Digital quantification method and device for non-linear modal uncertainty of condensate pump rotor

Abstract

The application provides a kind of condensate pump rotor nonlinear modal uncertainty digital quantification method and device, the method comprises: based on the dynamics model of condensate pump rotor and the coupling model of condensate pump rotor and fluid interaction, obtain the first nonlinear dynamics model of condensate pump rotor;Based on the sample in sample space, the nonlinear eigenvalue analysis of first nonlinear dynamics model is carried out, and the nonlinear eigenvalue corresponding to sample is obtained;Based on complex polynomial and the nonlinear eigenvalue corresponding to sample, obtain the complex surrogate model of condensate pump rotor nonlinear modal;Based on complex surrogate model, obtain the stability boundary of condensate pump rotor.The application establishes nonlinear dynamics model based on the interaction of condensate pump rotor and fluid, establishes complex surrogate model based on nonlinear eigenvalue, obtains the stability boundary of condensate pump rotor based on complex surrogate model, and realizes the quantification of condensate pump rotor nonlinear modal uncertainty.

Description

Technical Field

[0001] This invention relates to the field of marine nuclear power platform technology, and in particular to a digital quantification method and apparatus for nonlinear modal uncertainty of condensate pump rotor. Background Technology

[0002] Condensate pump rotors are an important component of the power system of marine nuclear power platforms. They are characterized by miniaturization and high speed, and the safety of their dynamic design is of great significance to ensuring the safe and stable operation of the power system.

[0003] The operating environment of condensate pump rotors is extremely harsh, making them highly sensitive to environmental factors. When the rotor's characteristic frequency approaches or equals the characteristic frequency of the external excitation, the condensate pump rotor will experience an increase in vibration response amplitude, affecting its safety. Furthermore, when the real part of the nonlinear mode of the condensate pump rotor is greater than zero, its vibration will diverge, with the vibration amplitude continuously increasing, ultimately leading to mechanical failure and loss of life. Therefore, in the dynamic design of condensate pump rotors, the rotor's nonlinear modes are one of the most important verification targets.

[0004] In traditional modal analysis of condensate pump rotors, two easily overlooked characteristics exist: nonlinearity and uncertainty. On the one hand, during operation, the condensate pump rotor undergoes intense interaction with the fluid, and the nonlinear fluid excitation force causes the rotor's modal characteristics to also exhibit nonlinearity; however, this nonlinear effect is almost never considered. On the other hand, various unavoidable uncertainties arise during the processing, manufacturing, and operation of the condensate pump rotor. These uncertainties manifest in material characteristics, geometric parameters, support parameters, and external excitations, leading to significant changes in the rotor's nonlinear modes and affecting its safety. In summary, the nonlinearity and uncertainty of the modes pose significant challenges to the safety assessment of condensate pump rotors.

[0005] In summary, there is an urgent need to develop a digital quantification method for the nonlinear modal uncertainty of condensate pump rotors that balances solution efficiency and accuracy, in order to assess the reliability of condensate pump rotors and ensure the safe and stable operation of the power system of marine nuclear power platforms. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a digital quantification method and apparatus for the nonlinear modal uncertainty of a condensate pump rotor.

[0007] This invention provides a digital quantification method for the nonlinear modal uncertainty of a condensate pump rotor, comprising:

[0008] Based on the dynamic model of the condensate pump rotor and the coupling model of the interaction between the condensate pump rotor and the fluid, the first nonlinear dynamic model of the condensate pump rotor is obtained.

[0009] Based on the samples in the sample space, perform nonlinear eigenvalue analysis on the first nonlinear dynamic model to obtain the nonlinear eigenvalues ​​corresponding to the samples;

[0010] Based on the complex polynomial and the nonlinear eigenvalues ​​corresponding to the sample, a complex proxy model of the nonlinear mode of the condensate pump rotor is obtained.

[0011] Based on the complex surrogate model, the stability boundary of the condensate pump rotor is obtained.

[0012] Optionally, the step of performing nonlinear eigenvalue analysis on the first nonlinear dynamic model based on samples in the sample space to obtain the nonlinear eigenvalues ​​corresponding to the samples includes:

[0013] Based on the physical parameters corresponding to the samples in the sample space and the first nonlinear dynamic model, a second nonlinear dynamic model is obtained.

[0014] The second nonlinear dynamic model is solved using the perturbation method, harmonic balance method, and Newton's iteration method to obtain the steady-state solution;

[0015] The steady-state solution is superimposed with periodic small perturbations and then fed into the second nonlinear dynamic model. The harmonic balance method is used to solve the model and obtain the nonlinear eigenvalues ​​corresponding to the samples.

[0016] Optionally, the step of solving the second nonlinear dynamic model based on the perturbation method, harmonic balance method, and Newton's iteration method to obtain a steady-state solution includes:

[0017] The second nonlinear dynamic model is solved using the perturbation method to obtain the assumed steady-state solution;

[0018] Substitute the assumed steady-state solution into the second nonlinear dynamic model, and use the harmonic balance method to obtain the residual equation corresponding to the second nonlinear dynamic model;

[0019] The second nonlinear dynamic model is iterated using Newton's iteration method, and the steady-state solution is obtained when the residual equation converges.

[0020] Optionally, before performing nonlinear eigenvalue analysis on the first nonlinear dynamic model based on samples in the sample space to obtain the nonlinear eigenvalues ​​corresponding to the samples, the process includes:

[0021] Based on the uncertainty dimension, obtain the Chebyshev polynomial zero tensor product space;

[0022] Random sampling is performed on the Chebyshev polynomial zero-point tensor product space, and the sample space is obtained when the uniformity of the sample is minimized.

[0023] Optionally, obtaining the stability boundary of the condensate pump rotor based on the complex surrogate model includes:

[0024] The random sample generated in the two-dimensional space is substituted into the complex proxy model to obtain the stability criterion corresponding to the random sample;

[0025] Based on the stability criterion, the stability boundary of the condensate pump rotor is obtained.

[0026] Optionally, the number of samples in the random sampling is determined based on the order of the Chebyshev polynomial and the uncertainty dimension.

[0027] The present invention also provides a digital quantification device for the nonlinear modal uncertainty of a condensate pump rotor, comprising:

[0028] The first acquisition module is used to acquire the first nonlinear dynamic model of the condensate pump rotor based on the dynamic model of the condensate pump rotor and the coupling model of the interaction between the condensate pump rotor and the fluid.

[0029] The second acquisition module is used to perform nonlinear eigenvalue analysis on the first nonlinear dynamic model based on samples in the sample space, and acquire the nonlinear eigenvalues ​​corresponding to the samples.

[0030] The third acquisition module is used to acquire a complex proxy model of the nonlinear mode of the condensate pump rotor based on the complex polynomial and the nonlinear eigenvalues ​​corresponding to the sample.

[0031] The fourth acquisition module is used to acquire the stability boundary of the condensate pump rotor based on the complex surrogate model.

[0032] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the digital quantification method for the nonlinear modal uncertainty of the condensate pump rotor as described in any of the above.

[0033] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a digital quantification method for the nonlinear modal uncertainty of a condensate pump rotor as described in any of the above claims.

[0034] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements a digital quantification method for the nonlinear modal uncertainty of a condensate pump rotor as described in any of the above claims.

[0035] The present invention provides a digital quantification method and apparatus for nonlinear modal uncertainty of condensate pump rotor. By establishing a nonlinear dynamic model based on the interaction between condensate pump rotor and fluid, establishing a complex surrogate model based on the nonlinear eigenvalues ​​of the nonlinear dynamic model, and obtaining the stability boundary of condensate pump rotor based on the complex surrogate model, the nonlinear modal uncertainty of condensate pump rotor is realized. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0037] Figure 1 This is one of the flowcharts illustrating the digital quantification method for the nonlinear modal uncertainty of a condensate pump rotor provided in this embodiment of the invention.

[0038] Figure 2 This is the second flowchart illustrating the digital quantification method for the nonlinear modal uncertainty of a condensate pump rotor provided in this embodiment of the invention.

[0039] Figure 3 This is a schematic diagram of the structure of the digital quantification device for the nonlinear modal uncertainty of the condensate pump rotor provided in an embodiment of the present invention;

[0040] Figure 4 This is a schematic diagram of the structure of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0042] Figure 1 This is one of the flowcharts illustrating the digital quantification method for the nonlinear modal uncertainty of a condensate pump rotor provided in this embodiment of the invention, such as... Figure 1As shown, this embodiment of the invention provides a method for quantifying the nonlinear modes of a condensate pump rotor, including:

[0043] Step 101: Based on the dynamic model of the condensate pump rotor and the coupling model of the interaction between the condensate pump rotor and the fluid, obtain the first nonlinear dynamic model of the condensate pump rotor.

[0044] Specifically, a dynamic model of the condensate pump rotor is established using the three-dimensional finite element method, and a coupling effect model between the condensate pump rotor and the fluid is established using the three-dimensional finite volume method. Preferably, hexahedral elements are used in both the three-dimensional finite element method and the three-dimensional finite volume method to improve the accuracy of the numerical simulation.

[0045] Figure 2 This is the second flowchart illustrating the digital quantification method for the nonlinear modal uncertainty of a condensate pump rotor provided in this embodiment of the invention. Figure 2 As shown, after establishing the dynamic model and the coupling model, the first nonlinear dynamic model of the condensate pump rotor is obtained based on the dynamic model and the coupling model. The expression of the first nonlinear dynamic model is shown below:

[0046]

[0047] In the formula, M is the mass matrix; C is the damping matrix; K is the stiffness matrix; and u(t) is the displacement vector in the time domain. The velocity vector in the time domain f is the acceleration vector in the time domain. mech (t) represents the mechanical excitation load, mainly including unbalanced loads, loads caused by pre-deformation, and nonlinear loads related to faults; f fluid (u,t) represents the fluid excitation load, which mainly includes the coupling force between the condensate pump rotor and the fluid, the support reaction force provided by the fluid at the bearing, etc., and t represents time.

[0048] Step 102: Perform nonlinear eigenvalue analysis on the first nonlinear dynamic model based on the samples in the sample space to obtain the nonlinear eigenvalues ​​corresponding to the samples.

[0049] Specifically, the sample space is a sparse sample space with high discreteness and sufficient sampling obtained by sparsely sampling the tensor product space of Chebyshev polynomial zeros.

[0050] Based on the first nonlinear dynamic model, a second nonlinear dynamic model is obtained based on the physical parameters corresponding to the samples in the sample space. A series of solutions are performed on the second nonlinear dynamic model to obtain the nonlinear eigenvalues ​​corresponding to the samples.

[0051] Optionally, before performing nonlinear eigenvalue analysis on the first nonlinear dynamic model based on samples in the sample space to obtain the nonlinear eigenvalues ​​corresponding to the samples, the process includes:

[0052] Based on the uncertainty dimension, obtain the Chebyshev polynomial zero tensor product space;

[0053] Random sampling is performed on the Chebyshev polynomial zero-point tensor product space, and the sample space is obtained when the uniformity of the sample is minimized.

[0054] Specifically, the expression for the zeros of the k-th order Chebyshev polynomial is as follows:

[0055]

[0056] In the formula, α is the zero vector of the k-th order Chebyshev polynomial, and θ w Let w be the angle value, and w ranges from 1 to k+1, where k is the order of the Chebyshev polynomial.

[0057] When the uncertainty dimension is n, the expression for the Chebyshev polynomial zero tensor product space is as follows:

[0058]

[0059] In the formula, α is the tensor product space of the zeros of the Chebyshev polynomial, α1 is the vector of zeros of the Chebyshev polynomial corresponding to the first uncertainty factor, α2 is the vector of zeros of the Chebyshev polynomial corresponding to the second uncertainty factor, and α... n Let be the zero vector of the Chebyshev polynomial corresponding to the nth uncertainty factor.

[0060] The Chebyshev polynomial zero tensor product space is a dense sample space, where each sample corresponds to a Chebyshev polynomial zero vector. The large number of samples in this dense space makes it difficult to perform uncertain quantization, leading to the curse of dimensionality. To overcome this problem, sparse sampling of the dense sample space is necessary.

[0061] The specific process of sparse sampling in a dense sample space is as follows: repeatedly randomly sample the dense space samples until the uniformity of the sampled samples reaches the minimum, and the required sample space can be obtained. The obtained sample space is the sparse sample space.

[0062] The expression for evaluating sample evenness is as follows:

[0063]

[0064] In the formula, α pLet α be the p-th sample in the sample space, where p ranges from 1 to G-1, and G is the total number of samples in the sample space. q Let q be the q-th sample in the sample space, where the value of q ranges from p+1 to G-1.

[0065] Optionally, the number of samples in the random sampling is determined based on the order of the Chebyshev polynomial and the uncertainty dimension.

[0066] Specifically, the dense spatial sample is subjected to repeated random sampling, and the number of samples in each random sampling is determined by the order of the Chebyshev polynomial and the uncertainty dimension.

[0067] The expression for the number of samples in a random sampling is as follows:

[0068] N = 2(n+k)! / (n!k!)

[0069] Where N represents the number of samples, n represents the dimension of uncertainty, k represents the order of the Chebyshev polynomial, and ! represents the factorial.

[0070] Table 1 compares the computational efficiency of dense and sparse sample spaces. When the order of the Chebyshev polynomial is 4, as the uncertainty dimension increases from 3 to 7, the time saved by the sparse sample space compared to the dense sample space increases from 44.00% to 99.16%. The higher the uncertainty dimension, the more significant the time-saving effect of the sparse sample space becomes, indicating that the sparse sampling method provided in this embodiment can play a greater role in high-dimensional uncertainty problems and can effectively overcome the curse of dimensionality.

[0071] Table 1 Comparison of computational efficiency between dense and sparse sample spaces.

[0072]

[0073] The quantification method for the nonlinear modes of the condensate pump rotor provided in this embodiment of the invention can effectively reduce the number of samples, overcome the curse of dimensionality, and improve computational efficiency by randomly sampling the tensor product space of the Chebyshev polynomial zeros.

[0074] Optionally, the step of performing nonlinear eigenvalue analysis on the first nonlinear dynamic model based on samples in the sample space to obtain the nonlinear eigenvalues ​​corresponding to the samples includes:

[0075] Based on the physical parameters corresponding to the samples in the sample space and the first nonlinear dynamic model, a second nonlinear dynamic model is obtained.

[0076] The second nonlinear dynamic model is solved using the perturbation method, harmonic balance method, and Newton's iteration method to obtain the steady-state solution;

[0077] The steady-state solution is superimposed with periodic small perturbations and then fed into the second nonlinear dynamic model. The harmonic balance method is used to solve the model and obtain the nonlinear eigenvalues ​​corresponding to the samples.

[0078] Specifically, the random parameters of a sample are the zero vectors of the Chebyshev polynomial corresponding to that sample. After determining the sample, the random parameters of the sample need to be mapped to the values ​​of the actual physical variables, which are the physical parameters.

[0079] The physical parameters of a sample can be determined based on its random parameters and the maximum and minimum values ​​of the corresponding physical variables.

[0080] The expressions for the physical parameters corresponding to the sample are as follows:

[0081]

[0082] In the formula, H k H represents the physical parameters corresponding to the sample. max H represents the maximum value of the physical variable H. min α represents the minimum value of the physical variable H. k Let represent the vector of zeros of the Chebyshev polynomial, where k is a positive integer greater than or equal to 1.

[0083] The physical parameters are related to the mass matrix M, damping matrix C, stiffness matrix K, and mechanical excitation load f. mech (t) and fluid excitation load f fluid The parameters related to (u,t) can include physical parameters such as material properties and geometric dimensions. Changes in these physical parameters will affect the mass matrix M, damping matrix C, stiffness matrix K, and mechanical excitation load f. mech (t) and fluid excitation load f fluid The values ​​of (u,t) can be adjusted to change the expression of the nonlinear dynamic model.

[0084] Therefore, the mass matrix M, damping matrix C, stiffness matrix K, and mechanical excitation load f are determined based on the physical parameters corresponding to the samples in the sample space. mech (t) and fluid excitation load f fluid (u,t), thereby further determining the second nonlinear dynamic model, which is a model with different parameters from the first nonlinear dynamic model.

[0085] The second nonlinear dynamic model is solved to obtain the steady-state solution. The solution process requires the use of the perturbation method, the harmonic balance method, and Newton's iteration method.

[0086] Optionally, the step of solving the second nonlinear dynamic model based on the perturbation method, harmonic balance method, and Newton's iteration method to obtain a steady-state solution includes:

[0087] The second nonlinear dynamic model is solved using the perturbation method to obtain the assumed steady-state solution;

[0088] Substitute the assumed steady-state solution into the second nonlinear dynamic model, and use the harmonic balance method to obtain the residual equation corresponding to the second nonlinear dynamic model;

[0089] The second nonlinear dynamic model is iterated using Newton's iteration method, and the steady-state solution is obtained when the residual equation converges.

[0090] Specifically, since the motion of the condensate pump rotor is periodic, the mechanical and fluid excitation loads associated with the rotor's motion are also periodic. By using the perturbation method to solve the second nonlinear dynamic model, the assumed steady-state solution corresponding to u(t) in the second nonlinear dynamic model can be obtained.

[0091] u(t), f mech (t) and f fluid The Fourier decomposition expressions corresponding to (t) are shown below:

[0092]

[0093]

[0094]

[0095] In the formula, u(t) is the displacement vector in the time domain, and f mech (t) represents the mechanical excitation load, f fluid (u,t) represents the fluid excitation load, j represents the order of the harmonic term, and U j Let u(t) be the harmonic component of the displacement vector. For mechanical excitation load f mech The harmonic components of (t), For fluid excitation load f fluid The harmonic components of (u,t), where i is the imaginary unit, are... Ω represents the rotor speed.

[0096] By substituting the assumed steady-state solution into the second nonlinear dynamic model and applying the harmonic balance method, the residual equation of the dynamic model in the frequency domain can be obtained.

[0097] The expression for the residual equation is as follows:

[0098] R=Z(Ω)UF mech+F fluid (U)

[0099] In the formula, R is the residual vector, and the other matrices and vectors in the residual equation can be represented as:

[0100]

[0101]

[0102]

[0103] In the formula, U is a vector composed of displacement harmonic components, and F mech Let F be a vector composed of harmonic components of the mechanical excitation load. fluid It is a vector composed of harmonic components of fluid-excited load.

[0104] Z(Ω) = diag(…A -3 A -2 A -1 A0A1A2A3…)

[0105] A j =-j 2 Ω 2 M+ijΩC+K,j∈(-∞,+∞)

[0106] In the formula, Z(Ω) is the dynamic stiffness matrix, Ω represents the rotor speed, j is the order of the harmonic term, M is the mass matrix, C is the damping matrix, K is the stiffness matrix, and i is the imaginary unit.

[0107] The second nonlinear dynamic model is solved iteratively using the Newton-Raphson method. When the magnitude of the residual vector in the residual equation is less than the preset convergence value, the solution corresponding to this value is the steady-state solution of the second nonlinear dynamic model.

[0108] The iterative process of Newton's iteration method is as follows: solve the second nonlinear dynamic model to obtain the motion response of the condensate pump rotor. Substitute it into fluid dynamics software (such as FLUENT, CFX software, etc.) to obtain the fluid excitation force. Substitute the fluid excitation force into the second nonlinear dynamic model to obtain the motion response of the condensate pump rotor. Repeat the above process to obtain the nonlinear steady-state solution of the condensate pump rotor.

[0109] Since the range of j is from negative infinity to positive infinity, it means that j can take any integer value and is unbounded. Therefore, in order to make A j To make it bounded and solvable, we need to truncate the order of j. Let N be the order of the harmonic term truncation. h This means that the absolute value of j is greater than N. h All items must be discarded.

[0110] After obtaining the steady-state solution u * Based on this, a periodic small perturbation is superimposed. The expression for the periodic small perturbation δu is as follows:

[0111]

[0112] In the formula, δ represents the disturbance sign, δu represents the small displacement disturbance, λ represents the nonlinear eigenvalue, and S j Let represent the harmonic components of the frequency domain eigenvector S, where j is the order of the harmonic term and i is the imaginary unit, i.e., Ω represents the rotor speed, N h This is the order of the harmonic term cutoff.

[0113] The vibration response after disturbance is u * +δu, u * Substituting +δu into the second nonlinear dynamic model and applying the harmonic balance method again, we can obtain the nonlinear eigenvalue equation, the expression of which is shown below:

[0114] (λ 2 B2+2λB1+B0)S=0

[0115] In the formula:

[0116]

[0117]

[0118]

[0119] B 1,k =irΩM+C,r∈[-N h N h ]

[0120]

[0121] In the formula, λ is the nonlinear eigenvalue, S is the frequency domain eigenvector, Z(Ω) is the dynamic stiffness matrix, U is a vector composed of displacement harmonic components, and F is F mech and F fluid The sum of these terms, where M is the mass matrix, C is the damping matrix, Ω represents the rotor speed, and N... h This is the order of the harmonic term cutoff.

[0122] By performing generalized eigenvalue analysis on the nonlinear eigenvalue equation, we can obtain the nonlinear eigenvalues, which are expressed as follows:

[0123] λ=iω+ξ

[0124] In the formula, λ is the nonlinear eigenvalue, the imaginary part ω is the nonlinear characteristic frequency, i is the imaginary unit, and ξ is the stability criterion. A real part ξ greater than zero means the system is unstable, less than zero means the system is stable, and equal to zero means the system is critically stable.

[0125] Step 103: Based on the complex polynomial and the nonlinear eigenvalues ​​corresponding to the sample, obtain the complex surrogate model of the nonlinear mode of the condensate pump rotor.

[0126] Specifically, the nonlinear eigenvalues ​​corresponding to all samples are collected to form a vector Y, that is, vector Y is [λ1λ2…λ]. N ] T .

[0127] The expression for a complex polynomial is shown below:

[0128]

[0129] In the formula,

[0130] β=[β 0,0,…,0 β 1,0,…,0 β 0,1,…,0 …β 0,0,…,1 β 2,0,…,0 β 1,1,…,0 …β 0,0,…,ku ]

[0131]

[0132] Substituting the random parameters of each sample into an efficient complex polynomial, we can obtain a matrix Ψ composed of the X vectors corresponding to the samples. The expression for matrix Ψ is as follows:

[0133]

[0134] Substitute the vector Y, composed of the nonlinear eigenvalues ​​corresponding to all samples, into the complex polynomial, and solve the complex polynomial using the least squares method to obtain the coefficients β of each term, i.e.:

[0135] β=(Ψ T Ψ) -1 Ψ T Y

[0136] Where Y is the vector composed of the nonlinear eigenvalues ​​corresponding to the sample, and Ψ is the matrix composed of the X vectors corresponding to the sample.

[0137] The complex polynomial with determined coefficients is the complex surrogate model of the nonlinear modes of the condensate pump rotor.

[0138] Step 104: Based on the complex surrogate model, obtain the stability boundary of the condensate pump rotor.

[0139] Specifically, the nonlinear eigenvalue boundaries of the complex surrogate model are determined. Based on the boundaries of the nonlinear eigenvalues, the boundaries of the nonlinear characteristic frequency and the unstable speed range are obtained. The boundaries of the unstable speed range are the boundaries of the stability criterion. Based on the boundaries of the stability criterion, the stability boundaries of the condensate pump rotor can be determined.

[0140] Optionally, obtaining the stability boundary of the condensate pump rotor based on the complex surrogate model includes:

[0141] The random sample generated in the two-dimensional space is substituted into the complex proxy model to obtain the stability criterion corresponding to the random sample;

[0142] Based on the stability criterion, the stability boundary of the condensate pump rotor is obtained.

[0143] Specifically, a large number of random samples are generated in a two-dimensional space. It is generally recommended that the number of samples be greater than 10,000. Each sample is substituted into a complex surrogate model to obtain the complex polynomial corresponding to each sample, which is the stability criterion.

[0144] Based on the stability criteria corresponding to all samples, a contour map is drawn where the stability criterion equals 0. This is the boundary of the stability criterion, which means that the condensate pump rotor cannot operate within the boundary of the stability criterion, i.e., in the region where the stability is greater than zero, in order to avoid rotor instability, which could cause devastating damage to the unit or even casualties.

[0145] The digital quantification method for nonlinear modal uncertainty of condensate pump rotor provided in this invention considers the nonlinearity of the interaction between the condensate pump rotor and the fluid, as well as the nonlinearity related to faults. It establishes an analysis method for the nonlinear modes of condensate pump rotor. Compared with the modal results that ignore nonlinearity, the nonlinear modal results obtained based on this invention are more consistent with the actual situation and have more important reference value for the design of condensate pump rotor.

[0146] The digital quantification method for nonlinear modal uncertainty of condensate pump rotor provided in this invention takes into account the unavoidable uncertainties in the design, manufacturing and operation of condensate pump rotor, which can enhance the accuracy of nonlinear modal evaluation of condensate pump rotor and improve the design level of propulsion condensate pump rotor.

[0147] The following describes the digital quantification device for the nonlinear modal uncertainty of the condensate pump rotor provided by the present invention. The digital quantification device for the nonlinear modal uncertainty of the condensate pump rotor described below and the digital quantification method for the nonlinear modal uncertainty of the condensate pump rotor described above can be referred to in correspondence with each other.

[0148] Figure 3This is a schematic diagram of the structure of the digital quantification device for the nonlinear modal uncertainty of the condensate pump rotor provided in an embodiment of the present invention, as shown below. Figure 3 As shown, the present invention also provides a digital quantification device for the nonlinear modal uncertainty of a condensate pump rotor, comprising: a first acquisition module 301, a second acquisition module 302, a third acquisition module 303, and a fourth acquisition module 304, wherein:

[0149] The first acquisition module 301 is used to acquire the first nonlinear dynamic model of the condensate pump rotor based on the dynamic model of the condensate pump rotor and the coupling model of the interaction between the condensate pump rotor and the fluid.

[0150] The second acquisition module 302 is used to perform nonlinear eigenvalue analysis on the first nonlinear dynamic model based on samples in the sample space, and acquire the nonlinear eigenvalues ​​corresponding to the samples.

[0151] The third acquisition module 303 is used to acquire a complex surrogate model of the nonlinear mode of the condensate pump rotor based on the complex polynomial and the nonlinear eigenvalues ​​corresponding to the sample.

[0152] The fourth acquisition module 304 is used to acquire the stability boundary of the condensate pump rotor based on the complex proxy model.

[0153] Optionally, the second acquisition module 302 includes: a first acquisition submodule, a second acquisition submodule, a third acquisition submodule, and a fourth acquisition submodule, wherein:

[0154] The first acquisition submodule is used to substitute the physical parameters corresponding to the samples in the sample space into the first nonlinear dynamic model to obtain the second nonlinear dynamic model.

[0155] The second acquisition submodule is used to solve the second nonlinear dynamic model based on the perturbation method, harmonic balance method and Newton's iteration method to obtain the steady-state solution;

[0156] The third acquisition submodule is used to superimpose periodic small perturbations on the steady-state solution and input them into the second nonlinear dynamic model, and use the harmonic balance method to solve the problem to obtain the nonlinear eigenvalues ​​corresponding to the sample.

[0157] Optionally, the third acquisition submodule is specifically used to: solve the second nonlinear dynamic model using the perturbation method to obtain the assumed steady-state solution;

[0158] Substitute the assumed steady-state solution into the second nonlinear dynamic model, and use the harmonic balance method to obtain the residual equation corresponding to the second nonlinear dynamic model;

[0159] The second nonlinear dynamic model is iterated using Newton's iteration method, and the steady-state solution is obtained when the residual equation converges.

[0160] Optionally, the device further includes: a fifth acquisition module and a sixth acquisition module; wherein:

[0161] The fifth acquisition module is used to acquire the Chebyshev polynomial zero tensor product space based on the uncertainty dimension.

[0162] The sixth acquisition module is used to randomly sample the Chebyshev polynomial zero-point tensor product space and acquire the sample space when the uniformity of the sample is minimized.

[0163] Optionally, the fourth acquisition module 304 is specifically used to: substitute the samples in the two-dimensional space into the complex surrogate model to obtain the stability criterion corresponding to the samples in the two-dimensional space;

[0164] Based on the stability criterion, the stability boundary of the condensate pump rotor is obtained.

[0165] Optionally, the number of samples in the random sampling is determined based on the order of the Chebyshev polynomial and the uncertainty dimension.

[0166] Specifically, the digital quantification device for nonlinear modal uncertainty of condensate pump rotor provided in this application embodiment can realize all the method steps implemented in the above method embodiment and can achieve the same technical effect. Here, the parts that are the same as those in the method embodiment and the beneficial effects will not be described in detail.

[0167] Figure 4 This is a schematic diagram of the structure of the electronic device provided in the embodiment of the present invention, such as... Figure 4As shown, the electronic device may include: a processor 410, a communication interface 420, a memory 430, and a communication bus 440, wherein the processor 410, the communication interface 420, and the memory 430 communicate with each other through the communication bus 440. The processor 410 can call logical instructions in the memory 430 to execute a digital quantification method for the uncertainty of the nonlinear modes of the condensate pump rotor. This method includes: obtaining a first nonlinear dynamic model of the condensate pump rotor based on the dynamic model of the condensate pump rotor and the coupling model of the interaction between the condensate pump rotor and the fluid; performing nonlinear eigenvalue analysis on the first nonlinear dynamic model based on samples in the sample space to obtain the nonlinear eigenvalues ​​corresponding to the samples; obtaining a complex surrogate model of the nonlinear modes of the condensate pump rotor based on a complex polynomial and the nonlinear eigenvalues ​​corresponding to the samples; and obtaining the stability boundary of the condensate pump rotor based on the complex surrogate model.

[0168] Furthermore, the logical instructions in the aforementioned memory 430 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0169] On the other hand, the present invention also provides a computer program product, which includes a computer program that 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 digital quantification method for the uncertainty of the nonlinear modes of the condensate pump rotor provided by the above methods. The method includes: obtaining a first nonlinear dynamic model of the condensate pump rotor based on a dynamic model of the condensate pump rotor and a coupling model of the interaction between the condensate pump rotor and the fluid; performing nonlinear eigenvalue analysis on the first nonlinear dynamic model based on samples in the sample space to obtain nonlinear eigenvalues ​​corresponding to the samples; obtaining a complex surrogate model of the nonlinear modes of the condensate pump rotor based on a complex polynomial and the nonlinear eigenvalues ​​corresponding to the samples; and obtaining the stability boundary of the condensate pump rotor based on the complex surrogate model.

[0170] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a digital quantification method for the uncertainty of nonlinear modes of a condensate pump rotor provided by the methods described above. This method includes: obtaining a first nonlinear dynamic model of the condensate pump rotor based on a dynamic model of the condensate pump rotor and a coupling model of the interaction between the condensate pump rotor and the fluid; performing nonlinear eigenvalue analysis on the first nonlinear dynamic model based on samples in a sample space to obtain nonlinear eigenvalues ​​corresponding to the samples; obtaining a complex surrogate model of the nonlinear modes of the condensate pump rotor based on a complex polynomial and the nonlinear eigenvalues ​​corresponding to the samples; and obtaining the stability boundary of the condensate pump rotor based on the complex surrogate model.

[0171] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0172] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0173] In the embodiments of this application, the terms "first," "second," etc., are used to distinguish similar objects, and not to describe a specific order or sequence. It should be understood that such terms can be used interchangeably where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first" and "second" are generally of the same class, and the number of objects is not limited; for example, the first object can be one or more.

[0174] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A digital quantification method for the nonlinear modal uncertainty of a condensate pump rotor, characterized in that, include: Based on the dynamic model of the condensate pump rotor established using the three-dimensional finite element method and the coupling interaction model between the condensate pump rotor and the fluid established using the three-dimensional finite volume method, the first nonlinear dynamic model of the condensate pump rotor is obtained. Based on the samples in the sample space, perform nonlinear eigenvalue analysis on the first nonlinear dynamic model to obtain the nonlinear eigenvalues ​​corresponding to the samples; Based on the complex polynomial and the nonlinear eigenvalues ​​corresponding to the sample, a complex proxy model of the nonlinear mode of the condensate pump rotor is obtained. Based on the complex surrogate model, the stability boundary of the condensate pump rotor is obtained; Before performing nonlinear eigenvalue analysis on the first nonlinear dynamic model based on samples in the sample space to obtain the nonlinear eigenvalues ​​corresponding to the samples, the process includes: Based on the uncertainty dimension, obtain the Chebyshev polynomial zero tensor product space; Random sampling is performed on the Chebyshev polynomial zero-point tensor product space, and the sample space is obtained when the uniformity of the sample is minimized.

2. The digital quantification method for the nonlinear modal uncertainty of a condensate pump rotor according to claim 1, characterized in that, The nonlinear eigenvalue analysis of the first nonlinear dynamic model based on samples in the sample space to obtain the nonlinear eigenvalues ​​corresponding to the samples includes: Based on the physical parameters corresponding to the samples in the sample space and the first nonlinear dynamic model, a second nonlinear dynamic model is obtained. The second nonlinear dynamic model is solved using the perturbation method, harmonic balance method, and Newton's iteration method to obtain the steady-state solution; The steady-state solution is superimposed with periodic small perturbations and then fed into the second nonlinear dynamic model. The harmonic balance method is used to solve the model and obtain the nonlinear eigenvalues ​​corresponding to the samples.

3. The digital quantification method for the nonlinear modal uncertainty of a condensate pump rotor according to claim 2, characterized in that, The step of solving the second nonlinear dynamic model based on the perturbation method, harmonic balance method, and Newton's iteration method to obtain the steady-state solution includes: The second nonlinear dynamic model is solved using the perturbation method to obtain the assumed steady-state solution; Substitute the assumed steady-state solution into the second nonlinear dynamic model, and use the harmonic balance method to obtain the residual equation corresponding to the second nonlinear dynamic model; The second nonlinear dynamic model is iterated using Newton's iteration method, and the steady-state solution is obtained when the residual equation converges.

4. The digital quantification method for the nonlinear modal uncertainty of a condensate pump rotor according to claim 1, characterized in that, The process of obtaining the stability boundary of the condensate pump rotor based on the complex surrogate model includes: The random sample generated in the two-dimensional space is substituted into the complex proxy model to obtain the stability criterion corresponding to the random sample; Based on the stability criterion, the stability boundary of the condensate pump rotor is obtained.

5. The digital quantification method for the nonlinear modal uncertainty of a condensate pump rotor according to claim 1, characterized in that, The number of samples in the random sampling is determined based on the order of the Chebyshev polynomial and the uncertainty dimension.

6. A digital quantification device for the nonlinear modal uncertainty of a condensate pump rotor, characterized in that, include: The first acquisition module is used to acquire the first nonlinear dynamic model of the condensate pump rotor by using the dynamic model based on the condensate pump rotor established by the three-dimensional finite element method and the coupling interaction model between the condensate pump rotor and the fluid established by the three-dimensional finite volume method. The second acquisition module is used to perform nonlinear eigenvalue analysis on the first nonlinear dynamic model based on samples in the sample space, and acquire the nonlinear eigenvalues ​​corresponding to the samples. The third acquisition module is used to acquire a complex proxy model of the nonlinear mode of the condensate pump rotor based on the complex polynomial and the nonlinear eigenvalues ​​corresponding to the sample. The fourth acquisition module is used to acquire the stability boundary of the condensate pump rotor based on the complex surrogate model. The device further includes: The fifth acquisition module is used to obtain the Chebyshev polynomial zero-point tensor product space based on multiple preset uncertainty dimensions. The sixth acquisition module is used to randomly sample the Chebyshev polynomial zero-point tensor product space and acquire the sample space when the uniformity of the sample is minimized.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the digital quantification method for the nonlinear modal uncertainty of the condensate pump rotor as described in any one of claims 1 to 5.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the digital quantification method for the nonlinear modal uncertainty of the condensate pump rotor as described in any one of claims 1 to 5.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the digital quantification method for the nonlinear modal uncertainty of the condensate pump rotor as described in any one of claims 1 to 5.

Images