data of the blade after fatigue life;

[0046] (3) According to the measured stiffness value, the parameters of equation (24) are estimated, and the partial derivatives of μ and λ are calculated respectively, and their respective partial derivatives are set to 0, that is, As shown in formula (25), the maximum likelihood estimates of parameters μ and λ are obtained;

[0047]

[0048] Further, the optimization of the life extension evaluation time period to determine the optimal evaluation time period is to determine the optimal evaluation time period by obtaining the expected cost rate of blade evaluation. When the expected cost rate of evaluation is the lowest, the blade life extension evaluation time period is optimal. The expected cost rate of blade evaluation is the ratio of the expected evaluation cost to the expected time length. The specific method includes:

[0049] For the degradation process of blade degradation performance monotonically decreasing, if the degradation value ΔE at the service age ta is measured, a , the blade reliability at time ta+T is:

[0050]

[0051] The expected length of the blade life extension assessment cycle is:

[0052]

[0053] Definition c p represents the cost of evaluating the blades according to the life extension assessment plan, c f It represents the cost loss caused by the failure of the blade not being evaluated at time t k (k=0,1,2,L) Evaluate whether the blade continues to run until time t k+1 , or immediately implement the cost c p Preventive treatment, if the blade at time t k Run to t k+1 If the process fails, the implementation cost is c f The sudden failure of blades will inevitably cause additional costs. f >c p >0;

[0054] The expected cost of blade assessment during the renewal cycle is:

[0055] C r =c p R(t|t a ,ΔE a )+c f [1-R(t|t a ,ΔE a )] (19)

[0056] According to the relevant theory of the renewal process, the expected cost rate of blade evaluation is:

[0057]

[0058] Formula (20) minimizes the expected cost rate of blade evaluation, and the corresponding time is the optimal blade life extension evaluation time period:

[0059]

[0060] Beneficial technical effects of the present invention:

[0061] 1. The present invention constructs a blade stiffness degradation life extension assessment method based on the inverse Gaussian process, accurately estimates the inverse Gaussian process parameters through the maximum likelihood estimation method, and derives the cumulative distribution function of the blade life, the cumulative distribution function of the remaining service life and the reliability function, analyzes the changing trend of the blade life and reliability, and finally calculates the optimal life extension assessment time period with the goal of minimizing the expected cost rate, and gives the optimal blade life extension assessment strategy, thereby achieving a win-win situation of reliability and economic benefits in the life extension assessment of wind turbine blades.

[0062] 2. The wind turbine blade life extension assessment method based on the inverse Gaussian process of the present invention can simulate the nonlinear degradation process of blade stiffness over time and predict the remaining service life and reliability of the blade, providing important data support and analysis tools for the optimal blade life extension decision. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is a schematic diagram of blade degradation modeling and remaining service life prediction in an embodiment of the present invention;

[0064] Figure 2 This is a diagram of the entire life of a blade in an embodiment of the present invention;

[0065] Figure 3 This is a flow chart of a wind turbine blade life extension assessment method based on an inverse Gaussian process in an embodiment of the present invention;

[0066] Figure 4 Schematic diagram of the blade life extension assessment time period in an embodiment of the present invention;

[0067] Figure 5 This is a diagram showing the overall idea of ​​parameter estimation in an embodiment of the present invention;

[0068] Figure 6 is a probability density function diagram of blade stiffness degradation predicted based on the inverse Gaussian process in an application example of the present invention;

[0069] Figure 7 is a cumulative distribution function diagram of blade stiffness degradation predicted based on an inverse Gaussian process in an application example of the present invention;

[0070] Figure 8 is a cumulative distribution function diagram of blade stiffness degradation predicted based on an inverse Gaussian process in an application example of the present invention;

[0071] Fig. 9 It is a cumulative distribution function diagram of the remaining service life of the blade predicted based on the inverse Gaussian process in the application example of the present invention;

[0072] Fig.10 is a diagram of blade reliability function predicted based on inverse Gaussian process in an application example of the present invention;

[0073] Fig.11A curve diagram showing the expected cost rate of blade evaluation in an application example of the present invention changing over time;

[0074] Fig.12 It is a schematic diagram of a method for determining an optimal evaluation period of a blade in an application example of the present invention; DETAILED DESCRIPTION

[0075] The technical solution of the present invention will be described clearly and completely in conjunction with the embodiments below. 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.

[0076] Example

[0077] During the use of wind turbine blades, the action of cyclic loads will cause fatigue damage. As the number of working cycles accumulates, the blades made of composite materials will show the characteristics of fatigue damage. From the perspective of macroscopic phenomenology, this damage is manifested as a gradual decrease in the overall stiffness of the blade. The blade regularized stiffness E K It is defined as the ratio of the stiffness measured during service to the initial stiffness, with a maximum value of 1. The damage development related to the change in composite stiffness of the blade due to fatigue is as follows: Figure 1 As shown. With the continuous operation of the wind turbine, the blade stiffness gradually decreases due to fatigue damage, thus affecting the performance and service life of the blade. When the residual stiffness of the blade is reduced to a certain critical level, its load-bearing capacity or stability may drop significantly, eventually leading to failure or damage of the blade. According to the IEC 61400 standard, when the stiffness of the blade drops by 10% and cannot be recovered, it can be regarded as a key indicator of blade failure. When the residual stiffness of the blade is less than 90% of its initial stiffness, large deformation or fracture may occur, resulting in catastrophic consequences. As shown Figure 1 As shown in Figure 1, the stiffness degradation trajectory of the blade shows a strictly monotonically decreasing trend over time. Therefore, the inverse Gaussian process can be used to fit this degradation trajectory, and it is considered that the entire life of the blade obeys the inverse Gaussian distribution. The diachronic degradation trajectory describes the stiffness degradation process of the blade after the load during service, while the future degradation trajectory predicts the stiffness degradation process at t k The stiffness changes after the time point. When the blade stiffness degrades to the critical value E rc The service life of the blade reaches the end when the blade has been in service for time t k The probability density function of the remaining useful life distribution also obeys the inverse Gaussian process.

[0078] The research goal of the wind turbine blade degradation process established based on the inverse Gaussian process is to predict the remaining service life of the blade. The blade life is defined as the time when the random degradation amount {Y(t), t≥0} first reaches the failure threshold. The basic principle is as follows Figure 1 When the random degradation process {Y(t), t≥0} reaches the preset failure threshold E for the first time rc When the blade degradation reaches or exceeds the set threshold, the operation must be stopped for blade maintenance to ensure safety and reliability. Using the concept of first arrival time, the life span T D Defined as:

[0079] T D = inf{t|Y(t)≥E rc ,t>0} (1)

[0080] The key to predicting the remaining service life of blades based on random degradation process is to solve the life T D The probability density function of the remaining service life T l The probability distribution of the blade life is predicted. Figure 2 As shown in the figure, the total service life is the design life plus the extended life. The length of the extended life depends on the conclusion of the life extension assessment. When the blade reaches the design life, a life assessment is performed to give the remaining service life and determine the length of the life extension. If the blade is in service during the extended life stage, another life extension assessment is required after a certain period of time.

[0081] The Cumulative Distribution Function (CDF) represents the probability that the random variable Y is less than or equal to y for all real numbers y, denoted as F(y). The cumulative distribution function is defined as:

[0082] F(y)=Pr(Y≤y) (2)

[0083] Where: P r Represents probability.

[0084] The derivation of the cumulative distribution function is usually based on the distribution characteristics of random variables. For the Y continuous random variable, its probability density function is f(y), then its CDF is:

[0085]

[0086] The probability density function (PDF) describes the probability density of a continuous random variable near a certain value point. For a continuous random variable Y, its probability density function is usually denoted as f(y) and satisfies the following conditions:

[0087] (1) f(y) is non-negative for all y;

[0088] (2) The sum of the probability densities over all possible ranges of values ​​(or, in other words, the integral over the entire domain) is equal to 1;

[0089] The probability density function is defined as:

[0090]

[0091] The probability density function is usually derived from the cumulative distribution function. For a continuous random variable Y, its probability density function is the derivative of the cumulative distribution function, that is:

[0092]

[0093] The distribution characteristics of random variables can be described by the cumulative distribution function and the probability density function. The cumulative distribution function shows the probability that the random variable takes a value not greater than a certain value, while the probability density function reflects the probability density of the random variable around a specific value. For continuous random variables, these two functions are interrelated. The probability density function can be obtained by taking the derivative of the cumulative distribution function, and conversely, the cumulative distribution function can be obtained by integrating the probability density function.

[0094] The mathematical definition of the inverse Gaussian process {Y(t), t≥0} is described as follows:

[0095] (1) For any 0<t1<t2<t3<t4, the increments Y(t4)-Y(t3) and Y(t2)-Y(t1) are independent of each other, that is, Y(t) has independent increments;

[0096] (2) For any t>s≥0, the increment Y(t)-Y(s) obeys the inverse Gaussian distribution IG(Λ(t)-Λ(s),λ[Λ(t)-Λ(s)] 2 ), Λ(t) is a monotonically growing function with respect to time t, IG(a,b) represents the inverse Gaussian distribution, and its probability density function is:

[0097]

[0098] The cumulative distribution function is:

[0099]

[0100] Where: Φ(·) represents the cumulative distribution function of the normal distribution. Let Λ(0) = 0 and Y(0) = 0, and Y(t) obeys the inverse Gaussian distribution IG(Λ(t),λΛ(t)) with mean Λ(t) and variance Λ(t) / λ 2 ).

[0101] Considering the monotonicity of the inverse Gaussian degradation process, T D The cumulative distribution function of is:

[0102] Pr(T D ≤t)=Pr(Y≥y)=1-F IG (y; Λ(t), λΛ 2 (t)) (8)

[0103] A wind turbine blade life extension assessment method based on an inverse Gaussian process comprises: defining a degradation variable as the degree of stiffness degradation of a blade, selecting an inverse Gaussian process to describe the distribution of the degradation variable, wherein monotonically increasing, independent increments and inverse Gaussian distribution are determined as their specific forms, determining shape parameters and scale parameters by a maximum likelihood estimation method, and establishing an inverse Gaussian process model of wind turbine blade degradation; assessing the life of the blade using the established inverse Gaussian process model to ensure that it meets the safety limit life of reliability, and optimizing the assessment cycle to determine when to conduct the next assessment.

[0104] (1) Inverse Gaussian process modeling of wind turbine blades

[0105] The strictly monotonic IG process is used to describe the blade stiffness performance degradation process. Let Y(t) be the degradation characteristic of the blade at time t. The blade degradation trajectory Y(t) obeys the IG process and has the following properties:

[0106] ①Y(t)=0;

[0107] ②Y(t) has independent increments, that is, for any 0<t1<t2<t3<t4, Y(t4)-Y(t3) and Y(t2)-Y(t1) are independent random variables;

[0108] ③ The degenerate increment Y(t)-Y(s) obeys the IG distribution, that is, Y(t)-Y(s)~IG(μΔΛ,λ(ΔΛ) 2 )(0≤s<t), where ΔΛ=Λ(t)-Λ(s), Λ(t) is a monotonically increasing function, and Λ(0)=0; when the random variable Y(t)~IG(μΛ(t),λΛ 2 (t)), where the shape parameter μ is a function of the load level; the scale parameter λ is a constant independent of the load level; Λ(t) is a monotonically increasing function related to time, in the form of a linear or power function; according to the properties of the IG process, the probability density function of Y(t) is:

[0109]

[0110] The cumulative distribution function is:

[0111]

[0112] Where: Φ(·)—standard normal distribution function;

[0113] (2) Determine the cumulative distribution function of blade life

[0114] If the failure threshold of blade stiffness is E rc , then the life span T D The performance degradation reaches E for the first time rc Time:

[0115] T D = inf{t|Y(t)≥E rc ,t>0} (11)

[0116] According to formula (11), T D The cumulative distribution function of is:

[0117]

[0118] (3) Determine the remaining service life distribution and reliability of blades

[0119] ① Distribution of blade remaining service life

[0120] Assume that the blade is in service until time t a No failure, and the stiffness Y degrades to E a , then the cumulative distribution function of the remaining service life Tr of the blade is expressed as:

[0121]

[0122] The remaining service life distribution of the blade calculated by formula (13) utilizes the degradation value and working time of the blade at the current moment, and the result can better reflect the change of the health status of the blade;

[0123] The probability density function of the remaining useful life is:

[0124]

[0125] (2) Blade reliability

[0126] Given that the IG process has a strict monotonicity characteristic, the blade life T D The reliability function can be expressed as:

[0127] R(t)=Pr(T D >t)=Pr(Y<E rc )=1-F(t) (15)

[0128] So the reliability function of the blade is:

[0129]

[0130] (4) Life extension assessment strategy based on life information

[0131] Due to the influence of multiple factors such as operation and maintenance plans, the inspection and evaluation cycle of blades usually has great uncertainty. On the one hand, in order to ensure that the performance of blades meets the use requirements, reduce the risk of blade failure during the evaluation interval, and promptly discover and deal with potential problems, it is necessary to shorten the inspection cycle and increase the evaluation frequency. However, frequent evaluations will not only significantly increase costs, but may also shorten the actual service life of the blades and reduce their effective operating time. On the other hand, although extending the evaluation cycle can reduce the inspection cost and improve the efficiency of blade use, it also increases the risk of blade failure during the evaluation interval. Too long a cycle may lead to higher safety risks. On the premise of ensuring that the performance of the blades meets the standards, the goal of the study is to find an evaluation strategy to achieve the optimal goals of the longest effective working time, the lowest evaluation cost, and the longest remaining service life of the blades. Based on the remaining service life prediction and working time distribution estimation of blade degradation data, the optimal life extension evaluation strategy of blades is explored.

[0132] ① Evaluation cycle length

[0133] According to the life extension assessment plan, the life extension assessment requires that the blade performance variables be evaluated once every certain period of time T to determine whether the blade has reached the failure point, such as Figure 4 shown.

[0134] In order to determine the optimal evaluation time period, it is necessary to obtain the expected cost rate of blade evaluation, which is the ratio of the expected evaluation cost to the expected time length. When the expected cost rate is the lowest, the blade life extension evaluation time period is optimal. Figure 4 As shown, when a blade fails between the kth and k+1th life extension assessments, once the blade failure is discovered, disposal measures such as repair or scrapping should be taken immediately.

[0135] For a degradation process in which the degradation performance decreases monotonically, if the service age t is measured, a The degradation value ΔE at a , at t a The reliability at time +T is:

[0136]

[0137] The expected length of the blade life extension assessment cycle is:

[0138]

[0139] Definition c p represents the cost of evaluating the blades according to the life extension assessment plan, c f It means that the cost loss caused by blade failure is not evaluated. k(k=0,1,2,L) Evaluate whether the blade continues to run until time t k+1 , or immediately implement the cost c p If the blade is at time t k Run to t k+1 If the process fails, the implementation cost is c f Sudden blade failure is bound to cause additional costs, so c f >c p >0.

[0140] ②Optimal time period

[0141] The expected cost during the renewal period is:

[0142] C r =c p R(t|t a ,ΔE a )+c f [1-R(t|t a ,ΔE a )] (19)

[0143] According to the theory of renewal process, the expected cost rate of blades is:

[0144]

[0145] Formula (20) minimizes the expected cost rate, and the corresponding time is the optimal evaluation time of the blade:

[0146]

[0147] Maximum likelihood estimation is a statistical method that aims to determine the parameters of the probability density function associated with a sample set, with the goal of finding a phylogenetic tree that can generate the observed data with a high probability. The steps of this method are: given a probability distribution F(t), assuming its probability density function is f(t), and the parameters of the distribution are μ, λ, a sample Ym containing m values ​​is drawn from the distribution, and then the probability of the occurrence of sample Ym is calculated through the probability density function f(t).

[0148] In this embodiment, the maximum likelihood estimation method is used to estimate the parameters μ and λ, and the most likely values ​​of the distribution parameters μ and λ are found to maximize the possibility of this sampling. The specific process is as follows: Figure 5 shown.

[0149] The blade is subjected to fatigue test, and m measurements are performed during the test. Then t1, t2, L t m The measured values ​​at the time are Y1, Y2, LY m . Note ΔY j =Yj -Y j-1 , is the leaf at time t j-1 and t j The stiffness degradation between j =t j -t j-1 , j = 1, 2, ... m. The logarithmic likelihood function of the blade stiffness degradation is:

[0150]

[0151] The log-likelihood function is:

[0152]

[0153] Where: μ, λ are the parameters to be estimated.

[0154] The blade stiffness degradation follows the IG process, E(t)~IG(μΛ(t),λΛ 2 (t)). Λ(t) is in the form of a linear or power function. Let Λ(t) = t, ΔΛ(t) = Λ(t j )-Λ(t j-1 ) = t j -t j-1 The degradation of blade stiffness ΔE(t j ) obeys the IG distribution, that is, ΔE(t j )~IG(μΛ(t j ),λΛ 2 (t j )). The stiffness degradation of the blade is ΔE(t j ) is:

[0155]

[0156] Application Examples

[0157] In the span direction of the blade, a concentrated load is applied to the section so that each section of the blade is subjected to a bending moment load in a specific direction, and the stiffness value under these fatigue vibration times is measured. This stiffness value is the performance degradation data of the blade after fatigue life. According to the life t = 0.145, 0.25, 0.315, 0.75, 1, the blade loading section is loaded with test loads, and the normalized stiffness data of the blade is measured respectively, as shown in Table 1. The stiffness degradation data set is (0, 1), (0.145, 0.9826), (0.25, 0.9788), (0.315, 0.9771), (0.75, 0.9616), (1, 0.94211).

[0158] Table 1 Blade stiffness degradation data table

[0159]

[0160] The maximum likelihood estimation method is used to estimate the parameters of equation (24). The partial derivatives of μ and λ are calculated respectively, and their respective partial derivatives are set to 0, that is, As shown in formula (25).

[0161]

[0162] Based on the blade stiffness degradation test data in Table 1, the maximum likelihood estimation of parameters μ and λ is solved, and the results are shown in Table 2.

[0163] Table 2 IG degradation process parameter estimation table

[0164]

[0165] Substituting the estimated parameter values ​​μ, λ into equations (9), (10), (12), (13) and (16), we can obtain the probability density function of stiffness degradation, the cumulative distribution function of stiffness degradation, the cumulative distribution function of life, the cumulative distribution function of remaining service life and the reliability function of this type of blade based on the inverse Gaussian process. The results are as follows: Figures 6 to 10 shown.

[0166] The probability density function of blade stiffness degradation predicted by inverse Gaussian process is as follows: Figure 6 As shown in the figure, the horizontal axis represents the failure threshold time, the vertical axis represents the probability density of blade stiffness degradation, and the curve is bell-shaped, with a peak at 30 years, indicating that the probability of the blade maintaining the initial stiffness before this moment is the highest. As time goes by, the curve moves to the right and the peak gradually decreases, indicating that the blade stiffness gradually degrades and the probability of maintaining the initial stiffness gradually decreases. The shape and position of the curve are affected by parameters, such as the shape parameter μ and the scale parameter λ. Due to the use of the inverse Gaussian process for modeling, the curve shows a typical right-skewed distribution characteristic. This means that in the early stages of stiffness degradation, the degradation rate is slow and the probability density is high; as the degradation deepens, the degradation rate accelerates and the probability density gradually decreases.

[0167] The cumulative distribution function of blade stiffness degradation based on the inverse Gaussian process is as follows: Figure 7 As shown in the figure, the horizontal axis represents the failure threshold time, and the vertical axis represents the cumulative distribution probability of blade stiffness degradation. The curve shows a monotonically decreasing trend, starting from 1 and gradually approaching 0. The shape and position of the curve are determined by the parameters, reflecting the degradation law of blade stiffness over time. The monotonically decreasing trend of the curve shows that with the increase of time and the degradation of blade stiffness, the probability of blade failure also gradually increases. This cumulative distribution function can be converted into the cumulative distribution function of blade life and reliability, and its curve trend is opposite to the life distribution.

[0168] The cumulative distribution function of blade life based on the inverse Gaussian process is as follows: Figure 8 As shown in the figure, the horizontal axis is the life span, and the vertical axis is the cumulative distribution probability of the blade life span. The curve also shows a monotonically increasing trend, starting from 0 and gradually approaching 1. The curve reflects the probability distribution of the blade life span, indicating the probability of blade failure at different time points. The curve shows an S-shaped increasing trend, indicating that the probability of blade failure gradually increases with the passage of time. After 20 years of service, the probability of blade failure of this type of blade gradually increases, showing a rapid upward trend. Corresponding to the expiration of the blade design life, the probability of blade failure increases during the extended use period.

[0169] Set t a and E a are all 0, and the cumulative distribution function of the remaining useful life of the blade based on the inverse Gaussian process is as follows: Fig. 9 As shown in the figure, the horizontal axis is the remaining service life, and the vertical axis is the cumulative distribution probability of the remaining service life. The curve also shows a monotonically increasing trend, starting from 0 and gradually approaching 1. The curve reflects the probability distribution of the remaining service life of the blade at the current moment, indicating that the probability of failure of the blade increases with the increase of the remaining service life, and it is close to failure after 30 years. The curve shows a monotonically increasing trend, indicating that the cumulative probability of the remaining service life of the blade gradually increases with the passage of time. The cumulative distribution curve of the remaining service life of the blade shows a similar distribution to the cumulative distribution function curve of its life, reflecting the consistency of blade performance.

[0170] The curve of blade reliability function changing with time is as follows: Fig.10 As shown in the figure, the horizontal axis is the life time, and the vertical axis is the reliability. The curve shows an inverse S-shaped increasing trend, starting from 1 and gradually approaching 0. The curve reflects the change of blade reliability over time. The lower the reliability, the higher the risk of blade failure. The curve shows a monotonically decreasing trend, indicating that the reliability of the blade gradually decreases with the passage of time. In the initial design life stage of the blade service, the blade is at a relatively high reliability of more than 0.9.

[0171] According to the blade stiffness degradation data, the stiffness degradation IG process is established, and the blade life cumulative distribution function, remaining service life cumulative distribution function and reliability function are solved with estimated parameters to obtain the blade life distribution and reliability distribution. The life extension evaluation is carried out based on the blade remaining service life cumulative distribution function. Fig. 9 As the service life of the blade increases, the stiffness gradually decreases, and the blade's remaining service life gradually decreases. After exceeding the design life by 20 years, the possibility of blade failure increases rapidly. When the blade service life exceeds 30 years, the cumulative distribution function value of the remaining service life will be close to 1, and the blade's remaining service life will be close to 0. Fig.10As shown in the figure, the blade design life is 20 years, and its reliability is above 0.9. The blade life extension assessment is carried out, and the blade life within the reliability of 0.9 is calculated. By reducing the blade reliability, its life can be moderately extended. However, for blades with lower reliability, the possibility of blade failure increases rapidly. It can be seen that the inverse Gaussian process is suitable for modeling the nonlinear degradation process of wind turbine blade stiffness over time. For the blade life and reliability function established with blade stiffness as an indicator, the blade life extension assessment can be effectively carried out. The results reflect the advantages of the inverse Gaussian process, such as the ability to model highly nonlinear models, the ability to establish degradation processes using fewer data points, and the ability to capture performance trends over time.

[0172] Solve equations (17)-(19) and substitute them into equation (20) to obtain the curve of blade evaluation expected cost rate changing with time: Fig.11 As shown in the figure, the horizontal axis is time, and the vertical axis is the expected cost rate of the evaluation. The curve shows a fluctuating trend, and there is a minimum point, and the corresponding time is the optimal evaluation time period. The curve reflects the changes in the expected cost rate of the blade under different evaluation time periods, and the minimum value corresponds to the optimal economic evaluation plan. The curve shows a trend of first decreasing and then increasing, which shows that in the early stage of blade service, appropriately extending the evaluation cycle can reduce the evaluation cost; but as the blade performance deteriorates, the evaluation cycle needs to be shortened to reduce the risk of failure, which leads to an increase in the evaluation cost. Therefore, the point corresponding to the optimal evaluation time period is the best solution to achieve the lowest cost rate. The process of determining the optimal evaluation period of the blade is as follows Fig.12 By calculating the expected cost rate under different evaluation time periods, the lowest point of the expected cost rate is found, and the time corresponding to this point is the optimal evaluation time period. This method comprehensively considers the evaluation cost and failure risk to seek the optimal economic benefit.

[0173] Set t a and E a All are 0, the preventive maintenance cost C p =60, maintenance cost after failure C r =60000, as described in formula (20), calculate the minimum expected cost rate for evaluation. Fig.11 The expected cost rate curve over time is given. Through this figure, the point on the curve corresponding to the minimum cost rate is found, and the approximately optimal blade life extension assessment time period T = 2 years is found, and the minimum cost per unit time is C = 63.

[0174] The present invention aims to formulate the optimal life extension strategy, studies the relationship between blade stiffness degradation modeling and remaining service life, establishes the blade stiffness degradation process of the inverse Gaussian process, defines the blade life using the concept of first arrival time, and derives the expression of the blade remaining service life distribution and reliability function. The parameters of the inverse Gaussian degradation process are estimated by the maximum likelihood estimation method, and the variation law of the blade life distribution, reliability function and optimal evaluation time period is analyzed by calculation. A blade life extension evaluation method based on the inverse Gaussian degradation process and a method for determining the optimal blade life extension evaluation time period based on minimizing the expected cost rate are proposed. The following conclusions are drawn:

[0175] The cumulative distribution function of the blade's remaining service life predicted based on the inverse Gaussian process shows a monotonically increasing trend. As the service life of the blade increases, the stiffness gradually decreases, and the blade's remaining service life gradually decreases. When the cumulative distribution function value of the blade's remaining service life is close to 1, the blade's remaining service life is close to 0. The curve of the blade reliability function changing with time shows an inverse S-shaped decreasing trend. This trend clearly reflects the relationship between the decrease in blade reliability and time, that is, as time increases, the risk of blade failure increases accordingly. However, within a certain range of reliability reduction, the life of the blade is expected to be moderately extended. The optimal life extension assessment cycle of the blade shortens with the increase in the service time of the blade. In the early stage of blade life extension, the performance is good and the reliability is high. Appropriately increasing the assessment cycle can effectively reduce the assessment cost. At the end of service, the reliability of the blade decreases, and the possibility of failure between two assessments increases. It is required to shorten the assessment cycle and reduce the risk of failure.

[0176] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the technical solution and conceptual invention of the present invention should be included in the protection scope of the present invention.

Claims

1. A wind turbine blade life extension assessment method based on inverse Gaussian process, characterized in that: include: (1) Define the degradation variable of wind turbine blades as the degree of blade stiffness degradation, use the inverse Gaussian process to describe the blade stiffness degradation process, and establish the inverse Gaussian process model of the blade stiffness degradation process; (2) Use the established inverse Gaussian process model to evaluate the blade life to ensure that it meets the safety limit life of reliability; (3) Optimize the life extension assessment time period to determine the optimal assessment time period to determine when to conduct the next assessment.

2. The wind turbine blade life extension assessment method based on inverse Gaussian process according to claim 1 is characterized in that: The specific method of establishing the inverse Gaussian process model of the blade stiffness degradation process includes: S1, inverse Gaussian process modeling of blade stiffness degradation; The inverse Gaussian process with strict monotonicity is used to describe the blade stiffness performance degradation process. Let Y(t) be the degradation characteristic of the blade at time t. The blade stiffness degradation Y(t) obeys the IG process and has the following properties: ①, Y(t) = 0; ②, Y(t) has independent increments, that is, for any 0<t1<t2<t3<t4, Y(t4)-Y(t3) and Y(t2)-Y(t1) are independent random variables; ③ The degenerate increment Y(t)-Y(s) obeys the IG distribution, that is, Y(t)-Y(s)~IG(μΔΛ,λ(ΔΛ) 2 )(0≤s<t), where ΔΛ=Λ(t)-Λ(s), Λ(t) is a monotonically increasing function, and Λ(0)=0; when the random variable Y(t)~IG(μΛ(t),λΛ 2 (t)), where the shape parameter μ is a function of the load level; the scale parameter λ is a constant independent of the load level; Λ(t) is a monotonically increasing function related to time, in the form of a linear or power function; according to the properties of the IG process, the probability density function expression of Y(t) is: The cumulative distribution function expression of Y(t) is: Where: Φ(·)—standard normal distribution function; S2. Determine the expression of the cumulative distribution function of blade life; If the failure threshold of blade stiffness is E rc , then the blade life T D The performance degradation reaches E for the first time rc Time: T D =inf{t|Y(t)≥E rc ,t>0} (11) According to formula (11), T D The cumulative distribution function expression is:

3. The wind turbine blade life extension assessment method based on inverse Gaussian process according to claim 2 is characterized in that: The specific method of blade life assessment includes: S1. Determine the cumulative distribution function and probability density function of the remaining useful life of the blade and the expression of the blade reliability function based on the established inverse Gaussian process model; The expression of the cumulative distribution function of the remaining service life of the blade is determined by: assuming that the blade is in service until time t a No failure, and the stiffness Y degrades to E a , then the remaining service life of the blade is T r The cumulative distribution function of is expressed as: The probability density function of the remaining service life of the blade is expressed as: The blade life T D The reliability function is expressed as: R(t)=Pr(T D >t)=Pr(Y<E rc )=1-F(t) (15) Therefore, the blade reliability function is expressed as: S2. The maximum likelihood estimation method is used to estimate the parameters μ and λ in the inverse Gaussian process model. The estimated parameter values ​​μ and λ are substituted into equations (9), (10), (12), (13) and (16) respectively to obtain the probability density function of blade stiffness degradation, the cumulative distribution function of blade stiffness degradation, the cumulative distribution function of blade life, the cumulative distribution function of blade remaining service life and the blade reliability function based on the inverse Gaussian process. The life extension assessment is carried out based on the cumulative distribution function of blade remaining service life.

4. The method for evaluating the life extension of wind turbine blades based on inverse Gaussian process according to claim 3 is characterized in that: The steps of estimating the parameters μ, λ in the inverse Gaussian process model using the maximum likelihood estimation method are: (1) The blade is subjected to fatigue test. During the test, m measurements are performed. Then t1, t2, L t m The measured values ​​at the time are Y1, Y2, LY m , record ΔY j =Y j -Y j-1 , is the leaf at time t j-1 and t j The stiffness degradation between j =t j -t j-1 , j = 1, 2, ... m, the likelihood function of blade stiffness degradation can be obtained as: The log-likelihood function is: Where: μ, λ—are the parameters to be estimated; The blade stiffness degradation follows the IG process, E(t)~IG(μΛ(t),λΛ 2 (t)), Λ(t) is in the form of a linear or power function, assuming Λ(t) = t, ΔΛ(t) = Λ(t j )-Λ(t j-1 ) = t j -t j-1 , the degradation of blade stiffness ΔE(t j ) obeys the IG distribution, that is, ΔE(t j )~IG(μΛ(t j ),λΛ 2 (t j )), then the blade stiffness degradation ΔE(t j ) is: (2) Apply concentrated loads to the cross-section in the span direction of the blade so that each cross-section of the blade is subjected to a bending moment load in a specific direction, and measure the stiffness value under the action of these fatigue vibration times. The stiffness value is the performance degradation data of the blade after fatigue life; (3) According to the measured stiffness value, the parameters of equation (24) are estimated, and the partial derivatives of μ and λ are calculated respectively, and their respective partial derivatives are set to 0, that is, As shown in formula (25), the maximum likelihood estimates of parameters μ and λ are obtained; 5. The wind turbine blade life extension assessment method based on inverse Gaussian process according to claim 4 is characterized in that: The optimization of the life extension evaluation time period to determine the optimal evaluation time period is to determine the optimal evaluation time period by obtaining the expected cost rate of blade evaluation. When the expected cost rate of evaluation is the lowest, the blade life extension evaluation time period is optimal. The expected cost rate of blade evaluation is the ratio of the expected evaluation cost to the expected time length. The specific method includes: For the degradation process of blade degradation performance monotonically decreasing, if the service age t is measured, a The degradation value ΔE at a , at t a The blade reliability at time +T is: The expected length of the blade life extension assessment cycle is: Definition c p represents the cost of evaluating the blades according to the life extension assessment plan, c f It represents the cost loss caused by the failure of the blade not being evaluated at time t k (k=0,1,2,L) Evaluate whether the blade continues to run until time t k+1 , or immediately implement the cost c p Preventive treatment, if the blade at time t k Run to t k+1 If the process fails, the implementation cost is c f The sudden failure of blades will inevitably cause additional costs. f >c p >0; The expected cost of blade assessment during the renewal cycle is: C r =c p R(t|t a ,ΔE a )+c f [1-R(t|t a ,ΔE a )] (19) According to the relevant theory of the renewal process, the expected cost rate of blade evaluation is: Formula (20) minimizes the expected cost rate of blade evaluation, and the corresponding time is the optimal blade life extension evaluation time period:

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