Model reduction based equivalent simulation acceleration method for full-scale launch vehicle modal testing

Abstract

The application provides a launch vehicle full rocket modal test equivalent simulation acceleration method based on model order reduction, and relates to the technical field of model order reduction, which comprises the following steps: calculating attitude control modal gain according to the bending modal parameters of the working second state full rocket finite element model, and determining the sweep frequency interval according to the adjacent modal gain sign inversion relationship; under the swing engine swing core excitation, determining the zero point interval according to the in-phase displacement response of the interstage separation docking surface, the inertial measurement unit installation section and the swing engine swing core, and forming a zero point compensation base from the response vectors on both sides of the zero point interval. The zero point compensation base is used for augmenting the common order reduction base, and the augmented order reduction base and the common order reduction base are used for solving respectively in the zero point interval and other frequencies in the sweep frequency interval. When the reconstructed response maintains the sign inversion relationship of the interstage separation docking surface response and the attitude control modal gain, the full rocket equivalent simulation result is output, so that the number of full order solving in dense sweep frequency is reduced and the key local response is maintained.

Description

Technical Field

[0001] This application relates to the field of model reduction technology, specifically to an accelerated method for equivalent simulation of full-rocket modal tests of launch vehicles based on model reduction. Background Technology

[0002] During flight, a launch vehicle undergoes propellant consumption, engine operating state changes, and interstage state changes. Different flight moments correspond to different mass distributions and structural dynamic characteristics. Full-rocket modal testing can obtain parameters such as modal frequencies, mode shapes, and damping, and can be used to verify the full-rocket finite element model. Due to limitations in test cycle, test configuration, and boundary simulation conditions, full-rocket modal testing typically cannot cover all operational seconds. Therefore, it is necessary to use the verified finite element modeling method to perform equivalent simulations of other operational seconds.

[0003] The full-length finite element model of the rocket has a large number of degrees of freedom. When performing frequency response analysis, the dynamic equations formed by the mass matrix, damping matrix, and stiffness matrix need to be solved for each sampling frequency. As the output frequency or the number of operating seconds increases, the computational complexity of full-order frequency sweep also increases. Existing techniques can reduce the model dimensionality using modal truncation, substructure modal synthesis, or the Krylov subspace method, and then use the reduced-order model to calculate the frequency response.

[0004] Existing model reduction methods typically focus on reducing the solution scale of the dynamic equations. When the launch vehicle structure is complex and the number of analyzed frequencies is large, the limited modal information retained during the reduction process may not be sufficient to accurately reflect the full frequency response characteristics, thus affecting the equivalent comparison between the reduced results and the full-rocket modal test results. Summary of the Invention

[0005] This application provides an accelerated method for equivalent simulation of full-rocket modal tests of launch vehicles based on model order reduction, which solves the problem that the existing model order reduction process does not retain the local response characteristics between adjacent bending modes, making it difficult to balance computational efficiency and the accuracy of frequency response of interstage separation docking surfaces in the equivalent simulation of the full-rocket launch vehicle.

[0006] To solve the above-mentioned technical problems, this application adopts the following technical solution: Obtain the full-length finite element model of the rocket in its working state; The attitude control mode gain is calculated based on the bending mode parameters of the whole rocket finite element model, and the sweep frequency interval is determined by the adjacent bending mode frequencies with opposite signs of the attitude control mode gain. Using the oscillating engine center as the excitation point, the full-order response at discrete sampling frequencies within the sweep frequency range is solved. The full-order response includes the response vector and the in-phase displacement response of the inter-stage separation docking surface, the inertial navigation system mounting section, and the oscillating engine center. When the in-phase displacement response of the docking surface reverses sign between adjacent discrete sampling frequencies, the in-phase displacement response of the inertial navigation system mounting section does not reverse sign, and the in-phase displacement response of the oscillating engine center does not reverse sign and the amplitude is not zero, the interval between adjacent discrete sampling frequencies is determined to be the zero point interval. The response vectors on both sides of the zero interval are normalized and the difference is obtained to obtain the zero compensation basis; A common reduced-order basis is formed by bending modal parameters, and the zero-point compensation basis is added to the common reduced-order basis to obtain an augmented reduced-order basis; The reconstruction response and reduced-order attitude control mode gain are obtained by solving for other frequencies in the zero-point interval and the frequency sweep interval using the augmented reduced-order basis and the common reduced-order basis, respectively. When the reconstructed response reproduces the in-phase displacement response of the docking surface with the reverse sign, and the reduced-order attitude control mode gain reproduces the attitude control mode gain with the reverse sign, the equivalent simulation results of the entire rocket are obtained.

[0007] Optionally, the boundary verification of the zero-point interval includes: The interval between adjacent discrete sampling frequencies with opposite signs of the in-phase displacement response of the docking surface is marked as the candidate interval; Candidate intervals with opposite signs at both ends of the candidate interval are eliminated from the inertial navigation system mounting section or the oscillating engine oscillating center in phase displacement response. Within the reserved candidate interval, the verification sampling frequency is set and the full-arrow finite element model is solved to obtain the verification full-order response; The candidate interval boundary is iteratively updated based on the comparison between the amplitude of the in-phase displacement response of the docking surface in the full-order verification response and the amplitudes at both ends of the candidate interval, until the amplitude of the in-phase displacement response of the docking surface in the full-order verification response is simultaneously lower than the amplitudes at both ends of the current candidate interval. The current candidate interval is determined as the zero interval, and the response vectors on both sides of the zero interval are recorded.

[0008] Optionally, the formation of the zero-point compensation base includes: Extract the in-phase displacement response of the oscillating engine center from the two response vectors. The amplitudes of the in-phase displacement responses of the two oscillating engine centers are not zero. The amplitudes of the two in-phase displacement responses are used as the normalization references for the corresponding response vectors. The two response vectors are normalized according to the corresponding normalization benchmark to obtain two normalized response vectors; The zero-point compensation basis is obtained by subtracting the two normalized response vectors.

[0009] Optionally, the construction of the augmented order-reducing basis includes: Calculate the projection residual of the zero-point compensation basis relative to the common reduced-order basis; According to the orthogonality criterion used by the finite element solver under the inner product of the mass matrix, if the projected residual contains components independent of the common reduced basis, then the projected residual is normalized and added to the common reduced basis to obtain a candidate reduced basis; if the projected residual does not contain independent components, then the common reduced basis is used as a candidate reduced basis. The candidate reduced-order basis is used to solve and reconstruct the response in the zero-point interval to obtain the candidate reduced-order response; When the candidate reduced order response fails to pass the in-phase shift response sign verification at the two boundary sampling frequencies, the boundary projection residual of the corresponding response vector relative to the candidate reduced order basis is calculated, and the independent components determined according to the orthogonality criterion are normalized and added to the candidate reduced order basis, and the zero interval is solved again. Candidate reduced-order bases verified by in-phase shift response symbols are used as augmented reduced-order bases.

[0010] Optionally, the formation of the full-rocket equivalent simulation results includes: An augmented reduced-order basis is used to solve for the zero-point interval, and the reduced-order response within the interval is obtained. The frequency located outside the zero interval within the swept frequency range is solved by using a common reduced-order basis to obtain the reduced-order response outside the interval; The intra-interval reduced-order response and the extra-interval reduced-order response are reconstructed to full-order coordinates using augmented reduced-order basis and common reduced-order basis, respectively, to obtain the intra-interval reconstructed response and the extra-interval reconstructed response. By connecting the reconstructed responses within the interval and the reconstructed responses outside the interval in order of sampling frequency, the reconstructed response is obtained. Calculate the reduced-order attitude control mode gain based on the bending mode parameters of the reduced-order model formed by the augmented reduced-order basis; By comparing the reconstructed response vectors at the two boundary sampling frequencies with the corresponding response vectors, the boundary consistency results are obtained. When the boundary consistency results show that the signs of the in-phase displacement responses of the docking surface, the inertial navigation system mounting section, and the oscillating engine center are consistent in the two sets of response vectors, the reconstructed response maintains the opposite sign of the in-phase displacement response of the docking surface and the local minimum of the response amplitude, and the reduced attitude control mode gain has the same opposite sign relationship with the attitude control mode gain, the reconstructed response is taken as the equivalent simulation result of the whole rocket.

[0011] Optionally, the solution for the full-order response includes: Apply a lateral equivalent excitation to the center of the oscillating engine along the pitch or yaw direction of the entire rocket; The displacement responses of the docking surface, inertial navigation system mounting section, and oscillating engine center are extracted along the same direction as the lateral equivalent excitation.

[0012] Optionally, obtaining the in-phase shift response includes: Using the phase of the lateral equivalent excitation as the phase reference, the displacement responses of the docking surface, the inertial navigation system mounting section, and the oscillating engine center are projected along the phase reference to obtain the in-phase displacement responses of the docking surface, the inertial navigation system mounting section, and the oscillating engine center.

[0013] Optionally, the formation of a shared reduced-order substrate includes: From the bending modal parameters, select bending modal vectors whose modal frequencies are outside the zero interval, perform quality normalization on the bending modal vectors, and form a common reduced-order basis with the quality normalized bending modal vectors.

[0014] Optionally, the composition of the shared reduced-order basis includes: The mass-normalized bending mode vectors corresponding to two adjacent bending modes in the frequency sweep interval are used as the basis vectors of the common reduced-order basis.

[0015] Optionally, the output process of the full-rocket equivalent simulation results includes: An augmented reduced-order basis is used to solve for the zero-point interval, yielding the reduced-order response within the interval. A shared reduced-order basis is used to solve for the frequencies within the swept frequency interval but outside the zero-point interval, yielding the reduced-order response outside the interval. The reduced-order responses within the interval and outside the interval are reconstructed to full-order coordinates using the augmented and shared reduced-order basis, respectively, yielding the reconstructed responses within and outside the interval. The reconstructed responses within and outside the interval are connected in the order of sampling frequencies to form the reconstructed response, and the full-arrow equivalent simulation result is output.

[0016] The technical solution provided in this application has the following beneficial effects: This application first determines the search frequency band for the full-order response based on the inverse sign relationship of the attitude control mode gain, and then identifies local zeros by combining the response sign relationships of the interstage separation docking surface, the inertial navigation system mounting section, and the oscillating engine center. The response vectors on both sides of the zero-point interval are normalized and differentially divided to form a zero-point compensation basis, which is used to augment the common reduced-order basis. The zero-point interval is solved using the augmented reduced-order basis, while frequencies within the sweep interval but outside the zero-point interval are solved using the common reduced-order basis, thereby reducing the repeated solution of the full-order dynamic equations while maintaining the inverse sign relationship of the in-phase displacement response of the interstage separation docking surface and the inverse sign relationship of the attitude control mode gain. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application 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 application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1A flowchart illustrating the accelerated method for equivalent simulation of full-rocket modal testing of a launch vehicle based on model order reduction, provided in this application embodiment; Figure 2 A schematic diagram showing the positional relationship between the interstage separation docking surface, the inertial navigation system mounting section, and the oscillating engine center, provided for embodiments of this application. Figure 3 This is a schematic diagram of zero-point interval identification and boundary verification provided in an embodiment of this application; Figure 4 This is a schematic diagram illustrating the construction of the zero-point compensation basis and the augmented order reduction basis provided in the embodiments of this application; Figure 5 This is a schematic diagram illustrating the reconstruction, connection, and verification of responses inside and outside the interval provided in an embodiment of this application. Detailed Implementation

[0019] To enable those skilled in the art to better understand the present application, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are merely some embodiments of the present application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] like Figure 1 As shown, this embodiment provides an accelerated method for equivalent simulation of full-rocket modal tests of launch vehicles based on model order reduction, including the following steps: S101, Obtain the full-length finite element model of the rocket in its working state; S102, calculate the attitude control mode gain based on the bending mode parameters of the whole rocket finite element model, and determine the sweep frequency interval by the adjacent bending mode frequencies with opposite signs of the attitude control mode gain; S103, with the swing engine center as the excitation point, solve the full-order response at the discrete sampling frequency within the sweep frequency range, and obtain the response vector as well as the in-phase displacement response of the interstage separation docking surface, the inertial navigation system installation section and the swing engine center; S104. When the in-phase displacement response of the interstage separation docking surface is reversed between adjacent discrete sampling frequencies, the in-phase displacement response of the inertial navigation system installation section is not reversed, and the in-phase displacement response of the oscillating engine center is not reversed and the amplitude is not zero, the interval between adjacent discrete sampling frequencies is determined to be the zero point interval. S105, normalize the response vectors on both sides of the zero interval to obtain the difference, and obtain the zero compensation basis; S106, a common reduced-order basis is formed by bending modal parameters, and the zero-point compensation basis is added to the common reduced-order basis to obtain an augmented reduced-order basis; S107, using augmented reduced-order basis and common reduced-order basis respectively, solve for other frequencies in the zero-point interval and frequency sweep interval to obtain the reconstruction response and reduced-order attitude control mode gain; S108, when the in-phase displacement response of the reconstructed response reproduction level is reversed and the attitude control mode gain of the reduced-order attitude control mode gain is reversed, the equivalent simulation results of the whole rocket are obtained.

[0021] Execute S101 to obtain the full-rocket finite element model in the operational second state. The operational second state represents the rocket body configuration and mass state corresponding to the selected flight time. Based on the flight time sequence, obtain the stage combination, remaining propellant mass, engine operating state, interstage connection state, and mass distribution for that moment in the simulation, and write this data into the finite element modeling structure verified by full-rocket modal testing. The full-rocket finite element model includes a mass matrix, a damping matrix, and a stiffness matrix. The main load-bearing structure of the rocket body can use beam elements, shell elements, or a combination of beam and shell elements; the equipment mass and propellant mass are updated according to the operational second state. The above element types and matrix assembly belong to existing techniques in finite element structural dynamics.

[0022] After completing the working second-state update, the bending modal parameters used to calculate the attitude control modal gain are obtained via S102. Modal analysis is performed on the full-rocket finite element model to obtain the bending modal vectors and generalized mass arranged according to the modal frequencies. For example, the existing Block Lanczos modal extraction method can be used to obtain the bending modal parameters. The bending modal parameters include modal frequencies, bending modal vectors, and generalized mass; the subsequent shared reduced-order basis is also formed from the bending modal vectors in the bending modal parameters.

[0023] Attitude control modal gain is used to represent the directional relationship of a single-order bending mode between the oscillating engine center and the inertial navigation system (INS) mounting section. For the i-th order bending mode, the lateral displacement of the oscillating engine center along the pitch or yaw direction is extracted from the bending mode vector, and the mode shape slope is obtained from the section rotation angle of the INS mounting section. The attitude control modal gain is calculated according to the following formula: In the formula, Let i be the attitude control mode gain of the i-th bending mode. For the lateral displacement of the swing engine's pivot point, The slope of the mode shape at the inertial navigation system mounting section. This refers to the generalized mass. The generalized mass is calculated from the mass matrix and the bending mode vector, and satisfies the following conditions when the mass matrix is ​​in positive definiteness: If the sign is greater than 0, the sign of the attitude control modal gain depends on the directional combination of the lateral displacement of the oscillating engine center and the slope of the mode shape at the inertial navigation system mounting section. When the bending mode vector is reversed globally, the two quantities involved in the multiplication are reversed synchronously, and the attitude control modal gain retains its original sign.

[0024] Subsequently, the attitude control mode gains of adjacent bending modes are compared pairwise along the direction of increasing modal frequency. When the signs of two adjacent attitude control mode gains are opposite, the modal frequencies of the corresponding two bending modes are used directly as boundaries, and the area between the two boundaries is defined as a frequency sweep interval. The frequency sweep interval is generated by the modal frequency of the current operating second state, and the interval width varies with the distance between the two modal frequencies. This interval represents the frequency band where the attitude control direction of adjacent bending modes changes, and serves as the frequency range for the next step of solving the full-order response.

[0025] After determining the frequency sweep interval, S103 uses the oscillating engine's center of rotation as the excitation point to solve for the full-order response at the discrete sampling frequencies. For example... Figure 2 As shown, the interstage separation docking surface is determined along the entire rocket axis, and the inertial measurement unit (INS) mounting section and the yaw engine center are determined on both sides of the INS mounting surface. The INS mounting section corresponds to the section where the inertial measurement unit is located, and the yaw engine center corresponds to the rotation center of the engine's pitch or yaw yaw. The INS separation docking surface is located between two positions, so that the three positions can reflect the spatial response relationship between the INS mounting section, the INS separation docking surface, and the yaw engine center.

[0026] When performing pitch direction analysis, a lateral equivalent excitation is applied to the center of the oscillating engine along the overall pitch direction of the rocket, and three displacement responses are extracted along the same direction. When performing yaw direction analysis, all quantities are uniformly expressed in the yaw direction. For example, the lateral equivalent excitation can be a unit harmonic load. Under linear frequency response conditions, uniform scaling of the load amplitude will cause the response to scale proportionally, and the sign relationship of the responses at the three locations will remain consistent.

[0027] Discrete sampling frequencies are obtained between the two boundaries of the frequency sweep interval. Initial sampling can be done by taking points at equal intervals, and subsequent sampling positions are adjusted based on the response comparison results of S104. For example, nine full-order sampling frequencies are set in the frequency sweep interval to find adjacent sampling frequencies where local response changes occur; the final 201 frequency points to be output are solved by the reduced-order model. The nine initial sampling frequencies correspond to eight equal divisions of the frequency sweep interval, and the 201 output frequencies correspond to one two-hundredth of the frequency sweep interval's frequency resolution. The specific number is set according to the frequency resolution required for the equivalent simulation. Increasing the initial sampling frequency helps shorten the initially identified candidate interval, while decreasing the initial sampling frequency reduces the number of full-order solutions.

[0028] The full-order response is obtained by solving the full-rocket finite element model at discrete sampling frequencies, including in-phase displacement response and response vector. Using the phase of the lateral equivalent excitation as a reference, the reset displacement response of each degree of freedom is projected onto the excitation phase direction and arranged according to the degree of freedom order of the full-rocket finite element model, forming a real-valued response vector. Then, components along the excitation direction for the interstage separation docking surface, the inertial navigation system mounting section, and the oscillating engine center are extracted from the response vector to obtain three in-phase displacement responses. Since the in-phase displacement responses consist of real components under a common phase reference, their signs and amplitudes can be directly compared.

[0029] like Figure 3 As shown, after obtaining the full-order response at discrete sampling frequencies, S104 first identifies candidate intervals and then verifies the boundaries of the candidate intervals. The in-phase displacement responses of the inter-stage separation docking surfaces are compared in frequency order. When the signs of the responses at adjacent discrete sampling frequencies are opposite, the interval between the two sampling frequencies is marked as a candidate interval. Next, the in-phase displacement responses of the inertial navigation system (INS) mounting section and the oscillating engine center at the two boundaries of the same candidate interval are compared. If the signs of the INS mounting section or the oscillating engine center are reversed at the two boundaries, the corresponding candidate interval is deleted; if both positions retain their original signs, the oscillating engine center responses at the two boundaries are further checked to see if they can be used as a normalization reference. First, the larger value of the two oscillating engine center response amplitudes is checked according to the non-zero criterion under the current floating-point precision of the finite element solver; after the larger value passes the non-zero criterion, the ratio of the smaller value to the larger value is calculated, and the ratio is compared with the relative zero tolerance currently used by the finite element solver. When the ratio is higher than the relative zero tolerance, it is confirmed that the responses of both oscillating engine centers are not numerically zero and the candidate interval is retained. When the larger value fails to pass the non-zero criterion or the ratio is not higher than the relative zero tolerance, the verification sampling frequency is increased within the candidate interval. The corresponding boundary is replaced with the sampling frequency corresponding to the verification response of the same sign that passes the above zero criterion, and the candidate interval is re-verified. The non-zero criterion and relative zero tolerance use the values ​​in the current floating-point precision setting of the finite element solver, so that the judgment does not change with the response magnitude or unit system. This can distinguish the local response changes of the inter-stage separation docking surface from the case of simultaneous commutation at the three positions, and avoid using zero or numerical zero as the normalization divisor.

[0030] After retaining the candidate intervals, a verification sampling frequency is set between the two boundaries, and the verification full-order response is solved. For example, the midpoint frequency between the two boundaries is used as the verification sampling frequency. When the amplitude of the in-phase displacement response at the inter-stage separation docking surface at the verification sampling frequency is simultaneously lower than the amplitudes of the in-phase displacement responses at both boundaries, the current candidate interval contains a local minimum, and the sampling frequencies of the two boundaries and their corresponding response vectors are recorded. When the amplitude of the in-phase displacement response at the verification sampling frequency is not simultaneously lower than the amplitudes of the in-phase displacement responses at both boundaries, the candidate interval boundaries with the same sign are replaced with the verification sampling frequency according to the sign of the in-phase displacement response of the inter-stage separation docking surface in the verification full-order response, and a new verification sampling frequency is set within the updated candidate interval. The relative magnitudes of the current verification full-order response and the responses at the two boundaries constitute the boundary conditions for local minima, and the boundary update process is driven by response feedback. After verification, the interval between the two boundaries is taken as the zero-point interval.

[0031] The zero-point interval reflects the cancellation of contributions from adjacent bending modes at the interstage separation interface with frequency. The in-phase displacement response at the interstage separation interface reverses sign on both sides of the zero-point interval and forms a local minimum within the interval. The inertial navigation system mounting section and the oscillating engine oscillator center retain their original signs, indicating that the sign reversal occurs at the interstage separation interface. This response relationship will be used to form the zero-point compensation basis.

[0032] like Figure 4 As shown, after the zero-point interval is determined, S105 extracts the in-phase displacement response of the oscillating engine center from the two boundary response vectors. S104, in addition to confirming that the two oscillating engine center responses do not have reversed signs, also confirms, according to the zero-value criterion currently used by the finite element solver, that neither response is numerically zero. Therefore, the two responses can be used as the normalization reference for the corresponding response vectors. Normalization is used to eliminate the overall scale difference between the two boundary response vectors caused by the different excitation transmission amplitudes. The zero-point compensation basis is formed according to the following formula: In the formula, As a zero-point compensation base, and The response vectors corresponding to the two boundaries of the zero interval. and This represents the in-phase displacement response of the oscillating engine center in the corresponding response vector. After normalizing the amplitude of the oscillating engine center response, the common components of the two response vectors at the excitation position are unified; after subtraction, the difference components formed by the zero crossing of the interstage separation docking surface are retained, thereby obtaining the response direction that needs to be supplemented for the shared reduced-order basis.

[0033] Based on the zero-point compensation basis, S106 constructs an augmented reduced-order basis. First, bending mode vectors with modal frequencies outside the zero-point interval are selected from the bending modal parameters, with at least two adjacent bending mode vectors within a defined sweep interval chosen. The selected bending mode vectors are then mass-normalized and arranged into a common reduced-order basis according to their modal frequencies. The mass normalization employs existing methods from finite element modal analysis, ensuring that each basis vector has a uniform scale under the inner product of the mass matrix.

[0034] Next, the projected residuals of the zero-compensation basis relative to the common reduced-order basis and the mass norm of the projected residuals are calculated. Then, based on the orthogonality criterion used by the finite element solver under the inner product of the mass matrix, it is determined whether the projected residuals contain independent components. The calculation relationships are as follows: ; In the formula, For the projection residual, To achieve a shared reduced-order basis for quality orthogonal normalization, M is the quality matrix. This is an orthogonal compensation vector. The projected residual retains components in the zero-point compensation basis that cannot be represented by a shared reduced-order basis. When the finite element solver uses absolute orthogonality tolerance, the orthogonality criterion is to compare the mass norm of the projected residual under the inner product of the mass matrix with the absolute orthogonality tolerance of the same caliber. When the finite element solver uses relative orthogonality tolerance, the mass norm of the corresponding vector before projection is used as a reference, and the ratio of the mass norm of the projected residual to the reference norm is compared with the relative orthogonality tolerance. Both methods ensure that the comparison quantity and the orthogonality tolerance have the same dimensions or are both dimensionless, thus unaffected by changes in vector scale and unit system. The comparison results show that if the projected residual contains independent components, the projected residual is mass normalized; if it does not contain independent components, the current reduced-order basis is retained. The absolute orthogonality tolerance or relative orthogonality tolerance uses the values ​​in the current orthogonality settings of the finite element solver, without the need for a separate judgment threshold.

[0035] The orthogonality criterion indicates that when the projected residual contains independent components, the quality-normalized projected residual is added to the common reduced-order basis; when it does not contain independent components, the common reduced-order basis is used as a candidate reduced-order basis. The candidate reduced-order basis is used to solve and reconstruct the zero-point interval response, yielding the candidate reduced-order response. When the candidate reduced-order response passes the in-phase shift response sign verification at the two boundary sampling frequencies, the candidate reduced-order basis is used as the augmented reduced-order basis; if it fails verification, the boundary projection residual of the corresponding response vector relative to the candidate reduced-order basis is calculated, and the independent components in the boundary projection residual are processed according to the same orthogonality criterion. When no independent compensation vector is added, the common reduced-order basis directly serves as the augmented reduced-order basis; if S108 fails verification subsequently, the full-arrow equivalent simulation result is not output.

[0036] After determining the augmented reduced-order basis, the process transitions to the interval-based solution in S107. The mass matrix, damping matrix, stiffness matrix, and the equivalent lateral excitation load applied to the oscillating engine center of the full-rocket finite element model are projected onto the corresponding reduced-order basis to form the reduced-order dynamic equations. The matrix projection can use the existing Galerkin projection. The augmented reduced-order basis is used to solve for the zero-point interval, obtaining the reduced-order response within the interval; the shared reduced-order basis is used to solve for the frequencies within the sweep frequency interval but outside the zero-point interval, obtaining the reduced-order response outside the interval.

[0037] like Figure 5 As shown, after solving for the frequencies inside and outside the interval, augmented and shared reduced-order bases are used respectively to reconstruct the reduced-order responses inside and outside the interval to full-order coordinates, obtaining the reconstructed responses inside and outside the interval. Both reconstruction processes use the degree-of-freedom arrangement of the full-arrow finite element model, thus corresponding to the same nodes, directions, and cross-sectional positions. The two boundary sampling frequencies of the zero-point interval are included in the reconstructed response inside the interval, and the reconstructed responses inside and outside the interval are connected in order of increasing sampling frequency to form the reconstructed response.

[0038] To verify whether the reduced-order model maintains the attitude control direction, bending mode parameters are obtained from the reduced-order model formed by the augmented reduced-order basis. After the reduced-order mode vector is reconstructed to full-order coordinates through the augmented reduced-order basis, the lateral displacement of the oscillating engine center and the mode shape slope of the inertial navigation system mounting section are extracted from the reconstructed mode vector. Then, combined with the generalized mass of the reduced-order mode, the reduced-order attitude control mode gain is obtained according to the calculation relationship of S102. According to the modal frequency order, the two full-order bending modes that determine the frequency sweep interval are paired with the corresponding two reduced-order bending modes one order at a time, so that the comparison objects of the two sets of attitude control mode gains are consistent.

[0039] Finally, step S108 is executed. The response vectors of the reconstructed response at the two boundary sampling frequencies are compared with the corresponding response vectors recorded in S104 to obtain the boundary consistency results. The boundary consistency results show that the signs of the interstage separation docking surface, the inertial navigation system mounting section, and the in-phase displacement response of the oscillating engine center are consistent in both sets of response vectors. Furthermore, when the reconstructed response maintains the inverse sign relationship of the interstage separation docking surface and the local minimum, it is confirmed that the reduced-order result reproduces the zero-point response. When the corresponding two reduced-order attitude control mode gains have the same inverse sign order as the two full-order attitude control mode gains, it is confirmed that the inverse sign relationship of the attitude control mode gains is reproduced. After both inverse sign relationships are verified, the reconstructed response is used as the equivalent simulation result of the entire rocket.

[0040] The following is a set of illustrative normalized values ​​used to illustrate zero-point interval identification. The lower boundary of the sweep interval is denoted as 0, and the upper boundary as 1. The frequency position within the interval is obtained by subtracting the lower boundary frequency from the actual frequency and then dividing by the sweep interval width. The responses at the three positions are uniformly normalized using the amplitude of the oscillating engine center response at the left boundary of the zero-point interval. Table 1 is only used to show the identification relationship between candidate intervals and local minima. When forming the zero-point compensation basis, the response vectors corresponding to the normalized oscillating engine center response amplitudes at the left and right boundaries are still normalized according to S105. The calculation results are shown in Table 1.

[0041] Table 1. Examples of normalized responses for zero-point interval identification

[0042] Table 1 and the following results are illustrative values ​​used to demonstrate the judgment and verification process. In Table 1, the interstage separation docking surface responses at 0.45 and 0.55 have opposite signs, and the absolute value of the response at 0.50 is lower than both boundaries. The inertial navigation system mounting section and the oscillating engine oscillator center maintain the same sign at the three frequency positions; therefore, 0.45 to 0.55 constitutes a zero-point interval. When using a shared reduced-order basis, the interstage separation docking surface responses at the two boundaries are +0.070 and +0.030, failing to reproduce the opposite sign relationship. After adding the zero-point compensation basis, the responses at the two boundaries are +0.110 and -0.080, and the minimum absolute response within the interval is 0.006. The adjacent full-order attitude control mode gains are +0.460 and -0.380, and the corresponding reduced-order attitude control mode gains are +0.440 and -0.360. The two sets of attitude control mode gains have the same opposite sign order.

[0043] Continuing with the illustrative frequency configuration described above, nine discrete sampling frequencies are used for the initial solution and boundary verification of the full-order response, while 201 output frequencies are solved by the reduced-order model. If the zero-point interval contains 21 output frequencies, the augmented reduced-order basis is used for these 21 frequencies, and the shared reduced-order basis is used for the 180 frequencies within the sweep interval but outside the zero-point interval. This set of numbers is used to illustrate the computational relationship between full-order sampling and reduced-order sweeping; the actual number of frequencies is determined based on the output frequency resolution and the number of boundary verifications. The full-rocket finite element model handles the initial sampling and boundary verification, while the remaining output frequencies are solved by the reduced-order dynamic equations. By comparing the number of full-order equation solutions and the total runtime under the same hardware, the same full-rocket finite element model, and the same solver, the computational difference between discrete full-order solutions and reduced-order frequency solutions can be obtained.

[0044] The reduced-order attitude control modal gain is only used to verify whether the reduced-order model maintains the inverse sign relationship of the attitude control modal gain and is not included in the output. After the two inverse sign relationships are verified, the reconstructed response formed by connecting them in the order of sampling frequencies is the equivalent simulation result of the entire rocket. The displacement frequency response of the entire rocket, as well as the responses of the interstage separation docking surface, the inertial navigation system mounting section, and the oscillating engine oscillator, can be extracted from the equivalent simulation result of the entire rocket. The extracted responses are compared with the responses of the same excitation direction and the same measurement position in the full-rocket modal test to evaluate the consistency between the simulation results and the experimental results.

[0045] The foregoing has provided a detailed description of the accelerated equivalent simulation method for full-rocket modal testing of a launch vehicle based on model order reduction, as provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and its core ideas. It should be noted that those skilled in the art can make various improvements and modifications to this application without departing from its principles, and these improvements and modifications also fall within the protection scope of this application.

Claims

1. A method for accelerating the equivalent simulation of full-rocket modal tests of launch vehicles based on model order reduction, characterized in that, include: Obtain the full-length finite element model of the rocket in its working state; The attitude control mode gain is calculated based on the bending mode parameters of the full rocket finite element model, and the sweep frequency interval is determined by the adjacent bending mode frequencies with opposite signs of the attitude control mode gain. Using the oscillating engine center as the excitation point, the full-order response at the discrete sampling frequency within the frequency sweep interval is solved. The full-order response includes the response vector and the inter-stage separation docking surface, the inertial navigation system mounting section, and the in-phase displacement response of the oscillating engine center. When the in-phase displacement response of the docking surface is reversed between adjacent discrete sampling frequencies, the in-phase displacement response of the inertial navigation system installation section is not reversed, and the in-phase displacement response of the swing engine center is not reversed and the amplitude is not zero, the interval between adjacent discrete sampling frequencies is determined to be a zero point interval. The response vectors on both sides of the zero-point interval are normalized and the difference is obtained to obtain the zero-point compensation basis; A common reduced-order basis is formed from the bending modal parameters, and the zero-point compensation basis is added to the common reduced-order basis to obtain an augmented reduced-order basis; The reconstruction response and reduced-order attitude control mode gain are obtained by solving the zero-point interval and other frequencies in the swept frequency interval using the augmented reduced-order basis and the common reduced-order basis, respectively. When the reconstructed response reproduces the in-phase displacement response of the docking surface with the opposite sign, and the reduced-order attitude control mode gain reproduces the attitude control mode gain with the opposite sign, the equivalent simulation result of the entire rocket is obtained.

2. The method according to claim 1, characterized in that, The boundary verification of the zero-point interval includes: The interval between adjacent discrete sampling frequencies with opposite signs of the in-phase displacement response of the docking surface is marked as a candidate interval; Candidate intervals with opposite signs at both ends of the candidate interval are eliminated from the inertial navigation system mounting section or the oscillating engine swing center in the same phase displacement response. Within the reserved candidate interval, a verification sampling frequency is set and the full-arrow finite element model is solved to obtain the verification full-order response; The candidate interval boundary is iteratively updated based on the comparison result between the in-phase displacement response amplitude of the docking surface in the full-order verification response and the amplitudes at both ends of the candidate interval, until the in-phase displacement response amplitude of the docking surface in the full-order verification response is simultaneously lower than the amplitudes at both ends of the current candidate interval. The current candidate interval is determined as the zero-point interval, and the response vectors on both sides of the zero-point interval are recorded.

3. The method according to claim 2, characterized in that, The formation of the zero-point compensation base includes: Extract the in-phase displacement response of the swing engine center from the two response vectors. The amplitudes of the in-phase displacement responses of the two swing engine centers are not zero. The amplitudes of the two in-phase displacement responses are used as the normalization references for the corresponding response vectors. The two response vectors are normalized according to the corresponding normalization benchmark to obtain two normalized response vectors; The zero-point compensation basis is obtained by subtracting the two normalized response vectors.

4. The method according to claim 3, characterized in that, The construction of the augmented order-reducing basis includes: Calculate the projection residual of the zero-point compensation basis relative to the common reduced-order basis; According to the orthogonality criterion used by the finite element solver under the inner product of the mass matrix, if the projection residual contains components independent of the common reduced basis, then the projection residual is normalized and added to the common reduced basis to obtain a candidate reduced basis; if the projection residual does not contain independent components, then the common reduced basis is used as the candidate reduced basis. The candidate reduced-order basis is used to solve and reconstruct the response in the zero-point interval to obtain the candidate reduced-order response; When the candidate reduced order response fails to pass the in-phase shift response sign verification at the two boundary sampling frequencies, the boundary projection residual of the corresponding response vector relative to the candidate reduced order basis is calculated, and the independent components determined according to the orthogonality criterion are normalized and added to the candidate reduced order basis, and the zero interval is solved again. The candidate reduced-order basis verified by the in-phase shift response symbol is used as the augmented reduced-order basis.

5. The method according to claim 4, characterized in that, The formation of the full-rocket equivalent simulation results includes: The zero-point interval is solved using the augmented reduced-order basis to obtain the reduced-order response within the interval; The frequency within the swept frequency range and outside the zero-point interval is solved using the common reduced-order basis to obtain the reduced-order response outside the interval; The intra-interval reduced-order response and the extra-interval reduced-order response are reconstructed to full-order coordinates using the augmented reduced-order basis and the common reduced-order basis, respectively, to obtain the intra-interval reconstructed response and the extra-interval reconstructed response. The reconstructed response is obtained by connecting the intra-interval reconstruction response and the extra-interval reconstruction response in order of sampling frequency. The reduced-order attitude control mode gain is calculated based on the bending mode parameters of the reduced-order model formed by the augmented reduced-order basis; By comparing the reconstructed response at the two boundary sampling frequencies with the corresponding response vectors, a boundary consistency result is obtained. When the boundary consistency results indicate that the signs of the in-phase displacement responses of the docking surface, the inertial navigation system mounting section, and the oscillating engine center in the two sets of response vectors are consistent, the reconstructed response maintains the in-phase displacement response of the docking surface with the opposite sign and the response amplitude is locally minimal, and the reduced attitude control mode gain has the same opposite sign relationship with the attitude control mode gain, the reconstructed response is taken as the equivalent simulation result of the entire rocket.

6. The method according to claim 1, characterized in that, The solution to the full-order response includes: A lateral equivalent excitation is applied to the swing center of the oscillating engine along the pitch or yaw direction of the entire rocket. The displacement responses of the docking surface, the inertial navigation system mounting section, and the oscillating engine center are extracted along the same direction as the lateral equivalent excitation.

7. The method according to claim 6, characterized in that, The acquisition of the in-phase shift response includes: Using the phase of the lateral equivalent excitation as the phase reference, the displacement responses of the docking surface, the inertial navigation system mounting section, and the oscillating engine center are projected along the phase reference to obtain the in-phase displacement responses of the docking surface, the inertial navigation system mounting section, and the oscillating engine center.

8. The method according to claim 1, characterized in that, The formation of the shared reduced-order substrate includes: The bending mode vectors whose modal frequencies are outside the zero-point interval are selected from the bending mode parameters. The bending mode vectors are then mass-normalized, and the mass-normalized bending mode vectors are used to form the common reduced-order basis.

9. The method according to claim 8, characterized in that, The shared reduced-order basis comprises: The mass-normalized bending mode vectors corresponding to two adjacent bending modes in the frequency sweep interval are used as the basis vectors of the common reduced-order basis.

10. The method according to claim 9, characterized in that, The output process of the full-rocket equivalent simulation results includes: The augmented reduced-order basis is used to solve the zero-point interval to obtain the reduced-order response within the interval; the common reduced-order basis is used to solve the frequencies within the swept frequency interval but outside the zero-point interval to obtain the reduced-order response outside the interval; the reduced-order response within the interval and the reduced-order response outside the interval are reconstructed to full-order coordinates using the augmented reduced-order basis and the common reduced-order basis respectively to obtain the reconstructed response within the interval and the reconstructed response outside the interval; the reconstructed response within the interval and the reconstructed response outside the interval are connected in the order of sampling frequency to form the reconstructed response and output the equivalent simulation result of the whole arrow.

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