Digital quantification method and device for steady-state response uncertainty of seawater pump rotor

Abstract

The application provides a kind of seawater pump rotor steady-state response uncertainty digital quantification method and device, the method comprises: based on the improved Chebyshev polynomial zero point, sample all target physical parameters, constitute sparse sample space;Based on the dynamics model of seawater pump rotor and Newton iteration method, determine the nonlinear steady-state response corresponding to each sample point in sparse sample space;Based on the corresponding nonlinear steady-state response of polynomial and sparse sample space, determine the proxy model of seawater pump rotor nonlinear steady-state response;Based on the proxy model of seawater pump rotor nonlinear steady-state response, determine the boundary corresponding to the nonlinear steady-state response of seawater pump rotor.The application uses improved sampling method, obtains representative sparse sample space, determines the corresponding nonlinear steady-state response of the sample point by Newton iteration method, greatly improves the solving efficiency and solving accuracy, completes the quantitative evaluation of the boundary value of rotor nonlinear steady-state response.

Description

Technical Field

[0001] This invention relates to the field of marine propulsion system technology, and in particular to a digital quantification method and apparatus for the uncertainty of steady-state response of seawater pump rotors. Background Technology

[0002] Seawater pumps are crucial equipment in marine propulsion systems. The design, manufacturing, operation, and maintenance of marine seawater pump rotors are subject to numerous uncertainties that can impact their operation. For example, limitations in manufacturing processes can lead to discrepancies between component dimensions and standard design dimensions; the material properties of the rotor inherently exhibit randomness; during service, the support conditions provided by bearings may deviate from rated operating conditions; and changes in the fluid environment and operating conditions can introduce randomness into the excitation force. These uncertainties result in uncertainties in the steady-state response of the seawater pump rotor. Even if the fluctuation level of each individual uncertainty parameter is small, the combined effect of all uncertainties can significantly impact the steady-state response of the seawater pump rotor. Therefore, considering the impact of uncertainties on the nonlinear steady-state response during the design and optimization of seawater pump rotors is of paramount importance for assessing rotor reliability, ensuring safe and stable operation, reducing significant economic losses, and preventing catastrophic accidents.

[0003] In summary, there is an urgent need to develop a computationally efficient, widely applicable, and highly stable method for quantifying the uncertainty of the nonlinear steady-state response of seawater pump rotors. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a digital quantification method and apparatus for the uncertainty of the steady-state response of a seawater pump rotor, which solves the technical problems of low solution efficiency, poor results, and randomness in solution accuracy when analyzing the nonlinear steady-state response of a seawater pump rotor in the prior art.

[0005] In a first aspect, the present invention provides a digital quantification method for the uncertainty of the steady-state response of a seawater pump rotor, comprising:

[0006] Based on the improved Chebyshev polynomial zeros, all target physical parameters are sampled to form a sparse sample space; the target physical parameters are multiple physical parameters that affect the nonlinear steady-state response of the seawater pump rotor.

[0007] Based on the dynamic model of the seawater pump rotor and Newton's iteration method, the nonlinear steady-state response corresponding to each sample point in the sparse sample space is determined.

[0008] Based on the polynomial and the nonlinear steady-state response corresponding to each sample point in the sparse sample space, a surrogate model for the nonlinear steady-state response of the seawater pump rotor is determined.

[0009] Based on a proxy model of the nonlinear steady-state response of the seawater pump rotor, the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor is determined.

[0010] Optionally, the sampling of all target physical parameters based on the improved Chebyshev polynomial zeros to form a sparse sample space includes:

[0011] Based on the zeros of the improved Chebyshev polynomial, the sampling points corresponding to each of the target physical parameters are determined.

[0012] If the sum of the number of sampling points corresponding to all the target physical parameters satisfies the preset truncation interval, the sample space formed by the sampling points corresponding to all the physical parameters is determined as the sparse sample space.

[0013] Optionally, the determination of the nonlinear steady-state response corresponding to each sample point in the sparse sample space based on the dynamic model of the seawater pump rotor and Newton's iteration method includes:

[0014] Based on Fourier transform and the constructed dynamic model of the seawater pump rotor, the first harmonic coefficient corresponding to the displacement of the seawater pump rotor and the second harmonic coefficient corresponding to the excitation force of the seawater pump rotor are determined.

[0015] Based on the harmonic balance method, and the first harmonic coefficient and the second harmonic coefficient, the frequency domain residual corresponding to the dynamic model of the seawater pump rotor is constructed.

[0016] Based on Newton's iteration method, an iterative process is performed on the constructed dynamic model of the seawater pump rotor until the value of the frequency domain residual is less than the preset convergence value, thereby determining the nonlinear steady-state response of the seawater pump rotor.

[0017] Optionally, the step of performing an iterative process on the constructed dynamic model of the seawater pump rotor based on the Newton iteration method until the value of the frequency domain residual is less than a preset convergence value, and determining the nonlinear steady-state response of the seawater pump rotor, includes:

[0018] Based on the time-frequency conversion method, the derivative of the excitation force of the seawater pump rotor with respect to the displacement of the seawater pump rotor is determined and used as the first iteration parameter;

[0019] Based on the first harmonic coefficient corresponding to the displacement of the seawater pump rotor, the second harmonic coefficient corresponding to the excitation force of the seawater pump rotor, the frequency domain residual, and the first iteration parameter, the iterative model is determined.

[0020] Based on the Newton-Raphson iteration method and the iteration model, an iterative process is performed on the constructed dynamic model of the seawater pump rotor.

[0021] Optionally, determining the surrogate model for the nonlinear steady-state response of the seawater pump rotor based on the polynomial and the nonlinear steady-state response corresponding to each sample point in the sparse sample space includes:

[0022] A steady-state response proxy model is constructed using efficient polynomials;

[0023] Based on the steady-state response proxy model and the first harmonic coefficient corresponding to the displacement of the seawater pump rotor, a loss function is constructed;

[0024] Based on the stochastic gradient descent method, the coefficient vector of the steady-state response surrogate model is determined when the loss function is minimized.

[0025] Optionally, the surrogate model based on the nonlinear steady-state response of the seawater pump rotor determines the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor, including:

[0026] The range of values ​​for each of the target physical parameters is divided into multiple equal parts to construct a new sample space;

[0027] Based on the steady-state response proxy model, determine the output results of all samples in the new sample space;

[0028] Based on the output results of all the samples, the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor is determined.

[0029] Secondly, the present invention also provides a digital quantification device for the uncertainty of the steady-state response of a seawater pump rotor, comprising:

[0030] The sampling module is used to sample all target physical parameters based on the zeros of the improved Chebyshev polynomial to form a sparse sample space; the target physical parameters are multiple physical parameters that affect the nonlinear steady-state response of the seawater pump rotor.

[0031] The first determining module is used to determine the nonlinear steady-state response corresponding to each sample point in the sparse sample space based on the dynamic model of the seawater pump rotor and Newton's iteration method.

[0032] The second determining module is used to determine the surrogate model of the nonlinear steady-state response of the seawater pump rotor based on the polynomial and the nonlinear steady-state response corresponding to each sample point in the sparse sample space.

[0033] The third determining module is used to determine the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor based on the proxy model of the nonlinear steady-state response of the seawater pump rotor.

[0034] Thirdly, 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 uncertainty of the steady-state response of a seawater pump rotor as described in the first aspect above.

[0035] Fourthly, 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 the digital quantification method for the uncertainty of the steady-state response of a seawater pump rotor as described in the first aspect above.

[0036] Fifthly, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the digital quantification method for the uncertainty of the steady-state response of a seawater pump rotor as described in any of the above-described methods.

[0037] The present invention provides a digital quantification method and apparatus for the uncertainty of the steady-state response of a seawater pump rotor. By sparsely sampling multiple physical parameters that affect the nonlinear steady-state response of the rotor, a small number of representative samples are obtained. The corresponding nonlinear steady-state response is determined for these sample points using the Newton-Raphson iteration method, which greatly improves the solution efficiency and solution accuracy, and completes the quantitative evaluation of the boundary values ​​of the rotor's nonlinear steady-state response. Attached Figure Description

[0038] 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.

[0039] Figure 1 This is one of the flowcharts illustrating the digital quantification method for the steady-state response uncertainty of a seawater pump rotor provided in this embodiment of the invention.

[0040] Figure 2 This is a schematic diagram of the improved Chebyshev polynomial zeros provided in the embodiments of the present invention;

[0041] Figure 3 This is a comparative schematic diagram of dense sample space and sparse sample space provided in the embodiments of the present invention;

[0042] Figure 4 This is the second flowchart illustrating the digital quantification method for the steady-state response uncertainty of a seawater pump rotor provided in this embodiment of the invention.

[0043] Figure 5This is a schematic diagram of the structure of the digital quantification device for the steady-state response uncertainty of a seawater pump rotor provided in an embodiment of the present invention;

[0044] Figure 6 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0045] 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.

[0046] Figure 1 This is one of the flowcharts illustrating the digital quantification method for the steady-state response uncertainty of a seawater pump rotor provided in this embodiment of the invention, such as... Figure 1 As shown, the method includes:

[0047] Step 101: Based on the improved Chebyshev polynomial zeros, sample all target physical parameters to form a sparse sample space; the target physical parameters are multiple physical parameters that affect the nonlinear steady-state response of the seawater pump rotor.

[0048] Specifically, seawater pump rotors are common core components in marine systems. Due to variations in manufacturing processes, material properties, long-term service, fluid environment, operating conditions, and other unforeseen failures, their design and operating parameters inevitably change and become uncertain. To assess the impact of various physical parameters on rotor reliability during the design of marine seawater pump rotors, and to optimize these parameters, thus ensuring their safe and stable operation, the following analysis is conducted. These physical parameters may include many types, each with a corresponding reasonable range of values. Based on specific application requirements, a selection of physical parameters are analyzed, such as bearing support parameters, material property parameters, blade surface quality spalling parameters, and dynamic / static clearance parameters.

[0049] In related technologies, the probabilistic nature of each physical parameter's value is typically used to process or statistically analyze these parameters. 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 do not possess probabilistic characteristics (uncertain factors) are usually represented as interval parameters, i.e., the maximum and minimum values ​​of the parameters that need to be determined are sufficient. This improves the practicality of the analytical methods.

[0050] For uncertain but bounded interval parameters, a dense sample space of Chebyshev zeros can be established based on nested grid technology, and a sparse grid technology can be used to sample the dense sample space to form a sparse sample space, thereby reducing the number of sample points and significantly improving analysis efficiency. In other words, this invention uses improved Chebyshev polynomial zeros to sample the physical parameters to be analyzed, generating corresponding sample points.

[0051] Step 102: Based on the dynamic model of the seawater pump rotor and Newton's iteration method, determine the nonlinear steady-state response corresponding to each sample point in the sparse sample space;

[0052] The aforementioned sparse sample space, after sparse sampling of the Chebyshev polynomial zero-point tensor product space, yields sample points with high discreteness, sufficient sampling, and strong representativeness.

[0053] Then, a dynamic model of the seawater pump rotor is constructed, considering the nonlinear characteristics of the external excitation force. The motion model of the rotor and the dynamic model of the seawater pump can be expressed as:

[0054]

[0055] In the formula, M is the mass matrix; C is the damping matrix, which includes the damping matrix caused by the gyroscopic effect; u(t) is the displacement vector of the rotor. Let be the rotor's velocity vector, u(t) be the rotor's acceleration vector; K is the stiffness matrix, representing the stiffness in the time domain; f ext (t) represents the external nonlinear excitation force vector. The external excitation force vector includes, but is not limited to, the combined load of unbalanced forces, bearing loads, fluid excitation forces, etc.

[0056] For each sample point in the sparse sample space, Newton's iteration method and the aforementioned dynamic model of the seawater pump rotor are applied to determine the corresponding nonlinear steady-state response. The results are then organized to form a frequency response curve composed of the output results of all nonlinear steady-state responses.

[0057] Step 103: Based on the polynomial and the nonlinear steady-state response corresponding to each sample point in the sparse sample space, determine the surrogate model of the nonlinear steady-state response of the seawater pump rotor.

[0058] Specifically, in order to quantify the impact of various uncertainties on the nonlinear steady-state response of the seawater pump rotor, a proxy model for the nonlinear steady-state response of the seawater pump rotor is introduced in the form of a polynomial.

[0059] Step 104: Based on the proxy model of the nonlinear steady-state response of the seawater pump rotor, determine the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor.

[0060] Specifically, by utilizing the aforementioned physical parameters for the seawater pump rotor design and their corresponding value ranges, combined with the surrogate model for the nonlinear steady-state response of the seawater pump rotor, the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor can be determined. If the nonlinear steady-state response corresponding to a certain sample point is not within this boundary range, it is determined that the data corresponding to that sample point may contain parameters that affect the normal operation of the rotor, and the relevant physical parameters for the seawater pump rotor design need to be adjusted.

[0061] The present invention provides a digital quantification method for the uncertainty of the steady-state response of a seawater pump rotor. By sparsely sampling multiple parameters that affect the nonlinear steady-state response of the rotor, a small number of representative samples are obtained. The Newton-Raphson iteration method is then used to quickly determine the nonlinear steady-state response corresponding to these sample points, which greatly improves the solution efficiency and accuracy, and completes the quantitative evaluation of the boundary values ​​of the rotor's nonlinear steady-state response.

[0062] Optionally, the sampling of all target physical parameters based on the improved Chebyshev polynomial zeros to form a sparse sample space includes:

[0063] Based on the zeros of the improved Chebyshev polynomial, the sampling points corresponding to each of the target physical parameters are determined.

[0064] If the sum of the number of sampling points corresponding to all the target physical parameters satisfies the preset truncation interval, the sample space formed by the sampling points corresponding to all the physical parameters is determined as the sparse sample space.

[0065] Specifically, the sparse sample space is determined using the improved Chebyshev polynomial zeros, including:

[0066] The results of sampling each physical parameter using Chebyshev polynomial zeros can be expressed as:

[0067]

[0068] Among them, H i H represents any one of several physical parameters that affect the nonlinear steady-state response of the rotor. i The range of values ​​for [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 This is the vector of zeros of the Chebyshev polynomial. The corresponding α k The number of possible values ​​determines the physical parameter H. i The corresponding number of samples is that.

[0069] Determine the highest order k (k>1) of the Chebyshev polynomial zeros and the corresponding Chebyshev polynomial zero vector α. k It can be represented as:

[0070]

[0071] Where, θ j This is the angle value.

[0072] Then, starting from the first zero of the k-th order Chebyshev polynomial, and discarding the zeros with even numbers, we can obtain the (k-1)-th order Chebyshev polynomial zeros.

[0073] Finally, repeat the above two steps until k = 2; when k = 1, the corresponding zero of the Chebyshev polynomial is the average value of the parameters in that interval.

[0074] By following the steps described above, samples of zeros of all orders can be obtained. This process yields the improved Chebyshev polynomial zeros, which exhibit nesting.

[0075] Figure 2 This is a schematic diagram of the improved Chebyshev polynomial zeros provided in an embodiment of the present invention, as shown below. Figure 2 As shown, when k=4, the physical parameter H i There are 9 corresponding Chebyshev polynomial zeros; according to the improved Chebyshev polynomial zeros, the zeros with even numbers are discarded, and the physical parameter H is obtained when k=3. i The corresponding improved Chebyshev polynomial has 5 zeros; discarding the even-numbered zeros again, we obtain the physical parameter H when k=2. i The corresponding improved Chebyshev polynomial has 3 zeros. When k=1, the physical parameter H... i The corresponding improved Chebyshev polynomial has one zero, which is the physical parameter H. i The corresponding value when taking the average.

[0076] The total number of physical parameters affecting the rotor's nonlinear steady-state response is n. u The number of uncertain factors is n. u That is, the uncertainty dimension is n u According to the Chebyshev zeros in related techniques, the order of each dimension is equal. Therefore, n u Dense sample space Θ of k-dimensional uncertainty problem d This can be represented by the tensor product as:

[0077]

[0078] The number of samples in the dense sample space is Let n represent the Chebyshev zero vector of the nth uncertainty factor, where n represents 1 to n. u Any positive integer between 0 and 1.

[0079] The present invention uses an improved Chebyshev polynomial zero, and the number of sampling points for each physical parameter can be different. The dense sample obtained above is sampled again to obtain a sparse sample space.

[0080] This sparse sample space consists of tensor products of zeros in each dimension, denoted by i. j Let represent the order of the j-th dimension. Then the sum of the orders of all dimensions can be denoted as . Based on the convergence of the data, a preset cutoff interval is set, and the upper and lower limits of the sparse grid cutoff level are denoted as L1 and L2, respectively. Then the sparse sample space Θ... c This can be represented by the tensor product as:

[0081]

[0082] When the number of physical parameters (uncertainties) affecting the rotor's nonlinear steady-state response is 2, and the order k = 4, by setting the upper limit of the preset cutoff interval to 5 and the lower limit to 4, it is possible to complete the processing of dense sample spaces (such as...). Figure 3 Sampling (as shown in (a)) yields a sparse matrix sample space (such as...) Figure 3 (as shown in (b)). The sparse sample space is composed of... and The sparse grid has 29 sample points due to the overlap between the three tensor products. Compared to the 81 sample points of the dense grid, the application of sparse grid technology significantly reduces the number of sample points, thus greatly improving analysis efficiency.

[0083] For each sample point in the sparse sample space, the corresponding nonlinear steady-state response is determined, and the results are organized to form a frequency response curve composed of the output results of all nonlinear steady-state responses.

[0084] Optionally, the determination of the nonlinear steady-state response corresponding to each sample point in the sparse sample space based on the dynamic model of the seawater pump rotor and Newton's iteration method includes:

[0085] Based on Fourier transform and the constructed dynamic model of the seawater pump rotor, the first harmonic coefficient corresponding to the displacement of the seawater pump rotor and the second harmonic coefficient corresponding to the excitation force of the seawater pump rotor are determined.

[0086] Based on the harmonic balance method, and the first harmonic coefficient and the second harmonic coefficient, the frequency domain residual corresponding to the dynamic model of the seawater pump rotor is constructed.

[0087] Based on Newton's iteration method, an iterative process is performed on the constructed dynamic model of the seawater pump rotor until the value of the frequency domain residual is less than the preset convergence value, thereby determining the nonlinear steady-state response of the seawater pump rotor.

[0088] Specifically, the dynamic model of a seawater pump can be expressed as:

[0089]

[0090] The nonlinear displacement and periodic nonlinear excitation force of the seawater pump rotor are expressed using Fourier series through Fourier transform. The specific formula is as follows:

[0091]

[0092]

[0093] Among them, U j F is the j-th harmonic coefficient of the displacement vector u(t); ext,j The external excitation force vector f ext The j-th harmonic coefficient of (t); Ω represents the rotor speed. Because higher-order harmonic coefficients have a smaller impact on displacement and external excitation force, and to save computational resources, a truncated approach is usually adopted, using a finite number of harmonic coefficients to estimate the Fourier series of the rotor displacement vector and the Fourier series of the rotor's external excitation force. Where N... h This is the harmonic cutoff number. All harmonic coefficients corresponding to the rotor's displacement vector can be expressed as U = {U...} j},j={-N h ,-N h +1,…,N h -1,N h The harmonic coefficients corresponding to the rotor's excitation force vector can be expressed as F. ext ={F ext,j},j={-N h ,-N h +1,…,N h -1,N h}

[0094] Using the harmonic balance method, the frequency domain residual corresponding to the dynamic model of the seawater pump rotor can be expressed as:

[0095] R=Z(Ω)UF ext ;

[0096] In the formula, R represents the frequency domain residual corresponding to the rotor's dynamic model, and U is the displacement harmonic vector, which can be expressed as: F ext The excitation force harmonic vector can be expressed as: Z(Ω) is a dynamic matrix representing the linear stiffness in the frequency domain, and its expression is:

[0097]

[0098] A j =-j 2 Ω 2 M+ijΩC+K,j∈[-N h ,+N h ];

[0099] The time-domain dynamic equations are transformed into the frequency domain using the above transformation. Then, Newton's iteration method is employed to perform an iterative process on the constructed dynamic model of the seawater pump rotor. The iterative equations corresponding to this process can be expressed as:

[0100]

[0101] Among them, two adjacent steady-state solutions are (Ω) (k-1) U (k-1) ) and (Ω (k) U (k) ), where k is the number of the steady-state solution.

[0102] The iterative process continues until the frequency domain residual is less than a preset convergence value, at which point the steady-state solution of the dynamic model of the seawater pump rotor is obtained. This preset convergence value can be set according to requirements; to ensure high accuracy of the analysis results, it can be set to 1×10⁻⁶. -9 .

[0103] All the above steps are as follows Figure 4 As shown, Figure 4 This is the second flowchart illustrating the digital quantification method for the steady-state response uncertainty of a seawater pump rotor provided in this embodiment of the invention.

[0104] Optionally, the step of performing an iterative process on the constructed dynamic model of the seawater pump rotor based on the Newton iteration method until the value of the frequency domain residual is less than a preset convergence value, and determining the nonlinear steady-state response of the seawater pump rotor, includes:

[0105] Based on the time-frequency conversion method, the derivative of the excitation force of the seawater pump rotor with respect to the displacement of the seawater pump rotor is determined and used as the first iteration parameter;

[0106] Based on the first harmonic coefficient corresponding to the displacement of the seawater pump rotor, the second harmonic coefficient corresponding to the excitation force of the seawater pump rotor, the frequency domain residual, and the first iteration parameter, the iterative model is determined.

[0107] Based on the Newton-Raphson iteration method and the iteration model, an iterative process is performed on the constructed dynamic model of the seawater pump rotor.

[0108] Specifically, the derivative of the excitation force of the seawater pump rotor with respect to the displacement of the seawater pump rotor in the iterative equation. It can be obtained through time-frequency conversion and can be represented by the Jacobian matrix, specifically as follows:

[0109]

[0110] Without loss of generality, the derivative of the p-th harmonic of the external excitation force vector with respect to the q-th harmonic of the displacement vector can be expressed as:

[0111]

[0112] Where p and q can both take values ​​of [-N] h ,+N h Let T = 2π / Ω be any integer in the equation, where T = 2π / Ω represents the rotor period. Through a deeper derivation of the above equation, it can be found that the derivative of the p-th harmonic component of the nonlinear external excitation force vector with respect to the q-th harmonic component of the displacement vector is the coefficient in the Fourier decomposition of the derivative in the time domain, i.e., the coefficient of the pq-th harmonic term. Therefore, the derivative... All elements of the corresponding Jacobian matrix can be expressed as coefficients of the Fourier decomposition of the time-domain derivative, where k represents the number of the steady-state solution. All elements of the Jacobian matrix can be obtained by performing only one Fourier decomposition on the time-domain derivative; this is the core principle of Newton's method.

[0113] For example, if the Fourier series of the displacement of the seawater pump rotor obtained by Fourier transform, and the Fourier series of the excitation force of the seawater pump rotor, retain a harmonic order of 10, then according to the traditional finite difference method, 21 finite difference operations are required. However, according to the Newton iteration method provided by this invention, only one Fourier decomposition is needed. In this case, the solution speed of the derivative of the external excitation force with respect to the displacement can be increased by at least 20 times. Furthermore, Fourier decomposition is faster than the finite difference method; therefore, the improvement in solution speed of this invention far exceeds 20 times.

[0114] Furthermore, in the time domain, the derivative of the external excitation force with respect to the displacement, i.e. It can be obtained explicitly. Therefore, the method for solving the derivative of external excitation force with respect to displacement established based on this invention is analytical, and its accuracy is much higher than that obtained by the finite difference method.

[0115] Optionally, determining the surrogate model for the nonlinear steady-state response of the seawater pump rotor based on the polynomial and the nonlinear steady-state response corresponding to each sample point in the sparse sample space includes:

[0116] A steady-state response proxy model is constructed using efficient polynomials;

[0117] Based on the steady-state response proxy model and the first harmonic coefficient corresponding to the displacement of the seawater pump rotor, a loss function is constructed;

[0118] Based on the stochastic gradient descent method, the coefficient vector of the steady-state response surrogate model is determined when the loss function is minimized.

[0119] Specifically, after determining 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 surrogate model, which is specifically expressed as:

[0120]

[0121] Where, β T k is the transpose of the β vector, where β represents the coefficient vector composed of polynomial coefficients, and X represents the polynomial vector composed of polynomials corresponding to all target physical parameters. u This is the polynomial truncation order, which is generally taken as 4 or 5, or the value of the truncation order can be appropriately increased according to the number of uncertain factors; Here are the polynomial coefficients, and X represents the vector of sample points corresponding to all target physical parameters. Indicates the nth u The exponential term corresponding to each target physical parameter (uncertainty factor), Indicates the first The power of the power represents the coordinates of the sample points in the sparse sample space.

[0122] Based on the steady-state response surrogate model and the path-dependent coordinate system, a loss function is constructed, which can be expressed as follows:

[0123]

[0124] Where N is the total number of all sample points in the sparse sample space, U i Let represent the rotor displacement of the seawater pump rotor corresponding to the i-th sample point. By repeatedly executing the stochastic gradient descent method to minimize the loss function, the coefficient vector of the corresponding steady-state response surrogate model is determined.

[0125] Optionally, the surrogate model based on the nonlinear steady-state response of the seawater pump rotor determines the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor, including:

[0126] The range of values ​​for each of the target physical parameters is divided into multiple equal parts to construct a new sample space;

[0127] Based on the steady-state response proxy model, determine the output results of all samples in the new sample space;

[0128] Based on the output results of all the samples, the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor is determined.

[0129] Specifically, once the coefficient vector of the steady-state response surrogate model is determined, the steady-state response value of any sample point can be calculated using this steady-state response surrogate model.

[0130] The range of values ​​corresponding to all physical parameters (uncertain factors) affecting the rotor is divided into several equal parts to form a new sample space for the steady-state response surrogate model. The value of the physical parameter corresponding to each sample point is substituted into the steady-state response surrogate model to obtain the corresponding output results. When the maximum and minimum values ​​of the interval are determined, the boundary of the nonlinear steady-state response of the rotor is obtained, and the uncertainty quantification result of the semilinear steady-state response of the rotor is obtained.

[0131] The present invention provides a digital quantification method for the uncertainty of the steady-state response of a seawater pump rotor. By sparsely sampling multiple physical parameters that affect the nonlinear steady-state response of the seawater pump rotor, a small number of representative samples are obtained. The corresponding nonlinear steady-state response is determined for these sample points using the Newton-Raphson iteration method, which greatly improves the solution efficiency and solution accuracy, and completes the quantitative evaluation of the boundary values ​​of the rotor's nonlinear steady-state response.

[0132] The following describes the digital quantification device for the steady-state response uncertainty of a seawater pump rotor provided by the present invention. The digital quantification device for the steady-state response uncertainty of a seawater pump rotor described below and the digital quantification method for the steady-state response uncertainty of a seawater pump rotor described above can be referred to in correspondence.

[0133] Figure 5 This is a schematic diagram of the structure of the digital quantification device for the steady-state response uncertainty of a seawater pump rotor provided in an embodiment of the present invention, as shown below. Figure 5 As shown, the device includes:

[0134] The sampling module 501 is used to sample all target physical parameters based on the zeros of the improved Chebyshev polynomial to form a sparse sample space; the target physical parameters are multiple physical parameters that affect the nonlinear steady-state response of the seawater pump rotor.

[0135] The first determining module 502 is used to determine the nonlinear steady-state response corresponding to each sample point in the sparse sample space based on the dynamic model of the seawater pump rotor and Newton's iteration method.

[0136] The second determining module 503 is used to determine the surrogate model of the nonlinear steady-state response of the seawater pump rotor based on the polynomial and the nonlinear steady-state response corresponding to each sample point in the sparse sample space.

[0137] The third determining module 504 is used to determine the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor based on the proxy model of the nonlinear steady-state response of the seawater pump rotor.

[0138] Optionally, in the process of sampling all target physical parameters based on the zeros of the improved Chebyshev polynomial to form a sparse sample space, the sampling module 501 is specifically used for:

[0139] Based on the zeros of the improved Chebyshev polynomial, the sampling points corresponding to each of the target physical parameters are determined.

[0140] If the sum of the number of sampling points corresponding to all the target physical parameters satisfies the preset truncation interval, the sample space formed by the sampling points corresponding to all the physical parameters is determined as the sparse sample space.

[0141] Optionally, in the process of determining the nonlinear steady-state response corresponding to each sample point in the sparse sample space based on the dynamic model of the seawater pump rotor and Newton's iteration method, the first determining module 502 is specifically used for:

[0142] Based on Fourier transform and the constructed dynamic model of the seawater pump rotor, the first harmonic coefficient corresponding to the displacement of the seawater pump rotor and the second harmonic coefficient corresponding to the excitation force of the seawater pump rotor are determined.

[0143] Based on the harmonic balance method, and the first harmonic coefficient and the second harmonic coefficient, the frequency domain residual corresponding to the dynamic model of the seawater pump rotor is constructed.

[0144] Based on Newton's iteration method, an iterative process is performed on the constructed dynamic model of the seawater pump rotor until the value of the frequency domain residual is less than the preset convergence value, thereby determining the nonlinear steady-state response of the seawater pump rotor.

[0145] Optionally, the step of performing an iterative process on the constructed dynamic model of the seawater pump rotor based on the Newton iteration method until the value of the frequency domain residual is less than a preset convergence value, and determining the nonlinear steady-state response of the seawater pump rotor, includes:

[0146] Based on the time-frequency conversion method, the derivative of the excitation force of the seawater pump rotor with respect to the displacement of the seawater pump rotor is determined and used as the first iteration parameter;

[0147] Based on the first harmonic coefficient corresponding to the displacement of the seawater pump rotor, the second harmonic coefficient corresponding to the excitation force of the seawater pump rotor, the frequency domain residual, and the first iteration parameter, the iterative model is determined.

[0148] Based on the Newton-Raphson iteration method and the iteration model, an iterative process is performed on the constructed dynamic model of the seawater pump rotor.

[0149] Optionally, in the process of determining the surrogate model of the nonlinear steady-state response of the seawater pump rotor based on the polynomial and the nonlinear steady-state response corresponding to each sample point in the sparse sample space, the second determining module 503 is specifically used for:

[0150] A steady-state response proxy model is constructed using efficient polynomials;

[0151] Based on the steady-state response proxy model and the first harmonic coefficient corresponding to the displacement of the seawater pump rotor, a loss function is constructed;

[0152] Based on the stochastic gradient descent method, the coefficient vector of the steady-state response surrogate model is determined when the loss function is minimized.

[0153] Optionally, the third determining module 504, in the process of determining the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor based on the surrogate model of the nonlinear steady-state response of the seawater pump rotor, is specifically used for:

[0154] The range of values ​​for each of the target physical parameters is divided into multiple equal parts to construct a new sample space;

[0155] Based on the steady-state response proxy model, determine the output results of all samples in the new sample space;

[0156] Based on the output results of all the samples, the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor is determined.

[0157] It should be noted that the apparatus provided in this embodiment of the invention can implement all the method steps implemented in the above method embodiment and can achieve the same technical effect. Therefore, the parts and beneficial effects that are the same as those in the method embodiment will not be described in detail here.

[0158] Figure 6 This is a schematic diagram of the structure of the electronic device provided by the present invention, such as... Figure 6 As shown, the electronic device may include a processor 610, a communication interface 620, a memory 630, and a communication bus 640, wherein the processor 610, the communication interface 620, and the memory 630 communicate with each other via the communication bus 640. The processor 610 can call logical instructions in the memory 630 to execute any of the digital quantification methods for the steady-state response uncertainty of the seawater pump rotor provided in the above embodiments, for example:

[0159] Based on the improved Chebyshev polynomial zeros, all target physical parameters are sampled to form a sparse sample space; the target physical parameters are multiple physical parameters that affect the nonlinear steady-state response of the seawater pump rotor.

[0160] Based on the dynamic model of the seawater pump rotor and Newton's iteration method, the nonlinear steady-state response corresponding to each sample point in the sparse sample space is determined.

[0161] Based on the polynomial and the nonlinear steady-state response corresponding to each sample point in the sparse sample space, a surrogate model for the nonlinear steady-state response of the seawater pump rotor is determined.

[0162] Based on a proxy model of the nonlinear steady-state response of the seawater pump rotor, the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor is determined.

[0163] Furthermore, the logical instructions in the aforementioned memory 630 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.

[0164] Optionally, the sampling of all target physical parameters based on the improved Chebyshev polynomial zeros to form a sparse sample space includes:

[0165] Based on the zeros of the improved Chebyshev polynomial, the sampling points corresponding to each of the target physical parameters are determined.

[0166] If the sum of the number of sampling points corresponding to all the target physical parameters satisfies the preset truncation interval, the sample space formed by the sampling points corresponding to all the physical parameters is determined as the sparse sample space.

[0167] Optionally, the determination of the nonlinear steady-state response corresponding to each sample point in the sparse sample space based on the dynamic model of the seawater pump rotor and Newton's iteration method includes:

[0168] Based on Fourier transform and the constructed dynamic model of the seawater pump rotor, the first harmonic coefficient corresponding to the displacement of the seawater pump rotor and the second harmonic coefficient corresponding to the excitation force of the seawater pump rotor are determined.

[0169] Based on the harmonic balance method, and the first harmonic coefficient and the second harmonic coefficient, the frequency domain residual corresponding to the dynamic model of the seawater pump rotor is constructed.

[0170] Based on Newton's iteration method, an iterative process is performed on the constructed dynamic model of the seawater pump rotor until the value of the frequency domain residual is less than the preset convergence value, thereby determining the nonlinear steady-state response of the seawater pump rotor.

[0171] Optionally, the step of performing an iterative process on the constructed dynamic model of the seawater pump rotor based on the Newton iteration method until the value of the frequency domain residual is less than a preset convergence value, and determining the nonlinear steady-state response of the seawater pump rotor, includes:

[0172] Based on the time-frequency conversion method, the derivative of the excitation force of the seawater pump rotor with respect to the displacement of the seawater pump rotor is determined and used as the first iteration parameter;

[0173] Based on the first harmonic coefficient corresponding to the displacement of the seawater pump rotor, the second harmonic coefficient corresponding to the excitation force of the seawater pump rotor, the frequency domain residual, and the first iteration parameter, the iterative model is determined.

[0174] Based on the Newton-Raphson iteration method and the iteration model, an iterative process is performed on the constructed dynamic model of the seawater pump rotor.

[0175] Optionally, determining the surrogate model for the nonlinear steady-state response of the seawater pump rotor based on the polynomial and the nonlinear steady-state response corresponding to each sample point in the sparse sample space includes:

[0176] A steady-state response proxy model is constructed using efficient polynomials;

[0177] Based on the steady-state response proxy model and the first harmonic coefficient corresponding to the displacement of the seawater pump rotor, a loss function is constructed;

[0178] Based on the stochastic gradient descent method, the coefficient vector of the steady-state response surrogate model is determined when the loss function is minimized.

[0179] Optionally, the surrogate model based on the nonlinear steady-state response of the seawater pump rotor determines the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor, including:

[0180] The range of values ​​for each of the target physical parameters is divided into multiple equal parts to construct a new sample space;

[0181] Based on the steady-state response proxy model, determine the output results of all samples in the new sample space;

[0182] Based on the output results of all the samples, the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor is determined.

[0183] It should be noted that the electronic device provided in this embodiment of the invention can implement all the method steps implemented in the above method embodiment and can achieve the same technical effect. Here, the parts and beneficial effects that are the same as or corresponding to the method embodiment in this embodiment will not be described in detail.

[0184] 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 is able to execute the digital quantification method for the steady-state response uncertainty of the seawater pump rotor provided in the above embodiments.

[0185] In another aspect, 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 the digital quantification method for the uncertainty of the steady-state response of the seawater pump rotor provided in the above embodiments.

[0186] 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.

[0187] 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.

[0188] 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 uncertainty of the steady-state response of a seawater pump rotor, characterized in that, include: Based on the improved Chebyshev polynomial zeros, all target physical parameters are sampled to form a sparse sample space. The target physical parameters are multiple physical parameters that affect the nonlinear steady-state response of the seawater pump rotor; Based on the dynamic model of the seawater pump rotor and Newton's iteration method, the nonlinear steady-state response corresponding to each sample point in the sparse sample space is determined. Based on the dynamic model of the seawater pump rotor and Newton's iteration method, the nonlinear steady-state response corresponding to each sample point in the sparse sample space is determined, including: Based on Fourier transform and the constructed dynamic model of the seawater pump rotor, the first harmonic coefficient corresponding to the displacement of the seawater pump rotor and the second harmonic coefficient corresponding to the excitation force of the seawater pump rotor are determined. Based on the harmonic balance method, and the first harmonic coefficient and the second harmonic coefficient, the frequency domain residual corresponding to the dynamic model of the seawater pump rotor is constructed. Based on the time-frequency conversion method, the derivative of the excitation force of the seawater pump rotor with respect to the displacement of the seawater pump rotor is determined and used as the first iteration parameter; Based on the first harmonic coefficient corresponding to the displacement of the seawater pump rotor, the second harmonic coefficient corresponding to the excitation force of the seawater pump rotor, the frequency domain residual, and the first iteration parameter, the iterative model is determined. Based on the Newton iteration method and the iteration model, an iterative process is performed on the constructed dynamic model of the seawater pump rotor until the value of the frequency domain residual is less than the preset convergence value, thereby determining the nonlinear steady-state response of the seawater pump rotor. This requires only one Fourier decomposition of the derivative in the time domain; Based on the polynomial and the nonlinear steady-state response corresponding to each sample point in the sparse sample space, a surrogate model for the nonlinear steady-state response of the seawater pump rotor is determined. Based on a proxy model of the nonlinear steady-state response of the seawater pump rotor, the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor is determined.

2. The digital quantification method for the uncertainty of the steady-state response of a seawater pump rotor according to claim 1, characterized in that, The method of sampling all target physical parameters based on the improved Chebyshev polynomial zeros to form a sparse sample space includes: Based on the zeros of the improved Chebyshev polynomial, the sampling points corresponding to each of the target physical parameters are determined. If the sum of the number of sampling points corresponding to all the target physical parameters satisfies the preset truncation interval, the sample space formed by the sampling points corresponding to all the physical parameters is determined as the sparse sample space.

3. The digital quantification method for the uncertainty of the steady-state response of a seawater pump rotor according to claim 1, characterized in that, The surrogate model for determining the nonlinear steady-state response of the seawater pump rotor, based on the polynomial and the nonlinear steady-state response corresponding to each sample point in the sparse sample space, includes: A steady-state response proxy model is constructed using efficient polynomials; Based on the steady-state response proxy model and the first harmonic coefficient corresponding to the displacement of the seawater pump rotor, a loss function is constructed; Based on the stochastic gradient descent method, the coefficient vector of the steady-state response surrogate model is determined when the loss function is minimized.

4. The digital quantification method for the uncertainty of the steady-state response of a seawater pump rotor according to claim 1, characterized in that, The surrogate model based on the nonlinear steady-state response of the seawater pump rotor determines the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor, including: The range of values ​​for each of the target physical parameters is divided into multiple equal parts to construct a new sample space; Based on the steady-state response proxy model, determine the output results of all samples in the new sample space; Based on the output results of all the samples, the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor is determined.

5. A digital quantification device for the uncertainty of the steady-state response of a seawater pump rotor, characterized in that, include: The sampling module is used to sample all target physical parameters based on the zeros of the improved Chebyshev polynomial to form a sparse sample space. The target physical parameters are multiple physical parameters that affect the nonlinear steady-state response of the seawater pump rotor; The first determining module is used to determine the nonlinear steady-state response corresponding to each sample point in the sparse sample space based on the dynamic model of the seawater pump rotor and Newton's iteration method. Based on the dynamic model of the seawater pump rotor and Newton's iteration method, the nonlinear steady-state response corresponding to each sample point in the sparse sample space is determined, including: Based on Fourier transform and the constructed dynamic model of the seawater pump rotor, the first harmonic coefficient corresponding to the displacement of the seawater pump rotor and the second harmonic coefficient corresponding to the excitation force of the seawater pump rotor are determined. Based on the harmonic balance method, and the first harmonic coefficient and the second harmonic coefficient, the frequency domain residual corresponding to the dynamic model of the seawater pump rotor is constructed. Based on the time-frequency conversion method, the derivative of the excitation force of the seawater pump rotor with respect to the displacement of the seawater pump rotor is determined and used as the first iteration parameter; Based on the first harmonic coefficient corresponding to the displacement of the seawater pump rotor, the second harmonic coefficient corresponding to the excitation force of the seawater pump rotor, the frequency domain residual, and the first iteration parameter, the iterative model is determined. Based on the Newton iteration method and the iteration model, an iterative process is performed on the constructed dynamic model of the seawater pump rotor until the value of the frequency domain residual is less than the preset convergence value, thereby determining the nonlinear steady-state response of the seawater pump rotor. This requires only one Fourier decomposition of the derivative in the time domain; The second determining module is used to determine the surrogate model of the nonlinear steady-state response of the seawater pump rotor based on the polynomial and the nonlinear steady-state response corresponding to each sample point in the sparse sample space. The third determining module is used to determine the boundary corresponding to the nonlinear steady-state response of the seawater pump rotor based on the proxy model of the nonlinear steady-state response of the seawater pump rotor.

6. 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 program, it implements the digital quantification method for the uncertainty of the steady-state response of the seawater pump rotor as described in any one of claims 1 to 4.

7. 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 uncertainty of the steady-state response of the seawater pump rotor as described in any one of claims 1 to 4.

8. 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 uncertainty of the steady-state response of the seawater pump rotor as described in any one of claims 1 to 4.

Images