Rotor response uncertainty quantification method and device based on path-dependent coordinate system

Abstract

The present invention provides a method and device for quantifying rotor response uncertainty based on a path-dependent coordinate system. The method includes: determining multiple physical parameters that affect the nonlinear steady-state response of the rotor, and corresponding value ranges; sampling all physical parameters based on the zero points of an improved Chebyshev polynomial to form a sparse sample space; determining the coordinate transformation corresponding to the nonlinear steady-state response of each sample point in the sparse sample space based on the path-dependent coordinate system; determining the coefficient vector of a constructed steady-state response proxy model based on the nonlinear steady-state response of each sample point after the coordinate transformation; and determining the boundary corresponding to the nonlinear steady-state response of the rotor based on the steady-state response proxy model. The present invention adopts an improved sampling method to obtain a representative sparse sample space, performs coordinate transformation on these samples to overcome the multi-solution problem, and combines the steady-state response proxy model to complete the quantitative evaluation of the boundary value of the nonlinear steady-state response of the rotor.

Description

Technical Field

[0001] The present invention relates to the field of heat exchange technology, and in particular to a method and device for quantifying rotor response uncertainty based on a path-dependent coordinate system. Background Art

[0002] The Brayton cycle, using supercritical carbon dioxide as a working fluid, boasts high thermal efficiency, high power density, and low cost, and holds promising application prospects in the field of marine energy and power. Turbine rotors, the core components of supercritical carbon dioxide cycle systems, are subject to inevitable variations and uncertainties in their design and operating parameters due to manufacturing variations, long service life, harsh operating conditions, and unforeseen failures. These include random fluctuations in bearing support parameters, material properties, blade surface quality spalling, and dynamic-static clearance variations. Even if the fluctuation level of each uncertainty parameter is relatively small, the accumulation of these uncertainties can significantly impact the nonlinear steady-state response of the turbine rotor. Therefore, when designing and optimizing marine supercritical carbon dioxide turbine rotors, considering the impact of these uncertain parameters on the nonlinear steady-state response is crucial for assessing rotor reliability, ensuring safe and stable operation, and mitigating significant economic losses and catastrophic accidents.

[0003] Currently, traditional uncertainty quantification methods for the nonlinear steady-state response of turbine rotors have the following two defects: First, traditional interval methods can only handle nonlinear steady-state responses with single-solution characteristics, where a single-solution characteristic means that each frequency has a unique steady-state response solution corresponding to it. However, for turbine rotors with nonlinearity, their frequency response curves may have multiple corresponding steady-state response solutions at certain frequencies, that is, there is a multi-solution phenomenon, in which case traditional interval methods are no longer applicable; Second, traditional interval methods use the zero points of Chebyshev polynomials as the basis for constructing the sample space. However, when performing sparse sampling based on Chebyshev zeros, a random sampling strategy is required, which will lead to uneven distribution of the sample space and affect the accuracy of the final determination of the steady-state response of the turbine rotor. Summary of the Invention

[0004] In response to the problems existing in the prior art, the present invention provides a rotor response uncertainty quantification method and device based on a path-dependent coordinate system, which is used to solve the problem in the prior art that the accuracy of the final determination of the nonlinear steady-state response of the turbine rotor is low due to inappropriate sample data.

[0005] In a first aspect, the present invention provides a method for quantifying rotor response uncertainty based on a path-dependent coordinate system, comprising:

[0006] Determining a plurality of physical parameters that affect the nonlinear steady-state response of the rotor, and a value range of each of the physical parameters;

[0007] Based on the improved Chebyshev polynomial zero points, all the physical parameters are sampled to form a sparse sample space;

[0008] Determining a coordinate transformation corresponding to a nonlinear steady-state response of each sample point in the sparse sample space based on a path-dependent coordinate system;

[0009] Determining a coefficient vector of a constructed steady-state response proxy model according to the nonlinear steady-state response of each sample point after coordinate transformation;

[0010] Based on the steady-state response proxy model, a boundary corresponding to the nonlinear steady-state response of the rotor is determined.

[0011] Optionally, sampling all the physical parameters based on the improved Chebyshev polynomial zero points to form a sparse sample space includes:

[0012] Determining a sampling point corresponding to each of the physical parameters based on the improved Chebyshev polynomial zero point;

[0013] When the sum of the numbers of the sampling points corresponding to all the physical parameters satisfies a preset cutoff interval, a sample space formed by the sampling points corresponding to all the physical parameters is determined as a sparse sample space.

[0014] Optionally, before determining the coordinate transformation corresponding to the nonlinear steady-state response of each sample point in the sparse sample space based on the path-dependent coordinate system, the method includes:

[0015] Based on all the physical parameters and the value ranges of the physical parameters, determining a nonlinear steady-state response corresponding to an average value of the physical parameters as a reference response;

[0016] The first response curve corresponding to the reference response is divided into equal parts, and according to the right-hand rule, the local coordinate system corresponding to each of the equal division points is determined to form the path-dependent coordinate system.

[0017] Optionally, determining the coordinate transformation corresponding to the nonlinear steady-state response of each sample point in the sparse sample space based on the path-dependent coordinate system includes:

[0018] In the first response curve, sequentially determining tangent lines corresponding to designated equally divided points in the path-dependent coordinate system;

[0019] Obtaining a nonlinear steady-state response of any sample point in the sparse sample space as a response to be determined;

[0020] If the first normal line and a straight line connecting any two consecutive steady-state solutions in the second response curve have an intersection, and the coordinates of the intersection are within the coordinate range corresponding to the any two consecutive steady-state solutions, then determining the coordinate transformation corresponding to the second response curve based on the coordinates of the designated equally divided point and the coordinates of the intersection;

[0021] The second response curve is a response curve corresponding to the response to be determined; and the first normal line is a straight line perpendicular to the tangent line corresponding to the designated equally divided point.

[0022] Optionally, determining the coefficient vector of the constructed steady-state response proxy model according to the nonlinear steady-state response of each sample point after coordinate transformation includes:

[0023] The steady-state response surrogate model is constructed using efficient polynomials;

[0024] constructing a loss function based on the steady-state response agent model and the path-dependent coordinate system;

[0025] Based on the stochastic gradient descent method, a coefficient vector of the steady-state response proxy model is determined when the loss function is minimized.

[0026] Optionally, determining a boundary corresponding to the nonlinear steady-state response of the rotor based on the steady-state response proxy model includes:

[0027] Divide the value range of each physical parameter into multiple equal parts to construct a new sample space;

[0028] Determining output results of all samples in the new sample space based on the steady-state response proxy model;

[0029] Based on the output results of all the samples, a boundary corresponding to the nonlinear steady-state response of the rotor is determined.

[0030] Optionally, the method for determining the nonlinear steady-state response includes:

[0031] Based on Fourier transform and the constructed motion model of the rotor, determining a first harmonic coefficient corresponding to the displacement of the rotor and a second harmonic coefficient corresponding to the exciting force of the rotor;

[0032] Constructing a frequency domain residual corresponding to the motion model of the rotor based on a harmonic balance method, the first harmonic coefficient, and the second harmonic coefficient;

[0033] Based on the nonlinear arc length method, when the value of the frequency domain residual corresponding to the motion model of the rotor and the value of the arc length residual corresponding to the rotor are both less than a preset convergence value, the corresponding steady-state solution is used as the nonlinear steady-state response of the rotor.

[0034] In a second aspect, the present invention further provides a rotor response uncertainty quantification device based on a path-dependent coordinate system, comprising:

[0035] A determination module, configured to determine a plurality of physical parameters that affect the nonlinear steady-state response of the rotor, and a value range of each of the physical parameters;

[0036] A sampling module, configured to sample all the physical parameters based on the improved Chebyshev polynomial zero points to form a sparse sample space;

[0037] a transformation module, configured to determine, based on a path-dependent coordinate system, a coordinate transformation corresponding to a nonlinear steady-state response of each sample point in the sparse sample space;

[0038] An agent module, configured to determine a coefficient vector of a constructed steady-state response agent model according to the nonlinear steady-state response of each sample point after coordinate transformation;

[0039] A boundary module is used to determine a boundary corresponding to the nonlinear steady-state response of the rotor based on the steady-state response proxy model.

[0040] In a third aspect, the present invention further provides an electronic 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 program, the rotor response uncertainty quantification method based on the path-dependent coordinate system as described in the first aspect above is implemented.

[0041] In a fourth aspect, the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the rotor response uncertainty quantification method based on the path-dependent coordinate system as described in the first aspect above.

[0042] In a fifth aspect, the present invention further provides a computer program product, comprising a computer program, which, when executed by a processor, implements any of the above-described methods for quantifying rotor response uncertainty based on a path-dependent coordinate system.

[0043] The rotor response uncertainty quantification method and device based on the path-dependent coordinate system provided by the present invention obtain a small number of representative samples by sparse sampling of multiple parameters affecting the nonlinear steady-state response of the rotor, and determine the nonlinear steady-state response after coordinate transformation of these sample points. This overcomes the problem of multiple solutions of the rotor response curve in related technologies, and combines with the steady-state response proxy model to complete the quantitative evaluation of the boundary value of the rotor's nonlinear steady-state response. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the present invention or the prior art, a brief introduction is given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0045] Figure 1 1 is a flow chart of a method for quantifying rotor response uncertainty based on a path-dependent coordinate system provided by an embodiment of the present invention;

[0046] Figure 2 1 is a schematic diagram of the improved Chebyshev polynomial zero points provided by an embodiment of the present invention;

[0047] Figure 3 is a schematic diagram comparing a dense sample space and a sparse sample space provided by an embodiment of the present invention;

[0048] Figure 4 is a schematic diagram of several nonlinear steady-state response curves in a sparse sample space provided by an embodiment of the present invention;

[0049] Figure 5 is a schematic diagram of a path-dependent coordinate system provided by an embodiment of the present invention;

[0050] Figure 6 1 is a schematic diagram of the uncertainty quantification results of the rotor response based on the path-dependent coordinate system provided by an embodiment of the present invention;

[0051] Figure 7 1 is a schematic structural diagram of a rotor response uncertainty quantification device based on a path-dependent coordinate system provided by an embodiment of the present invention;

[0052] Figure 8 It is a structural diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0053] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0054] Figure 1 is a flow chart of a rotor response uncertainty quantification method based on a path-dependent coordinate system provided by an embodiment of the present invention, such as Figure 1 As shown, the method includes:

[0055] Step 101: determining a plurality of physical parameters that affect the nonlinear steady-state response of the rotor, and a value range of each physical parameter;

[0056] Specifically, turbine rotors are core components of supercritical CO2 circulation systems. Due to manufacturing deviations, long service life, harsh operating conditions, and unforeseen failures, their design and operating parameters are subject to inevitable changes and uncertainty. To evaluate the impact of various physical parameters on rotor reliability during the design of supercritical CO2 turbine rotors for ships, the relevant physical parameters of the turbine rotor design are optimized to ensure safe and stable operation of the turbine rotor. The relevant physical parameters of the turbine rotor design may include many types, and each parameter has a corresponding reasonable range of values. Based on the specific application requirements, a selection of these physical parameters is selected for analysis, such as bearing support parameters, material property parameters, blade surface quality spalling parameters, and dynamic and static clearance parameters.

[0057] Step 102: based on the improved Chebyshev polynomial zero points, sampling all the physical parameters to form a sparse sample space;

[0058] Related technologies often use the probabilistic nature of the values ​​of physical parameters to process or perform statistical analysis on them. However, in industrial applications, it is often difficult to determine the probability distribution characteristics of each physical parameter using probabilistic methods. Therefore, physical parameters that lack probabilistic characteristics (uncertain factors) are often expressed as interval parameters, that is, the maximum and minimum values ​​of the parameter to be determined are sufficient. This improves the practicality of the analysis method.

[0059] In addition, the present invention uses the improved Chebyshev polynomial zero point to sample each physical parameter to be analyzed and generate corresponding sample points.

[0060] The improved Chebyshev polynomial zeros specifically include:

[0061] The results of sampling the zero points of Chebyshev polynomials for each physical parameter can be expressed as:

[0062]

[0063] Among them, H i represents any one of the multiple physical parameters that affect the nonlinear steady-state response of the rotor, the physical parameter H i The value range of [H i,min ,H i,max ], that is, the maximum value is H i,max , the minimum value is H i,min , k is a positive integer greater than or equal to 1, α k is the zero vector of Chebyshev polynomial. The corresponding α kHow many values ​​does the physical parameter H have? i That's how many samples there are.

[0064] Determine the highest order k (k>1) of the Chebyshev polynomial zero point and the corresponding Chebyshev polynomial zero point vector α k It can be expressed as:

[0065]

[0066] Among them, θ j is the angle value.

[0067] Then, starting from the first zero of the k-order Chebyshev polynomial zeros and discarding the zeros with even numbers, we can get the k-1-order Chebyshev polynomial zeros;

[0068] Finally, repeat the above two steps until k=2; when k=1, the corresponding zero point of the Chebyshev polynomial is the average value of the interval parameter.

[0069] Through the above steps, samples of all order zeros can be obtained. The above process is the improved Chebyshev polynomial zeros, and the improved Chebyshev polynomial zeros are nested.

[0070] When the highest order k = 4, the schematic diagram of the zero points of the nested Chebyshev polynomial is as follows Figure 2 As shown. When k = 4, the physical parameter H i There are 9 corresponding zeros of the Chebyshev polynomial. According to the improved zeros of the Chebyshev polynomial, the zeros with even numbers are discarded, and when k=3, the physical parameter H is obtained. i The corresponding improved Chebyshev polynomial has 5 zeros. Once again discarding the even-numbered zeros, we get the physical parameter H when k=2. i The corresponding improved Chebyshev polynomial has 3 zero points. When k = 1, the physical parameter H i The corresponding improved Chebyshev polynomial has one zero point, which is the physical parameter H i The corresponding average value.

[0071] The above physical parameters that affect the nonlinear steady-state response of the rotor are n in total. u That is, the number of uncertain factors is n u , that is, the uncertainty dimension is n u According to the Chebyshev zeros in the related art, the order of each dimension is equal. Then n u Dense sample space Θ for k-dimensional uncertainty problems d It can be expressed as a tensor product:

[0072]

[0073] The number of samples in the dense sample space is The Chebyshev zero vector representing the nth uncertainty factor, where n represents the number from 1 to n. u Any positive integer between .

[0074] The present invention adopts the improved Chebyshev polynomial zero point, and the number of sampling points of each physical parameter can be different. The dense samples obtained above are sampled again to obtain a sparse sample space.

[0075] The sparse sample space is composed of the tensor product of the zero points of each dimension, i j Represents the order of the jth dimension, then the sum of the orders of all dimensions can be recorded as i sum =i1+i2+…+i n , According to the convergence of the data, a preset truncation interval is set, and the upper and lower limits of the sparse grid truncation level are recorded as L1 and L2 respectively, then the sparse sample space Θ c It can be expressed as a tensor product:

[0076]

[0077] When the number of physical parameters (uncertainty factors) that affect the nonlinear steady-state response of the rotor is 2 and the order k = 4, by setting the upper limit of the preset truncation interval to 5 and the lower limit to 4, the dense sample space (such as Figure 3 (a) in the figure) to obtain a sparse matrix sample space (as shown in Figure 3 As shown in (b)). The sparse sample space is composed of and Since there is overlap between the three tensor products above, the number of sample points in the sparse grid is 29. Compared with the 81 sample points in the dense grid, it can be seen that the application of sparse grid technology greatly reduces the number of sample points and can greatly improve the analysis efficiency.

[0078] The corresponding nonlinear steady-state response is determined for each sample point in the sparse sample space, and the corresponding results are sorted to form a frequency response curve composed of the output results of all nonlinear responses.

[0079] Specific methods for determining nonlinear steady-state responses include:

[0080] Based on Fourier transform and the constructed motion model of the rotor, determining a first harmonic coefficient corresponding to the displacement of the rotor and a second harmonic coefficient corresponding to the exciting force of the rotor;

[0081] Constructing a frequency domain residual corresponding to the motion model of the rotor based on a harmonic balance method, the first harmonic coefficient, and the second harmonic coefficient;

[0082] Based on the nonlinear arc length method, when the value of the frequency domain residual corresponding to the motion model of the rotor and the value of the arc length residual corresponding to the rotor are both less than a preset convergence value, the corresponding steady-state solution is used as the nonlinear steady-state response of the rotor.

[0083] Considering the nonlinear characteristics of the external exciting force, the motion model of the rotor can be expressed by the corresponding control equation:

[0084]

[0085] Where M is the mass matrix; C is the damping matrix, including the damping matrix caused by the gyroscopic effect; u(t), and They represent the rotor displacement vector, rotor velocity vector and rotor acceleration vector respectively; K is the stiffness matrix, which represents the stiffness in the time domain; f ext (t) is the external nonlinear excitation force vector, which includes but is not limited to the composite load of unbalanced force, bearing load, fluid excitation force, etc.

[0086] Through Fourier transform, the nonlinear displacement and periodic nonlinear exciting force of the turbine rotor are expressed by Fourier series. The specific expression formula is:

[0087]

[0088]

[0089] Among them, U j is the jth harmonic coefficient of the displacement vector u(t); F ext,j is the external exciting force vector f ext (t) is the jth harmonic coefficient; Ω represents the rotor speed. Because the high-order harmonic coefficients have little effect on the displacement and external exciting force, and in order to save computing resources, a truncation method is usually adopted to estimate the Fourier series of the rotor displacement vector and the Fourier series of the rotor's external exciting force using a limited number of harmonic term coefficients. Where N h is the harmonic cutoff number. All harmonic coefficients corresponding to the rotor displacement vector can be expressed as U = {U j},j={-N h ,-N h +1,…,N h -1,N h}, all harmonic coefficients corresponding to the rotor exciting force vector can be expressed as F ext ={F ext,j},j={-Nh ,-N h +1,…,N h -1,N h}.

[0090] Applying the harmonic balance method, the frequency domain residual corresponding to the rotor motion model can be expressed as:

[0091] R=Z(Ω)UF ext ;

[0092] Where R represents the frequency domain residual corresponding to the rotor motion model, and U is the displacement harmonic vector, which can be expressed as F ext is the exciting force harmonic vector, which can be expressed as Z(Ω) is a dynamic matrix that represents the linear stiffness in the frequency domain. Its expression is:

[0093]

[0094] A j =-j 2 Ω 2 M+ijΩC+K,j∈[-N h ,+N h ];

[0095] Through the above transformation, the dynamic equation in the time domain is converted to the frequency domain. Then, the nonlinear arc length method is used to determine the iterative arc length Δl corresponding to the frequency domain curve corresponding to the above frequency domain residual.

[0096] Assume that the two adjacent steady-state solutions corresponding to the above frequency domain residual are (Ω (k-1) , U (k-1) ) and (Ω (k) , U (k) ), where k is the number of the steady-state solution. Then the displacement increment ΔU can be defined as the difference between the displacement harmonic vectors of two adjacent steady-state solutions, that is, ΔU (k) =U (k) -U (k-1) , and define the speed harmonic increment ΔΩ as the speed difference between two adjacent steady-state solutions, that is, ΔΩ (k) =Ω (k) -Ω (k-1) . Then the arc length residual equation between any two adjacent steady-state solutions is satisfied:

[0097] a=(ΔU) 2 +(ΔΩ) 2 -(Δl) 2 ;

[0098] Where a represents the arc length residual, and Δl represents the arc length involved in the iteration.

[0099] Combining the frequency domain residual and arc length residual corresponding to the above rotor motion model, the augmented residual equation of the arc length method iteration is determined as:

[0100]

[0101] Based on the arc length method, the steady-state solution is predicted and corrected. In the prediction process, based on the known steady-state solution, the next adjacent steady-state solution is predicted, which can be specifically expressed as:

[0102]

[0103] Among them, U (k+1，0) and Ω (k+1，0) Represents the steady-state solution determined during the prediction process. It should be noted that the predicted solution (Ω (k+1，0) , U (k+1，0) ) is based on two known steady-state solutions (Ω (k-1) , U (k-1) ) and (Ω (k) , U (k) ) is different from the final steady-state solution (Ω (k+1) , U (k+1) ), and the final steady-state solution needs to be obtained through subsequent multiple correction processes.

[0104] The corresponding correction process can be expressed as:

[0105]

[0106] Among them, K t Represents the derivative of the frequency domain residual vector R with respect to the displacement harmonic vector U, q t Represents the derivative of the frequency domain residual vector R with respect to the speed Ω, and K t and q t Both are vectors or matrices. The following describes the solution method of the two derivatives in detail.

[0107] The first derivative K t It can be expressed as:

[0108]

[0109] Among them, the exciting force harmonic vector F ext Derivative of the displacement harmonic vector U The detailed expression is:

[0110]

[0111] Without loss of generality, the derivative of the p-order harmonic of the external exciting force vector with respect to the q-order harmonic of the displacement vector can be expressed as:

[0112]

[0113] Among them, p and q can both be [-N h , +N h ] is any integer in , T = 2π / Ω represents the period of the rotor.

[0114] The second derivative q t It can be expressed as:

[0115]

[0116] During the iterative correction process, to avoid excessive iterations, if convergence is not achieved after a specified number of iterations, the corresponding derivative is updated and the iteration process is repeated. Typically, the specified number of iterations is set to 10.

[0117] Each iteration uses the finite difference method. The corresponding first derivative K t and the second derivative q t The relevant parameters can be expressed as:

[0118]

[0119]

[0120]

[0121] The above correction process is continued until the frequency domain residual and arc length residual in the augmented residual equation are both less than the preset convergence value, and the corresponding result is determined to be a steady-state solution. The preset convergence value here is set to 1×10 -9 , ensuring that the analysis results have high accuracy.

[0122] For each sample point in the sparse sample space, nonlinear response analysis is performed according to the above method to determine the nonlinear steady-state response corresponding to any sample point. The results are collected and organized to form a frequency response curve composed of all nonlinear response output results. Figure 4 This is a schematic diagram of several nonlinear steady-state response curves in a sparse sample space provided by an embodiment of the present invention, which are determined based on the steady-state response curves corresponding to five typical sample points in the sparse sample space.

[0123] Step 103: determining the coordinate transformation corresponding to the nonlinear steady-state response of each sample point in the sparse sample space based on the path-dependent coordinate system;

[0124] After constructing the method for determining the nonlinear steady-state response, in order to avoid the situation where a set of physical parameters corresponds to multiple steady-state solutions, the original coordinate system needs to be transformed so that a set of physical parameters corresponds to a single steady-state solution.

[0125] The specific solution is to determine the nonlinear steady-state response corresponding to the average value of the physical parameters based on the above-mentioned physical parameters of the rotor and the range of values ​​of the physical parameters. Based on the response curve corresponding to the nonlinear steady-state response, in order to unify the dimensions of the coordinate system or facilitate the visualization of the response results, the corresponding response amplitude is converted into a generalized amplitude. Based on the response curve composed of the generalized amplitude and the speed, a path-dependent coordinate system is established, and all frequency response curve data are mapped to the path-dependent coordinate system.

[0126] Take the logarithm with base 10 of the response amplitude and multiply it by the corresponding multiple to form a generalized amplitude, so that the generalized amplitude and the speed are in the same dimension, and then based on the nonlinear steady-state response corresponding to the average value of the physical parameter, divide the response curve into M equal parts according to the total length, where the value of M can be set according to the accuracy requirement. If high accuracy is required, the corresponding M value is set to a larger value. Otherwise, the M value is set to a smaller value. Establish a local coordinate system at each equal division point. The horizontal axis of the local coordinate system is the tangent slope of the equal division point, and the vertical axis is perpendicular to the horizontal axis, that is, the normal of the equal division point, which satisfies the right-hand rule. The local coordinate systems of all the above-mentioned equal division points constitute a path-dependent coordinate system, and the corresponding schematic diagram is shown as follows. Figure 5 shown.

[0127] Optionally, determining the coordinate transformation corresponding to the nonlinear steady-state response of each sample point in the sparse sample space based on the path-dependent coordinate system includes:

[0128] In the first response curve, sequentially determining tangent lines corresponding to designated equally divided points in the path-dependent coordinate system;

[0129] Obtaining a nonlinear steady-state response of any sample point in the sparse sample space as a response to be determined;

[0130] If the first normal line and a straight line connecting any two consecutive steady-state solutions in the second response curve have an intersection, and the coordinates of the intersection are within the coordinate range corresponding to the any two consecutive steady-state solutions, then determining the coordinate transformation corresponding to the second response curve based on the coordinates of the designated equally divided point and the coordinates of the intersection;

[0131] The second response curve is a response curve corresponding to the response to be determined; and the first normal line is a straight line perpendicular to the tangent line corresponding to the designated equally divided point.

[0132] Specifically, after determining the path-dependent coordinate system, in the first response curve corresponding to the benchmark response, tangent lines corresponding to designated equally divided points in the path-dependent coordinate system are sequentially determined;

[0133] The jth equal division point is (x j ,y j ), the slope of the tangent line in the horizontal direction can be approximately replaced by the slope of the secant line corresponding to the two adjacent points before and after the j-th equally divided point, which can be expressed as:

[0134]

[0135] The direction is consistent with the vertical axis and passes through the jth equally divided point (x j ,y j ), that is, the normal line perpendicular to the above tangent line (first normal line), the corresponding equation is:

[0136]

[0137] Obtain the nonlinear steady-state response corresponding to any sample point in the above sparse sample space as the response to be determined. For example, the two adjacent steady-state solutions on the response curve of the sth sample are (m i ,n i ) and (m i+1 ,n i+1 ), then the equation of the line connecting these two steady-state solutions is:

[0138]

[0139] Combine the above two straight line equations to obtain the intersection point (u, v) of the two straight lines. If u∈[m i ,m i+1 ], the intersection point is the intersection point of the response curve of the sth sample and the vertical axis of the local coordinate system of the jth equally divided point. If the horizontal coordinate of the intersection point does not satisfy the horizontal coordinate values ​​of the two adjacent steady-state solutions, the value of i is increased by 1 to determine the intersection point of the next adjacent steady-state solution and the local coordinate system of the jth equally divided point.

[0140] When the intersection coordinates are determined, the abscissa of the intersection in the local coordinate system of the jth equally divided point is 0, and the ordinate is:

[0141]

[0142] Repeat the above steps until all sample points in the sparse sample space determine the corresponding coordinate transformation of the steady-state response in the local coordinate system of the jth equally divided point.

[0143] Then, the corresponding coordinate transformation of all sample points in the sparse sample space in the local coordinate system of the next equally divided point j+1 of the response curve of the reference response is determined.

[0144] By performing the above steps on all equally divided points on the response curve of the benchmark response, the nonlinear steady-state responses of all sample points in the sparse sample space are coordinate transformed, completing the mapping of the frequency response curve data to the path-dependent coordinate system.

[0145] Step 104: determining a coefficient vector of a constructed steady-state response proxy model according to the nonlinear steady-state response of each sample point after coordinate transformation;

[0146] After determining the coordinate transformation of the nonlinear steady-state response of all sample points in the sparse sample space, an efficient polynomial is used to construct a steady-state response proxy model, which is specifically expressed as:

[0147]

[0148] Among them, β T is the transpose of the β vector, β represents the coefficient vector composed of polynomial coefficients, and X represents the polynomial vector composed of polynomials corresponding to all physical parameters. u is the polynomial truncation order, which is generally 4 or 5, or the truncation order can be appropriately increased according to the number of uncertain factors; are polynomial coefficients, X represents the sample point vector corresponding to all physical parameters, Indicates the nth u The exponential term corresponding to the physical parameter (uncertain factor), Indicates the The sample point vector is the coordinate of the sample point in the sparse sample space.

[0149] Based on the steady-state response agent model and the path-dependent coordinate system, a loss function is constructed. The specific loss function can be expressed as follows:

[0150]

[0151] Among them, N is the total number of all sample points in the sparse sample space, φ i Represents the ordinate of the i-th sample point in the path-dependent coordinate system. Repeatedly perform the stochastic gradient descent method to minimize the loss function and determine the coefficient vector of the corresponding steady-state response agent model.

[0152] Step 105: Determine a boundary corresponding to the nonlinear steady-state response of the rotor based on the steady-state response proxy model.

[0153] After the coefficient vector of the steady-state response proxy model is determined, the steady-state response value of any sample point can be calculated using the steady-state response proxy model.

[0154] The value ranges corresponding to all physical parameters (uncertain factors) affecting the rotor are divided into several equal parts to form a new sample space for the steady-state response proxy model. The value of the physical parameter corresponding to each sample point is substituted into the steady-state response proxy model to obtain the corresponding output result. When the maximum and minimum values ​​of the interval are determined, the boundary of the nonlinear steady-state response of the above rotor is obtained, as shown in Figure 6 As shown in Figure 3, the uncertainty quantification results of the nonlinear steady-state response of the rotor are shown.

[0155] The rotor response uncertainty quantification method based on the path-dependent coordinate system provided by the present invention obtains a small number of representative samples by sparse sampling of multiple parameters affecting the nonlinear steady-state response of the rotor, and determines the nonlinear steady-state response after coordinate transformation of these sample points. This overcomes the problem of multiple solutions of the rotor response curve in related technologies, and combines with the steady-state response proxy model to complete the quantitative evaluation of the boundary value of the rotor's nonlinear steady-state response.

[0156] The rotor response uncertainty quantification device based on the path-dependent coordinate system provided by the present invention is described below. The rotor nonlinear steady-state response uncertainty quantification device described below and the rotor nonlinear steady-state response uncertainty quantification method described above can be referenced to each other.

[0157] Figure 7 is a schematic diagram of the structure of a rotor response uncertainty quantification device based on a path-dependent coordinate system provided by an embodiment of the present invention, such as Figure 7 As shown, the device includes:

[0158] A determination module 701 is configured to determine a plurality of physical parameters that affect the nonlinear steady-state response of the rotor, and a value range of each of the physical parameters;

[0159] A sampling module 702 is configured to sample all the physical parameters based on the improved Chebyshev polynomial zero points to form a sparse sample space;

[0160] A transformation module 703 is configured to determine a coordinate transformation corresponding to a nonlinear steady-state response of each sample point in the sparse sample space based on a path-dependent coordinate system;

[0161] The proxy module 704 is configured to determine a coefficient vector of a constructed steady-state response proxy model according to the nonlinear steady-state response of each sample point after coordinate transformation;

[0162] The boundary module 705 is configured to determine a boundary corresponding to the nonlinear steady-state response of the rotor based on the steady-state response proxy model.

[0163] Optionally, in the process of sampling all the physical parameters based on the improved Chebyshev polynomial zero points to form a sparse sample space, the sampling module 702 is specifically configured to:

[0164] Determining a sampling point corresponding to each of the physical parameters based on the improved Chebyshev polynomial zero point;

[0165] When the sum of the numbers of the sampling points corresponding to all the physical parameters satisfies a preset cutoff interval, a sample space formed by the sampling points corresponding to all the physical parameters is determined as a sparse sample space.

[0166] Optionally, before determining the coordinate transformation corresponding to the nonlinear steady-state response of each sample point in the sparse sample space based on the path-dependent coordinate system, the transformation module 703 is further configured to:

[0167] Based on all the physical parameters and the value ranges of the physical parameters, determining a nonlinear steady-state response corresponding to an average value of the physical parameters as a reference response;

[0168] The first response curve corresponding to the reference response is divided into equal parts, and according to the right-hand rule, the local coordinate system corresponding to each of the equal division points is determined to form the path-dependent coordinate system.

[0169] Optionally, in the process of determining the coordinate transformation corresponding to the nonlinear steady-state response of each sample point in the sparse sample space based on the path-dependent coordinate system, the transformation module 703 is specifically configured to:

[0170] In the first response curve, the normal lines corresponding to the designated equally divided points in the path-dependent coordinate system are sequentially determined;

[0171] Obtaining a nonlinear steady-state response of any sample point in the sparse sample space as a response to be determined;

[0172] If a normal line corresponding to the designated equally divided point intersects a straight line connecting any two consecutive steady-state solutions in the second response curve, and the coordinates of the intersection are within the coordinate range corresponding to the any two consecutive steady-state solutions, then determining a coordinate transformation corresponding to the second response curve based on the coordinates of the designated equally divided point and the coordinates of the intersection;

[0173] The second response curve is a response curve corresponding to the response to be determined.

[0174] Optionally, in the process of determining the coefficient vector of the constructed steady-state response proxy model according to the nonlinear steady-state response of each sample point after coordinate transformation, the proxy module 704 is specifically configured to:

[0175] The steady-state response surrogate model is constructed using efficient polynomials;

[0176] constructing a loss function based on the steady-state response agent model and the path-dependent coordinate system;

[0177] Based on the stochastic gradient descent method, a coefficient vector of the steady-state response proxy model is determined when the loss function is minimized.

[0178] Optionally, in the process of determining the boundary corresponding to the nonlinear steady-state response of the rotor based on the steady-state response proxy model, the boundary module is specifically configured to:

[0179] Divide the value range of each physical parameter into multiple equal parts to construct a new sample space;

[0180] Determining output results of all samples in the new sample space based on the steady-state response proxy model;

[0181] Based on the output results of all the samples, a boundary corresponding to the nonlinear steady-state response of the rotor is determined.

[0182] Optionally, the device further includes a response module, which, in the process of determining the nonlinear steady-state response, is specifically configured to:

[0183] Based on Fourier transform and the constructed motion model of the rotor, determining a first harmonic coefficient corresponding to the displacement of the rotor and a second harmonic coefficient corresponding to the exciting force of the rotor;

[0184] Constructing a frequency domain residual corresponding to the motion model of the rotor based on a harmonic balance method, the first harmonic coefficient, and the second harmonic coefficient;

[0185] Based on the nonlinear arc length method, when the value of the frequency domain residual corresponding to the motion model of the rotor and the value of the arc length residual corresponding to the rotor are both less than a preset convergence value, the corresponding steady-state solution is used as the nonlinear steady-state response of the rotor.

[0186] It should be noted here that the above-mentioned device provided by the present invention can implement all the method steps implemented in the above-mentioned method embodiment and can achieve the same technical effects. The parts and beneficial effects that are the same as those in the method embodiment will not be described in detail here.

[0187] Figure 8 Schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. Figure 8As shown, the electronic device may include: a processor 810, a communication interface 820, a memory 830, and a communication bus 840, wherein the processor 810, the communication interface 820, and the memory 830 communicate with each other via the communication bus 840. The processor 810 may call the logic instructions in the memory 830 to execute any of the rotor response uncertainty quantification methods based on the path-dependent coordinate system provided in the above embodiments, for example:

[0188] Determining a plurality of physical parameters that affect the nonlinear steady-state response of the rotor, and a value range of each of the physical parameters;

[0189] Based on the improved Chebyshev polynomial zero points, all the physical parameters are sampled to form a sparse sample space;

[0190] Determining a coordinate transformation corresponding to a nonlinear steady-state response of each sample point in the sparse sample space based on a path-dependent coordinate system;

[0191] Determining a coefficient vector of a constructed steady-state response proxy model according to the nonlinear steady-state response of each sample point after coordinate transformation;

[0192] Based on the steady-state response proxy model, a boundary corresponding to the nonlinear steady-state response of the rotor is determined.

[0193] In addition, the logic instructions in the above-mentioned memory 830 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0194] Optionally, sampling all the physical parameters based on the improved Chebyshev polynomial zero points to form a sparse sample space includes:

[0195] Determining a sampling point corresponding to each of the physical parameters based on the improved Chebyshev polynomial zero point;

[0196] When the sum of the numbers of the sampling points corresponding to all the physical parameters satisfies a preset cutoff interval, a sample space formed by the sampling points corresponding to all the physical parameters is determined as a sparse sample space.

[0197] Optionally, before determining the coordinate transformation corresponding to the nonlinear steady-state response of each sample point in the sparse sample space based on the path-dependent coordinate system, the method includes:

[0198] Based on all the physical parameters and the value ranges of the physical parameters, determining a nonlinear steady-state response corresponding to an average value of the physical parameters as a reference response;

[0199] The first response curve corresponding to the reference response is divided into equal parts, and according to the right-hand rule, the local coordinate system corresponding to each of the equal division points is determined to form the path-dependent coordinate system.

[0200] Optionally, determining the coordinate transformation corresponding to the nonlinear steady-state response of each sample point in the sparse sample space based on the path-dependent coordinate system includes:

[0201] In the first response curve, sequentially determining tangent lines corresponding to designated equally divided points in the path-dependent coordinate system;

[0202] Obtaining a nonlinear steady-state response of any sample point in the sparse sample space as a response to be determined;

[0203] If the first normal line and a straight line connecting any two consecutive steady-state solutions in the second response curve have an intersection, and the coordinates of the intersection are within the coordinate range corresponding to the any two consecutive steady-state solutions, then determining the coordinate transformation corresponding to the second response curve based on the coordinates of the designated equally divided point and the coordinates of the intersection;

[0204] The second response curve is a response curve corresponding to the response to be determined; and the first normal line is a straight line perpendicular to the tangent line corresponding to the designated equally divided point.

[0205] Optionally, determining the coefficient vector of the constructed steady-state response proxy model according to the nonlinear steady-state response of each sample point after coordinate transformation includes:

[0206] The steady-state response surrogate model is constructed using efficient polynomials;

[0207] constructing a loss function based on the steady-state response agent model and the path-dependent coordinate system;

[0208] Based on the stochastic gradient descent method, a coefficient vector of the steady-state response proxy model is determined when the loss function is minimized.

[0209] Optionally, determining a boundary corresponding to the nonlinear steady-state response of the rotor based on the steady-state response proxy model includes:

[0210] Divide the value range of each physical parameter into multiple equal parts to construct a new sample space;

[0211] Determining output results of all samples in the new sample space based on the steady-state response proxy model;

[0212] Based on the output results of all the samples, a boundary corresponding to the nonlinear steady-state response of the rotor is determined.

[0213] Optionally, the method for determining the nonlinear steady-state response includes:

[0214] Based on Fourier transform and the constructed motion model of the rotor, determining a first harmonic coefficient corresponding to the displacement of the rotor and a second harmonic coefficient corresponding to the exciting force of the rotor;

[0215] Constructing a frequency domain residual corresponding to the motion model of the rotor based on a harmonic balance method, the first harmonic coefficient, and the second harmonic coefficient;

[0216] Based on the nonlinear arc length method, when the value of the frequency domain residual corresponding to the motion model of the rotor and the value of the arc length residual corresponding to the rotor are both less than a preset convergence value, the corresponding steady-state solution is used as the nonlinear steady-state response of the rotor.

[0217] It should be noted here that the above-mentioned electronic device provided by the embodiment of the present invention can implement all the method steps implemented by the above-mentioned method embodiment and can achieve the same technical effect. The parts and beneficial effects that are the same or corresponding to the method embodiment in this embodiment will not be described in detail here.

[0218] On the other hand, the present invention also provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the rotor response uncertainty quantification method based on the path-dependent coordinate system provided in the above embodiments.

[0219] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to execute the rotor response uncertainty quantification method based on the path-dependent coordinate system provided in the above embodiments.

[0220] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0221] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, or of course, by hardware. Based on this understanding, the essence of the above technical solution or the part that contributes to the existing technology can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or certain parts of the embodiments.

[0222] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A rotor response uncertainty quantification method based on a path-dependent coordinate system, characterized in that: include: Determining a plurality of physical parameters that affect the nonlinear steady-state response of the rotor, and a value range of each of the physical parameters; Based on the improved Chebyshev polynomial zero points, all the physical parameters are sampled to form a sparse sample space; Determining a coordinate transformation corresponding to a nonlinear steady-state response of each sample point in the sparse sample space based on a path-dependent coordinate system; Determining a coefficient vector of a constructed steady-state response proxy model according to the nonlinear steady-state response of each sample point after coordinate transformation; determining a boundary corresponding to the nonlinear steady-state response of the rotor based on the steady-state response proxy model; Before determining the coordinate transformation corresponding to the nonlinear steady-state response of each sample point in the sparse sample space based on the path-dependent coordinate system, the method includes: Based on all the physical parameters and the value ranges of the physical parameters, determining a nonlinear steady-state response corresponding to an average value of the physical parameters as a reference response; The first response curve corresponding to the reference response is divided into equal parts, and according to the right-hand rule, a local coordinate system corresponding to each of the equal division points is determined to form the path-dependent coordinate system; The determining, based on the path-dependent coordinate system, the coordinate transformation corresponding to the nonlinear steady-state response of each sample point in the sparse sample space includes: In the first response curve, sequentially determining tangent lines corresponding to designated equally divided points in the path-dependent coordinate system; Obtaining a nonlinear steady-state response of any sample point in the sparse sample space as a response to be determined; If the first normal line and a straight line connecting any two consecutive steady-state solutions in the second response curve have an intersection, and the coordinates of the intersection are within the coordinate range corresponding to the any two consecutive steady-state solutions, then determining the coordinate transformation corresponding to the second response curve based on the coordinates of the designated equally divided point and the coordinates of the intersection; The second response curve is a response curve corresponding to the response to be determined; and the first normal line is a straight line perpendicular to the tangent line corresponding to the designated equally divided point.

2. The rotor response uncertainty quantification method based on the path-dependent coordinate system according to claim 1 is characterized in that: The method of sampling all the physical parameters based on the improved Chebyshev polynomial zero point to form a sparse sample space includes: Determining a sampling point corresponding to each of the physical parameters based on the improved Chebyshev polynomial zero point; When the sum of the numbers of the sampling points corresponding to all the physical parameters satisfies a preset cutoff interval, a sample space formed by the sampling points corresponding to all the physical parameters is determined as a sparse sample space.

3. The rotor response uncertainty quantification method based on a path-dependent coordinate system according to claim 1, characterized in that: The step of determining the coefficient vector of the constructed steady-state response proxy model according to the nonlinear steady-state response of each sample point after coordinate transformation includes: The steady-state response surrogate model is constructed using efficient polynomials; constructing a loss function based on the steady-state response agent model and the path-dependent coordinate system; Based on the stochastic gradient descent method, a coefficient vector of the steady-state response proxy model is determined when the loss function is minimized.

4. The rotor response uncertainty quantification method based on a path-dependent coordinate system according to claim 1, characterized in that: The determining, based on the steady-state response proxy model, a boundary corresponding to the nonlinear steady-state response of the rotor includes: Divide the value range of each physical parameter into multiple equal parts to construct a new sample space; Determining output results of all samples in the new sample space based on the steady-state response proxy model; Based on the output results of all the samples, a boundary corresponding to the nonlinear steady-state response of the rotor is determined.

5. The rotor response uncertainty quantification method based on a path-dependent coordinate system according to any one of claims 1 to 4, characterized in that: The method for determining the nonlinear steady-state response includes: Based on Fourier transform and the constructed motion model of the rotor, determining a first harmonic coefficient corresponding to the displacement of the rotor and a second harmonic coefficient corresponding to the exciting force of the rotor; Constructing a frequency domain residual corresponding to the motion model of the rotor based on a harmonic balance method, the first harmonic coefficient, and the second harmonic coefficient; Based on the nonlinear arc length method, when the value of the frequency domain residual corresponding to the motion model of the rotor and the value of the arc length residual corresponding to the rotor are both less than a preset convergence value, the corresponding steady-state solution is used as the nonlinear steady-state response of the rotor.

6. A rotor response uncertainty quantification device based on a path-dependent coordinate system, characterized in that: include: A determination module, configured to determine a plurality of physical parameters that affect the nonlinear steady-state response of the rotor, and a value range of each of the physical parameters; A sampling module, configured to sample all the physical parameters based on the improved Chebyshev polynomial zero points to form a sparse sample space; a transformation module, configured to determine, based on a path-dependent coordinate system, a coordinate transformation corresponding to a nonlinear steady-state response of each sample point in the sparse sample space; An agent module, configured to determine a coefficient vector of a constructed steady-state response agent model according to the nonlinear steady-state response of each sample point after coordinate transformation; a boundary module, configured to determine a boundary corresponding to the nonlinear steady-state response of the rotor based on the steady-state response proxy model; Before determining the coordinate transformation corresponding to the nonlinear steady-state response of each sample point in the sparse sample space based on the path-dependent coordinate system, the method includes: Based on all the physical parameters and the value ranges of the physical parameters, determining a nonlinear steady-state response corresponding to an average value of the physical parameters as a reference response; The first response curve corresponding to the reference response is divided into equal parts, and according to the right-hand rule, a local coordinate system corresponding to each of the equal division points is determined to form the path-dependent coordinate system; The determining, based on the path-dependent coordinate system, the coordinate transformation corresponding to the nonlinear steady-state response of each sample point in the sparse sample space includes: In the first response curve, sequentially determining tangent lines corresponding to designated equally divided points in the path-dependent coordinate system; Obtaining a nonlinear steady-state response of any sample point in the sparse sample space as a response to be determined; If the first normal line and a straight line connecting any two consecutive steady-state solutions in the second response curve have an intersection, and the coordinates of the intersection are within the coordinate range corresponding to the any two consecutive steady-state solutions, then determining the coordinate transformation corresponding to the second response curve based on the coordinates of the designated equally divided point and the coordinates of the intersection; The second response curve is a response curve corresponding to the response to be determined; and the first normal line is a straight line perpendicular to the tangent line corresponding to the designated equally divided point.

7. An electronic 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 program, the rotor response uncertainty quantification method based on the path-dependent coordinate system as described in any one of claims 1 to 5 is implemented.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the rotor response uncertainty quantification method based on a path-dependent coordinate system as claimed in any one of claims 1 to 5 is implemented.

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