A parameter identification method and device for a dual-time-delay feedback control system for aerodynamic elasticity and an aircraft

Abstract

The application relates to the technical field of power equipment response prediction, in particular to a parameter identification method for a double-time-lag feedback control system facing aerodynamic elasticity and an aircraft. The method comprises the following steps: collecting original observation data; performing filtering processing on the original observation data to obtain filtered observation data; obtaining complete observation data through a kinematic state model; determining an optimal discrete prediction step number and performing local time window division; determining the difference between predicted response data and real observation data in a local prediction window, and updating a target function containing a regularization term according to the difference; and finally outputting identified parameters to adjust a control law to suppress flutter. The application realizes a good balance among parameter identification accuracy, noise resistance robustness and calculation efficiency, and has wide engineering applicability.

Description

Technical Field

[0001] This application relates to the field of power equipment response prediction technology, and in particular to a parameter identification method, device, electronic equipment and aircraft for a dual time-delay feedback control system for aeroelasticity resistance. Background Technology

[0002] In aerospace and high-end equipment manufacturing, the dynamic behavior of complex mechanical structures is influenced by factors such as nonlinear damping, external excitation, and time-delay feedback, often exhibiting complex dynamic phenomena such as multiple steady states, bifurcation, and even chaos. Parameter identification for these nonlinear vibration time-delay systems helps reveal the system's dynamic mechanisms, assess its state, and provide a basis for control design. For controlled vibration systems, time delays are prevalent in sensing, control, and execution processes, and these delays often significantly alter the system's stability, bifurcation characteristics, and response patterns. Especially under chaotic conditions, history dependence and initial trajectory sensitivity are coupled, making it easier for small deviations in long-term responses to accumulate and amplify. Furthermore, actual observation data are often affected by environmental noise and measurement disturbances. Under fine sampling step sizes, sample correlation increases, information redundancy intensifies, and local sensitive information characterizing parameter changes is easily masked by noise. Therefore, for noisy, fine-sampling nonlinear chaotic time-delay systems, it is necessary to propose parameter identification methods that combine stability and noise resistance. Summary of the Invention

[0003] To address the aforementioned problems, embodiments of this application provide a parameter identification method, apparatus, electronic device, and aircraft for a dual time-delay feedback control system oriented towards aeroelasticity resistance, which can solve at least one of the problems in the prior art.

[0004] According to one aspect of the embodiments of this application, a parameter identification method for aeroelastic dual-time-delay feedback control system is proposed. The method includes: acquiring raw observation data for the dual-time-delay feedback control system; performing filtering processing on the raw observation data based on local polynomial regression to obtain filtered observation data; if there are missing parameters in the filtered observation data, constructing a state model based on the missing parameters, and using the state model to complete the missing parameters in the filtered observation data to obtain complete observation data, wherein the missing parameters are one of velocity and acceleration; calculating the average absolute rate of change of the dual-time-delay feedback control system based on the raw observation data, and calculating the average absolute rate of change based on the average absolute rate of change. The optimal discrete prediction step number is determined by the rate, the sampling step size of the original observation data, and a preset signal-to-noise ratio adjustment factor. The product of the optimal discrete prediction step number and the sampling step size of the original observation data is used as a single local prediction window. The complete time window of the original observation data is composed of multiple local prediction windows. For each local prediction window, the response prediction is performed on the real observation data at the beginning of the local prediction window to obtain the predicted response data at the end of the local prediction window. The difference between the predicted response data and the real observation data at the end of the local prediction window is determined, and the preset objective function is updated according to the difference. The objective function is related to the identification parameters and the sensitivity matrix. After each of the local prediction windows has completed updating the objective function, the final objective function is output, and the final identification parameters are extracted from the final objective function. Based on the final identification parameters, the control law of the dual time-delay feedback control system is adjusted to suppress the aeroelastic flutter behavior of the physical object.

[0005] In the above scheme, the dynamic control equation of the dual time-delay feedback control system is: ; in, Generalized displacements characterizing the principal modes of an aircraft wing or structural component. Characterizing response speed, Characterizing the response acceleration, The natural frequency of the structure, The van der Pol type nonlinear damping coefficient is used to characterize the self-excited characteristics of stall flutter. Duffing-type cubic nonlinear stiffness coefficients are used to characterize the large deformation hardening / softening properties of materials. External periodic harmonic excitation, and These respectively constitute displacement feedback and velocity feedback control loops for flutter suppression on aerodynamic surfaces; the preset objective function and the system history state function in the sensitivity matrix explicitly depend on the delayed displacement, delayed velocity, and delayed acceleration.

[0006] In the above scheme, constructing a state model based on the missing parameter includes: if the missing parameter is velocity, then constructing a three-dimensional state model to characterize the displacement-acceleration joint observation mode, the three-dimensional state model including displacement, velocity and acceleration; if the missing parameter is acceleration, then constructing a four-dimensional state model to characterize the displacement-velocity joint observation mode, the four-dimensional state model including displacement, velocity, acceleration and jerk.

[0007] In the above scheme, the missing parameters of the filtered observation data are filled in using the state model to obtain the complete observation data. This includes: acquiring the filtered observation data after filtering based on local multinomial regression; combining the preset transient observation error distribution; using the discrete kinematic evolution equations corresponding to the three-dimensional or four-dimensional state model to perform forward filtering state prediction on the system state; using the observation information of future moments in the entire time series to perform reverse smoothing correction on the result of the forward filtering state prediction to obtain a posterior estimated state sequence that satisfies global kinematic consistency; and converting the posterior estimated state sequence into a continuous time history function through interpolation to extract the missing velocity or acceleration in the filtered observation data, thereby obtaining the complete observation data.

[0008] In the above scheme, updating the preset objective function based on the difference includes: solving for the parameter correction amount through the difference and the sensitivity matrix; superimposing the parameter correction amount onto the current identification parameters to complete the iterative update of the identification parameters until the difference satisfies a preset convergence condition, wherein the preset convergence condition is the minimization of the difference.

[0009] According to another aspect of the embodiments of this application, a parameter identification device for a dual time-delay feedback control system for aeroelasticity is proposed, including an acquisition module, a filtering module, a state reconstruction module, a window adaptive module, and an identification iteration module.

[0010] According to another aspect of the embodiments of this application, an electronic device is proposed, including a memory and a processor, wherein the processor implements the above-described parameter identification method when executing a program stored in the memory.

[0011] According to another aspect of the embodiments of this application, an aircraft is proposed, the aircraft including a sensor assembly, a flight control computer, and aerodynamic control surfaces; the flight control computer, as the aforementioned electronic device, performs the parameter identification method to suppress aeroelastic flutter behavior.

[0012] The beneficial effects of this application are: First, to address the parameter identification problem of aeroelastic dual-time-delay feedback control system, a multi-step response prediction framework based on a local prediction window was established, and the theoretical calculation results were applied to the updating of the aircraft control law and the suppression of physical flutter, forming a complete engineering application closed loop.

[0013] Second, a multi-step response prediction framework was established. Based on the original observation data, a joint optimization framework of "smoothing processing, missing parameter completion, and multi-step local prediction" was introduced to effectively solve the identification problem under conditions of fine sampling, strong noise, and missing data types of observations.

[0014] Compared with existing technologies, this application achieves a better balance between parameter identification accuracy, noise robustness and computational efficiency, and has wide engineering applicability. Attached Figure Description

[0015] Figure 1 A flowchart illustrating the parameter identification method for a dual time-delay feedback control system for aeroelasticity resistance provided in this application embodiment; Figure 2 This application provides an overall logical framework diagram for its embodiments. Figure 3 A flowchart for optimizing response data provided in the embodiments of this application; Figure 4 A flowchart illustrating the state recovery process for auxiliary state reconstruction provided in this application embodiment; Figure 5 A flowchart of multi-step response sensitivity identification provided for embodiments of this application. Detailed Implementation

[0016] To enable those skilled in the art to better understand the solutions of this application, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0017] It should be noted that while some processes described in the specification, claims, and accompanying drawings include multiple steps appearing in a specific order, it should be clearly understood that these steps may not be performed in the order they appear herein, or may be performed in parallel. The step numbers are merely used to distinguish different steps and do not themselves represent any execution order. Furthermore, descriptions such as "first," "second," or "objective" in this document are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. "Multiple" in this document refers to at least two.

[0018] It is worth noting that in the specific embodiments of this application, data related to status response data and dynamic change characteristics are involved. When the above embodiments of this application are applied to specific products or technologies, permission or consent from the target object is required, and the collection, use, and processing of related data must comply with relevant laws, regulations, and standards. For example, when an embodiment of this application needs to obtain data related to status response data and dynamic change characteristics, separate permission or consent from the target object can be obtained through pop-up windows or redirection to a confirmation page. After obtaining separate permission or consent from the target object, the data related to status response data and dynamic change characteristics used to enable the embodiment of this application to operate normally can then be obtained.

[0019] The following provides a detailed description of the specific implementation methods of the embodiments of this application: Please see Figure 1 , Figure 1 This is a flowchart illustrating the parameter identification method for a dual time-delay feedback control system for aeroelasticity resistance provided in this application embodiment. Figure 1 The parameter identification method shown for aeroelastic dual-time-delay feedback control system includes: Step 210: Collect raw observation data for the dual-time-delay feedback control system; Step 220: Perform filtering processing on the original observation data based on local multinomial regression to obtain filtered observation data; Step 230: If there are missing parameters in the filtered observation data, a state model is constructed based on the missing parameters, and the missing parameters are filled in the filtered observation data through the state model to obtain the complete observation data after filling in the missing parameters. The missing parameters are either velocity or acceleration. Step 240: Calculate the average absolute rate of change of the dual time-delay feedback control system based on the original observation data, and determine the optimal discrete prediction step based on the average absolute rate of change, the sampling step size of the original observation data, and the preset signal-to-noise ratio adjustment factor. The product of the optimal discrete prediction step and the sampling step size of the original observation data is used as a single local prediction window. The complete time window of the original observation data is composed of multiple local prediction windows. Step 250: For each of the local prediction windows, perform response prediction on the actual observation data at the start time of the local prediction window to obtain the predicted response data at the end time of the local prediction window, determine the difference between the predicted response data and the actual observation data at the end time of the local prediction window, and update the preset objective function according to the difference. The objective function is related to the identification parameters and the sensitivity matrix. Step 260: After updating the objective function in each of the local prediction windows, output the final objective function and extract the final identification parameters from the final objective function; based on the final identification parameters, adjust the control law of the dual time-delay feedback control system to suppress the aeroelastic flutter behavior of the physical object.

[0020] Specifically, in combination Figure 2 As shown, Figure 2 A diagram illustrating the overall parameter identification process and the data interaction relationships between the three functional modules: First, the raw observation data (or state response data) of the aeroelastic dual-time-delay feedback control system are acquired; then, the data optimization module is used ( Figure 2 Module 1) performs noise reduction, window adjustment, and effective data filtering on the raw observation data to improve the quality of the input data; Further utilize the auxiliary state reconstruction module ( Figure 2 Module 2 in the module restores missing state information, making the system's historical state more complete; finally, the multi-step response sensitivity identification module is used to recover the missing state information. Figure 2 (Module 3) updates the parameters based on the optimized state data and outputs the final identification result.

[0021] The data transmission relationship between the three modules is as follows: raw observation data → data quality improvement → status information completion → parameter sensitivity analysis → parameter identification result output and control law adjustment.

[0022] Specifically, for module one, its internal operational logic is as follows: Figure 3 As shown, combined with Figure 3 The following steps will be explained in detail: Step S101: Obtain the raw observation data of the dual time-delay feedback control system.

[0023] Specifically, the system acquires state response data (i.e., raw observation data) during operation through sensors. This state response data may include dynamic response data such as displacement, velocity, and acceleration. Because the raw observation data is easily affected by environmental disturbances, sensing errors, and high-frequency noise during actual acquisition, it usually contains a certain degree of uncertainty and requires further processing.

[0024] Step S102: Calculate the local dynamic change characteristics based on the observation data.

[0025] Specifically, time-scale analysis is performed on the input state response data to obtain information that reflects the degree of local dynamic changes, and the time window scale in subsequent data processing is determined based on this information.

[0026] Here, to quantify the effective response rate of change per unit time, this embodiment first performs coarse pre-smoothing on the original observation data, and then defines the average absolute rate of change (i.e., dynamic change characteristics). For single-channel observations... Then there is ; in, Sampling time The corresponding coarsely smoothed observation data, Let be the sampling step size. Divide the difference between adjacent time points by the sampling step size to obtain the local rate of change, and average it to obtain the average absolute rate of change.

[0027] Step S103: Determine the adaptive filtering window based on the local change characteristics.

[0028] Specifically, the filtering window is dynamically adjusted based on the differences in the rate of response change within different time regions; this is the adaptive filtering window of this application. In regions with slow response changes, noise suppression is improved; in regions with significant response changes, data feature preservation is enhanced, thereby avoiding the loss of effective dynamic information caused by a fixed window.

[0029] Step S104: Smooth the observation data.

[0030] Specifically, the influence of random noise is reduced by smoothing filtering (specifically, Savitzky-Golay filtering based on local multinomial regression, or SG filtering for short) while preserving the peaks, inflection points, and trends in the response curve, thus providing a stable data foundation for subsequent parameter identification and obtaining filtered observation data.

[0031] Step S105: Filter highly redundant sampling points according to the local prediction time scale to reduce redundant calculations and improve the efficiency of subsequent optimization calculations.

[0032] Through the above steps, optimized historical response data (i.e., the filtered response data described in this application) can be obtained.

[0033] Specifically, for module two, its internal operational logic is as follows: Figure 4 As shown, combined with Figure 4 The following steps will be explained in detail: It should be noted that the RTS (Rauch-Tung-Striebel) smoother is not an identification algorithm, but rather used to complete historical states, ensuring continuous-time integration and providing a complete state for local predictions. The RTS smoother only serves to assist in state recovery and does not participate in parameter updates.

[0034] Combination Figure 2 As shown, this embodiment provides a state recovery method for situations where observation information is incomplete.

[0035] Step S201: Input the preprocessed observation data (i.e., the filtered observation data).

[0036] Step S202: Determine the state recovery mode based on the currently available types of observation variables.

[0037] Specifically, based on the actual measurement conditions, it is determined whether the currently input observation data belongs to the displacement and velocity observation mode (corresponding to the displacement-velocity joint observation mode) or the displacement and acceleration observation mode (corresponding to the displacement-acceleration joint observation mode).

[0038] Step S203: Establish corresponding state models according to different observation modes.

[0039] Specifically, when velocity information is missing, a three-dimensional state model containing displacement, velocity, and acceleration is established; when acceleration information is missing, a higher-order state variable "jerk" is introduced to establish a four-dimensional state model containing displacement, velocity, acceleration, and jerk, in order to improve the ability to describe rapidly changing processes during state recovery.

[0040] Step S204: Obtain the complete state sequence (complete observation data after completion) using the smoothing estimation method.

[0041] Specifically, by combining forward state prediction with backward information correction, the historical state is optimized and estimated so that the recovered state satisfies the global consistency law of system kinematics.

[0042] Step S205: Construct a continuous historical state function based on the recovery results.

[0043] By using interpolation, discrete states are converted into continuous forms, providing complete state information for subsequent calculations of dynamical systems with historical dependencies.

[0044] Specifically, for Module 3, its internal operational logic is as follows: Figure 5 As shown, combined with Figure 5 The following steps will be explained in detail: Step S301: Input the processed historical state data (i.e., the aforementioned complete observation data).

[0045] Step S302: Establish a local prediction window based on historical responses.

[0046] Unlike traditional long-term continuous prediction methods, this embodiment divides the overall time range into multiple local prediction regions and uses local historical states as the starting point for prediction.

[0047] Step S303: Perform response prediction within each local prediction window.

[0048] Step S304: Construct the parameter update objective function and calculate the response sensitivity matrix.

[0049] An optimization objective is established based on the difference between the predicted response and the actual observed response, and the direction of parameter adjustment is determined using response-sensitive information.

[0050] Step S305: Perform parameter iterative update.

[0051] Specifically, the parameters to be identified are continuously adjusted based on the current calculation results (parameter correction amount), and it is determined whether the optimization process meets the convergence condition. If the convergence condition is not met, the historical prediction window is updated and the calculation continues; if the convergence condition is met (residual minimization), the final identification parameters are output, and the dual time-delay feedback control law in the flight control computer is adjusted in real time using the identification parameters to drive the actuators to suppress wing flutter.

[0052] Parameter identification framework based on sensitivity analysis: For dynamical systems with unknown parameters, their discrete time intervals can be collected. (Sampling step size is) h The response data on the measurement data (i.e., the original observation data) is denoted as: ; including superscript The variable represents the measurement data. , They are respectively in The displacement, velocity, and acceleration response observed at all times.

[0053] To improve the stability of parameter identification under chaotic response conditions, this embodiment discretizes the time domain and performs parameter identification within each finite time window. The local integration strategy of resetting the initial value using the observation value is adopted, that is, using the time... The observed data are used as the initial conditions for calculating the local response and sensitivity, thereby obtaining the time... The numerical response. The calculated response obtained from equation (1) is denoted as... ; in, For the predicted response data at each time point, Represents displacement. Represents speed, Represents acceleration. To identify parameters.

[0054] Given a known system structure model, the parameter identification problem can be formulated as a weighted least squares optimization problem, i.e., within the parameter feasible region. The objective function is to find a set of optimal parameters that minimizes the weighted residual between the calculated and measured responses. ; in, For the optimal parameter vector, The objective function is the weighted residual. This is the weight matrix, used to balance the contributions of different observation components to the residuals.

[0055] For nonlinear least squares problems, an iterative strategy is typically used to gradually approximate the optimal solution based on initial parameter values. The core of this approach lies in finding the parameter corrections near the current estimates. ; in, This represents the parameter adjustment for the k-th iteration. At the current estimated value... A first-order Taylor expansion of the response function in the vicinity yields the locally linearized relation. ; in, This represents the response residual under the current parameters. This represents the response sensitivity matrix. The original nonlinear optimization problem can be approximately transformed into a linear least squares problem within a local neighborhood: ; in, The response sensitivity matrix, as shown in equation (9), is composed of column vectors of the first-order partial derivatives of the response vector with respect to each parameter to be identified. This indicates the number of parameters to be identified.

[0056] ; Since local linearization is only effective within the neighborhood of the current estimate, a trust region constraint is further introduced when solving equation (8). ; in, >0 represents the radius of the trust region.

[0057] To evaluate the degree of approximation between the linearized model and the original objective function, a consistency index is introduced.

[0058] ; When the consistency index is satisfied ; Then the current iteration step is considered acceptable.

[0059] Since the sensitivity matrix may be ill-conditioned and the observed data is noisy, the problem corresponding to Equation (10) is often ill-posed; at the same time, the trust region constraint also increases the solution complexity. To improve the solution stability, this embodiment further introduces Tikhonov regularization. ; in, It is the identity matrix. This is a regularization term.

[0060] From equation (13), it can be seen that when As the value gradually increases, the parameter correction amount will be gradually compressed, thus having ; Furthermore, in Nearby residuals First-order expansion ; Substituting equation (15) into the linearized objective function and expanding it, we get: ; Therefore, the consistency index can be further written as ; Combining equation (14), we can obtain ; This indicates that as the regularization parameter increases, the consistency between the linearized model and the original nonlinear objective function gradually improves, thus indicating the existence of a certain critical parameter. , making when The consistency criterion is satisfied at that time. In actual calculations, The initial values ​​can be determined by the L-curve method and adaptively adjusted by introducing a magnification factor. Within this iterative framework, the parameter estimation sequence ultimately satisfies... ; This embodiment proposes a multi-step response sensitivity method based on resetting initial values ​​using local time windows. The basic idea is to decompose the original long-term global evolution process into a series of short-term local evolution processes, and at each time point, reset the initial integral value using observation data, then apply the result within the interval... Local integration and sensitivity calculations are performed within the local time window. Specifically, at the beginning of each local time window... At the local integral, the observed data is used as the initial value; for the historical states required for the time delay term, the corresponding historical function is constructed by interpolating the observed data, and the interval integral is completed accordingly. Numerical integration is used. Since the local predicted response is compared with the observed data only within a finite time scale, this method can effectively reduce the accumulation and amplification of errors during long-term integration, thereby improving the convergence stability and computational accuracy of the parameter identification process.

[0061] From the perspective of residual construction, traditional full-time integration methods match a single long-term predicted trajectory with the entire observation data, while multi-step methods construct predicted responses and residuals separately within multiple local time windows, and then aggregate the local residuals for parameter updates. The former is susceptible to the long-term divergence of chaotic trajectories, while the latter, by resetting the initial values ​​multiple times, keeps the residuals within a finite time scale, thereby improving the reliability of local gradient information.

[0062] Therefore, multi-step prediction is essentially a multi-step integral response construction process based on resetting the initial value within a local time window. Its core lies in suppressing the error accumulation caused by the long-term divergence of chaotic trajectories through local prediction within a finite time scale, and the key to its implementation lies in the reasonable selection of the discrete prediction step size. .when If the value is too large, chaotic error accumulation will occur during long-term integration; when Too small, local time window The dynamic increment within the response will decrease, and the gradient information of the response sensitivity will be easily dominated by random noise.

[0063] To estimate the intensity of high-frequency random noise, this embodiment uses the second-order difference method to process the observation data. Let the observation data... ,in For a genuine response, If the noise is independent and identically distributed Gaussian white noise, then the noise standard deviation is... ; To quantify the effective response rate of change per unit time, this embodiment first performs coarse pre-smoothing on the observed data, and then defines the average absolute rate of change. For single-channel observations... Then there is ; For multi-source observations, a joint average absolute rate of change can be constructed in the normalized observation space, and the equivalent noise intensity can be defined accordingly. To ensure the local time window The effective response increment within the signal is significantly greater than the noise disturbance, so a signal-to-noise ratio adjustment factor is introduced.

[0064] ; in, To balance the preservation of dynamic information and noise suppression, this embodiment uses 16 based on the system's dynamic characteristics. Therefore, the optimal number of discrete prediction steps is... for ; From this, we obtain It can provide a suitable time window scale for subsequent multi-step local prediction and response sensitivity calculation.

[0065] SG filtering and adaptive window design: To obtain more reliable local gradient information and initial values ​​for time-delay integrals, a more robust smoothing process needs to be introduced. This embodiment uses SG filtering to perform polynomial fitting and smoothing of the local data, and adaptively adjusts the filtering window based on changes in the system's local dynamics. Since a fixed window cannot simultaneously achieve both noise reduction in the stable region and feature preservation in the violent oscillation region, this embodiment adjusts the filtering window... Compared with the optimal discrete prediction steps obtained above Perform coupled design.

[0066] To avoid the filtering process weakening the effective high-frequency dynamic information within the prediction window, the theoretical span of the SG filter window should be smaller than the corresponding prediction window. Therefore, a scale reduction factor is introduced. (Considering both noise reduction strength and data fidelity, this embodiment uses empirical values.) The ideal window span is defined as... ; Meanwhile, considering the requirement of minimum sample size for local polynomial fitting, a lower bound constraint needs to be applied to the discrete window. ; To ensure that the SG filter window length satisfies odd-number symmetry, the final adaptive window is written as: ; The adaptive window design can suppress high-frequency noise while preserving dynamic features such as local peaks, inflection points and curvature as much as possible, thus providing a stable observation data basis for subsequent parameter identification.

[0067] To address the computational burden under full-frequency observation conditions, a sparse sampling strategy is introduced. This utilizes the optimal step size of the prediction window. As the sampling index span Only when At that time, the computational load is relatively small and the observational data information is utilized more fully, and the numerical solution is more stable.

[0068] For multi-step prediction across the entire window, the starting points of all time-domain sub-intervals participate: ; The starting point is identified after sparse sampling: ; The objective function then becomes: ; By using a sparse sampling mechanism, the tedious numerical integration calculation is transformed into an efficient information extraction process, and dimensionality reduction processing of the massive sensitivity matrix is ​​achieved.

[0069] To address the missing system state variables in dual-delay vdPD systems under different observation modes, an RTS smoother is introduced to reconstruct the missing data types using kinematic properties, thereby improving the quality of the history function.

[0070] The research object of this embodiment is an excited vdPD oscillator with double time-delay feedback, and its dynamic control equations are as follows: ; To construct the gradient direction of the objective function within a multi-step time window, it is necessary to calculate the system state's response sensitivity to the parameters to be identified. Let the parameter vector be... Then the sensitivity of acceleration to each parameter can be written as: ; Due to time delay parameter The sensitivity term explicitly depends on the delayed acceleration. In cases where observations are incomplete, it is necessary to reconstruct the corresponding missing states stably. This embodiment introduces an auxiliary state reconstruction method based on an RTS smoother. It should be noted that the data participating in RTS smoothing is an observation sequence that has already undergone adaptive SG filtering.

[0071] 1. Three-dimensional RTS smoother under displacement-acceleration observations In the displacement-acceleration joint observation mode, the system lacks velocity state, and therefore adopts... The constructed three-dimensional state vector can satisfy the requirements for historical state recovery. In discrete form, the constant acceleration kinematic model is expressed as follows: ; in, This represents the index of the discrete sampling time, where h is the sampling step size. This represents the random perturbation of the acceleration state during the discrete update process, used to characterize the deviation between the real motion and the ideal constant acceleration model. It is typically assumed that... The noise is zero-mean Gaussian white noise, and the covariance matrix is ​​denoted as . ,but , The specific form is as follows: ; in, The Jerk noise intensity parameters are set. For strongly nonlinear vdPD systems, to prevent the filter from over-smoothing abrupt acceleration peaks and causing amplitude truncation, this embodiment provides a large tolerance for process noise. This allows the filter to maintain the stability of the integral velocity term even when fitting drastic changes in acceleration. In the displacement-velocity joint observation mode, the value after SG filtering can be directly obtained. and In the Kalman filter observation model, the observed data equals the superposition of the true state and the measurement noise. Therefore, the algebraic equations for each observation channel are as follows: ; in, and Represent The transient observation errors introduced by the displacement and acceleration channels are discussed. This embodiment assumes that both errors follow a Gaussian white noise distribution with a mean of zero. and During the simulation data generation phase, the system was injected with noise levels. The controlled global Gaussian white noise sequence can be obtained as follows: ; in, and The noise levels are set for the displacement and acceleration channels respectively (in this embodiment, they are set to 3% and 8% respectively).

[0072] The 3D RTS smoother starts from the initial moment and continuously predicts and corrects forward using current observations to obtain an instantaneous state estimate at each moment. After processing the entire time series, it uses observation information from future moments to correct the estimates of past moments. The resulting velocity is smoother and more stable, conforming to kinematic consistency over the entire time period.

[0073] Since the state model of a three-dimensional RTS assumes that the acceleration does not change much within a sampling interval, as shown in equation (32), this assumption is generally acceptable for low-frequency, weakly nonlinear, or stationary systems, but it is not applicable to the dual-time-delay vdPD system studied in this embodiment. This is because the acceleration of this system is affected not only by the linear inertia and damping terms, but also by the nonlinear stiffness term. External incentives and two time-delayed feedback terms and The combined effect of acceleration and displacement often results in acceleration changing faster than displacement and velocity. If a three-dimensional model is still used, acceleration can only be considered a passively following implicit state, leading to insufficient degrees of freedom in its evolution and problems such as suppressed peak acceleration, phase lag, and excessive smoothing of sharp local changes. In the parameter identification process, acceleration is not only used for the integral solution of the time-delay state equation, but also directly participates in… The construction of the sensitivity term means that this distortion will further affect the accuracy of the sensitivity matrix. Therefore, this embodiment no longer uses a three-dimensional RTS in the displacement-velocity mode, but instead introduces a four-dimensional higher-order RTS smoother.

[0074] 2. Four-dimensional RTS smoother under displacement-velocity observation In the displacement-velocity joint observation mode, if a three-dimensional state model is still used, the acceleration can only be approximated by velocity difference, making it difficult to balance numerical smoothness and historical state accuracy. Therefore, it is necessary to introduce a higher-order state extension. When the system recognizes the use of displacement-velocity combined observation, A four-dimensional state vector is required. The description states that jerk acceleration (Jerk) needs to be introduced at this point. This is considered the highest-order state, thus improving the continuity and smoothness of acceleration recovery. Within a sampling step... Inner displacement at the next moment From the current displacement ,speed acceleration and accelerometer Together, they determine the velocity and acceleration; similarly, the jerk remains approximately constant within this time step, affected only by unmodeled higher-order perturbations. In discrete form, this relationship can be expressed as a system of equations: ; in, This represents the random perturbation of the jerk state during the discrete update process. To characterize higher-order nonlinear dynamics, this embodiment models it as a jerk process driven by white noise, typically assuming... The noise is zero-mean Gaussian white noise, and the covariance matrix is ​​denoted as . Based on the laws of continuous kinematic integrals, The specific form of the derivation is as follows: ; in, The parameters for the set acceleration noise intensity are defined. By extrapolating the unknown white noise excitation to a higher-order Snap level, the acceleration... At the underlying physical logic level, it becomes accelerometer. The absolute integral term. Because integration has the mathematical smoothing property of suppressing abrupt changes, this embodiment provides a high degree of tolerance for process noise. This physical dimension expansion mechanism mandates that the reconstructed acceleration must be a linear path possessing... The analysis of the smooth curve of continuity fundamentally eliminates the high-frequency noise spikes generated by reverse deduction.

[0075] In the displacement-velocity joint observation mode, the values ​​after SG pre-filtering can be directly obtained. and At this point, the algebraic equations relating the various observation channels are as follows: ; in, and Represent The transient observation errors introduced by the displacement and velocity channels at different times are also considered. Similarly, this embodiment assumes that both of these errors follow a Gaussian white noise distribution with a mean of zero. and , and They respectively satisfy: ; in, and The noise levels are set for the displacement and velocity channels respectively (in this embodiment, they are set to 3% and 5% respectively).

[0076] For the strongly nonlinear, strongly time-delay coupled system studied in this embodiment, its acceleration does not change slowly, but often exhibits local sharp increases or decreases. Therefore, only by incorporating the jerk into the state can the filter have sufficient degrees of freedom to describe this higher-order change. The acceleration driven by the jerk maintains the amplitude and phase position better than the acceleration obtained from 3D RTS reconstruction, and is more suitable as... The auxiliary acceleration in the sensitivity section.

[0077] The RTS smoother introduced in this embodiment does not change or replace the dual-time-delay dynamic system to be identified. Instead, it aims to compensate for missing physical states by using simple and stable Newtonian kinematic relationships when observations are incomplete. After obtaining the RTS-smoothed state sequence, this embodiment further transforms it into a continuous-time history function through interpolation. This ensures that the displacement history, velocity history, and delayed acceleration required for local time-delay integration, as well as the delayed acceleration required for sensitivity construction, can all be stably provided by the state trajectory after SG preprocessing and RTS smoothing, providing stable and reliable data for subsequent identification problems.

[0078] In summary, compared with the prior art, this embodiment has at least the following beneficial effects: (1) By adaptively processing the observation data, the adverse effects of noise on the parameter identification process can be reduced, while the retention of effective dynamic response information can be improved.

[0079] (2) By introducing a local prediction and state reconstruction mechanism, the accumulation of errors during long-term prediction can be reduced, and the stability of parameter estimation of complex nonlinear systems can be improved.

[0080] (3) By adopting corresponding state recovery strategies for different observation modes, more continuous and reliable system state information can be obtained when the measurement information is incomplete.

[0081] (4) By deeply binding the pure calculation method with the control law adjustment action, not only is the robustness and accuracy of the parameter identification process of complex dynamic system improved, but also good physical engineering protection is achieved.

[0082] (5) This application not only provides method protection, but also system-level protection for devices, electronic equipment and aircraft, with a wide coverage and high implementation efficiency.

[0083] According to another aspect of the embodiments of this application, an aircraft is also proposed, the aircraft including a sensor assembly, a flight control computer, and aerodynamic control surfaces. The sensor assembly is used to collect raw observation data, and the flight control computer, as the aforementioned electronic device, executes a parameter identification method and adjusts the time-delay feedback control law of the aerodynamic control surfaces in real time according to the identified system dynamic parameters, so as to physically suppress the aeroelastic flutter behavior of the wing.

[0084] The above is a detailed description of the embodiments of this application. However, this application is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of this application. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A parameter identification method for a dual time-delay feedback control system resistant to aeroelasticity, characterized in that, The method includes: Collect raw observation data for the dual-time-delay feedback control system; The original observation data is filtered based on local multinomial regression to obtain filtered observation data. If there are missing parameters in the filtered observation data, a state model is constructed based on the missing parameters, and the missing parameters are filled in the filtered observation data through the state model to obtain the complete observation data. The missing parameter is one of velocity or acceleration. The average absolute rate of change of the dual time-delay feedback control system is calculated based on the original observation data. The optimal discrete prediction step is determined based on the average absolute rate of change, the sampling step size of the original observation data, and the preset signal-to-noise ratio adjustment factor. The product of the optimal discrete prediction step and the sampling step size of the original observation data is used as a single local prediction window. The complete time window of the original observation data is composed of multiple local prediction windows. For each local prediction window, the actual observation data at the start time of the local prediction window is used to predict the response data at the end time of the local prediction window, the difference between the predicted response data and the actual observation data at the end time of the local prediction window is determined, and the preset objective function is updated according to the difference. The objective function is related to the identification parameters and the sensitivity matrix. After each of the local prediction windows has completed updating the objective function, the final objective function is output, and the final identification parameters are extracted from the final objective function. Based on the final identification parameters, the control law of the dual time-delay feedback control system is adjusted to suppress the aeroelastic flutter behavior of the physical object.

2. The parameter identification method for a dual-time-delay feedback control system oriented towards aeroelasticity resistance according to claim 1, characterized in that, The dynamic control equations of the dual time-delay feedback control system are as follows: ； in, Generalized displacements characterizing the principal modes of an aircraft wing or structural component. Characterizing response speed, Characterizing the response acceleration, The natural frequency of the structure, The van der Pol type nonlinear damping coefficient is used to characterize the self-excited characteristics of stall flutter. Duffing-type cubic nonlinear stiffness coefficients are used to characterize the large deformation hardening / softening properties of materials. External periodic harmonic excitation, and These respectively constitute displacement feedback and velocity feedback control loops for flutter suppression on aerodynamic surfaces; the preset objective function and the system history state function in the sensitivity matrix explicitly depend on the delayed displacement, delayed velocity, and delayed acceleration.

3. The parameter identification method for a dual-time-delay feedback control system oriented towards aeroelasticity resistance according to claim 2, characterized in that, A state model is constructed based on the missing parameters, and the filtered observation data is then filled in with the missing parameters to obtain the complete observation data, including: If the missing parameter is velocity, then a three-dimensional state model is constructed to characterize the joint observation mode of displacement-acceleration, and the three-dimensional state model includes displacement, velocity and acceleration. If the missing parameter is acceleration, then a four-dimensional state model is constructed to characterize the displacement-velocity joint observation mode. The four-dimensional state model includes displacement, velocity, acceleration, and jerk. The filtered observation data after filtering based on local multinomial regression is obtained, and combined with the preset transient observation error distribution, the discrete kinematic evolution equations corresponding to the three-dimensional state model or four-dimensional state model are used to perform forward filtering state prediction of the system state. By using the observation information of future moments in the entire time series, the forward filtering state prediction result is reverse smoothed and corrected to obtain the posterior estimated state sequence that satisfies global kinematic consistency. The posterior estimated state sequence is transformed into a continuous-time history function by interpolation, and the output is used to extract the missing velocity or acceleration in the filtered observation data, thus obtaining the complete observation data after completion.

4. The parameter identification method for a dual time-delay feedback control system oriented towards aeroelasticity resistance according to claim 3, characterized in that, Calculate the average absolute rate of change of the dual-time-delay feedback control system based on the original observation data, and determine the optimal number of discrete prediction steps, including: The original observation data is coarsely smoothed to obtain coarsely smoothed observation data; each sampling time of the original observation data is obtained, and the sampling step size is defined as every two adjacent sampling times. For each sampling time, the difference between the coarsely smoothed observation data corresponding to the sampling time and the coarsely smoothed observation data corresponding to the next sampling time is obtained, and the difference is divided by the sampling step size to obtain the local rate of change corresponding to the sampling time. The average absolute rate of change of the dual time-delay feedback control system is obtained by summing the local change rates corresponding to each of the sampling times and then dividing by the number of sampling times. The optimal number of discrete prediction steps is obtained by dividing the product of the signal-to-noise ratio adjustment factor and the preset equivalent noise intensity by the product of the average absolute rate of change and the sampling step size.

5. The parameter identification method for a dual-time-delay feedback control system oriented towards aeroelasticity resistance according to claim 4, characterized in that, The step of performing response prediction on the actual observation data at the start time of the local prediction window to obtain the predicted response data at the end time of the local prediction window includes: The identification parameters of the objective function at the start time of the local prediction window are determined, and the actual observation data at the start time is input into the preset historical state function for sensitivity differentiation to obtain the prediction response data at the end time of the local prediction window.

6. The parameter identification method for a dual time-delay feedback control system oriented towards aeroelasticity resistance according to claim 5, characterized in that, Determining the difference between the predicted response data and the actual observed data at the end of the local prediction window includes: The actual observation data at the end time of the local prediction window is input into a preset sensitivity matrix to obtain displacement sensitivity, velocity sensitivity and acceleration sensitivity. Determine the predicted displacement sensitivity, predicted velocity sensitivity, and predicted acceleration sensitivity in the predicted response data; The displacement sensitivity difference is obtained by subtracting the displacement sensitivity from the predicted displacement sensitivity. The difference between the velocity sensitivity and the predicted velocity sensitivity is obtained; The difference between the acceleration sensitivity and the predicted acceleration sensitivity is obtained as the acceleration sensitivity difference value. The difference is defined as the difference between the displacement sensitivity, the velocity sensitivity, and the acceleration sensitivity.

7. The parameter identification method for a dual time-delay feedback control system oriented towards aeroelasticity resistance according to claim 6, characterized in that, Update the preset objective function based on the differences, including: The parameter correction amount is obtained by using the difference and the sensitivity matrix; The parameter correction amount is superimposed on the current identification parameter to complete the iterative update of the identification parameter until the difference meets the preset convergence condition, which is the minimization of the difference.

8. A parameter identification device for a dual time-delay feedback control system resistant to aeroelasticity, characterized in that, include: The data acquisition module is used to acquire raw observation data for the dual-time-delay feedback control system. The filtering module is used to perform filtering processing on the original observation data based on local multinomial regression to obtain filtered observation data. The state reconstruction module is used to construct a state model based on the missing parameters if there are missing parameters in the filtered observation data, and to fill in the missing parameters in the filtered observation data to obtain the complete observation data after completion. The window adaptive module is used to calculate the average absolute rate of change of the system and determine the optimal number of discrete prediction steps, and to divide the local prediction window; The identification iteration module is used to perform multi-step response prediction within each local prediction window, update the objective function and identification parameters according to the difference between the predicted response and the actual observed data, output the final identification parameters, and adjust the control law of the dual time-delay feedback control system based on the final identification parameters.

9. An electronic device, characterized in that, include: At least one processor; and a memory communicatively connected to the at least one processor; The memory stores a computer program that can be executed by the at least one processor, which is then executed by the at least one processor to enable the at least one processor to perform the parameter identification method for a dual time-delay feedback control system for aeroelasticity as described in any one of claims 1-7.

10. An aircraft, characterized in that, This includes sensor components, flight control computer, and aerodynamic control surfaces; The sensor assembly is used to collect raw observation data, and the flight control computer, as an electronic device as described in claim 9, executes the parameter identification method of the dual time-delay feedback control system for aeroelasticity as described in any one of claims 1-9.

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