Method for simulating wideband random vibration effect in space launch phase

Abstract

The application discloses a spaceflight launching stage wide-frequency random vibration effect simulation method, relates to the technical field of spaceflight engineering and structural dynamics, and comprises the following steps: S001, a multi-physical field coupling model containing thermal load, aerodynamic disturbance and wide-frequency random vibration input is constructed, a variable parameter driving mechanism is adopted to dynamically map material properties and boundary conditions, and a time-varying response curve of structural inherent frequency is acquired; S002, based on the time-varying response curve, modal energy distribution data are loaded, frequency intersection and energy transfer trends are identified, and a response prediction benchmark of a modal overlap region is established. Through thermal-flow-vibration coupling modeling and modal energy analysis, the application realizes early warning and active inhibition of modal jump, forms a closed-loop vibration risk inhibition mechanism through frequency regulation and parameter calibration, significantly improves the response stability and safety of the structure in the launching stage, and has good engineering practicability and innovation.

Description

Technical Field

[0001] This invention relates to the fields of aerospace engineering and structural dynamics, specifically to a method for simulating broadband random vibration effects during the space launch phase. Background Technology

[0002] "Simulation of Broadband Random Vibration Effects During Space Launch" refers to modeling and simulating the vibration environment experienced by a spacecraft during its launch from a launch vehicle. This simulation covers a wide frequency range and exhibits random characteristics, assessing the dynamic response and potential damage risks of the structure under such complex vibration excitations. Due to multi-source excitations during launch, including engine combustion, aerodynamic fluctuations, and structural resonance, strong random vibration loads are generated in the 10Hz to 2000Hz frequency range and even wider. These loads are characterized by uncertain amplitude variations, complex spectral composition, and high energy density, potentially leading to structural fatigue, fastener loosening, or failure of sensitive instruments. To ensure the safety and reliability of spacecraft under these extreme conditions, simulation technology is used to construct a broadband random vibration model based on tested or standard power spectral density (PSD) curves. Combined with finite element dynamics analysis, the acceleration response, stress distribution, and resonance risk of key components are calculated, guiding structural optimization design and vibration-resistant reinforcement scheme development. This type of simulation is a fundamental step in aerospace engineering environmental adaptability design and ground verification testing.

[0003] Multiphysics coupled random vibration response simulation can be effectively used to simulate broadband random vibration effects during space launch. Its core function lies in comprehensively considering the coupled effects of multiple physical excitations on the structure in a complex environment, thereby improving the realism and completeness of vibration response prediction. During spacecraft launch, the structure is not only subjected to broadband random vibration excitation, but also to multiple effects such as high-temperature heat flow, aerodynamic pulsation, and non-uniform loads caused by propellant combustion. These factors are coupled with each other, causing phenomena such as changes in material stiffness, local thermal expansion and contraction, structural frequency drift, or nonlinear changes in damping characteristics. Multiphysics coupled simulation integrates thermal-structural-fluid-random vibration excitation into a unified modeling framework, which can dynamically simulate the actual response process of the structure under broadband vibration environment, capturing the interactive effects that are ignored in single-physics simulation. For example, when local thermal expansion causes changes in structural prestress, it may cause local modal frequencies to approach a certain excitation frequency band, thereby increasing the risk of resonance. Therefore, this method not only improves the accuracy of vibration response prediction, but also provides a more reliable decision-making basis for the vibration isolation design and thermal protection system optimization of spacecraft structures, making it an indispensable simulation tool for the extremely complex environmental conditions during the launch phase.

[0004] The existing technology has the following shortcomings:

[0005] During spacecraft launch, structural systems are typically situated in a rapidly changing multiphysics environment involving thermal, fluid, and structural coupling, simultaneously subjected to multiple excitations such as high-speed airflow impact, transient thermal loading, and broadband random vibration. Under these complex conditions, the local stiffness of structural materials may undergo nonlinear changes due to factors such as temperature rise, thermal stress redistribution, or aerodynamic pressure fluctuations, leading to dynamic drift of the natural mode frequencies over time. Particularly in simulations of random vibration responses under multiphysics coupling, modal responses originally in different frequency bands may briefly overlap at a certain moment due to frequency drift, resulting in enhanced intermodal coupling and inducing the so-called "modal energy jump" phenomenon. This phenomenon manifests as a sudden transfer of vibrational energy from one mode to another within an extremely short time, causing nonlinear amplification of local amplitudes and resulting in unexpected structural forced responses.

[0006] Because such intermodal abrupt responses are highly transient, concealed, and nonlinear, conventional modeling methods based on linear mode decomposition or steady-state PSD inputs are difficult to effectively identify and predict, easily leading to excessively biased assessments of vibration risks in critical structural components. If such modal jumps occur in weak points such as load-bearing components, sensitive electronic equipment, or interface connection areas, they can easily trigger serious consequences such as loosening of fasteners, exacerbation of local fatigue cracks, or even instantaneous structural instability, severely threatening the structural integrity and mission safety during spacecraft launch.

[0007] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0008] The purpose of this invention is to provide a broadband random vibration effect simulation method during the space launch phase. Through thermal-fluid-vibration coupling modeling and modal energy analysis, it can achieve early warning and active suppression of modal jumps. Furthermore, through frequency regulation and parameter calibration, it forms a closed-loop vibration risk suppression mechanism, which significantly improves the response stability and safety of the structure during the launch phase. It has good engineering applicability and innovation, thereby solving the problems mentioned in the background technology.

[0009] To achieve the above objectives, the present invention provides the following technical solution: a method for simulating broadband random vibration effects during aerospace launch, comprising the following steps:

[0010] S001, a multi-physics coupled model including thermal load, aerodynamic disturbance and broadband random vibration input is constructed. A variable parameter driving mechanism is used to dynamically map material properties and boundary conditions to obtain the time-varying response curve of the structure's natural frequency.

[0011] S002, based on time-varying response curves, load modal energy distribution data, identify frequency convergence and energy transfer trends, and establish a response prediction benchmark for modal overlap regions;

[0012] S003, the response prediction benchmark is used for response analysis in the energy focusing region, modal transition triggering features are extracted, and a judgment threshold standard for modal energy mutation is constructed;

[0013] S004, Based on the judgment threshold standard, establish the modal risk time evolution sequence, output the structural modal stability level, and generate a modal response evolution heatmap;

[0014] S005, based on the modal response evolution heatmap, implements active intervention in structural response, and achieves active separation of modal frequencies before transition triggering by controlling the load field and adjusting structural parameters;

[0015] S006, after active frequency separation, updates the parameter mapping relationship in the coupled model, calibrates the frequency drift prediction curve, forms an adaptive vibration risk closed-loop suppression mechanism, and achieves stable control of the structural response.

[0016] Preferably, step S001 includes:

[0017] Before constructing the multiphysics coupling model, we first obtain the physical field boundary input data of thermal load, aerodynamic disturbance and broadband random vibration input;

[0018] A three-dimensional finite element geometric model covering the propulsion section, mid-section connecting tube section, payload compartment, fairing, and structural bulkhead was established. The material properties in the model were set based on temperature-dependent functions, and the boundary conditions were dynamically adjusted according to the launch phase.

[0019] Heat flux density, aerodynamic force and random vibration power spectral density are applied to the outer shell of the structure, connection nodes and load-bearing parts respectively;

[0020] The temperature field, stiffness matrix and modal frequencies of the structure are solved iteratively within each time step to generate response curves of the structure’s natural frequencies as a function of time.

[0021] Preferably, step S002 includes:

[0022] The structure's natural frequency response curve is divided into continuous time windows at equal time intervals. In each time window, the frequencies and modal energy values ​​of multiple modes are extracted to construct a modal energy spectrum.

[0023] The modal energy spectrum maps of each time window are stitched together in chronological order to form a three-dimensional evolution map, and regions where the frequency trajectories gradually approach each other and the modal energy density continues to increase are identified.

[0024] When the frequency difference between two modes is less than 3 Hz and the energy increases by more than 50% in each of two consecutive time windows, it is identified as a modal frequency overlap region.

[0025] Extract the center value of the intersection frequency, the change of the modal frequency difference, and the modal energy transfer characteristics to establish a response prediction benchmark for the unexpected modal coupling region.

[0026] Preferably, the steps for establishing a response prediction baseline for the unexpected modal coupling region include:

[0027] For the identified modal frequency overlap region, the energy change rate and direction features are extracted, and the growth rate and decay rate of modal energy are recorded within a continuous time window;

[0028] To determine whether there is a unidirectional energy transfer characteristic, when the energy of the first mode decreases and the energy of the adjacent mode increases, and the frequency difference between the two approaches zero, it is marked as a mode energy transition behavior;

[0029] The start and end times of energy transitions, frequency changes, energy mutation amplitudes, and transfer directions are recorded as a set of characteristics.

[0030] Based on feature groups, a set of response prediction benchmark parameters is constructed, including time window number, intersection frequency center, frequency difference change, energy transfer directionality and amplitude, to identify high-risk regions of modal transitions in the structure.

[0031] Preferably, step S003 includes:

[0032] Acceleration, displacement, and strain response data from multiple measurement points within the modal frequency overlap region are extracted to construct a modal-level response dataset;

[0033] Within the modal energy focusing region, local variation analysis is performed on the response data to extract acceleration jump, displacement envelope distortion, strain increase and modal period variation values;

[0034] The above response change features are organized into a modal transition trigger feature dataset, and recognition templates are formed based on historical simulation cases;

[0035] Based on the identification template, threshold standards for acceleration, strain, displacement, period, and energy are constructed. When any mode meets more than three threshold conditions within a continuous time window, it is marked as a high-risk mode transition state.

[0036] Preferably, step S004 includes:

[0037] The modal response data was divided into continuous time periods of 0.2 seconds each, and the peak acceleration, peak strain, modal frequency change rate and energy density change of the corresponding nodes of each mode were extracted.

[0038] Based on the judgment threshold criteria, each mode is marked with a status in each time period, generating a time series containing time, mode number, risk level and triggering physical quantity;

[0039] By mapping the main action region of the modal vibration mode to the risk level, the correlation between time, mode and structural spatial region is established;

[0040] Construct a modal response evolution heatmap with time as the horizontal axis, structural region as the vertical axis, and color intensity representing risk level, and output the risk level evolution curve of each region of the structure.

[0041] Preferably, step S005 includes:

[0042] Based on the modal response evolution heatmap, identify the modal transition trigger risk region where the frequency difference is less than 3Hz and the energy density increases continuously;

[0043] Apply a sinusoidal excitation load with an amplitude of 30N and a frequency within ±10Hz of the target modal frequency at the maximum response node in the region of near modal frequencies, control the application time to be no less than 1 second, and apply it along the direction of the main mode.

[0044] Active separation of modal frequencies is achieved by shifting the modal frequency from 0.5Hz to 1.5Hz through load perturbation;

[0045] Simultaneously, the boundary condition constraint stiffness and local structural stiffness parameters are adjusted to increase the modal frequency distance to more than 5 Hz, thereby decoupling the modal coupling relationship.

[0046] Preferably, step S006 includes:

[0047] After the frequency active separation is completed, the thermal load field distribution, aerodynamic disturbance pressure gradient and structural boundary stiffness parameters are obtained. Combined with the strain response value and material elastic modulus change at the intervention point, the input parameters and attribute matrix of the multiphysics coupling model are updated, and a structural parameter mapping table is established.

[0048] By loading a unified heat flux, power spectral density curve and aerodynamic disturbance model, time-step modal frequency evolution analysis is performed, and the frequency drift trend prediction curve is calibrated.

[0049] By setting the rate of frequency change, the growth rate of modal energy density, and the peak strain of key nodes as judgment criteria, a closed-loop adaptive control mechanism for random vibration risk is constructed.

[0050] Intervention data and response results are stored in a response evolution history database for subsequent modal response prediction and intervention strategy optimization.

[0051] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0052] This invention dynamically constructs an integrated thermo-fluid-vibration coupled model to obtain the evolution trajectory of structural frequencies over time. Combined with modal energy distribution analysis, it identifies potential modal overlap and transition risk regions, and then constructs dynamic threshold standards and modal risk evolution sequences. This enables early warning of modal jumping phenomena and active suppression of local amplitude amplification. In particular, by precisely applying loads through frequency offset control and real-time adjustment of structural parameters, this method possesses the ability to perform feedforward intervention and adaptive calibration of modal responses, ultimately forming a closed-loop random vibration risk suppression mechanism. This not only improves simulation accuracy and risk identification capabilities but also significantly enhances the safety and dynamic stability of the structure under extreme launch environments, demonstrating outstanding engineering practical value and technological innovation. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0054] Figure 1 This is a flowchart of the method for simulating broadband random vibration effects during the space launch phase of the present invention. Detailed Implementation

[0055] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the description of this disclosure will be more complete and fully convey the concept of the exemplary embodiments to those skilled in the art.

[0056] This invention provides, for example Figure 1 The simulation method for broadband random vibration effects during the space launch phase, as shown, includes the following steps:

[0057] S001, construct a multi-physics coupled model that includes thermal load, aerodynamic disturbance and broadband random vibration input. Based on the dynamic changes of material property parameters and boundary condition parameters of the structural system, realize the dynamic mapping between model input and local structural stiffness through a variable parameter driving mechanism, and obtain the response curve of the structure's natural frequency evolution over time.

[0058] To address the complex environmental conditions encountered by spacecraft during launch, a simulation method is proposed to obtain the dynamic evolution of the structure's natural frequencies over time. This method comprehensively considers thermal loads, aerodynamic disturbances, and broadband random vibration inputs to construct a structural response model under multi-physics coupling, and achieves dynamic tracking of the structural modal response through multiple ordered steps.

[0059] The physical field boundary input data for coupled modeling is acquired. For the thermal load component, the radiative heat flux density of the structural surface is calculated using engine jet parameters and the nozzle's perspective factor on the structural parts. Combined with the forced convection heat transfer effect formed by the outer structure contacting the atmospheric boundary, the heat flux density value acting on each structural region per unit time is calculated using the energy conservation principle, forming a time-varying heat flux density input sequence. For aerodynamic disturbances, fluid dynamics simulation under unsteady flow conditions is used to simulate the surface pressure distribution of the spacecraft at each stage during atmospheric traversal, forming an aerodynamic loading sequence divided by time steps, covering the entire process from ignition, ascent, to first stage separation. For broadband random vibration input, the power spectral density curve in the 10Hz to 2000Hz frequency band is statistically obtained by analyzing the acceleration signals at key measurement points in the flight test data. Based on the frequency energy distribution differences at different stages of launch, it is subdivided into three specific stages: low-frequency start-up excitation, mid-frequency combustion stabilization excitation, and high-frequency structural resonance excitation. The three types of excitation are applied to the corresponding positions of the structural geometry model. The heat flux density is applied to the outer shell plates, the aerodynamic force is applied to the nose cone, the fairing and the compartment connection area, and the vibration excitation is applied to the load-bearing beams, structural nodes and equipment mounting surfaces.

[0060] A three-dimensional finite element geometric model of the main components of the launch structure was established. This model includes the propulsion section, mid-section connecting tube section, payload bay, fairing, structural bulkheads, and multiple load-bearing connection nodes. The structural material properties were not set with fixed parameters, but rather based on actual test data, establishing functional relationships between elastic modulus, shear modulus, and density at various temperature levels. Taking high-strength aluminum alloy as an example, its elastic modulus changes by more than 15% in the temperature range of -60℃ to 300℃; therefore, a piecewise fitting method was used to accurately describe the influence of temperature on material properties. The material properties of each finite element element were assigned temperature-related attribute parameters according to its thermal environment. Regarding boundary conditions, they were dynamically adjusted based on the actual constraint states of the structure at different flight stages. For example, axial limiting stiffness was applied at the base position during takeoff, tail clamping constraints were released when entering the sound barrier crossing phase, and transient connection release conditions were applied during the first and second stage separation phases. The evolution of these constraints was also set in a time-step manner to ensure that the structural state during the actual launch process was reflected.

[0061] A "three-dimensional finite element structural geometric model" refers to a fundamental modeling method that uses the actual structure of a spacecraft as a basis, discretizing the structure into a computational model composed of nodes and elements according to its true three-dimensional geometric shape, dimensional proportions, and component connection relationships. This allows for numerical simulation of its stress response, vibration characteristics, and physical behavior. In this step, the role of this three-dimensional finite element structural geometric model is to provide a unified mechanical calculation platform for the coupled analysis of various excitations such as thermal loads, aerodynamic disturbances, and broadband random vibrations. By performing detailed modeling of components such as the propulsion section, connecting cylinder section, bulkhead, fairing, load-bearing frame, and key connection nodes, it can not only accurately reflect the material distribution, structural connection methods, and the actual stress paths between components, but also dynamically calculate the local stiffness changes, modal frequency drift, and response characteristics of the structure based on the temperature field, aerodynamic field, and vibration input under different operating conditions. This model is the core carrier for subsequent modal energy transition identification, frequency evolution analysis, and risk assessment, directly determining the accuracy and reliability of multiphysics coupled response simulation.

[0062] During the structural analysis, the aforementioned thermal loads, aerodynamic forces, and vibration excitations are applied using a uniform time-stepping method. Within each time step, heat flux density, air pressure distribution, and vibration spectrum inputs are applied sequentially to calculate the structure's temperature field, stress field, and deformation response at the current time point. This yields updated values ​​for the material stiffness of each element and the overall structural boundary reactions at that time step. Subsequently, the updated material stiffness and boundary responses are used to construct the stiffness matrix of the entire structure, and the eigenvalue problem is solved based on this matrix to obtain the structure's natural frequencies and modal shapes at that moment. This solution process requires pre-loading thermal stress caused by temperature and deformation effects caused by aerodynamic loads to ensure accurate capture of the structure's dynamic characteristics under actual load conditions. By progressively advancing the solution, the structural modalities at each time step are solved throughout the entire launch phase, constructing a full-cycle response sequence of the structure's natural frequencies evolving over time.

[0063] The natural frequency data across all time steps were systematically organized to create a frequency evolution curve plotted with time on the horizontal axis and natural frequency on the vertical axis. This plot illustrates the dynamic changes in modal frequencies under coupled thermo-aerodynamic-vibration loads, reflecting whether there are significant trends of modal frequency shifting, convergence, or transition. Furthermore, by overlaying the modal frequency curves with the external vibration excitation frequency bands, the potential for frequency proximity or resonance risks can be identified, providing fundamental data support for subsequent modal energy migration assessment and modal jump identification. Simultaneously, this response curve set can also be used in the structural optimization design phase to target and reinforce thermally sensitive or flexible areas of the structure, reducing frequency drift sensitivity and improving the overall dynamic stability and reliability of the structure during launch.

[0064] The purpose of this step is to provide a more physically realistic and predictively accurate modeling foundation for the structural dynamic response of spacecraft under the complex load environment during the launch phase, thereby enabling precise tracking and evaluation of the time-varying characteristics of natural frequencies. During spacecraft launch, the structural system is simultaneously subjected to multiple excitations, including high-temperature heat flux, unsteady aerodynamic forces, and broadband random vibrations. These physical effects are not statically superimposed but change dramatically over time and are coupled with each other, causing continuous dynamic evolution of the structure's local stiffness, boundary constraint state, and modal characteristics. If traditional static or linear modeling methods are used, it will be impossible to capture key response behaviors such as local stiffness relaxation caused by thermal expansion and contraction, boundary softening caused by aerodynamic disturbances, or energy migration excited in the structure by random vibrations, thus seriously affecting the accuracy of vibration risk assessment. Therefore, this step constructs a multiphysics coupled model with joint loading of thermal, aerodynamic, and vibration fields, and combines the real-time changing characteristics of structural material properties and boundary conditions. A variable parameter driving mechanism is used to dynamically map the local structural stiffness, enabling the model to continuously update the natural frequency and modal response results throughout the launch phase. The final output of the structural natural frequency response curve not only reflects the trend of the system's modal stability change, but also provides basic data support for identifying modal overlap, predicting modal jump risk, and formulating structural intervention strategies. It is the starting point and key foundation in the multiphysics vibration risk identification and control process.

[0065] S002, based on the response curve, load the modal energy distribution data within a continuous time window, identify frequency intersection regions and energy transfer trends, determine the modal frequency overlap region and high-risk points of modal transition, and establish a response prediction benchmark for the unexpected modal coupling region;

[0066] To identify potential modal overlap regions and modal energy transition behaviors in structures under multiphysics coupling environments, modal energy distribution analysis and unexpected modal coupling prediction are proposed based on previously obtained response curves of the structure's natural frequencies over time. By analyzing the characteristics of modal frequency and corresponding energy changes during continuous temporal evolution, a high-risk region identification process for structural vibration response is constructed, specifically including the following steps:

[0067] The structural frequency response curve of the entire launch phase is divided into several consecutive time windows with equal time intervals. The duration of each time window is set to 0.2 seconds to cover sufficient frequency variation information without over-compressing the transient response. Within each time window, the frequency values ​​of all first to sixth order modes are extracted, and the acceleration time history of each mode at the measurement point is obtained from the structural response data of the corresponding time period. The square of the acceleration of each mode is integrated and multiplied by the equivalent mass of the corresponding mode to calculate its modal energy value within that time window. The energy values ​​of all modes are distributed with frequency as the horizontal axis to form a modal energy spectrum diagram under that time window, reflecting the energy distribution characteristics at different frequencies.

[0068] By vertically stitching together the modal energy spectrum maps within all time windows in chronological order, a three-dimensional evolution map of modal energy is formed, with time as the horizontal axis, frequency as the vertical axis, and energy as the numerical value. In this map, the trajectory of each modal frequency over time, as well as the fluctuation trend of energy density at the corresponding frequencies, can be clearly observed. By observing the energy "convergence bands" or "energy islands" in the map, regions where frequency trajectories gradually converge and where two modal energies simultaneously and rapidly increase within adjacent time windows can be identified. Regions with potential modal frequency overlap and enhanced coupling are identified based on the criterion that the frequency difference between two modes is less than 3 Hz and the corresponding energy density increases by more than 50% in each of two consecutive time windows.

[0069] The "energy convergence zone" or "energy island" structure refers to a high-energy region formed by a significant increase and aggregation of modal energy density in certain frequency areas within a continuous time period in a three-dimensional spectrum of modal energy distribution over time and frequency. Specifically, when the frequency trajectories of two or more modes gradually approach each other over time, and the energy density in that frequency range continuously increases, it will appear as a high-energy ridge extending along the time direction in the three-dimensional spectrum, called a "convergence zone." If this aggregation phenomenon suddenly intensifies within a small time window and frequency range, forming a local protrusion that stands out prominently against the surrounding low-energy background, it resembles an "island" and is called an "energy island."

[0070] The specific steps for identifying "convergence zones" or "energy islands" are as follows:

[0071] Modal frequency response and modal energy distribution data are plotted as a three-dimensional map with time as the horizontal axis, frequency as the vertical axis, and energy density as color or height.

[0072] Observe whether two or more modal frequency curves in the frequency trajectory of the spectrum gradually converge in a certain area, forming a clear trend of frequency convergence. At the same time, check whether the color of the frequency segment gradually transitions from cool color to warm color (representing an increase in energy).

[0073] In these regions where frequencies gradually overlap, observe whether there is a pattern of significant energy increase within a continuous time window, specifically manifested as a deepening of the energy color or a sudden increase in energy value near that frequency. If the energy value increases by more than 50% within two consecutive time windows, accompanied by a decrease in the frequency difference between the two modes to below 3Hz, it can be preliminarily identified as a convergence zone; if a sudden peak forms in this region, with both frequency and time range concentrated within a small window, energy much higher than the surrounding frequency bands, and energy growth extremely rapid, it can be identified as an energy island.

[0074] These identifications can clearly identify which modalities exhibit potential reinforcing interaction trends, providing an intuitive and quantitative basis for further identifying modal transition risks and developing response intervention strategies.

[0075] For the identified modal frequency overlap regions, energy change rate and direction features are further extracted. Specifically, for two modes with similar frequencies, their energy change curves are recorded within continuous time windows. If it is found that the energy of one mode decreases rapidly within two time windows, while the energy of the other mode increases at a similar rate, and the frequency difference between the two modes remains close to zero during this period, it can be identified as a sudden energy migration between modes, either from high to low frequency or from low to high frequency. This type of energy "jump" phenomenon is a typical sign of an impending modal transition. The start and end times of the corresponding time windows, modal frequency values, energy change amplitude, and transition direction are extracted and recorded as a complete feature set.

[0076] The aforementioned feature set data is used to establish a response prediction benchmark for unexpected modal coupling regions. This benchmark includes the following parameters: time window number, center value of intersection frequency, difference between initial and final frequencies between modes, relative rate of change of modal energy, duration of alternating energy growth and decay, and unidirectional energy transfer index. These parameters comprehensively characterize the mutual interference intensity between modes and their influence on the structural vibration energy distribution. Based on this, high-risk modal overlap sections can be identified in subsequent structural response calculations, and these areas can be subject to focused monitoring, response intervention, or structural optimization design. The establishment of the response prediction benchmark not only improves the pre-emptiveness of modal transition identification but also provides quantitative input conditions for the vibration isolation design stage.

[0077] The purpose of this step is to deeply identify the potential convergence behavior between structural modes caused by frequency drift in a multiphysics coupled environment, as well as the resulting energy transfer trends. This allows for the early detection of high-risk areas in the structural vibration response where modal coupling enhancement and modal energy transitions may occur, and the establishment of a predictive response benchmark. During the spacecraft launch phase, the coupling effects of thermal loads, aerodynamic disturbances, and broadband random vibrations on the structural system cause dynamic changes in modal frequencies over time. Originally separated modal frequencies may gradually approach or overlap at a certain point in time. If multiple modal energies simultaneously increase, the risk of resonance superposition and abrupt changes in local response will be significantly increased. This step involves jointly analyzing the time response curves of the structure's natural frequencies with modal energy distribution data, using a time-window segmentation method to construct a time-frequency spectrum of modal energy, and further analyzing whether there are sudden increases in energy density in areas where frequency trajectories are close. By identifying spectral feature structures such as "energy convergence zones" and "energy islands," it is possible to determine which modes may experience rapid energy migration, thereby pinpointing high-risk points for modal transitions. Based on this, a response prediction benchmark is established, including indicators such as frequency intersection intervals, energy growth rates, intermodal frequency differences, and energy transfer directions. This provides a quantitative basis for subsequent modal transition identification, modal risk level classification, and proactive intervention design. This step not only enhances the foresight and intelligence of modal response analysis but also realizes the transformation from passive response assessment to proactive risk prediction, making it a key technical link in the multiphysics random vibration risk control process.

[0078] S003 uses the response prediction benchmark as input conditions to perform refined modal response analysis on the energy focusing region, extracts modal transition triggering features and local energy surge parameters, and constructs a judgment threshold standard for modal energy mutation.

[0079] To further extract transition precursor features with engineering prediction value from the modal frequency overlap region and modal energy convergence trend identified in the previous stage, and to construct a judgment criterion for structural modal transition behavior, this step proposes a refined modal response analysis method based on response prediction benchmarks. This method mainly includes the following steps:

[0080] From the established modal response prediction benchmark, regions with significant energy accumulation were selected as the analysis objects. Within these energy-accumulating regions, response data from multiple measurement points within the corresponding time window were extracted, including nodal acceleration time histories, displacement responses, and strain outputs at key structural locations for each mode. A time window of 0.2 seconds was selected, and the sampling rate was increased to 1000Hz to ensure that the rapid changes in high-frequency modes were fully captured. These data were then organized into time series according to modal order to construct a modal-level response dataset, providing a data foundation for subsequent dynamic feature extraction. During data processing, special attention was paid to the locations of nodes where drastic response fluctuations occurred when modal frequencies were close together, especially in weak structural areas such as connection nodes, beam ends, and shell boundaries.

[0081] Based on the aforementioned high-precision response data, a local analysis was performed on the changes in the modal response before and after the energy peak to extract sensitive physical quantities related to modal transitions. These include: the increase in acceleration peak value within a very short time, the waveform distortion of the displacement envelope curve, the increase ratio of the strain curve between adjacent sampling points, and the continuous trend of the modal period length. The judgment criterion is: if the peak acceleration of a certain mode changes from below the mean to more than 1.5 times above the mean within five consecutive sampling points, and the peak envelope of the displacement response changes from symmetrical to asymmetrical, while the strain value at the corresponding node increases by more than 30% within 0.01 seconds, then it can be determined as a triggering behavior before a modal transition is about to occur. This type of response change often occurs when the modal frequencies are highly similar and the non-uniform stiffness region of the structure is aggravated by external coupling excitation, and is a typical precursor to the transfer of energy between structural modes from the first-order mode to a higher-order mode or in the opposite direction.

[0082] After identifying significant changes in the aforementioned physical quantities, these changes were constructed into a set of feature indicators, organized by time points into a modal transition trigger feature dataset. This dataset consists of the following: mode number, sampling time, maximum acceleration and its rate of change, strain growth rate, period length change, and corresponding energy increase. Each set of data records the characteristic trajectory of a potential transition event. Subsequently, five historical simulation cases with known modal transitions were selected for comparative analysis. The most representative trigger feature combinations were extracted, such as the triple joint feature of "displacement increase exceeding 40% and period shortening by 15% accompanied by energy increase exceeding twice the previous window value," forming a template for transition behavior identification for subsequent high-risk area judgment.

[0083] Based on the aforementioned feature dataset and recognition template, physical quantity threshold standards are constructed to determine whether a modal transition is imminent. Specific standards include: a peak acceleration increase threshold set to 1.5 times the mean; a strain growth threshold of 0.0008 mm / mm; a displacement increase exceeding the previous window by 40%; a periodic rate of change threshold set to 10%; and an energy density increase exceeding 200% of the previous time window. After setting these values ​​as fixed thresholds, modal responses within continuous time windows are monitored in real time. When any mode simultaneously meets three or more threshold conditions within a specified time window, it is automatically marked as a high-risk modal transition state. This judgment standard can be deployed during response analysis to provide early warnings for high-risk structural regions, and can also be combined with subsequent response evolution heatmaps for targeted intervention and control of the structure.

[0084] The purpose of this step is to identify key physical triggering signals before modal transitions by performing high-resolution analysis on regions of overlapping modal frequencies and regions of rapid energy accumulation. Based on this, a scientific and quantitative judgment threshold is established for real-time early warning of potential modal energy mutation events during structural vibration response. Spacecraft are subjected to multi-physics coupled excitation during launch, and the structural modal frequencies change dynamically over time. Different modes may couple due to frequency proximity, causing energy to rapidly transfer from one mode to another within a short period. This modal transition can trigger a sudden increase in local structural response. If not identified in time, it can easily lead to local fatigue, fastening failure, or interface damage. Therefore, based on the established response prediction benchmark, this step conducts a more detailed modal response analysis on regions with high energy density and frequency convergence characteristics, extracting precursor features such as sudden acceleration changes, sudden strain increases, and rapid shortening of vibration periods. Combined with the amplitude and rate of modal energy density mutations, typical physical response modes before modal transitions occur are summarized. Furthermore, by combining extensive simulation data with actual flight test experience, quantifiable judgment indicators and numerical thresholds are extracted, such as peak acceleration exceeding 1.5 times the average, strain rate exceeding 30%, and energy rate exceeding 200% per unit time, thus constructing a multidimensional judgment standard for modal energy mutation. These standards can be embedded into the structural response analysis process to assess in real time whether the structure is currently in a high-risk state of modal transition, thereby providing a clear triggering basis for subsequent proactive intervention or structural reinforcement. This step transforms modal transition identification from experience-based judgment to a data-driven scientific quantification process, and is a key link in the transformation of modal energy mutation prediction from trend analysis to event judgment, significantly improving the accuracy of structural response safety assessment and the foresight of response decisions.

[0085] S004. Based on the judgment threshold standard, establish a time evolution evaluation sequence of modal risk, output the modal stability level of each region of the structure in different time periods, generate a modal response evolution heatmap of the weak parts of the structure, and form the modal risk level evolution trajectory.

[0086] To monitor the modal stability changes of a structure under multi-physics coupled excitation in real time, and to dynamically assess the structural modal risk level in both time and space by combining the previously established modal energy mutation judgment threshold, this step proposes a modal risk time evolution evaluation based on the judgment threshold standard. Through phased processing of structural response data, modal risk quantification, spatial mapping, and graphical visualization, the risk trajectory of key structural components under the entire launch load process is constructed. Specifically, the steps are as follows:

[0087] Based on the established judgment threshold criteria, a temporal resolution is set for the entire launch phase, dividing the structural modal response data into a series of time segments. The time interval is set to 0.2 seconds per segment to ensure sufficient resolution for phenomena such as modal frequency drift and drastic response fluctuations. Within each time segment, for all structural modes, the corresponding physical quantities of the response at each node are extracted, including peak acceleration, peak strain, modal frequency change rate, and energy density change per unit time. In practice, if the rate of acceleration change exceeds 150% of the average of the previous time segment, the strain rate exceeds 25%, the modal frequency change exceeds 2Hz, and the energy density increase exceeds 200%, then based on the comparison results of the corresponding indicators in the judgment threshold criteria, the mode is marked as "stable," "critical," or "unstable," and a set of time series structures is generated, recording the time point, mode number, corresponding risk level label, and triggering physical parameters.

[0088] Establish the correlation between modal risk levels and structural spatial regions. The influence range of each mode on the structure is determined by its mode shape, which is obtained from previous modal analysis. Taking the first bending mode as an example, its influence area is mainly concentrated in the central axial region of the load-bearing shell; the second torsional mode is concentrated around the head cone connecting ring and the fairing. Based on this, the modal risk level labels in the time series are mapped to the main influence areas of their corresponding mode shapes, realizing the construction of a three-dimensional risk index linkage relationship of "time + mode + spatial region". For the modal response results within a specific time period, it can be clearly pointed to which part of the structure is in which risk level state. This process forms a one-to-one correspondence between key structural units and modal response risks, which is used for the next step of map construction.

[0089] After establishing the aforementioned spatial and temporal distribution relationships, a modal response evolution heatmap is generated. The heatmap uses time as the horizontal axis and structural spatial region numbers as the vertical axis, with color intensity representing risk levels. Green represents "stable," yellow represents "critical," and red represents "unstable." Each block represents the risk state of a specific structural component within a certain time period, and these blocks are arranged chronologically to form a risk evolution trajectory. For example, when analyzing the time segment from the 2nd to the 5th second of the launch phase, it was observed that the outer ring region of the tail section bulkhead was in a "critical" or "unstable" state for six consecutive time periods, indicating the presence of continuous modal transition disturbances in this region, which should be a priority target for subsequent response control. This heatmap visually reveals how modal disturbances develop in time and are distributed spatially, providing a foundation for global perception of structural vibration behavior.

[0090] Based on the heatmap, a risk level time series is established for each key region of the structure, forming a modal risk level evolution curve. The horizontal axis of this curve represents time, and the vertical axis represents the risk level code value (0 for stable, 1 for critical, and 2 for unstable). The risk level evolution curve of each structural region clearly reflects the start time, duration, and highest level of modal disturbance. For example, if a region of a connecting beam is found to continuously rise from level code 0 at 1.0 seconds to level code 2 at 1.6 seconds, and then slowly decline after maintaining this for 2 seconds, it indicates that there is a risk of continuous modal aggregation in this region, and frequency shifting or stiffness correction intervention should be carried out in conjunction with the next step of intervention mechanism. By comparing the evolution curves of multiple regions, it is also possible to identify whether there are mutually reinforcing segments in the propagation path of different modal responses in the structure. If multiple adjacent regions enter an unstable state at the same time period, it means that there is a local resonance coupling zone in the structure, which can be used to indicate the risk of resonance in the entire structure.

[0091] The purpose of this step is to apply the previously established modal transition judgment threshold standard to the entire process analysis of structural modal response, enabling a quantitative, dynamic, and continuous assessment of the modal risk of the spacecraft structure at different time periods and in different space locations during the launch phase. It outputs clear temporal evolution trends and spatial distribution characteristics, thus providing a visualized decision-making basis for subsequent structural response control and design optimization. Specifically, under the multiple excitations of thermal, aerodynamic, and random vibration, the modal frequencies, modal energies, and response characteristics of the structure change dynamically over time, easily leading to modal frequency overlap, energy transitions, and sudden increases in local response. These phenomena are highly transient and localized; without continuous tracking, high-risk response points are easily missed. This step sets a uniform time step (e.g., 0.2 seconds) to extract the response physical quantities of key modes within each time period, such as acceleration, strain, frequency change rate, and modal energy density change, and compares them with the judgment threshold standard to determine the risk level of the mode within that time period, classifying it as stable, critical, or unstable. Simultaneously, this risk level information is mapped to specific areas of the structure, forming a three-dimensional relationship of "time-space-risk level". Furthermore, a modal response evolution heatmap is constructed using color coding to visually display the change path of modal stability in different parts of the structure throughout the launch process, identifying modal response sensitive areas and weak points. The heatmap reveals which areas are in a sustained critical state, which areas experience transient instability, and how risks spread or concentrate within the structure. Finally, by extracting the risk level change sequence of each area, a modal risk level evolution trajectory is generated, providing a quantitative basis for active frequency intervention, structural stiffness adjustment, or local structural reinforcement. This step effectively extends from modal abrupt change judgment to full-process risk evolution management, and is a core component of the modal transition prediction system, possessing high engineering practicality, forward-looking perspective, and innovative value.

[0092] S005, based on the modal response evolution heatmap, implement active intervention control of structural response, apply frequency offset regulation load field, and achieve active separation of modal frequencies before modal transition is triggered by adjusting boundary condition parameters or modifying local structural stiffness parameters, thereby decoupling the coupling relationship between modes;

[0093] To prevent the dynamic convergence of modal frequencies during structural vibration from causing energy coupling amplification, abrupt changes in structural response, and local fatigue failure, a proactive intervention method combining modal response evolution heatmaps is proposed. By identifying risk regions before modal transitions are triggered and applying structural intervention measures, previously overlapping modal frequencies are effectively separated in both time and frequency dimensions, decoupling the modes and thus keeping the structural vibration response within a controllable range. This implementation process includes the following steps:

[0094] Based on the modal response evolution heatmap, regions within the structure that are persistently in a "critical" or "high-risk" state are identified. The location and duration of the red areas in the heatmap are analyzed, and combined with the modal numbers and frequency values, it is determined whether two or more modes exhibit frequency similarities within a certain time period. A region is identified as a modal transition trigger risk area if the modal frequency difference is less than 3 Hz and the modal energy density increases by more than 200% over three consecutive time periods. Further extraction of local vibration mode data confirms the location of nodes with the largest modal deformation amplitude, and the corresponding structural sub-segment number, modal number, frequency value, and risk occurrence time range are recorded as the basis for subsequent intervention operations.

[0095] For identified high-risk areas, the load application method is precisely controlled to actively shift the structural modal frequencies in time, reducing the probability of modal overlap. At the node with the largest structural deformation, a sinusoidal excitation load with an amplitude of 30N and a frequency within ±10Hz of the target modal frequency is applied using a mechanical excitation device. The duration of this load is set to be no less than 1 second, and the direction of application is consistent with the direction of the principal mode. This operation can change the local prestress state, causing a temporary disturbance in the structural stiffness, thereby shifting the natural frequency of the target mode to a higher or lower frequency direction by 0.5Hz to 1.5Hz in a short period of time, ultimately achieving decoupling of the two modal frequencies. After the load is applied, the changes in the structural frequency response are monitored in real time to confirm whether the modal frequencies separate within a safe interval of more than 3Hz.

[0096] Precise load control refers to the application of external excitation loads with specific frequencies, amplitudes, directions, locations, and durations to specific modal frequencies and sensitive structural locations during structural dynamic regulation. This allows for controllable disturbance of the local stiffness or prestress state of the structure, thereby adjusting the modal frequency position. To achieve this, precise and controllable excitation devices such as electromagnetic vibrators, piezoelectric actuators, or hydraulic micro-impact devices can be used. Electromagnetic vibrators are suitable for high-frequency (above 100Hz) vibration regulation, and the load frequency and amplitude can be precisely controlled by adjusting the current input. Piezoelectric actuators are suitable for small amplitude, high-response frequency domains and can be integrated into the structural surface for fine-tuning frequency control. Hydraulic micro-impact devices are suitable for areas with large structural dimensions and high stiffness, and can apply pulsed forces within a range of 0.1-1 seconds to change the local stress field. Before applying the load precisely, based on the modal vibration results, select the node with the largest structural displacement response or the concentrated modal energy density as the application point. The application direction should be consistent with the main direction of the mode. Gradually adjust the excitation frequency within the range of ±5Hz of the modal frequency, control the amplitude between 10N and 50N, and control the duration between 0.5 seconds and 1.5 seconds. Confirm whether the modal frequency shift has been achieved through real-time response feedback, thereby effectively suppressing the modal coupling trend.

[0097] While controlling the load, physical adjustments are made to the structural boundary and local stiffness parameters in high-risk areas. Boundary condition adjustments include removing axial limiting devices or adding radial limiting devices in the connection area, reducing or increasing boundary constraint stiffness by 20%, thereby causing a controllable drift in modal frequencies. Stiffness parameter adjustments include adding 2mm thick aluminum alloy reinforcing ribs to high-response modal areas, or attaching a three-dimensional fiber reinforcement layer to the inner surface of the thin-walled structure, increasing the local stiffness of that area by 12% to 18%. These changes in structural physical parameters will further expand the target modal frequency shift range, increasing the frequency distance between it and adjacent modes to more than 5Hz, ensuring that modal response energy no longer couples and superimposes.

[0098] After completing frequency regulation and structural physical intervention, modal response heatmaps are generated and analyzed again. By comparing the color changes of high-risk areas in the heatmaps before and after intervention, it is confirmed whether the original high-risk areas have changed from red to yellow or green, i.e., the risk state has changed from "high" to "critical" or "stable". At the same time, the modal frequency response curves are compared to determine whether the modal frequencies have been completely separated. If frequency convergence or energy surges still exist after intervention, the amplitude of the regulation load is increased to 40N, or the local stiffness is further increased by 10%, and the control process is repeated until the modal frequencies are completely decoupled. All intervention parameters and response changes are recorded and compiled into an operation log, including load type, frequency, duration, intervention location in the structure, stiffness change measures, and modal frequency response trends, to establish a structural regulation database and provide a reference for the next intervention.

[0099] The purpose of this step is to proactively intervene before modal transitions actually occur but before the structure enters a high-risk evolutionary state, based on the identification results of the modal response evolution heatmap. This involves pre-regulating and decoupling the structure's modal frequencies to block energy coupling paths between modes and prevent serious consequences such as sudden increases in local amplitude, weakened stiffness, or fatigue failure caused by frequency overlap or energy jumps between modes. Under the coupling effect of multiphysics fields, the modal frequencies of aerospace structures exhibit a trend of change over time. Originally widely spaced modal frequencies may gradually converge due to changes in thermal stiffness, aerodynamic disturbances, or evolution of boundary conditions. Once they enter the convergence region, frequency locking or modal coupling can easily occur, triggering nonlinear response behavior and increasing the risk of structural instability. Therefore, after identifying the region where the modal frequency approaches and the modal energy continuously increases through heat mapping in the previous step, this step actively alters the evolution path of the modal frequency by applying frequency offset load fields, adjusting structural boundary constraints (such as releasing limits or reinforcing supports), and adjusting local stiffness (such as reinforcing ribs and attaching stiffening materials), thereby achieving separation in the spatial and frequency dimensions before the transition is triggered. Through this proactive intervention process, directional control of modal behavior can be quickly achieved without affecting the overall load-bearing capacity of the structure, preventing the continuous accumulation of energy in the high-energy response region and protecting critical components from resonance excitation and fatigue impact. This step elevates structural response control from passive response analysis to proactive intervention design, and is a key link in achieving closed-loop suppression of structural vibration risks, possessing significant engineering practical value and innovation.

[0100] S006 After the active separation of modal frequencies is completed, the dynamic mapping relationship of structural parameters in the multiphysics coupling model is updated, the frequency drift trend prediction curve is calibrated, and a closed-loop suppression mechanism for random vibration risk with adaptive control capability is constructed to achieve stable control of the structural vibration response process.

[0101] To ensure the long-term stability of the structural vibration response after active modal frequency separation and to prevent modal transitions and energy abrupt changes caused by the reconvergence of modal frequencies due to thermal, aerodynamic, or boundary disturbances, a stochastic vibration closed-loop suppression mechanism based on real-time structural parameter updates and response prediction correction was constructed. This mechanism possesses the capabilities of adaptive structural state identification, automatic frequency trend calibration, and dynamic judgment of control conditions, enabling continuous regulation of the structure's modal stability under multi-physics coupled conditions. The process specifically includes the following steps:

[0102] After completing the active frequency separation operation, the thermal load field distribution of the structure under its current state is obtained (unit: W / m). 2The system collects aerodynamic disturbance pressure gradients (in Pa / m) and structural boundary stiffness parameters (in N / m). It also collects strain response values ​​at intervention points (e.g., the maximum strain at the mid-node of the connecting beam changes from 480 με to 620 με) and local material elastic modulus changes (e.g., the material stiffness within the control area decreases from 68 GPa to 65 GPa). These physical parameter changes and response parameters are used as input conditions and rewritten into the input items of the multiphysics coupling analysis model. The structural material and boundary property matrices are then updated. Finally, a structural parameter mapping table is generated, containing timestamps, spatial node numbers, stiffness coefficients, thermal stress distributions, and modal frequency values, achieving full synchronization between structural input parameters and response states.

[0103] Based on the updated structural parameters, a uniform heat flux input (set to 9 kW / m²) is loaded onto the modeling platform. 2 Power spectral density curves of random vibration input (frequency range 10Hz-2000Hz, peak value 0.05g) 2 Frequency response analysis was performed using a dynamic disturbance model (maximum pressure 4800 Pa) and an aerodynamic disturbance model (maximum pressure 4800 Pa). The frequency evolution paths of the first five modes were solved step-by-step (0.1 sec), resulting in a set of frequency change trend curves. This set of curves was then compared point-to-point with the modal frequency drift trend curves recorded before intervention to analyze whether the frequency shift trend of the current structure under the new state was stabilizing. If the rate of change of the new frequency curve did not exceed ±0.3 Hz / sec within five consecutive time steps, and the minimum frequency spacing between modes remained above 4.5 Hz, then the current structure's modal frequencies were determined to be in an effectively decoupled state.

[0104] After confirming that the current frequency trend has entered the stable decoupling region, real-time monitoring conditions are set, and a closed-loop adaptive control mechanism for random vibration risk is constructed. Three specific judgment criteria are set: First, a modal frequency change rate continuously exceeding 0.5 Hz / second is marked as a critical drift state; second, a modal energy density growth rate exceeding 200% within three consecutive time windows is marked as abnormal energy accumulation; third, a strain peak value at key nodes (such as engine compartment connecting rings and equipment compartment crossbeams) exceeding 1.6 times the historical average is marked as a local response mutation. If any one of these conditions is met, the frequency control operation is restarted. Otherwise, the current structural state is maintained, and modal response data continues to be dynamically updated every 0.2 seconds, automatically performing closed-loop calibration and parameter synchronization to ensure the long-term stability of the modal decoupling state.

[0105] All structural input parameters, modal frequency response results, risk assessment records, control trigger times, and operational parameters after intervention are uniformly compiled to establish a response evolution history database. The database includes: thermal load input curves, historical frequency response graphs, modal energy distribution curves, control intervention operation logs (including operation number, load amplitude, load frequency, and duration), structural boundary stiffness variation graphs, and a table of minimum modal frequency spacing variations. All data is stored in time-series format and updated after each new intervention. This database can serve as a system training sample for future modal response prediction and risk assessment of structures under similar multiphysics conditions, thereby significantly improving the response accuracy of structural modal control and the efficiency of intervention strategy selection.

[0106] The core function of this step is to promptly update the physical state and response model of the structure after the active separation of modal frequencies. This ensures that the multiphysics coupling analysis model maintains dynamic consistency with the actual structural behavior, thereby achieving closed-loop control and continuous suppression of random vibration risks. During the spacecraft launch phase, the structure is in a complex coupled environment involving high-speed flight, intense combustion, and drastic aerodynamic pressure changes. Thermal loads, aerodynamic disturbances, and broadband random vibrations continuously act on various regions of the structure, causing material stiffness, boundary conditions, and modal parameters to change over time. Although the preceding steps achieve temporary separation of modal frequencies, without continuous updates to the structural model input, subsequent modal frequencies may converge again due to structural stiffness evolution or overlapping external excitations, reigniting the risk of modal transitions and energy jumps.

[0107] Therefore, this step first uses structural monitoring and response results to backtrack, quantitatively analyzing the changes in key structural parameters such as stiffness, constraints, and stress field, and then inputs this data into the model to remap the structural state. Subsequently, based on the updated model, the frequency response curve over time is recalculated to calibrate the trend of modal frequency drift and determine whether the frequency decoupling state has long-term stability. If a potential frequency convergence trend is still detected, a risk triggering mechanism is immediately constructed by setting judgment conditions (such as frequency change rate, energy increase rate, and strain response amplitude) to activate the next round of control intervention, thus forming a closed-loop control process of "prediction—verification—intervention—re-prediction".

[0108] Ultimately, by recording model updates, risk identification, intervention strategy execution, and response feedback results in time series format, a response evolution database is constructed, enabling the intelligent evolution and improved adaptive capabilities of structural control strategies. This step ensures that, under uninterrupted flight and continuous excitation environments, structural response control no longer relies on static analysis but possesses continuous perception, dynamic judgment, and real-time intervention capabilities. This is a key technical step in realizing the transformation of structural modal stability management from "discrete control" to "continuous suppression."

[0109] The proposed "Simulation Method for Broadband Random Vibration Effects During Space Launch" effectively addresses the limitations of traditional linear modal analysis in identifying dynamic frequency drift and energy mutations under multi-physics coupling. This method enables precise modeling, prediction, and control of the actual dynamic response of structures under the combined effects of high-temperature heat flux, severe aerodynamic disturbances, and broadband random vibrations. By dynamically constructing an integrated heat-fluidity-vibration coupling model, the method obtains the evolution trajectory of structural frequencies over time. Combined with modal energy distribution analysis, it identifies potential modal overlap and transition risk regions, thereby constructing dynamic threshold standards and modal risk evolution sequences. This achieves early warning of modal jumps and active suppression of local amplitude amplification. In particular, through precise application of frequency offset-controlled loads and real-time adjustment of structural parameters, the method possesses the ability to perform feedforward intervention and adaptive calibration of modal responses, ultimately forming a closed-loop random vibration risk suppression mechanism. This not only improves simulation accuracy and risk identification capabilities but also significantly enhances the safety and dynamic stability of structures under extreme launch environments, demonstrating outstanding engineering practical value and technological innovation.

[0110] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A method for simulating broadband random vibration effects during space launch, characterized in that, Includes the following steps: S001, a multi-physics coupled model including thermal load, aerodynamic disturbance and broadband random vibration input is constructed. A variable parameter driving mechanism is used to dynamically map material properties and boundary conditions to obtain the time-varying response curve of the structure's natural frequency. S002, based on time-varying response curves, load modal energy distribution data, identify frequency convergence and energy transfer trends, and establish a response prediction benchmark for modal overlap regions; S003, the response prediction benchmark is used for response analysis in the energy focusing region, modal transition triggering features are extracted, and a judgment threshold standard for modal energy mutation is constructed; Step S003 includes: Acceleration, displacement, and strain response data from multiple measurement points within the modal frequency overlap region are extracted to construct a modal-level response dataset; Within the modal energy focusing region, local variation analysis is performed on the response data to extract acceleration jump, displacement envelope distortion, strain increase and modal period variation values; The above response change features are organized into a modal transition trigger feature dataset, and recognition templates are formed based on historical simulation cases; Based on the identification template, threshold standards for acceleration, strain, displacement, period and energy are constructed. When any mode meets more than three threshold conditions within a continuous time window, it is marked as a high-risk mode transition state. S004, Based on the judgment threshold standard, establish the modal risk time evolution sequence, output the structural modal stability level, and generate a modal response evolution heatmap; Step S004 includes: The modal response data was divided into continuous time periods of 0.2 seconds each, and the peak acceleration, peak strain, modal frequency change rate and energy density change of the corresponding nodes of each mode were extracted. Based on the judgment threshold criteria, each mode is marked with a status in each time period, generating a time series containing time, mode number, risk level and triggering physical quantity; By mapping the main action region of the modal vibration mode to the risk level, the correlation between time, mode and structural spatial region is established; Construct a modal response evolution heatmap with time as the horizontal axis, structural region as the vertical axis, and color intensity representing risk level, and output the risk level evolution curve of each region of the structure; S005, based on the modal response evolution heatmap, implements active intervention in structural response, and achieves active separation of modal frequencies before transition triggering by controlling the load field and adjusting structural parameters; Step S005 includes: Based on the modal response evolution heatmap, identify the modal transition trigger risk region where the frequency difference is less than 3Hz and the energy density increases continuously; Apply a sinusoidal excitation load with an amplitude of 30N and a frequency within ±10Hz of the target modal frequency at the maximum response node in the region of near modal frequencies, control the application time to be no less than 1 second, and apply it along the direction of the main mode. Active separation of modal frequencies is achieved by shifting the modal frequency from 0.5Hz to 1.5Hz through load perturbation; Simultaneously, the boundary condition constraint stiffness and local structural stiffness parameters are adjusted to increase the modal frequency distance to more than 5Hz, thereby decoupling the modal coupling relationship. S006, after active frequency separation, updates the parameter mapping relationship in the coupled model, calibrates the frequency drift prediction curve, forms an adaptive vibration risk closed-loop suppression mechanism, and achieves stable control of structural response. Step S006 includes: After the frequency active separation is completed, the thermal load field distribution, aerodynamic disturbance pressure gradient and structural boundary stiffness parameters are obtained. Combined with the strain response value and material elastic modulus change at the intervention point, the input parameters and attribute matrix of the multiphysics coupling model are updated, and a structural parameter mapping table is established. By loading a unified heat flux, power spectral density curve and aerodynamic disturbance model, time-step modal frequency evolution analysis is performed, and the frequency drift trend prediction curve is calibrated. By setting the rate of frequency change, the growth rate of modal energy density, and the peak strain of key nodes as judgment criteria, a closed-loop adaptive control mechanism for random vibration risk is constructed. Intervention data and response results are stored in a response evolution history database for subsequent modal response prediction and intervention strategy optimization.

2. The method for simulating broadband random vibration effects during the space launch phase according to claim 1, characterized in that, Step S001 includes: Before constructing the multiphysics coupling model, we first obtain the physical field boundary input data of thermal load, aerodynamic disturbance and broadband random vibration input; A three-dimensional finite element geometric model covering the propulsion section, mid-section connecting tube section, payload compartment, fairing, and structural bulkhead was established. The material properties in the model were set based on temperature-dependent functions, and the boundary conditions were dynamically adjusted according to the launch phase. Heat flux density, aerodynamic force and random vibration power spectral density are applied to the outer shell of the structure, connection nodes and load-bearing parts respectively; The temperature field, stiffness matrix and modal frequencies of the structure are solved iteratively within each time step to generate response curves of the structure’s natural frequencies as a function of time.

3. The method for simulating broadband random vibration effects during the space launch phase according to claim 1, characterized in that, Step S002 includes: The structure's natural frequency response curve is divided into continuous time windows at equal time intervals. In each time window, the frequencies and modal energy values ​​of multiple modes are extracted to construct a modal energy spectrum. The modal energy spectrum maps of each time window are stitched together in chronological order to form a three-dimensional evolution map, and regions where the frequency trajectories gradually approach each other and the modal energy density continues to increase are identified. When the frequency difference between two modes is less than 3 Hz and the energy increases by more than 50% in each of two consecutive time windows, it is identified as a modal frequency overlap region. Extract the center value of the intersection frequency, the change of the modal frequency difference, and the modal energy transfer characteristics to establish a response prediction benchmark for the unexpected modal coupling region.

4. The method for simulating broadband random vibration effects during the space launch phase according to claim 3, characterized in that, The steps for establishing a response prediction baseline for the unexpected modal coupling region include: For the identified modal frequency overlap region, the energy change rate and direction features are extracted, and the growth rate and decay rate of modal energy are recorded within a continuous time window; To determine whether there is a unidirectional energy transfer characteristic, when the energy of the first mode decreases and the energy of the adjacent mode increases, and the frequency difference between the two approaches zero, it is marked as a mode energy transition behavior; The start and end times of energy transitions, frequency changes, energy mutation amplitudes, and transfer directions are recorded as a set of characteristics. Based on feature groups, a set of response prediction benchmark parameters is constructed, including time window number, intersection frequency center, frequency difference change, energy transfer directionality and amplitude, to identify high-risk regions of modal transitions in the structure.

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