Response reconstruction-based folding wing rudder local nonlinear connection rigidity identification method

Abstract

The invention discloses a folding wing rudder local nonlinear connection stiffness identification method based on response reconstruction, which comprises the following steps: S1, establishing a finite element model of a folding wing rudder structure based on physical parameters of a folding wing rudder, correcting the finite element model, and obtaining a nominal linear frequency response function matrix of a structure system through the corrected finite element model; s2, obtaining a known external excitation signal of the folding wing rudder under the excitation effect and a displacement response signal at a measurable position of a structural system; s3, based on the nominal linear frequency response function matrix, a known external excitation signal and a displacement response signal at a measurable position, utilizing a displacement response and restoring force reconstruction algorithm to calculate and obtain a reconstruction displacement response and a reconstruction restoring force at a nonlinear connection position of the folded wing rudder; and S4, constructing a restoring force curve at the nonlinear connection position according to the reconstruction displacement response and the reconstruction restoring force, and identifying according to the restoring force curve to obtain the local nonlinear connection rigidity.

Description

Technical Field

[0001] This invention relates to the field of structural dynamics system identification technology, and in particular to a method for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction. Background Technology

[0002] To adapt to shipborne and airborne platforms, aircraft widely adopt folding wing rudder designs to meet the stringent space constraints during storage, transportation, and launch. However, due to factors such as kinematic pairs, manufacturing and assembly errors, and wear and tear, nonlinear characteristics such as gaps and friction at the folding points are unavoidable. This poses challenges to the high-precision modeling and dynamic characteristic prediction of folding wing rudders, severely impacting the design quality of the aircraft's servo elasticity and aeroelasticity, increasing flight risks in large airspace and wide speed ranges, and even causing structural damage and mission failure. Therefore, to meet the design requirements of folding wing rudders for aircraft, it is urgent to conduct research on nonlinear dynamic parameter identification methods for folding wing rudders with gaps, accurately obtain the nonlinear parameters at the connection points, and then establish a high-precision dynamic model of the folding wing rudder that considers gap nonlinearity, so as to achieve accurate and efficient prediction of the dynamic characteristics of the folding wing rudder.

[0003] However, it should be noted that most existing methods for identifying the stiffness of local nonlinear connections require accurate measurement of the response signal at the nonlinear connection location. However, for a series of nonlinear connection structural systems, such as folding wing rudders, space constraints or complex construction often prevent the deployment of sensors at the nonlinear connection locations, significantly reducing the engineering practicality of existing identification methods. Therefore, to overcome the identification bottleneck caused by the unknown or difficult-to-measure response at the nonlinear connection locations of folding wing rudders, researching a local nonlinear connection stiffness identification method based on response reconstruction is of great significance. This method can help effectively extract the nonlinear characteristics of the structural system when the true response at the nonlinear connection location cannot be obtained, thereby broadening the applicability of nonlinear dynamic parameter identification.

[0004] For those with local nonlinearity n For a structural system with degrees of freedom, based on the concept of output feedback, its time-domain dynamic equations can be expressed as: (1) in, , and These are the mass matrix, damping matrix, and stiffness matrix of the structural system, respectively. , and These are the displacement response, velocity response, and acceleration response in the time domain, respectively. for p The sum of nonlinear terms, where the type of nonlinearity of each component is described by the nonlinear description function. gj ( t )Decide, μ j These are local nonlinear parameters; f ( t ) represents the external stimulus within the time domain; L nj It is a non-linear position vector, typically taking values ​​of -1, 0, and 1.

[0005] Transforming equation (1) to the frequency domain yields: (2) in, , and These are the displacement response, external excitation, and nonlinear describing function in the frequency domain, respectively. Let be the nominal linear frequency response function matrix of the structural system.

[0006] Multiply both sides of equation (2) We can obtain: (3) Now, assuming that the structural system is only subjected to external excitation in the first degree of freedom, then equation (3) can be expressed as: (4) in, arrive The displacement response of the structural system for all degrees of freedom; arrive For all nominal linear frequency response functions of the structural system; arrive For all nonlinear description functions of the structural system; arrive These are all the local nonlinear parameters of the structural system; The external stimulus received for the first degree of freedom; The number of nonlinear degrees of freedom; subscript The location of the first nonlinear connection is the degree of freedom. arrive .

[0007] Equation (4) is the expansion of the entire dynamic equation. Since there are zero elements in the excitation terms on the right side, this equation can be further simplified. After simplification, the structural system's... The displacement response of one degree of freedom can be expressed as: (5) Assume the structural system has a known number of degrees of freedom in terms of displacement response. Then, from equation (5), we can obtain The displacement response for each degree of freedom is as follows: (6) Similarly, the displacement response at the unknown nonlinear connection location can be expressed as: (7) Combining equations (5) to (7), the displacement response at the local nonlinear connection location of the structural system can be reconstructed as follows: (8) Since the nonlinearity of the gap between the folding wing rudder exists within the structural system, namely between the inner and outer wing rudders, directly using the above response reconstruction method would result in a large matrix solution dimension and lead to significant numerical errors during the solution process. Therefore, it is necessary to simplify the reconstruction expression based on the structural characteristics of the folding wing rudder and further develop the response reconstruction method to identify the local nonlinear connection stiffness of the folding wing rudder. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction. Under the premise of knowing the nominal linear frequency response function matrix of the structural system, the displacement response and restoring force at the nonlinear connection location are reconstructed, thereby identifying the local nonlinear connection stiffness.

[0009] The objective of this invention is achieved through the following technical solution: A method for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction includes: S1. Establish a finite element model of the folding wing rudder structure based on the physical parameters of the folding wing rudder and correct it. Obtain the nominal linear frequency response function matrix of the structural system through the corrected finite element model. S2. Obtain the known external excitation signal of the folding wing rudder under excitation and the displacement response signal at the measurable position of the structural system; S3. Based on the nominal linear frequency response function matrix, the known external excitation signal, and the displacement response signal at the measurable position, the reconstructed displacement response and reconstructed restoring force at the nonlinear connection position of the folding wing rudder are calculated using the displacement response and restoring force reconstruction algorithm. S4. Based on the reconstructed displacement response and reconstructed restoring force, construct the restoring force curve at the nonlinear connection location, and identify the local nonlinear connection stiffness based on the restoring force curve.

[0010] Furthermore, in step S1, the density, Young's modulus and Poisson's ratio physical parameters are corrected based on the free modal tests of the inner wing rudder and the outer wing rudder, respectively, so that the finite element model matches the actual folding wing rudder structure, and the corrected finite element model is obtained. Furthermore, in step S3, the calculation of the reconstructed displacement response and reconstructed restoring force at the nonlinear connection position of the folding wing rudder using the displacement response and restoring force reconstruction algorithm specifically includes: establishing a simplified displacement response and restoring force reconstruction expression by utilizing the mechanical characteristic that the restoring forces between the inner and outer wing rudder connection nodes of the folding wing rudder are equal in magnitude and opposite in direction; substituting the nominal linear frequency response function matrix, the known external excitation signal, and the displacement response signal at the measurable position into the simplified displacement response and restoring force reconstruction expression, and solving for the reconstructed displacement response and reconstructed restoring force at the nonlinear connection position in the frequency domain; and performing an inverse Fourier transform on the reconstructed displacement response and reconstructed restoring force to obtain the reconstructed displacement response and reconstructed restoring force in the time domain.

[0011] Furthermore, in step S3, the displacement response and restoring force reconstruction expressions are simplified using the known external excitation signal and the restoring force coordination relationship between the inner and outer wing rudder connection nodes of the folding wing rudder. The simplified displacement response and restoring force reconstruction expressions are as follows: ; ; in, and These are the equivalent known displacement response required after the transformation and dimensionality reduction, and their corresponding equivalent nominal linear frequency response function matrix, respectively. The external stimulus received for the first degree of freedom; and These are the two known displacement responses required after the transformation and dimensionality reduction; arrive , arrive These are the nominal linear frequency response functions corresponding to the two known displacement responses, respectively; , arrive These are the reconstructed displacement response of the connecting node at its location and its corresponding nominal linear frequency response function, respectively. The restoring force on the outer wing rudder node of the upper connecting node; The restoring force is the force on the outer wing rudder node of the lower connecting node.

[0012] Furthermore, the restoring force between each pair of connected nodes exhibits an inverse relationship, that is: ; in, and These are the restoring force matrices on the outer wing rudder connection nodes and the inner wing rudder connection nodes, respectively.

[0013] Furthermore, in step S4, the local nonlinear connection stiffness is the slope of the restoring force curve. The nonlinear dynamic model of the structural system is improved by the local nonlinear connection stiffness, providing technical support for predicting the nonlinear dynamic characteristics of the structural system.

[0014] Furthermore, in step S2, the external excitation signal includes a white noise excitation signal and a sinusoidal excitation signal; the external excitation signal is acquired by a force sensor installed on the folding wing rudder.

[0015] Preferably, the present invention also provides a device for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction, comprising: The finite element model correction unit is used to establish and correct the finite element model of the folding wing rudder structure based on the physical parameters of the folding wing rudder. The nominal linear frequency response function matrix of the structural system is obtained through the corrected finite element model. The external excitation and displacement measurement unit is used to acquire the known external excitation signal of the folding wing rudder under excitation and the displacement response signal at the measurable position of the structural system. The reconstruction unit is used to calculate the reconstructed displacement response and reconstructed restoring force at the nonlinear connection position of the folding wing rudder based on the nominal linear frequency response function matrix, the known external excitation signal and the displacement response signal at the measurable position, using the displacement response and restoring force reconstruction algorithm. The local nonlinear connection stiffness identification unit is used to construct the restoring force curve at the nonlinear connection location based on the reconstructed displacement response and the reconstructed restoring force, and to identify the local nonlinear connection stiffness based on the restoring force curve.

[0016] The specific calculation process within the reconstruction unit includes: Utilizing the mechanical property that the restoring forces between the inner and outer wing rudders of a folding wing are equal in magnitude and opposite in direction, a simplified expression for the displacement response and restoring force reconstruction is established. Substituting the nominal linear frequency response function matrix, the known external excitation signal, and the displacement response signal at the measurable position into the simplified expression for the displacement response and restoring force reconstruction, the reconstructed displacement response and reconstructed restoring force at the nonlinear connection position are solved in the frequency domain. The reconstructed displacement response and reconstructed restoring force are then subjected to an inverse Fourier transform to obtain the reconstructed displacement response and reconstructed restoring force in the time domain.

[0017] Preferably, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the response-reconstruction-based folding wing rudder local nonlinear connection stiffness identification method.

[0018] Preferably, the present invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the response-reconstruction-based method for identifying the local nonlinear connection stiffness of a folding wing rudder.

[0019] Compared with the prior art, the beneficial effects of the technical solution of the present invention are: 1. This invention, based on the nominal linear frequency response function matrix of a structural system, utilizes response data from measurable locations (such as control surfaces where sensors can be easily installed) to reconstruct the displacement response and restoring force of local nonlinear connection locations (such as the interior of a concealed folding mechanism) through an algorithm. This method overcomes the physical bottleneck of folding wing control surfaces, where space constraints and structural complexity prevent the installation of sensors at connection locations, thus hindering the acquisition of response data. It achieves accurate identification of nonlinear parameters under "unknown response" conditions, greatly expanding the applicability of nonlinear dynamic parameter identification. It solves the technical problems of difficult sensor placement and inability to directly measure responses at nonlinear connection locations.

[0020] 2. This invention addresses the specific structural form of folding wing rudders by utilizing the physical property that the restoring forces between the inner and outer wing rudder connection nodes are "equal in magnitude and opposite in direction" to simplify the traditional full-dimensional response reconstruction matrix through dimensionality reduction. Compared to directly using general full-degree-of-freedom reconstruction methods, this invention significantly reduces the dimension of the matrix to be solved (e.g., halving the number of unknowns). This not only reduces the computational load in the matrix inversion process but, more importantly, effectively suppresses numerical truncation errors caused by ill-conditioned matrices or excessively large dimensions, thereby significantly improving the accuracy and robustness of the identification results and increasing computational efficiency.

[0021] 3. This invention is based on the frequency response function and input-output relationship, and is applicable to various excitation types such as white noise and sinusoidal noise. In actual engineering tests, the excitation type can be flexibly selected according to the field conditions, and effective identification can be achieved under any excitation type, reducing the stringent requirements on experimental conditions. It improves the versatility and engineering applicability of the identification method, and is not dependent on a specific excitation type.

[0022] 4. Step S1 uses the modified finite element model to obtain the nominal linear frequency response function matrix as a benchmark. This fully utilizes the existing linear finite element model resources from the folding wing rudder design phase, allowing identification to begin without establishing a complex fully nonlinear model. It can quickly feed the identified local nonlinear connection stiffness back into the linear finite element model, forming a design closed loop. This achieves the acquisition of nonlinear parameters based on a conventional linear model. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating the present invention.

[0024] Figure 2 This is a schematic diagram of the revised finite element model of the folding wing rudder.

[0025] Figure 3 This is a schematic diagram showing the location of the excitation point and the location of the response pickup point when specifically carrying out the displacement response and restoring force reconstruction of the folding wing rudder.

[0026] Figure 4a and Figure 4b These are schematic diagrams of the measured external excitation signals and displacement response signals under white noise excitation and sinusoidal excitation, respectively.

[0027] Figure 5a and Figure 5b These are schematic diagrams showing the reconstruction results of displacement response and restoring force at the nonlinear connection location under white noise excitation and sinusoidal excitation, respectively.

[0028] Figure 6a and Figure 6b These are schematic diagrams showing the results of identifying the local nonlinear connection stiffness at the upper connection position of the folding wing rudder under white noise excitation and sinusoidal excitation, respectively. Detailed Implementation

[0029] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0030] Example 1 This embodiment provides a method for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction, including the following steps: S1. Based on the physical parameters of the folding wing rudder, a finite element model of the folding wing rudder structure is established and corrected. The nominal linear frequency response function matrix of the structural system is obtained through the corrected finite element model. ; S2. Obtain the known external excitation signal of the folding wing rudder under excitation and the displacement response signal at the measurable position of the structural system; S3. Based on the nominal linear frequency response function matrix Given the external excitation signal and the displacement response signal at the measurable position, the reconstructed displacement response and reconstructed restoring force at the nonlinear connection position of the folding wing rudder are calculated using the displacement response and restoring force reconstruction algorithm. S4. Based on the reconstructed displacement response and reconstructed restoring force, construct the restoring force curve at the nonlinear connection location, and identify the local nonlinear connection stiffness based on the restoring force curve.

[0031] Specifically, in step S3: First, as shown in equation (6), when the number of degrees of freedom of the structural system with known displacement response is... That is, the known displacement response is arrive At this point, the restoring force at the nonlinear connection location of the structural system can be expressed by the known displacement response, as follows: (9) in, arrive The restoring force at all nonlinear connection locations; arrive for The nominal linear frequency response function corresponding to a known displacement response; arrive For all nonlinear description functions of the structural system; arrive These are all the local nonlinear parameters of the structural system; The external stimulus received for the first degree of freedom; The number of nonlinear degrees of freedom; subscript The location of the first nonlinear connection is the degree of freedom. arrive .

[0032] Based on equations (8) and (9), the displacement response at the nonlinear connection location can be determined respectively. and resilience Refactor. For the first... With each degree of freedom, the reconstruction result is further transformed from the frequency domain to the time domain, as follows: (10) in, and The first The time-domain reconstructed displacement response and time-domain reconstructed restoring force of each degree of freedom.

[0033] In step S4, it can be based on and Drawing the first The restoring force curves of each degree of freedom are obtained, and then the local nonlinear connection stiffness is obtained from the restoring force curves.

[0034] For example Figure 2 The folding wing shown has unknown information including the excitation point and the nonlinear connection stiffness between the two pairs of connecting nodes. If the derived restoring force and displacement reconstruction expressions are used directly for identification, at least five measurable locations' displacement responses are required. Figure 2 The structural features of the folding wing rudder shown simplify the expressions for response and restoring force reconstruction; specifically as follows: (11) (12) in, and These are the known displacement responses and their corresponding nominal linear frequency response function matrices required for reconstructing the folding wing rudder response and restoring force, respectively. and These are the restoring forces on the outer and inner wing rudder nodes, respectively, at the upper connecting nodes; similarly... and These are the restoring forces on the outer and inner wing rudder nodes of the lower connecting node, respectively.

[0035] As can be deduced, the restoring force between each pair of connected nodes exhibits an inverse relationship, that is: (13) in, and These are the restoring force matrices on the outer wing rudder connection nodes and the inner wing rudder connection nodes, respectively.

[0036] Substituting equation (13) into equations (11) and (12) respectively, we get: (14) (15) In this embodiment, the external excitation applied to the folding wing rudder can be measured by a force sensor mounted on it. Therefore, by substituting the external excitation as a known condition into equations (14) and (15), we can obtain: (16) (17) in, and These are the equivalent known displacement response required after the transformation and dimensionality reduction, and their corresponding equivalent nominal linear frequency response function matrix, respectively.

[0037] As can be seen, compared with equations (11) and (12), the solution dimensions of equations (16) and (17) have been significantly reduced, which is beneficial to reduce numerical errors in the solution process and improve computational efficiency.

[0038] Furthermore, by transforming equations (16) and (17) from the frequency domain to the time domain using equation (10), and plotting the restoring force curves at each nonlinear connection location, the stiffness identification of the local nonlinear connection can be achieved.

[0039] Preferably, a numerical example of a folding wing rudder structure system is used for illustration, along with accompanying drawings. A schematic diagram of the folding wing rudder's excitation and response points is shown below. Figure 3 As shown.

[0040] Let the stiffness of the torsion spring be White noise excitation and sinusoidal excitation are applied at the excitation point respectively, and the data is picked up. Figure 3 The displacement response signals of measuring points 1 and 2 and the force signal of the excitation point, such as Figure 4a and Figure 4b As shown.

[0041] In this process, the aforementioned response reconstruction-based method for identifying the local nonlinear connection stiffness of the folding wing rudder is used to identify the local nonlinear connection stiffness at the upper connection location. The calculation process is as follows: First, a finite element model of the folding wing rudder was created using commercial finite element software. Based on free modal tests, the physical parameters of the finite element model, such as density, Young's modulus, and Poisson's ratio, were corrected to ensure the model accurately reflects the actual folding wing rudder structure. Then, the mass and stiffness matrices of the corrected structural system were extracted, and the nominal linear frequency response function matrix of the structural system was calculated. ; Secondly, respectively as Figure 4a and Figure 4b The measured displacement response signal matrix shown is and external excitation signal Transform to the frequency domain, and in The nominal linear frequency response function matrix corresponding to the measured displacement response is selected. Based on the displacement response reconstruction expression and restoring force reconstruction expression derived in this embodiment, the relative displacement at the upper connection position is obtained. and resilience Finally, transform it to the time domain to obtain and ,like Figure 5a and Figure 5b As shown; Finally, respectively and Using the horizontal and vertical axes as the axes, plot the restoring force curve at the location of the nonlinear connection. The local nonlinear connection stiffness can be obtained by taking the slope of the restoring force curve.

[0042] Based on the above steps Figure 6a and Figure 6b The results of local nonlinear connection stiffness identification at the upper connection position of the folding wing rudder under white noise excitation and sinusoidal excitation are presented. The blue scatter points represent the reconstructed values ​​of the restoring force curve, and the red dashed line represents the theoretical values ​​of the restoring force curve. (Summary) Figures 5a to 6b It can be seen that the method of the present invention can accurately reconstruct the displacement response and restoring force at the nonlinear connection position of the folding wing rudder structure system, and then realize the accurate identification of the local nonlinear connection stiffness by drawing the restoring force curve.

[0043] In summary, addressing the urgent need for accurate understanding of local nonlinear connection stiffness characteristics in the design process of folding wing rudders, this invention proposes a response reconstruction-based method for identifying the local nonlinear connection stiffness of folding wing rudders. This method is applicable to the identification of local nonlinear connection stiffness in folding wing rudder structural systems. Numerical case studies of folding wing rudder structural systems demonstrate that the response reconstruction-based method provided by this invention can reconstruct the displacement response and restoring force at the nonlinear connection location based on the nominal linear frequency response function matrix of the structural system, thereby identifying the local nonlinear connection stiffness. This method exhibits good accuracy and robustness, providing a new approach for identifying the local nonlinear connection stiffness of complex structural systems.

[0044] Example 2 Based on the same inventive concept, this application also provides a response-reconstruction-based folding wing rudder local nonlinear connection stiffness identification device, which can be used to implement the method described in the above embodiments, as described in the following embodiments. Since the principle of the response-reconstruction-based folding wing rudder local nonlinear connection stiffness identification device is similar to the response-reconstruction-based folding wing rudder local nonlinear connection stiffness identification method, the implementation of this device can refer to the aforementioned method implementation, and repeated details will not be elaborated further. As used below, the terms "unit" or "module" can refer to a combination of software and / or hardware that implements a predetermined function. Although the system described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0045] Embodiments of the present invention provide a specific implementation of an identification device capable of implementing a response reconstruction-based method for identifying the local nonlinear connection stiffness of a folding wing rudder, specifically including the following: A response reconstruction-based local nonlinear connection stiffness identification device for folding wing rudders includes: The finite element model correction unit is used to establish and correct the finite element model of the folding wing rudder structure based on the physical parameters of the folding wing rudder. The nominal linear frequency response function matrix of the structural system is obtained through the corrected finite element model. The external excitation and displacement measurement unit is used to acquire the known external excitation signal of the folding wing rudder under excitation and the displacement response signal at the measurable position of the structural system. The reconstruction unit is used to calculate the reconstructed displacement response and reconstructed restoring force at the nonlinear connection position of the folding wing rudder based on the nominal linear frequency response function matrix, the known external excitation signal and the displacement response signal at the measurable position, using the displacement response and restoring force reconstruction algorithm. The local nonlinear connection stiffness identification unit is used to construct the restoring force curve at the nonlinear connection location based on the reconstructed displacement response and the reconstructed restoring force, and to identify the local nonlinear connection stiffness based on the restoring force curve.

[0046] The specific calculation process within the reconstructed unit includes: utilizing the mechanical property that the restoring forces between the inner and outer wing rudder connection nodes of the folding wing are equal in magnitude and opposite in direction, establishing simplified displacement response and restoring force reconstruction expressions; substituting the nominal linear frequency response function matrix, the known external excitation signal, and the displacement response signal at the measurable position into the simplified displacement response and restoring force reconstruction expressions, and solving for the reconstructed displacement response and reconstructed restoring force at the nonlinear connection position in the frequency domain; and performing an inverse Fourier transform on the reconstructed displacement response and reconstructed restoring force to obtain the reconstructed displacement response and reconstructed restoring force in the time domain.

[0047] Preferably, embodiments of this application also provide a specific implementation of an electronic device capable of implementing all steps in the response reconstruction-based folding wing rudder local nonlinear connection stiffness identification method described in the above embodiments. The electronic device specifically includes the following: Processor, memory, communications interface, and bus; The processor, memory, and communication interface communicate with each other via a bus; the communication interface is used to realize information transmission between server-side devices, metering devices, and user-side devices.

[0048] The processor is used to call the computer program in memory. When the processor executes the computer program, it implements all the steps in the response reconstruction-based method for identifying the local nonlinear connection stiffness of folding wing rudder in the above embodiments.

[0049] Embodiments of this application also provide a computer-readable storage medium capable of implementing all steps of the response-reconstruction-based folding wing rudder local nonlinear connection stiffness identification method in the above embodiments. The computer-readable storage medium stores a computer program that, when executed by a processor, implements all steps of the response-reconstruction-based folding wing rudder local nonlinear connection stiffness identification method in the above embodiments.

[0050] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. In particular, hardware + program embodiments are relatively simple in description because they are fundamentally similar to method embodiments; relevant parts can be referred to the descriptions in the method embodiments.

[0051] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0052] While this application provides method operation steps as shown in the embodiments or flowcharts, more or fewer operation steps may be included based on conventional or non-inventive labor. The order of steps listed in the embodiments is merely one possible execution order among many and does not represent the only execution order. In actual device or client product execution, the method can be executed in the order shown in the embodiments or drawings or in parallel (e.g., in a parallel processor or multi-threaded processing environment).

[0053] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0054] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0055] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0056] This invention is not limited to the embodiments described above. The above description of specific embodiments is intended to illustrate and explain the technical solutions of this invention. The specific embodiments described above are merely illustrative and not restrictive. Without departing from the spirit and scope of the claims, those skilled in the art can make many specific modifications based on the teachings of this invention, and these modifications all fall within the scope of protection of this invention.

Claims

1. A method for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction, characterized in that, include: S1. Establish a finite element model of the folding wing rudder structure based on the physical parameters of the folding wing rudder and correct it. Obtain the nominal linear frequency response function matrix of the structural system through the corrected finite element model. S2. Obtain the known external excitation signal of the folding wing rudder under excitation and the displacement response signal at the measurable position of the structural system; S3. Based on the nominal linear frequency response function matrix, the known external excitation signal, and the displacement response signal at the measurable position, the reconstructed displacement response and reconstructed restoring force at the nonlinear connection position of the folding wing rudder are calculated using the displacement response and restoring force reconstruction algorithm. S4. Based on the reconstructed displacement response and reconstructed restoring force, construct the restoring force curve at the nonlinear connection location, and identify the local nonlinear connection stiffness based on the restoring force curve.

2. The method for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction as described in claim 1, characterized in that, In step S1, the density, Young's modulus, and Poisson's ratio physical parameters of the inner and outer wing rudders are corrected based on free modal tests, respectively, so that the finite element model matches the actual folding wing rudder structure, thus obtaining the corrected finite element model.

3. The method for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction as described in claim 1, characterized in that, In step S3, the calculation of the reconstructed displacement response and reconstructed restoring force at the nonlinear connection position of the folding wing rudder using the displacement response and restoring force reconstruction algorithm specifically includes: establishing a simplified displacement response and restoring force reconstruction expression by utilizing the mechanical characteristic that the restoring forces between the inner and outer wing rudder connection nodes of the folding wing rudder are equal in magnitude and opposite in direction; substituting the nominal linear frequency response function matrix, the known external excitation signal, and the displacement response signal at the measurable position into the simplified displacement response and restoring force reconstruction expression, and solving for the reconstructed displacement response and reconstructed restoring force at the nonlinear connection position in the frequency domain; and performing an inverse Fourier transform on the reconstructed displacement response and reconstructed restoring force to obtain the reconstructed displacement response and reconstructed restoring force in the time domain.

4. The method for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction according to claim 3, characterized in that, In step S3, the displacement response and restoring force reconstruction expressions are simplified using the known external excitation signal and the restoring force coordination relationship between the inner and outer wing rudder connection nodes of the folding wing rudder. The simplified displacement response and restoring force reconstruction expressions are as follows: ； ； in, and These are the equivalent known displacement response required after the transformation and dimensionality reduction, and their corresponding equivalent nominal linear frequency response function matrix, respectively. The external stimulus received for the first degree of freedom; and These are the two known displacement responses required after the transformation and dimensionality reduction; arrive , arrive These are the nominal linear frequency response functions corresponding to the two known displacement responses, respectively; , arrive These are the reconstructed displacement response of the connecting node at its location and its corresponding nominal linear frequency response function, respectively. The restoring force on the outer wing rudder node of the upper connecting node; The restoring force is the force on the outer wing rudder node of the lower connecting node.

5. The method for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction according to claim 1, characterized in that, The restoring force between each pair of connected nodes exhibits an inverse relationship, that is: ； in, and These are the restoring force matrices on the outer wing rudder connection nodes and the inner wing rudder connection nodes, respectively.

6. The method for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction according to claim 1, characterized in that, In step S4, the local nonlinear connection stiffness is the slope of the restoring force curve. The nonlinear dynamic model of the structural system is improved by the local nonlinear connection stiffness, which provides technical support for predicting the nonlinear dynamic characteristics of the structural system.

7. The method for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction according to claim 1, characterized in that, In step S2, the external excitation signal includes a white noise excitation signal and a sinusoidal excitation signal; the external excitation signal is acquired by a force sensor installed on the folding wing rudder.

8. A device for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction, characterized in that, include: The finite element model correction unit is used to establish and correct the finite element model of the folding wing rudder structure based on the physical parameters of the folding wing rudder. The nominal linear frequency response function matrix of the structural system is obtained through the corrected finite element model. The external excitation and displacement measurement unit is used to acquire the known external excitation signal of the folding wing rudder under excitation and the displacement response signal at the measurable position of the structural system. The reconstruction unit is used to calculate the reconstructed displacement response and reconstructed restoring force at the nonlinear connection position of the folding wing rudder based on the nominal linear frequency response function matrix, the known external excitation signal and the displacement response signal at the measurable position, using the displacement response and restoring force reconstruction algorithm. A local nonlinear connection stiffness identification unit is used to construct a restoring force curve at the nonlinear connection location based on the reconstructed displacement response and the reconstructed restoring force, and to identify the local nonlinear connection stiffness based on the restoring force curve. The specific calculation process within the reconstruction unit includes: By utilizing the mechanical property that the restoring forces between the inner and outer wing rudders of a folding wing are equal in magnitude and opposite in direction, a simplified expression for displacement response and restoring force reconstruction is established. Substitute the nominal linear frequency response function matrix, the known external excitation signal, and the displacement response signal at the measurable position into the simplified displacement response and restoring force reconstruction expression, and solve in the frequency domain to obtain the reconstructed displacement response and reconstructed restoring force at the nonlinear connection position; perform an inverse Fourier transform on the reconstructed displacement response and reconstructed restoring force to obtain the reconstructed displacement response and reconstructed restoring force in the time domain.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method for identifying the local nonlinear connection stiffness of a folding wing rudder based on response reconstruction as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the response reconstruction-based method for identifying the local nonlinear connection stiffness of a folding wing rudder as described in any one of claims 1 to 7.

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