Distributed equivalent concentrated load identification method based on improvement

Abstract

The invention provides a distributed equivalent concentrated load identification method based on improvement, aiming at the problem that a transfer matrix at the inherent frequency of a structure is seriously ill-conditioned by a direct inversion method, a coefficient matrix is introduced to improve the condition number of the ill-conditioned matrix, and the load identification precision is improved; the frequency response function near the inherent frequency is corrected, and the average value of the frequency response function near the inherent frequency is used for replacing the frequency response function at the inherent frequency, so that the peak value of the identification load at the inherent frequency can be effectively reduced, and the stability and the calculation precision of the system are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerospace payload identification, and particularly relates to an improved distributed equivalent concentrated load identification method. Background Technique

[0002] The problem of dynamic load identification belongs to the second type of inverse problem in dynamics. According to whether the uncertainty of loads or system parameters is considered, it is mainly divided into two categories: deterministic dynamic load identification methods and stochastic dynamic load identification methods. Deterministic dynamic load identification methods generally include two types of identification methods: frequency domain methods and time domain methods. The frequency domain method is based on the structural dynamics equation in the discrete physical space or modal space, and the dynamic load is identified according to the relationship between the frequency response function of the system and the response spectrum in the frequency domain. The time domain method is a method based on the impulse response function. This method constructs the impulse response function by using the method of the forward problem of dynamics to establish the transfer relationship of the impulse response function, and performs an inverse operation on the transfer relationship, so as to use the measured response to inversely deduce the actual load.

[0003] The identification problem of deterministic dynamic loads has developed relatively maturely, and the research and development of identification methods for dynamic loads with stochastic characteristics are relatively imperfect. For loads with stochastic characteristics on aerospace engineering structures (such as gust loads, transonic fluctuating pressures, etc.), the significance of identifying their statistical characteristics is higher than that of identifying individual load samples. Therefore, the power spectral density of the load is generally identified by using the structural stochastic response power spectral density. More typical stochastic dynamic load identification methods include the direct inversion method of the frequency response matrix and the inverse virtual excitation method. These two methods provide theoretical support for stochastic dynamic load identification to a great extent. However, in an actual system, the frequency response matrix often has a large condition number at the natural frequency, and its numerical instability is more significant during the inversion process. Tiny measurement errors or noises will be amplified, resulting in a large deviation in the identification result of the excitation spectrum and being unable to accurately reflect the true excitation spectrum. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide an improved distributed equivalent concentrated load identification method. The solution of the present invention can solve the problems existing in the above prior art.

[0005] The technical solution of the present invention:

[0006] An improved distributed equivalent concentrated load identification method includes the following steps:

[0007] Step 1, establish a finite element model of the structure according to the geometric model and material properties of the typical structure of the aircraft, equivalent the distributed load it bears to P concentrated loads, and through finite element analysis, calculate the load and response transfer relationship matrix;

[0008] Step 2: Construct the response power spectral density matrix based on the response data of the typical structure of the aircraft obtained from actual flight measurements.

[0009] Based on the virtual excitation method, improve the condition number of the frequency response matrix according to the response power spectral density matrix and the introduced coefficient matrix, obtain the relationship between the virtual excitation and the virtual response, and then obtain the load power spectral density matrix of theoretical calculation.

[0010] Step 3: For the typical structure of the aircraft, conduct modal analysis to obtain the natural frequencies and frequency response function values of the typical structure of the aircraft. If the condition number of the frequency response matrix at the natural frequency ω i exceeds the permitted threshold, then select M frequency response function values H(ω i ) within the range of fluctuating by 5% above and below ω 1 ), H(ω 2 ), … H(ω M ), and calculate the average value, which is used as the corrected frequency response function to replace the frequency response function at the natural frequency ω i . Substitute the corrected load and response transfer relationship matrix into Step 1 to correct the obtained load and response transfer relationship matrix.

[0011] Step 4: Compare the load obtained from the load power spectral density matrix of theoretical calculation with the P concentrated loads equivalent to the distributed load. If the difference is within the permitted range, the load of theoretical calculation is valid.

[0012] Step 5: According to the response power spectral density matrix of the typical structure of the aircraft measured actually and the theoretical solution method in Step 2, obtain the load power spectral density matrix of the typical structure of the aircraft.

[0013] Further, the calculation of the load and response transfer relationship H(ω) is as follows:

[0014]

[0015] where ω is the analysis frequency, and H ij (ω) is the frequency response function between the i-th response and the j-th excitation, q is the total number of responses, and p ≤ q.

[0016] Further, the method for obtaining the power spectral density matrix of the excitation based on the virtual excitation method includes the following steps:

[0017] S1.1 Decompose the response power spectral density matrix Q yy (ω) of the typical structure of the aircraft as follows:

[0018]

[0019] where λ j and φ jThey are the j-th order eigenvalue and eigenvector of the Hermite matrix respectively, and m is the rank of S yy (ω), is the conjugate transpose of φ j ;

[0020] S1.2 Construct the virtual response y j and the virtual excitation f j as follows:

[0021]

[0022] f j = H(ω) + y j

[0023] where i is the imaginary unit and H(ω) + represents the generalized inverse of H(ω).

[0024] S1.3 Introduce the matrix Z to obtain the improved virtual excitation as

[0025] f j = (ZH(ω)) + Zy j

[0026] where Z satisfies

[0027] Zy j = ZH(ω)f j ,

[0028] the solutions of the two systems of equations are consistent, where cond(ZH(ω)) represents the condition number of ZH(ω).

[0029] S1.4 The expression of the load power spectral density matrix P yy (ω) is:

[0030]

[0031] Advantages of the present invention compared with the prior art:

[0032] (1) Aiming at the problem that the transfer matrix is seriously ill-conditioned at the structural natural frequency in the direct inversion method, the present invention introduces a coefficient matrix to improve the condition number of the ill-conditioned matrix, thereby improving the accuracy of load identification;

[0033] (2) By correcting the frequency response function near the natural frequency and using the mean value of the frequency response function near the natural frequency to replace the frequency response function at the natural frequency, the present invention can effectively reduce the peak value of the identified load at the natural frequency, improving the stability and calculation accuracy of the system. Brief Description of the Drawings

[0034] The accompanying drawings included are used to provide a further understanding of the embodiments of the present invention, which form a part of the specification, illustrate the embodiments of the present invention, and together with the written description, explain the principles of the present invention. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0035] Figure 1 It shows a schematic diagram of the steps of an improved distributed equivalent concentrated load identification method provided according to an embodiment of the present invention;

[0036] Figure 2 It shows a comparison schematic diagram of the self-power spectral density of the identified load provided according to an embodiment of the present invention. Detailed implementation manners

[0037] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and in no way limits the present invention and its application or use. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0038] It should be noted that the terms used herein are only for describing the specific implementation manners and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless otherwise clearly specified in the context, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0039] Unless otherwise specifically stated, the relative arrangements of components and steps, numerical expressions, and numerical values set forth in these embodiments do not limit the scope of the present invention. At the same time, it should be understood that for the sake of convenience in description, the dimensions of the various parts shown in the drawings are not drawn in actual proportional relationships. Technologies, methods, and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, the said technologies, methods, and devices should be regarded as part of the specification. In all the examples shown and discussed here, any specific values should be construed as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values. It should be noted that similar reference numerals and letters denote similar items in the following drawings, and thus, once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

[0040] As Figure 1 shown, according to an embodiment of the present invention, a method for identifying an improved distributed equivalent concentrated load is provided, including the following steps:

[0041] Step 1: Establish a finite element model of the structure according to the geometric model and material properties of the typical structure of the aircraft, equivalent the distributed load it bears to P concentrated loads, and through finite element analysis, calculate the load and response transfer relationship matrix;

[0042] Step 2: Construct the response power spectral density matrix according to the response data of the typical structure of the aircraft obtained from flight measurements;

[0043] Based on the virtual excitation method, improve the condition number of the frequency response matrix according to the response power spectral density matrix and the introduced coefficient matrix, obtain the relationship between the virtual excitation and the virtual response, and then obtain the load power spectral density matrix calculated theoretically; through this step, aiming at the problem that the transfer matrix is severely ill-conditioned at the natural frequencies of the structure in the direct inversion method, the coefficient matrix is introduced to improve the condition number of the ill-conditioned matrix, and the accuracy of load identification is improved;

[0044] Step 3: For the typical structure of the aircraft, perform modal analysis to obtain the natural frequencies and frequency response function values of the typical structure of the aircraft. If the condition number value of the frequency response matrix at the natural frequency ω i exceeds the permitted threshold, then select M frequency response function values H(ω i ) within the range of fluctuating 5% above and below ω 1 ), H(ω 2 ),... H(ω M ), and calculate the average value, which is used as the corrected frequency response function to replace the natural frequency ω iFor the frequency response function, substitute the corrected load and response transfer relationship matrix into Step 1 to correct the obtained load and response transfer relationship matrix; by correcting the frequency response function near the natural frequency and using the mean value of the frequency response function near the natural frequency to replace the frequency response function at the natural frequency, the peak value of the identified load at the natural frequency can be effectively reduced, and the stability and calculation accuracy of the system can be improved;

[0045] Step 4: Compare the load power spectral density matrix obtained by theoretical calculation with the P concentrated loads equivalent to the load and distributed load. If the difference is within the allowable range, the load obtained by theoretical calculation is valid;

[0046] Step 5: According to the response power spectral density matrix of the typical structure of the aircraft measured in actuality and the theoretical solution method in Step 2, obtain the load power spectral density matrix of the typical structure of the aircraft.

[0047] Further, in one embodiment, the calculation of the load and response transfer relationship H(ω) is as follows:

[0048]

[0049] where ω is the analysis frequency, and H ij (ω) is the frequency response function between the i-th response and the j-th excitation, q is the total number of responses, and p ≤ q.

[0050] Further, in one embodiment, the method for obtaining the power spectral density matrix of the excitation based on the virtual excitation method includes the following steps:

[0051] S2.1 Decompose the response power spectral density matrix Q yy (ω) of the typical structure of the aircraft as follows:

[0052]

[0053] where λ j and φ j are the j-th eigenvalue and eigenvector of this Hermite matrix respectively, m is the rank of S yy (ω), is the conjugate transpose of φ j ;

[0054] S2.2 Construct the virtual response y j and the virtual excitation f j as follows:

[0055]

[0056] f j = H(ω) + y j

[0057] where \(i\) is the imaginary unit, and \(H(\omega)\) + represents the generalized inverse of \(H(\omega)\).

[0058] S2.3 Introduce matrix \(Z\) to obtain the improved virtual excitation as

[0059] \(f\) j \(=(ZH(\omega))\) + \(Zy\) j

[0060] where \(Z\) satisfies

[0061] \(Zy\) j \(=ZH(\omega)f\) j ,

[0062] the solutions of the two systems of equations are consistent, where \(cond(ZH(\omega))\) represents the condition number of \(ZH(\omega)\).

[0063] S2.4 The expression of the load power spectral density matrix \(P\) yy \((\omega)\) is:

[0064]

[0065] To have a further understanding of an improved distributed equivalent concentrated load identification method provided by the present invention, the following will be described in detail with specific examples and drawings.

[0066] This patent discloses an improved distributed equivalent concentrated load identification method. Aiming at the problem that the transfer matrix is severely ill-conditioned at the natural frequencies of the structure in the direct inversion method, a method for improving the condition number is proposed, and the specific steps are as follows:

[0067] Step 1: Construct the relationship between \(q\) responses and loads considering the action of \(p\) distributed equivalent concentrated loads (\(p\leq q\)).

[0068] First, establish a finite element model of the structure according to the geometric model and material properties of the research object, equivalent the distributed load it bears to \(p\) concentrated loads, and calculate the load-response transfer relationship \(H(\omega)\) through finite element analysis.

[0069]

[0070] where \(\omega\) is the analysis frequency, and \(H\) ij \((\omega)\) is the frequency response function between the \(i\)-th response and the \(j\)-th excitation.

[0071] Step 2: Improve the condition number of the ill-conditioned matrix by introducing a diagonal matrix, and then invert the power spectral density of the true load.

[0072] Construct the power spectral density matrix of the response data based on the measured sensor data during flight (such as acceleration, strain, etc.).

[0073]

[0074] where Q PSDij (ω) is the cross-power spectral density of the i-th and j-th responses, and Q PSDii (ω) is the auto-power spectral density of the i-th response.

[0075] Since the power spectral density matrix is a Hermitian matrix, it can be decomposed as follows:

[0076]

[0077] where λ j and φ j are the j-th eigenvalue and eigenvector of this Hermitian matrix respectively, m is the rank of S yy (ω), is the conjugate transpose of φ j .

[0078] According to the virtual excitation method, it can be seen that the virtual response vector is caused by the virtual excitation vector f j , and then the virtual response y j and the virtual excitation f j are constructed based on each order of eigenpairs as follows:

[0079]

[0080] f j =H(ω) + y j

[0081] Since linear equations often face the problems of ill-conditioning and instability, here we introduce a matrix Z that satisfies

[0082] Zy j =ZH(ω)f j

[0083] cond(ZH(ω))<cond(H(ω))

[0084] On the premise that the solutions of the two equations before and after processing are kept consistent, the condition number of the transfer function at some frequencies is reduced. The improved virtual excitation after introducing the matrix is

[0085] f j =(ZH(ω)) + Zy j

[0086] Therefore, the load power spectral density matrix Pyy ($\omega$) can be expressed by virtual excitation as

[0087]

[0088] Step 3: According to the modal frequency, the peak error at the natural frequency

[0089] First, perform modal analysis on the research object to determine its natural frequencies ($\omega$ 1 , $\omega$ 2 , $\omega$ 3 , … $\omega$ n ). Since at the natural frequencies, the condition number of the frequency response function is relatively large, there is often a phenomenon of excessive peaks. To improve the stability and accuracy of the system, it is necessary to correct the frequency response function near the natural frequencies.

[0090] The specific approach is as follows: Select M frequency response function values H($\omega$ i ) within the range of fluctuating by 5% above and below the natural frequency $\omega$ 1 ), H($\omega$ 2 ), … H($\omega$ M ), and calculate the average value. The corrected frequency response function is:

[0091]

[0092] By using the average value of the frequency response functions near the natural frequency to replace the frequency response function at the natural frequency, it is possible to effectively reduce the peak value of the frequency response function at the natural frequency and improve the stability and calculation accuracy of the system.

[0093] In a specific embodiment, the calculation results using the existing technology and the present invention are as Figure 2 shown, indicating that the calculation results of the present invention are more accurate and have higher precision.

[0094] In summary, a method for identifying an improved distributed equivalent concentrated load provided by the present invention has at least the following advantages compared with the existing technology:

[0095] (1) The present invention addresses the problem of severe ill-conditioning of the transfer matrix at the structural natural frequencies in the direct inversion method, introduces a coefficient matrix to improve the condition number of the ill-conditioned matrix, and improves the accuracy of load calculation;

[0096] (2) The present invention corrects the frequency response function near the natural frequency with excessive peaks, uses the average value of the frequency response functions near the natural frequency to replace the frequency response function at the natural frequency, and can effectively reduce the peak value of the frequency response function at the natural frequency, improving the stability and calculation accuracy of the system.

[0097] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, various modifications and variations can be made to the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for identifying distributed equivalent concentrated loads based on an improvement, characterized in that: The following steps are involved: Step 1: Establish a finite element model of the structure based on the geometric model and material properties of the typical structure of the aircraft, and equate the distributed load it bears to P concentrated loads. After finite element analysis, calculate the load and response transfer relationship matrix; Step 2: construct the response power spectrum density matrix of the typical structure of the aircraft based on the response data obtained from actual flight measurements; Based on the virtual excitation method, the frequency response matrix condition number is improved according to the response power spectrum density matrix and the introduced coefficient matrix, the relationship between virtual excitation and virtual response is obtained, and then the load power spectrum density matrix calculated theoretically is obtained; Step 3: Perform modal analysis on the typical structure of the aircraft to obtain the natural frequency and frequency response function value of the typical structure of the aircraft. If the natural frequency ω i If the conditional value of the frequency response matrix at exceeds the permitted threshold, then select ω i The M frequency response function values ​​H(ω1), H(ω2), …H(ω M ), and calculate the average value as the modified frequency response function instead of the natural frequency ω i The frequency response function of the load and response transfer relationship matrix is ​​brought into the modified load and response transfer relationship matrix in step 1 to modify the obtained load and response transfer relationship matrix; Step 4: Compare the load obtained from the load power spectrum density matrix calculated theoretically with the P concentrated loads equivalent to the distributed loads. If the difference is within the allowable range, the load calculated theoretically is valid. Step five, according to the response power spectrum density matrix of the typical structure of the aircraft measured actually and the theoretical solution method of step two, the load power spectrum density matrix of the typical structure of the aircraft is obtained.

2. The improved distributed equivalent concentrated load identification method according to claim 1 is characterized in that: The calculation load and response transfer relationship H(ω) is: Where ω is the analysis frequency, H ij (ω) is the frequency response function between the ith response and the jth excitation, q is the total number of responses, and p≤q.

3. The improved distributed equivalent concentrated load identification method according to claim 2 is characterized in that: Based on the virtual excitation method, the method for obtaining the power spectrum density matrix of the excitation includes the following steps: S1.1 The response power spectrum density matrix Q of the typical structure of the aircraft yy (ω) is decomposed as follows: Among them, λ i and φ j are the jth eigenvalue and eigenvector of the Hermite matrix, m is S yy The rank of (ω), Yes j The conjugate transpose of ; S1.2 Construct virtual response y according to the characteristic pairs of each order j and virtual excitation f j as follows: f j =H(ω) + y j Where i is the imaginary unit, H(ω) + represents the generalized inverse of H(ω); S1.3 introduces the matrix Z and obtains the improved virtual excitation as f j =(ZH(ω)) + Zy j Among them, Z satisfies Zy j =ZH(ω)f j , The solutions of the two equations are consistent, where cond(ZH(ω)) represents the ZH(ω) condition number; S1.4 theoretically calculated load power spectrum density matrix P yy The expression of (ω) is:

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