CN102982196B

CN102982196B - Time frequency domain time varying structure modal parameter identification method based on time varying common demominator model

Info

Publication number: CN102982196B
Application number: CN201210424594.XA
Authority: CN
Inventors: 周思达; 刘莉; 董威利; 杨武; 马志赛; 贺媛媛
Original assignee: Beijing Institute of Technology BIT
Current assignee: Beijing Institute of Technology BIT
Priority date: 2012-10-30
Filing date: 2012-10-30
Publication date: 2015-02-25
Anticipated expiration: 2032-10-30
Also published as: CN102982196A

Abstract

The invention relates to a time frequency domain time varying structure modal parameter identification method based on a time varying common demominator model and belongs to the technical field of structural dynamics. Firstly, structural dynamics response signals measured and obtained by aircraft or spacecraft structures with the time varying characteristics under the work situations are analyzed in a time frequency mode to obtain a time relative power spectral function of non-parametric evaluation corresponding to time varying structures. Then, the time varying common demominator model is used as a parametric model of the time varying structural dynamics to evaluate to-be-evaluated parameters of the time varying common demominator model through a least squares methods of the time domain. Finally, the evaluated to-be-evaluated parameters of the time varying common demominator model is utilized to calculate the model frequency and the model damping ratio corresponding to the time varying common demominator model. The time frequency domain time varying structure modal parameter identification method based on the time varying common demominator model is suitable for model parameters recognition of time varying structure in the field of aircraft and spacecraft engineering application and has the advantages of being simple and convenient to use. Furthermore, users are low in participation degree.

Description

Time-frequency domain time-varying structure modal parameter identification method based on time-varying common score female model

Technical Field

The invention relates to a time-frequency domain time-varying structure modal parameter identification method based on a time-varying common score female model, and belongs to the technical field of structure dynamics.

Background

In real production and life, many engineering structures exhibit such time-varying characteristics as axle systems in train excitation, launch vehicles with gradual reduction of liquid fuel during flight, aircraft under the additive effect of aerodynamic forces, flexible deployable geometrically-variable spacecraft, rotating machinery, and the like.

In the domestic aerospace field, a large space station, a new generation of carrier rocket, a large flexible expansion type satellite and other new generation of spacecrafts are listed in the latest aerospace development planning of China, and become the main direction of the development of the Chinese spacecrafts for decades. The structures of large space stations, new-generation carrier rockets and large-flexibility expansion satellites have strong time-varying factors such as space docking problem of the future large space stations, rapid consumption of fuel quality of the active carrier rockets and the new-generation carrier rockets in the future, and space expansion of the large-flexibility expansion satellites without exception during operation. Therefore, as an important method and approach for analyzing the dynamics characteristics of the time-varying structure, the identification and research of the modal parameters of the time-varying structure will become one of the key points of the future spacecraft structure dynamics research. The modal parameter identification of the time-varying structure can identify the modal frequency, the modal vibration mode and the modal damping of the time-varying structure, the parameters have important physical significance, and powerful support can be provided for the application of the time-varying structure in the aspects of structure design, structure health monitoring, structure fault diagnosis, structure vibration control and the like.

According to the difference distinction of the adopted mathematical models, the existing time-varying structure modal parameter identification method mainly comprises four types:

the first type is a time-varying modal parameter identification method based on an online recursion technology, which is developed from the conventional time-invariant structure modal parameter identification.

The method is based on the traditional time-invariant structure modal parameter identification method, and is different in that data is considered sequentially at each moment, old data is gradually forgotten, new data is continuously added, and the estimated value of the modal parameter is corrected at each moment. Such methods suffer from two drawbacks: firstly, the selection problem of observation data and forgetting factors (algorithms) exists, compromise needs to be made between recognition accuracy and tracking capability, and the adaptability of relevant selection of different structures is difficult to solve; second, such methods are derived from the conventional modal parameter identification method, and require response information of both input and output of the structure, so that it is difficult to apply the method to the identification of the modal parameters of the structure, such as a flying spacecraft, which can only obtain output response signals.

The second category is modal parameter identification methods based on short-time invariant assumptions.

In the method, data (structural response) is divided into small time periods, the structural parameters are regarded as time-invariant in each time period, and then the identification values in each time period are processed by a certain data processing technology (such as curve fitting) to obtain the rule that the modal parameters change along with time. It features that the data information of previous sections is not used when estimating modal parameters in a later period, and a short data section must be selected for fast parameter variation structure to raise estimation precision. The method includes the currently common methods of recursive random subspace identification (N4SID) and Time-dependent autoregressive moving average (tamma) based on a state-space model. The time-varying structure modal parameter identification method of the method has the longest development time and is developed most perfectly. But some inherent problems limit its further development and application: firstly, the short-time invariant assumption limits the application of the method to the identification of fast-changing and mutation parameters; secondly, the method needs fixed and definite mathematical models such as a state space model, a time series autoregressive moving average model and the like, so that the problem of order fixing of the model in identification is very prominent, a false mode without physical significance is introduced due to uncertainty of the order of the model, the identification result is not available, and the problems of reasonable selection of the order of the model, judgment of the false mode and the like need further deep research; thirdly, there are some other problems with the two mainstream modal parameter identification methods based on short-time invariant assumptions, i.e. recursive random subspace identification and time-dependent autoregressive moving average model: the stacking subspace method based on the state space model inevitably uses QR decomposition, eigenvalue decomposition (EVD) or Singular Value Decomposition (SVD) technology, which inevitably brings complexity on the numerical implementation of the method, and further research is needed for large engineering structures, especially for the problems with online and rapid identification requirements; the design of a parameter tracking algorithm cannot be avoided in the identification method research based on the time series model, and although various improved least square methods and various filtering methods are continuously provided, the results of the same algorithm are very different when the same model uses different tracking algorithms and different models apply the same algorithm.

The third type is a time-varying modal parameter identification method of the artificial neural network.

Artificial neural networks have been widely used in the problem of nonlinear system identification, and have achieved good results but most of the research work is limited to time-invariant systems, and only popularized to time-variant systems in recent years. There are few published documents that use artificial neural networks for research in the field of time-varying modal parameter identification, which mainly focuses on mechanistic research for simple structures (systems). For a real complex structure, the problems of complex algorithm, low calculation efficiency, poor identification precision and the like exist.

The fourth method is a time-varying structure modal parameter identification method based on non-parametric time-frequency domain of time-frequency analysis.

From the viewpoint of signal analysis, the structure dynamics response signal of the time-varying structure in the working environment is a non-stationary random signal.

The classical fourier transform has been developed over a century into the most powerful analysis method and tool in the field of signal processing, which is mainly determined by its orthogonality and clear physical meaning, as well as fast and simple computational methods. However, since the fourier transform is time-integrated, the time-varying signal in the non-stationary signal is removed, and thus the signal is required to be stationary, and it is difficult to adequately characterize the time-varying non-stationary signal. In order to meet the requirements for analysis of abrupt and non-stationary signals, in 1946, Gabor proposed a windowed Fourier transform analysis method, also called short-time Fourier transform (STFT), which can implement a certain degree of time-frequency analysis by selecting a proper window function, but the time resolution and the frequency resolution are always limited by the width of the window function and cannot reach the optimum at the same time. In 1948, Ville proposed a well-known Wigner-Ville distribution (WVD). The energy-type time-frequency joint distribution has many excellent properties compared with other time-frequency distributions, such as true marginality, weak support, translation invariance and the like, and is a very useful non-stationary signal analysis tool. Since the multi-signal wiener-well distribution has cross terms, the application effect of the multi-signal wiener-well distribution can be limited in many occasions, so that researchers put forward various improved forms such as index distribution, generalized bilinear time-frequency distribution and the like on the basis of the cross terms, wherein the generalized bilinear time-frequency distribution is also called Cohen type energy time-frequency distribution. On the basis, methods such as Cohen time-frequency distribution and the like are proposed, and the time-frequency analysis methods are widely applied to non-stationary random signal analysis and achieve a plurality of satisfactory results.

In recent decades, due to the advantages of time-frequency analysis in terms of non-stationary random signal analysis, more and more researchers have applied time-frequency analysis to study time-varying and non-linear system identification. The identification of time-varying and nonlinear structural modal parameters by a time-frequency analysis method is also becoming one of the hot spots in the field of modal parameter identification research. In 2000, Ghanem expands a structural dynamics control differential equation on a series of wavelet bases, replaces original physical response with wavelet coefficients, and identifies modal parameters of a system by adopting a method for solving the expansion equation; zhang and Xu identified modal frequencies of structures in 2003 by Gabor transformation in response to a simple time-varying structure; in 2007, Rosman-Ghias adopts an analytic derivation mode to carry out WVD and SPWVD conversion on the response of a single-degree-of-freedom system and a three-degree-of-freedom system under free vibration, and the modal frequency and the damping ratio of the system are estimated according to the conversion result.

The existing time-frequency domain time-varying structure modal parameter identification methods based on time-frequency analysis are non-parametric, and although some methods can well identify the modal frequency of a time-varying structure, the non-parametric methods depend on subjective consciousness and experience of users to different degrees, and no good method for identifying the modal damping ratio of the time-varying structure under random excitation exists.

Disclosure of Invention

The invention provides a time-frequency domain time-varying structure modal parameter identification method of a time-varying common score female model aiming at the problem of identification of time-varying structure modal parameters of aircrafts and spacecrafts, which has the following basic ideas: firstly, performing time-frequency analysis on a structural dynamics response signal measured by an aircraft or spacecraft structure with time-varying characteristics in a working environment to obtain a non-parametrically estimated time-dependent power spectrum function corresponding to a time-varying structure, then estimating a parameter to be estimated of the time-varying common-minute female model by using a time-varying common-minute female model as a parametrization model of time-varying structure dynamics through a time-frequency domain least square method, and finally calculating the modal frequency and the modal damping ratio of the corresponding time-varying structure by using the estimated parameter to be estimated of the time-varying common-minute female model.

The method comprises the following concrete implementation steps:

step 1, setting sampling time and sampling frequency required by identification according to the working state of the identified aircraft or spacecraft time-varying structure, the interested time range and the main frequency range of the identified aircraft or spacecraft time-varying structure, such as about 0-20Hz of a carrier rocket, about 0-100Hz of a common satellite, about 0-10Hz of a large deployable satellite, about 0-50Hz of an airplane wing and the like, and collecting a structure dynamics response signal of the identification structure.

Step 2, randomly selecting reference signals from the response signals collected in the step 1, and respectively carrying out time-frequency analysis on each response signal by combining the reference signals to obtain a time-dependent power spectrum function G of the response signals_k(t_τ，ω_f). Wherein, t_τRepresenting time sample points, ω_fDenotes the frequency sampling point, subscript τ =1, 2_τ，f=1，2，...，N_f，N_τIs the number of time samples, N_fIs the number of frequency samples, k =1, 2_sN_r，N_sTo output the number of responses, N_rThe number of points is referenced in response to the signal.

The method adopts Smooth Pseudo Wigner-Ville distribution (SPWVD) to calculate the power spectrum function of the response signal of the identified structure, has simple implementation and high calculation efficiency, and can better inhibit cross terms in the distribution.

Step 3, establishing a time-varying common score mother model according to the sampling time, the sampling frequency and the time-varying characteristics of the identified aircraft or spacecraft as follows:

wherein, the numerator polynomial and the denominator polynomial are respectively:

wherein,for time-frequency basis functions (i and j orders for time and frequency polynomials, respectively, i =0, 1,2_t，j=0，1，2，...，n_ω，n_tIs a time polynomial order, n_ωFrequency polynomial order), molecular polynomial coefficients b_k，i，jAnd a common denominator a_i，jWrite as vector form:

B_{k, j} = {[b_{k, 0, j}, b_{k, 1, j}, . . ., b_{k, n_{t}, j}]}^{T},

A_{j} = {[a_{0, j}, a_{1, j}, . . ., a_{n_{t}, j}]}^{T} - - - (4)

order:

then there are:

and theta is a parameter vector to be estimated in the time-varying common denominator model.

And 4, obtaining a parameter vector theta to be estimated in the time-varying common-score mother model by adopting a least square parameter method.

The specific process is as follows:

defining a least squares cost function:

wherein,

and

wherein W_k(t_τ，ω_f) Is a weight function.

Obtaining a constrained common denominator parameter vector alpha' to be estimated by the following formula:

D′α′=b′ (10)

wherein,

order to

And calculating the molecular parameter vector beta to be estimated according to the following formula_k：

And obtaining a parameter vector theta to be estimated in the time-varying common denominator model, and further determining the time-varying common denominator model.

Step 5, according to the application requirements of the identified aircraft or spacecraft modal parameters, such as the control frequency of a carrier rocket vibration control system, the time interval requirement in the satellite structure health monitoring and the like, giving a time point t needing to calculate the modal parameters_τ′And calculating the given time t by using the common denominator parameter vector alpha obtained in the step 4 and the time-varying common denominator model_τ′Lower identified modal frequency f_rAnd modal damping ratio ξ_r：

Wherein Im and Re are respectively the imaginary part and the real part of the median value in brackets, and lambda_rIs t with a coefficient_τ′Denominator polynomial A (t) in time-varying common denominator model at time_τ′ω) is the frequency variable of the identified aircraft or spacecraft.

Advantageous effects

The invention provides a time-varying structure modal parameter identification method of a parameterized time-frequency domain based on time-frequency analysis from the viewpoint of the parameterized time-frequency domain, and the physical significance is clear; the method is suitable for modal parameter identification of time-varying structures in the field of aviation and aerospace engineering application, and has the characteristics of low participation of required users, and simplicity and convenience in use.

Drawings

FIG. 1 is a three degree of freedom spring-damper-mass system in an embodiment;

FIG. 2 is a diagram illustrating a random response SPWVD for a three-degree-of-freedom time-varying structure in an exemplary embodiment;

FIG. 3 illustrates modal parameters identified in an embodiment.

Detailed Description

For better illustration of the objects and advantages of the present invention, the present invention is further illustrated below by simulating the time-varying structure of an aircraft and a spacecraft in an operating state by a three-degree-of-freedom time-varying structure example under random excitation.

The three-degree-of-freedom spring-damper-mass system of the present embodiment is shown in fig. 1.

The parameter of the three-degree-of-freedom system is k₁=k₂=k₃=10⁵，c₁=1.0，c₂=0.5，c₃=0.5, initial mass m₁(0)=0.2，m₂(0)=0.1，m₃(0) = 0.1. The kinetic control equation of the system is as follows:

where M (t) is a time-varying quality matrix, M (t) = M₀(1-0.5t)，M₀As a mass matrix at the initial moment, a damping matrix and a stiffness matrix of

C = [\begin{matrix} 0.2 & 0 & 0 \\ 0 & 0.2 & 0 \\ 0 & 0 & 0.1 \end{matrix}],

C = [\begin{matrix} 1.5 & - 0.5 & 0 \\ - 0.5 & 1.0 & - 0.5 \\ 0 & - 0.5 & 0.5 \end{matrix}],

f (t) is a white noise excitation of amplitude 100 units applied in three degrees of freedom.

The excitation in this embodiment is artificial Gauss white noise that acts on the first degree of freedom of the system. The system response is calculated by using a Newmark-beta numerical integration method (gamma =0.5, beta-0.1), wherein the integration step size is 1/4096 s. The signal sampling frequency is 2048Hz and the sampling time is 1 s.

In this embodiment, the specific implementation steps of the modal frequency identification of the time-frequency domain time-varying structure based on the time-varying common denominator model are as follows:

step 1, three-degree-of-freedom acceleration is a response signal used for identification, the sampling frequency is 1024Hz, and the sampling time is 1 s.

And 2, taking the acceleration response signal of the first response point as a reference signal during time-frequency analysis, and obtaining a time-dependent power spectrum function of each response signal and the reference signal through smooth pseudo Wigner-Ville distribution. The 40-fold averaged smoothed pseudo-Wigner-Ville distribution is shown in FIG. 2.

Step 3, establishing a time-varying common score mother model, and then giving a time sampling number N in the time-varying common score mother model_τ=32, number of frequency samples N_f=256, time polynomial order n_t=5 and frequency polynomial order n_ω=32, and initializes the parameter vector θ to be estimated.

And 4, estimating a parameter vector theta by adopting a least square method. Wherein, W_k(t_τ，ω_f) For the weight function, this example is set to 1.

And 5, calculating the structural modal frequency and modal damping ratio at each moment according to the common denominator parameter vector alpha in the parameter vector theta.

The modal frequencies and modal damping ratios of the time-varying structure identified using the parameters of this example are shown in fig. 3, where the solid line is the identified value and the black circle is the theoretical value.

Therefore, the modal frequency of the time-varying structure can be well identified, and the modal damping ratio of the time-varying structure can be well identified. The modal frequency identification method is suitable for modal frequency identification of the time-varying structure of the working state because only the response signal of the structure is required as an input. On the other hand, in the whole process, the user only needs to set one preliminary parameter to obtain the final identification result of the modal frequency and the modal damping ratio, so that the user participation degree is low, and the use is very simple and convenient.

The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention, and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims

1. The time-frequency domain time-varying structure modal parameter identification method based on the time-varying common denominator model is characterized in that: the method comprises the following concrete steps:

step 1, setting sampling time and sampling frequency required by identification according to the working state of the identified aircraft or spacecraft time-varying structure, the interested time range and the main frequency range of the identified aircraft or spacecraft time-varying structure, and acquiring a structure dynamics response signal of the identification structure;

step 2, selecting reference signals from the response signals collected in step 1And respectively performing time-frequency analysis on each response signal in combination with the reference signal to obtain a time-dependent power spectrum function G of the response signal_k(t_τ,ω_f) (ii) a Wherein, t_τRepresenting time sample points, ω_fDenotes the frequency sampling point, with the index τ being 1,2_τ，f＝1,2,...,N_f，N_τIs the number of time samples, N_fN is the number of frequency samples, k ═ 1,2_sN_r，N_sTo output the number of responses, N_rReferencing points for the response signal;

wherein,is a time-frequency basis function, the time polynomial is of the order i, the frequency polynomial is of the order j, i is 0,1,2_t，j＝0,1,2,...,n_ω，n_tIs a time polynomial order, n_ωIs a frequency polynomial order, a molecular polynomial coefficient b_k,i,jAnd a common denominator a_i,jWrite as vector form:

B_{k, j} = {[b_{k, 0, j}, b_{k, 1, j}, . . ., b_{k, n_{t}, j}]}^{T}, A_{j} = {[a_{0, j}, a_{1, j}, . . ., a_{n_{t}, j}]}^{T} - - - (4)

order:

then there are:

the method comprises the following steps that theta is a parameter vector to be estimated in a time-varying common denominator model;

step 4, obtaining a parameter vector theta to be estimated in the time-varying common denominator model by adopting a least square parameter method;

the specific process is as follows:

the cost function of least squares is:

wherein,

and

wherein W_k(t_τ,ω_f) Is a weight function;

obtaining a constrained common denominator parameter vector alpha' to be estimated according to the following formula:

D'α'＝b' (10)

wherein,

order to

Thereby obtaining a parameter vector theta to be estimated in the time-varying common denominator model;

step 5, according to the application requirements of the modal parameters of the identified aircraft or spacecraft, giving a time point t at which the modal parameters need to be calculated_τ'And calculating the given time t by using the common denominator parameter vector alpha obtained in the step 4 and the time-varying common denominator model_τ'Lower identified modal frequency f_rAnd modal damping ratio ξ_r：

Wherein Im and Re are respectively the imaginary part and the real part of the median value in brackets, and lambda_rIs t with a coefficient_τ'Denominator polynomial A (t) in time-varying common denominator model at time_τ'ω) of the identified aviationFrequency variation of a spacecraft or spacecraft.

2. The time-frequency domain time-varying structure modal parameter identification method based on the time-varying common denominator model according to claim 1, characterized in that: the power spectrum function of the response signal of the identified structure is calculated using a smoothed pseudo Wigner-Ville distribution.