A hybrid uncertain dynamics analysis method for rotating blades based on chaotic polynomials

Abstract

The present invention discloses a method for analyzing the mixed uncertainty dynamics of rotating blades based on chaotic polynomials. The method performs sampling within a random uncertainty space to generate configuration nodes for numerical integration and corresponding integral weights. Sampling is performed within an interval range of interval uncertainty parameters. Each interval configuration point is regarded as a constant vector, and a generalized chaotic polynomial model is constructed using the Galerkin projection method to obtain the expectation and variance of the uncertainty response of the rotating blade system at each interval configuration point relative to the random variable. The Legendre interval expansion function is used to calculate the expectation and variance of the uncertainty response relative to the boundaries of the interval variable. The present invention has no special restrictions on the numerical method for solving the differential equation system and is a technical solution with universal applicability. It provides a new approach for analyzing the dynamic systems of rotating blades with random and interval mixed uncertainties and has high engineering practical value in aeroengines and wind turbines.

Description

Technical Field

[0001] The present invention relates to the field of mechanical system dynamics, and in particular to a mixed uncertainty dynamics analysis method for rotating blades based on chaos polynomials. Background Art

[0002] Rotating blade systems are ubiquitous in aircraft engines and wind turbines. Advances in science and technology have made these systems increasingly sophisticated and complex. This, coupled with the diversification of their operating environments, inevitably generates significant background noise and interference. Traditional dynamic analysis of rotating blade systems is based on deterministic system parameters, while internal and external uncertainties (such as load characteristics, material properties, geometric dimensions, boundary conditions, initial conditions, measurement deviations, and environmental factors) are often ignored. However, in complex rotating blade dynamic systems, even minor parameter changes can alter the system's response. In particular, the coupling of uncertain parameters can significantly alter certain responses and performance indicators. Rotating blade design solutions that ignore uncertainty, a relatively crude concept, can, in actual use, result in a decline in system performance or even in inestimable economic losses, seriously contradicting the development of refined design. The coupling of uncertainty and dynamics within rotating blade systems presents considerable challenges in conducting uncertain dynamic analysis of rotating blade systems.

[0003] In recent decades, a series of research advances have been made in the theory of stochastic uncertainty dynamics, based on probability theory and mathematical statistics. However, as the academic community's understanding of uncertainty continues to deepen, stochastic methods have significant limitations in quantitative characterization, modeling, and solution. These limitations are primarily manifested in the following aspects: First, determining the precise probability distribution of uncertainty parameters is a prerequisite for modeling and solving stochastic dynamics methods. However, this typically requires complete probabilistic information and knowledge, which is difficult or expensive to obtain in actual rotating blade dynamics systems. The greatest advantage of interval methods is that they can obtain a tight wrapper containing all possible solutions using limited information. However, relevant research results show that interval methods tend to produce conservative results. In actual rotating blade structures, due to different levels of uncertainty information, random parameters and interval parameters may coexist, resulting in mixed uncertainty.

[0004] Existing hybrid uncertainty dynamics methods all have some potential limitations. The computational efficiency of the Monte Carlo simulation-sweep hybrid method is extremely low and is only applicable to simple rotating blade dynamic systems. Random and interval perturbation methods based on Taylor series expansion are only applicable to rotating blade dynamic systems with small uncertainty levels and weak nonlinearity. The vertex method is limited to cases where the function is monotonic and cannot be applied to complex rotating blade dynamic systems. In addition, the rotating blade dynamic system model is often based on finite element or multibody system dynamics, forming a series of complex partial differential equations or differential algebraic equations. Conventional intrusive uncertainty methods require transformation and modification of the original dynamic model, which brings great inconvenience to the solution. Overall, research on hybrid uncertainty rotating blade dynamic systems is still in its early stages, and some core technologies still need to be resolved. It is necessary to develop a more general method to solve the response of rotating blade dynamic systems with hybrid uncertainties, which has practical engineering significance. Summary of the Invention

[0005] The purpose of the present invention is to provide a rotating blade mixed uncertainty dynamics analysis method based on chaotic polynomials, which can efficiently and accurately solve the rotating blade dynamics system containing random and interval mixed uncertainties.

[0006] The technical solution for implementing the present invention is: a method for analyzing the mixed uncertainty dynamics of rotating blades based on chaotic polynomials, comprising the following steps:

[0007] Step 1: Select random uncertainty parameters and interval uncertainty parameters from the load characteristics, material characteristics, and geometric characteristics of the rotating blade model, and set the random uncertainty parameter x R The distribution parameters of the rotating blade model and the interval uncertainty parameter z I The specific interval value of the chaotic polynomial, the order p H , the configuration level k of sparse grid sampling H , the order p of the Legendre polynomial L , the time length t of the rotating blade dynamics model calculation e and time step Δt;

[0008] Step 2: According to the random uncertainty parameter x in the rotating blade model R The distribution type of chaotic orthogonal polynomial basis function is determined;

[0009] Step 3: Based on the configuration level k of sparse grid sampling H , the sparse grid sampling strategy is used to sample in the random uncertainty space of the rotating blade model to generate the configuration nodes and corresponding integral weights of the numerical integration. The total number of sparse grid sampling points is recorded as N P;

[0010] Step 4: Use the optimal Latin square sampling method to obtain sampling points within the interval range of the interval uncertainty parameter in the rotating blade model. The total number of interval sampling points is N. I ;

[0011] Step 5: Initialize the loop count index j=0, where j is used to count the time iteration steps in the dynamics calculation of the rotating blade system;

[0012] Step 6: Initialize the loop counting index i=1, i is used to count the interval sample points;

[0013] Step 7: Initialize loop counting index k=1, where k is used to count sparse grid sample points;

[0014] Step 8: Set the interval sampling point z I (i) Sparse grid integration configuration node x R Substitute (k) into the original rotating blade system dynamics equations and use an appropriate numerical algorithm to calculate t j The actual dynamic response of the rotating blade system at time t, including blade root displacement, velocity and friction;

[0015] Step 9: If k = N p , continue; otherwise, set k = k + 1 and return to step 8;

[0016] Step 10: Use the Galerkin projection method to calculate the expansion coefficient of the chaotic polynomial to obtain t j Chaotic polynomial of the dynamic system response of rotating blades at time instant;

[0017] Step 11: Use the t constructed in step 10 j The chaotic polynomial model of the dynamic system response of the rotating blade at time t j The statistical moments of the moment rotating blade system response with respect to random parameters;

[0018] Step 12: If i=N I , continue; otherwise, set i=i+1 and return to step 7;

[0019] Step 13: Using N I The statistical moments of the dynamic response of the rotating blade system with respect to the random parameters are calculated, and the Legendre polynomials of the interval uncertainty parameters of the rotating blade dynamic system are constructed. The expansion coefficients of the Legendre polynomials are calculated based on the least squares method to obtain t j Legendre polynomials of moments;

[0020] Step 14: Use the Legendre polynomial model constructed in step 13 to construct the Legendre interval expansion function and calculate t j The interval boundary of the statistical moment of the dynamic response of the rotating blade system relative to the interval parameter;

[0021] Step 15: If j>t e / Δt, then output the interval boundary change of the dynamic response statistical moment of the rotating blade system; otherwise, set j=j+1 and return to step 6.

[0022] Furthermore, the random uncertainty parameters include the density ρ of the beam and the excitation amplitude P c , the interval uncertainty parameters include the blade speed ω and the friction coefficient μ of the tenon-mortise contact surface.

[0023] Further, step 11, using the t constructed in step 10 j The chaotic polynomial model of the dynamic system response of the rotating blade at time t j The statistical moment of the rotating blade system response relative to the random parameters at time instant is calculated as follows:

[0024] The interval vector η of the rotating blade system is fixed, and only the influence of the random vector ξ in the rotating blade system is considered, t j The response of the rotating blade system at time t is described by the chaotic polynomial modeling in step 10 as the uncertainty function

[0025]

[0026] Then, t j The statistical moment of the rotating blade system response at time t is given by j The expansion coefficients of the chaotic polynomial and the orthogonal polynomial basis functions are directly calculated at the moment t j The statistical moments of F(ξ,η) are calculated as follows:

[0027] μ(F(ξ,η))=a0(η) (1)

[0028]

[0029] Where μ(F(ξ,η)) is the mean and σ(F(ξ,η)) is the standard deviation.

[0030] Furthermore, in step 14, the Legendre polynomial model constructed in step 13 is used to construct a Legendre interval expansion function to calculate the interval boundary of the statistical moment of the dynamic response of the rotating blade system relative to the interval parameter. The specific method is:

[0031] t jThe statistical moments of the uncertainty function F(ξ,η) of the rotating blade system response at each moment are used to construct Legendre polynomials, which are expressed as:

[0032]

[0033]

[0034] The Legendre interval expansion function is used to perform interval operations on Equations (3) and (4). During the calculation, the Legendre orthogonal basis function is taken as a whole, and the exact interval of the 1-dimensional Legendre polynomial basis function is substituted into Equations (3) and (4). The interval operation is directly used to estimate the range of the interval function of Equations (3) and (4) to obtain t j The interval bounds of the statistical moments of the uncertainty function F(ξ,η) of the rotating blade system response at time instant.

[0035] Furthermore, in step 14, for the rotating blade system with a large interval uncertainty level, the sub-interval technique is used for preliminary processing.

[0036] A chaotic polynomial-based rotating blade mixed uncertainty dynamics analysis system realizes the chaotic polynomial-based rotating blade mixed uncertainty dynamics analysis based on the rotating blade mixed uncertainty dynamics analysis method.

[0037] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the chaotic polynomial-based rotating blade mixed uncertainty dynamics analysis is implemented based on the rotating blade mixed uncertainty dynamics analysis method.

[0038] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the processor implements a chaotic polynomial-based rotating blade hybrid uncertainty dynamics analysis based on the overhead line differential protection method and the rotating blade hybrid uncertainty dynamics analysis method.

[0039] Compared with the prior art, the present invention has the following significant advantages:

[0040] (1) It can efficiently process the rotating blade dynamic system containing random and interval mixed uncertainty parameters. Compared with the traditional method, this method can obtain similar calculation results, but the calculation efficiency is greatly improved.

[0041] (2) It has good applicability. Through secondary sampling, the rotating blade dynamic system containing random and interval uncertainty parameters is converted into a system containing only deterministic parameters. There are no special restrictions on the numerical method for solving the dynamic equations. It is a technical solution with universal applicability.

[0042] (3) It is a typical non-invasive technical solution. There is no need to change the expression of the rotating blade dynamic equations during the solution process, which greatly reduces the complexity of dynamic modeling and solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Flowchart of the hybrid uncertainty dynamics analysis method of rotating blades based on chaotic polynomials of the present invention;

[0044] Figure 2 Basis functions of Legendre polynomials of order 0 to 5 of the present invention and their precise interval graphs;

[0045] Figure 3 Finite element model diagram of the rotating cantilever beam blade of Example 1 of the present invention;

[0046] Figure 4 Example 1 of the present invention is a comparison chart of the calculation results of the method of the present invention and the calculation results of the traditional method. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0048] Combine Figure 1 ,The rotating blade mixed uncertainty dynamic analysis method based on chaotic polynomials,the specific steps are as follows:

[0049] Step 1: Select random uncertainty parameters and interval uncertainty parameters from the load characteristics, material characteristics, and geometric characteristics of the rotating blade model, and set the random uncertainty parameter x in the rotating blade model. R The distribution parameters of the rotating blade model and the interval uncertainty parameter z I The specific interval value of the chaotic polynomial, the order p H , the configuration level k of sparse grid sampling H , the order p of the Legendre polynomial L , the time length t of the rotating blade dynamics model calculation e and time step Δt;

[0050] Step 2: Determine the chaotic orthogonal polynomial basis function according to the distribution type of random uncertainty parameters in the rotating blade model.

[0051] To facilitate subsequent explanations, a brief introduction to the theory of chaotic polynomials is provided here. Note that these basic theories are not within the scope of the claims of this application. Chaotic polynomials approximate uncertain processes using a series of orthogonal polynomials with a specific distribution in an uncertain space. The general chaotic polynomial expansion of the function y(x) can be expressed as:

[0052]

[0053] Where, are the coefficients of the polynomial to be calculated, is a d-dimensional uncertainty variable ξ=[ξ1,ξ2,...,ξ d ]’s n-th order generalized chaotic polynomial;

[0054] For ease of description, formula (1) is usually expanded and renumbered according to some specific rules, and simplified to a form using only a single index:

[0055]

[0056] Where a i and Corresponding to the polynomial coefficients in formula (2) and polynomial basis functions

[0057] Note that Equation (2) is the sum of infinite terms in infinite-dimensional space. In order to reduce the amount of computation, it is usually truncated at p-order. The p-order PCE model can be rewritten as follows:

[0058]

[0059] Where S+1 is the number of retained items, calculated as follows:

[0060]

[0061] In equations (2) and (3), multidimensional, hypergeometric polynomials can be expressed as the tensor product of the corresponding 1-dimensional polynomial basis functions:

[0062]

[0063] Where, represents the k-th dimension uncertainty variable ξ kThe corresponding one-dimensional orthogonal polynomial basis function. Several orthogonal polynomial bases have been developed for chaotic polynomials, which have optimal correspondences with probability distribution types. For example: Hermite polynomials for Gaussian distribution, Legendre polynomials for uniform distribution, generalized Laguerre polynomials for Gamma distribution, Jacobi polynomials for Beta distribution, Charlier polynomials for Poisson distribution, Krawtchouk polynomials for binomial distribution, Meixner polynomials for negative binomial distribution, Hahn polynomials for hypergeometric distribution, etc.

[0064] Step 3: Based on the configuration level k of sparse grid sampling H , the sparse grid sampling strategy is used to sample in the random uncertainty space of the rotating blade model to generate the configuration nodes and corresponding integral weights of the numerical integration. The total number of sparse grid sampling points is recorded as N P The relevant theories of sparse grid sampling method can be found in the literature, and this application will not go into details here.

[0065] Step 4: Use the optimal Latin square sampling method to obtain sampling points within the interval range of the interval uncertainty parameter in the rotating blade model. The total number of interval sampling points is N. I .

[0066] Step 5: Initialize the loop count index j=0, where j is used to count the time iteration steps in the dynamics calculation of the rotating blade system.

[0067] Step 6: Initialize the loop counting index i=1, where i is used to count the interval sample points.

[0068] Step 7: Initialize the loop counting index k=1, where k is used to count the sparse grid sample points.

[0069] Step 8: Set the interval sampling point z I (i) Sparse grid integration configuration node x R Substitute (k) into the original rotating blade system dynamics equations and use an appropriate numerical algorithm to calculate t j The actual dynamic response of the rotating blade system at time t.

[0070] Step 9: If k = N p , continue; otherwise, set k=k+1 and return to step 8.

[0071] Step 10: Use the Galerkin projection method to calculate the expansion coefficient of the chaotic polynomial to obtain t j Chaotic polynomial of the dynamic response of a rotating blade system at time t.

[0072] Apply Galerkin projection to simultaneously project both sides of equation (3) onto orthogonal polynomials On, we can get:

[0073]

[0074] Due to the orthogonality of the basis functions, the expansion coefficient a of the chaotic polynomial model in formula (3) is i It can be expressed as:

[0075]

[0076] The denominator of the above equation is simply the inner product of the orthogonal polynomials, which is the tensor product of the corresponding 1-dimensional orthogonal polynomial basis. Therefore, the denominator can be viewed as the continuous product of the inner product of the 1-dimensional orthogonal polynomial basis:

[0077]

[0078] Where, It can be calculated very conveniently using chaotic polynomial basis functions.

[0079] The numerator of formula (7) can be calculated by To determine the expectations:

[0080]

[0081] Where f(ξ) is the joint probability density function of ξ. Equation (9) is the numerical integration of a multivariate function. The solution process for a complex nonlinear function such as a rotating blade system is extremely difficult. Numerical integration methods are generally used to solve it. Here, a sparse grid numerical integration method is used.

[0082] Step 11: Use the t constructed in step 10 j The chaotic polynomial model of the dynamic system response of the rotating blade at time t j The statistical moment of the rotating blade system response relative to the random parameter at time t. Since the interval vector η of the rotating blade system is fixed here, only the influence of the random vector ξ in the rotating blade system is considered, j The response of the rotating blade system at time t can be described as the uncertainty function through the chaotic polynomial modeling in step 10 Then, t j The statistical moment of the rotating blade system response at time t can be used j The expansion coefficients of the chaotic polynomial and the orthogonal polynomial basis functions are directly calculated at the moment t j The statistical moments (mean μ(F(ξ,η)) and standard deviation σ(F(ξ,η))) of time F(ξ,η) can be calculated as follows:

[0083] μ(F(ξ,η))=a0(η) (10)

[0084]

[0085] Step 12: If i=N I , continue; otherwise, set i=i+1 and return to step 7.

[0086] Step 13: Using N I The statistical moments of the dynamic response of the rotating blade system with respect to the random parameters are calculated, and the Legendre polynomials of the interval uncertainty parameters of the rotating blade dynamic system are constructed. The expansion coefficients of the Legendre polynomials are calculated based on the least squares method to obtain t j Legendre polynomial of the moment.

[0087] Step 14: Use the Legendre polynomial model constructed in step 13 to construct the Legendre interval expansion function and calculate t j The interval boundaries of the statistical moments of the dynamic response of the rotating blade system relative to the interval parameters.

[0088] t j The statistical moments of the uncertainty function F(ξ,η) of the rotating blade system response at each moment are used to construct Legendre polynomials, which can be expressed as:

[0089]

[0090]

[0091] The Legendre interval expansion function is used to perform interval operations on equations (12) and (13). When calculating, the Legendre orthogonal basis function is taken as a whole, and the exact interval of the 1-dimensional Legendre polynomial basis function (the basis function of the 0th to 5th order Legendre polynomial and its exact interval are as follows Figure 2 Substitute (as shown) into Equation (12) and Equation (13), and directly use interval operations to estimate the range of the interval function of Equation (12) and Equation (13) to obtain t j The interval bounds of the statistical moments of the uncertainty function F(ξ,η) of the rotating blade system response at time θ. For rotating blade systems with large interval uncertainty levels, subinterval techniques can be used to pre-process them. The relevant theory of subinterval techniques will not be elaborated here.

[0092] Step 15: If j>t e / Δt, then output the interval boundary change of the dynamic response statistical moment of the rotating blade system; otherwise, set j=j+1 and return to step 6.

[0093] Example

[0094] In order to verify the effectiveness of the solution of the present invention, the following experiment was conducted.

[0095] The dynamic response analysis of the rotating blade dynamic system with random and interval mixed uncertainty parameters described by the finite element method is applied. The rotating cantilever beam blade model is as follows: Figure 3 (a). In the figure, O-XYZ is the global coordinate system, with the origin O at the center of the blade. The blade system rotates about the Z axis at a rotational speed of ω. o-xyz is the local coordinate system, with the origin o at the blade root and parallel to the global coordinate system O-XYZ. The distance between the origin O of the global coordinate system and the origin o of the local coordinate system is R, which is the radius of the blade. X and x coincide with the midline of the beam, and y and z coincide with the midline of the cross section.

[0096] The main geometric and physical parameters of the beam are: the cross-sectional area of the beam A = bh, where b is the width of the blade and h is the height of the blade. The bending stiffness EI, E is the elastic modulus, I is the moment of inertia about the Z axis, I = bh 3 / 12. ρ is the density of the beam, l is the length of the blade, L is the length of the finite element unit, N is the number of units, x i is the distance from any point in the i-th unit to the front end of the unit. Divide it into 30 beam unit finite element models, and the root of the beam is Figure 3 (b) The mortise and tenon contact model shown. A simple harmonic excitation is applied to the vertical beam surface in the middle of the cantilever beam. Among them, P c is the excitation amplitude, n0 is the number of static blades in the front row, which is 5 here. is the initial phase of the excitation.

[0097] Consider a rotating blade dynamic system with mixed random and interval uncertainties, where: ρ and P c are random parameters that satisfy Gaussian distribution, and their average values are 7850 kg / m 3 and 500N, with standard deviations of 75kg / m 3and 5N; the blade speed ω and the tenon-mortise contact surface friction coefficient μ are interval parameters, and their interval values are [98, 102] rad / s and [0.196, 0.204], respectively. The forced vibration response of the root of the mortise-tenon rotating beam is analyzed. For this system, the Hermite basis function is used to describe the random parameters of the rotating blade model, and the Legendre basis function is used to describe the interval parameters of the rotating blade model, and a chaotic polynomial model is constructed. The order of the Hermite chaotic polynomial is 2, and the configuration level k in the sparse grid sampling method is set to 1; the order of the Legendre polynomial is 1, and for each interval vector, 3 subintervals are divided. The traditional Monte Carlo simulation-scanning hybrid algorithm is used to obtain the reference solution for comparative analysis. The number of samples in the Monte Carlo simulation is set to 1000, and 10 scanning points are taken in each interval in the scanning method, and the total number of scanning samples is 100. The interval boundaries of the mean and standard deviation of the dynamic response of some rotating blade systems are plotted on Figure 4 All calculations were performed on a desktop computer with 16GB of RAM and one CPU core, the processor model is Intel(R) Core(TM) i5-4590 with a clock frequency of 3.30GHz.

[0098] like Figure 4 As shown, the interval boundaries of the dynamic response statistical characteristics of the rotating blade finite element model obtained by the technical solution of the present application can approximate the results of the traditional Monte Carlo simulation-scanning hybrid method. In terms of calculation time, the chaotic polynomial method and the Monte Carlo simulation-scanning hybrid method took 3870.6s and 307883.1s respectively. Obviously, the computational efficiency of the chaotic polynomial is much higher than that of the traditional Monte Carlo simulation-scanning hybrid method. In short, the proposed chaotic polynomial-based rotating blade mixed uncertainty dynamic analysis method is similar to a secondary sampling method. It converts the rotating blade dynamic system containing random and interval mixed uncertainty parameters into a rotating blade dynamic system containing only deterministic parameters through secondary sampling without changing its expression. As a non-invasive method, it has no special restrictions on the numerical method for solving the differential equations of the rotating blade system and is a technical solution with universal applicability.

[0099] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0100] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A method for analyzing the mixed uncertainty dynamics of rotating blades based on chaotic polynomials, characterized by: The following steps are involved: Step 1: Select random uncertainty parameters and interval uncertainty parameters from the load characteristics, material characteristics, and geometric characteristics of the rotating blade model, and set the random uncertainty parameter x R The distribution parameters of the rotating blade model and the interval uncertainty parameter z I The specific interval value of the chaotic polynomial, the order p H , the configuration level k of sparse grid sampling H , the order p of the Legendre polynomial L , the time length t of the rotating blade dynamics model calculation e and time step Δt; Step 2: According to the random uncertainty parameter x in the rotating blade model R The distribution type of chaotic orthogonal polynomial basis function is determined; Step 3: Based on the configuration level k of sparse grid sampling H , the sparse grid sampling strategy is used to sample in the random uncertainty space of the rotating blade model to generate the configuration nodes and corresponding integral weights of the numerical integration. The total number of sparse grid sampling points is recorded as N P ; Step 4: Use the optimal Latin square sampling method to obtain sampling points within the interval range of the interval uncertainty parameter in the rotating blade model. The total number of interval sampling points is N. I ; Step 5: Initialize the loop count index j=0, where j is used to count the time iteration steps in the dynamics calculation of the rotating blade system; Step 6: Initialize the loop counting index i=1, i is used to count the interval sample points; Step 7: Initialize loop counting index k=1, where k is used to count sparse grid sample points; Step 8: Set the interval sampling point z I (i) Sparse grid integration configuration node x R Substitute (k) into the original rotating blade system dynamics equations and use an appropriate numerical algorithm to calculate t j The actual dynamic response of the rotating blade system at time t, including blade root displacement, velocity and friction; Step 9: If k = N p , continue; otherwise, set k = k + 1 and return to step 8; Step 10: Use the Galerkin projection method to calculate the expansion coefficient of the chaotic polynomial to obtain t j Chaotic polynomial of the dynamic system response of rotating blades at time instant; Step 11: Use the t constructed in step 10 j The chaotic polynomial model of the dynamic system response of the rotating blade at time t j The statistical moments of the moment rotating blade system response with respect to random parameters; Step 12: If i=N I ,continue; Otherwise, set i=i+1 and return to step 7; Step 13: Using N I The statistical moments of the dynamic response of the rotating blade system with respect to the random parameters are calculated, and the Legendre polynomials of the interval uncertainty parameters of the rotating blade dynamic system are constructed. The expansion coefficients of the Legendre polynomials are calculated based on the least squares method to obtain t j Legendre polynomials of moments; Step 14: Use the Legendre polynomial model constructed in step 13 to construct the Legendre interval expansion function and calculate t j The interval boundary of the statistical moment of the dynamic response of the rotating blade system relative to the interval parameter; Step 15: If j>t e / Δt, then output the interval boundary change of the dynamic response statistical moment of the rotating blade system; otherwise, set j=j+1 and return to step 6.

2. The method for analyzing mixed uncertainty dynamics of rotating blades based on chaotic polynomials according to claim 1 is characterized in that: The random uncertainty parameters include the beam density ρ and the excitation amplitude P c , the interval uncertainty parameters include the blade rotation speed ω and the friction coefficient ω of the tenon-mortise contact surface.

3. The method for analyzing mixed uncertainty dynamics of rotating blades based on chaotic polynomials according to claim 1 is characterized in that: Step 11, using the t constructed in step 10 j The chaotic polynomial model of the dynamic system response of the rotating blade at time t j The statistical moment of the rotating blade system response relative to the random parameters at time instant is calculated as follows: The interval vector η of the rotating blade system is fixed, and only the influence of the random vector ξ in the rotating blade system is considered, t j The response of the rotating blade system at time t is described by the chaotic polynomial modeling in step 10 as the uncertainty function Then, t j The statistical moment of the rotating blade system response at time t is given by j The expansion coefficients of the chaotic polynomial and the orthogonal polynomial basis functions are directly calculated at the moment t j The statistical moments of F(ξ,η) are calculated as follows: μ(F(ξ,η))a0(η) (1) Where μ(F(ξ,η)) is the mean and σ(F(ξ,η)) is the standard deviation.

4. The method for analyzing mixed uncertainty dynamics of rotating blades based on chaotic polynomials according to claim 3 is characterized in that: Step 14: Use the Legendre polynomial model constructed in step 13 to construct a Legendre interval expansion function to calculate the interval boundary of the statistical moment of the dynamic response of the rotating blade system relative to the interval parameter. The specific method is as follows: t j The statistical moments of the uncertainty function F(ξ,η) of the rotating blade system response at each moment are used to construct Legendre polynomials, which are expressed as: The Legendre interval expansion function is used to perform interval operations on Equations (3) and (4). During the calculation, the Legendre orthogonal basis function is taken as a whole, and the exact interval of the 1-dimensional Legendre polynomial basis function is substituted into Equations (3) and (4). The interval operation is directly used to estimate the range of the interval function of Equations (3) and (4) to obtain t j The interval bounds of the statistical moments of the uncertainty function F(ξ,η) of the rotating blade system response at time instant.

5. The method for analyzing mixed uncertainty dynamics of rotating blades based on chaotic polynomials according to claim 4 is characterized in that: Step 14: For the rotating blade system with large interval uncertainty level, the sub-interval technology is used for preliminary processing.

6. A rotating blade hybrid uncertainty dynamics analysis system based on chaotic polynomials, characterized in that: Based on the rotating blade hybrid uncertainty dynamics analysis method described in any one of claims 1 to 5, the rotating blade hybrid uncertainty dynamics analysis based on chaotic polynomials is realized.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the method for analyzing the mixed uncertainty dynamics of rotating blades according to any one of claims 1 to 5 is used to implement the mixed uncertainty dynamics analysis of rotating blades based on chaotic polynomials.

8. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, based on the rotating blade hybrid uncertainty dynamics analysis method according to any one of claims 1 to 5, a rotating blade hybrid uncertainty dynamics analysis based on chaotic polynomials is implemented.

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