CN106951654A - Complicated coupling structural dynamic characteristics parameter recognition methods based on bounded-but-unknown uncertainty - Google Patents

Abstract

The invention discloses a kind of complicated coupling structural dynamic characteristics parameter recognition methods based on bounded-but-unknown uncertainty.The present invention is mainly, interval method is used to the uncertain variable of agent structure, and the complicated coupling structural dynamic characteristics parameter identification with uncertain factor is converted into by the deterministic complicated coupling structural dynamic characteristics parameter of two classes based on first order Taylor series expansion and is recognized；And the identification of deterministic complicated coupling structural dynamic characteristics parameter is carried out on the basis of agent structure dynamic analysis；Turn complicated coupling structural dynamic characteristics parameter simultaneously is identified as Dynamic Load Identification, under LTI hypothesis, time domain internal load is represented by a series of superposition of pulse excitation kernel functions, and the response of agent structure can be got by the response of kernel function and the convolution of dynamic loading.The present invention can obtain the complicated coupling structural dynamic characteristics parameter interval that conventional method is difficult to determine exactly, and greatly reduce the number of times and cost of Physical Experiment.

Description

Complicated coupling structural dynamic characteristics parameter recognition methods based on bounded-but-unknown uncertainty

Technical field

The invention belongs to the calculating reverse technology field of parameter identification, and in particular to one kind considers complicated under uncertain factor The parameter identification method of coupled structure.

Background technology

With high speed, precise treatment, intellectuality, greenization and the proposition of the ultimate target such as integrated, corresponding machinery dress Standby also to turn into the complication system of multi- scenarios method, this complication system is coupled by a variety of functional parts, and such as electric chief axis system is by sliding Bearing, motor and spindle assemblies coupling.When studying the dynamic characteristics of a wherein functional part (abbreviation agent structure), phase mutual coupling The dynamic characteristics of the tactile functional part (abbreviation coupled structure) of splice grafting turns into the boundary condition or load-up condition of agent structure (referred to as Dynamic parameters).These dynamic parameters surely help really developer it is quick, accurate, economically and safely to main body The property indices of structure carry out prediction, evaluated and optimized.However as requiring that agent structure operates in high-precision, height Speed, high reliability state, coupled structure also become increasingly complex, and such as sliding bearing uses helicla flute oil pocket.Pass through numerical solution at present Method directly obtains the method for coupled structure dynamic parameters mainly for simple structure.For complicated coupling structure from direct problem Numerical solution angle be difficult all-sidedly and accurately to annotate.And rely on experimental tests to obtain complicated coupling structural dynamic characteristics parameter Method, its signal to noise ratio is relatively low, and precision is difficult to ensure that.The on-site identification such as boundary element method developed below method is because of measuring point and exciting etc. It is restricted.Limited by technology or economic condition, complicated coupling structural dynamic characteristics parameter is being difficult to carry out in some cases Direct measurement at all can not direct measurement.The measurement of agent structure response is relatively easy and accurate.Therefore, measurement is utilized The parameter identification technology that response carries out complicated coupling structural dynamic characteristics parameter is increasingly becoming engineering agent structure ginseng in practice A kind of indispensable important means of the acquisitions such as number, boundary condition and external applied load parameter, studies it and is moved in agent structure Many technical fields such as balance control, fault diagnosis and detection all have wide practical use.

Simultaneously because the complexity and the discreteness of material therefor of agent structure, and agent structure manufacture, install and The reasons such as measurement error, are inevitably present material character, geometric properties, boundary condition, primary condition and measured deviation etc. Error or uncertainty.Therefore, the accurate upper lower limit value for obtaining complicated coupling structural dynamic characteristics parameter can be these problems Research definite environmental condition is provided, there is important practical significance to the safety and reliability design of agent structure.

The content of the invention

It is an object of the invention to overcome scene to be difficult in complicated coupling structure to arrange measuring point, agent structure has not true The problems such as dynamic parameters qualitative and that complicated coupling structure directly can not be directly calculated with numerical computation method, there is provided one kind Complicated coupling structural dynamic characteristics parameter recognition methods based on bounded-but-unknown uncertainty.

The complicated coupling structural dynamic characteristics parameter recognition methods based on bounded-but-unknown uncertainty of the present invention, it is mainly, right The uncertain variable of agent structure uses interval method, and based on first order Taylor series expansion by with uncertain factor The identification of complicated coupling structural dynamic characteristics parameter is converted into the deterministic complicated coupling structural dynamic characteristics parameter identification of two classes, i.e., Uncertain variables midpoint complicated coupling structural dynamic characteristics parameter identification and complicated coupling structural dynamic characteristics parameter for The identification of the gradient of uncertain variable；And the identification of deterministic complicated coupling structural dynamic characteristics parameter is in agent structure Carried out on the basis of dynamic analysis, i.e., the power of agent structure is set up according to the dynamic (dynamical) basic analyzing method of agent structure Equation, and then the agent structure vibratory response by that can predict are learned, binding kineticses equation, foundation includes unknown complex coupled structure The identification equation of dynamic parameters；Turn the Dynamic Load Identification that is identified as of complicated coupling structural dynamic characteristics parameter simultaneously, online During property under constant hypothesis, time domain internal load is represented by a series of superposition of pulse excitation kernel functions, and the response of agent structure It can be got by the response of kernel function and the convolution of dynamic loading；By discretization convolution point, Dynamic Load Identification is being set up just To model；The pathosis during Dynamic Load Identification is handled with regularization method, complicated coupling structural dynamic characteristics parameter is obtained Coboundary and lower boundary.

Comprise the following steps that：

(1) complicated coupling structural dynamic characteristics parameter is converted into dynamic loading form；

(2) uncertain Dynamic Load Identification is made to be converted into certainty Dynamic Load Identification based on interval method；

Dynamic loading is carried out by first order Taylor series expansion at uncertain variables interval midpoint using interval method, when obtaining t Carve dynamic loading coboundary f^RAnd lower boundary f (t)^L(t) explicit expression：

Wherein, λ is uncertain variables；For single order local derviation of the dynamic loading to uncertain variables, finite difference calculus is used Partial differential equation are converted into algebraic equation solving using difference scheme；f(t,λ^c) it is dynamic at uncertain variables interval midpoint Load is recognized；

(3) for certainty Dynamic Load Identification, first according to the actual conditions of agent structure, selected with computer simulation method Select species, position and the quantity of response measuring point；

(4) by testing the dynamic response matrix q at measurement means acquisition each measuring point of agent structure；

(5) kernel function for responding each measuring point with each dynamic load effect point of finite element method to agent structure is responded, And set up kernel matrix G；In the case of known to transient response matrix q and kernel matrix G, dynamic loading matrix F is calculated：

Or q=GF；

(6) when having error or noise in the response data of measurement, regularization method processing is introduced, filtering letter is utilized Number f (α, σ_i) dynamic loading stable estimation：

In formula, q_δRepresent to include noisy agent structure transient response, U=[u₁,u₂,...,u_k] for G it is left it is unusual to Amount and V=[v₁,v₂,...,v_k] be G right singular vector, be two standardization orthogonal matrixes, σ_iTo be intrinsic in agent structure The small singular value of kernel matrix；

Because measurement error can by the infinitely amplification of small singular value so that its actual value of the estimate substantial deviation of dynamic loading, And cause obtain dynamic loading there is ill-posedness；And regularization method is by small singular value σ_iIt is modified to reduce this It is individual to deviate, realize the stability of dynamic loading；The method that such issues that Regularization is commonly used is that a kind of wave filter of introducing will be small strange Different value σ_iAmplification decay to noise.

(7) coboundary of corresponding complicated coupling structural dynamic characteristics parameter is obtained with according to the dynamic loading of identification interval Border.

The problem of present invention is difficult to accurately calculate its dynamic parameters in theory for complicated coupling structure and main body Structure has uncertain as caused by objective factor in itself, it is proposed that consider the complicated coupling structural dynamic of uncertain factor The recognition methods of characterisitic parameter.The present invention is carried out on the basis of agent structure dynamic analysis, using agent structure just Normal working condition, is combined with finite element simulation simulation, the agent structure power that the several measuring point measurements of reasonable Arrangement are readily available Learn response.Using the mapping relations of the dynamic response and complicated coupling structural dynamic characteristics parameter of measuring point, by complicated coupling knot The identification of structure dynamic parameters is converted into dynamic state loading identification, quick obtaining dynamic loading, is moved so as to obtain complicated coupling structure Force characteristic parameter.The method considers agent structure uncertain factor first, based on interval mathematical theory and first order Taylor series Complicated coupling structural dynamic characteristics parameter identification problem with uncertain factor is converted into two classes by the interval method of expansion Deterministic complicated coupling structural dynamic characteristics parameter recognizes problem；Secondly for deterministic complicated coupling structural dynamic characteristic Parameter identification problem is converted into dynamic loading form according to operating mode and acted in agent structure, propose by dynamic loading in time domain with one The impulse function of series is represented, builds direct problem using the instantaneous response analysis method of agent structure, with reference to regularization side Ill-conditioning problem in method processing complicated coupling structural dynamic characteristics parameter identification, obtains complicated coupling structural dynamic characteristics parameter Coboundary and lower boundary.Finally by the numerical example examine complicated coupling structural dynamic characteristics parameter recognition methods validity and Robustness.

The present invention only needs once to test with several measuring points with regard to the upper of energy quick obtaining complicated coupling structural dynamic characteristics parameter Lower value.The present invention can not only accurately and effectively obtain the complicated coupling structural dynamic characteristic that some conventional methods are difficult to determine simultaneously Parameter is interval, and greatly reduces the number of times and cost of Physical Experiment, with preferable practical value.

Beneficial effects of the present invention specific manifestation is as follows：

(1) the inventive method can quickly set up agent structure using uncertain factor in interval method processing agent structure Analysis model, it is certain problem processing to turn uncertain problem, there is actual application value in engineering.

(2) present invention interacts the coupled relation between complicated coupling system with dynamic loading, based on calculating reverse skill Art using relation between agent structure and complicated coupling structure, as long as several measuring points in test subject structure just can it is quick, The dynamic parameters of complicated coupling structure are stably recognized, engineering site can be solved tired in the test of layouting of complicated coupling structure Difficult problem.

Brief description of the drawings

Fig. 1 is the FB(flow block) of the inventive method.

Fig. 2 is the rotor subject structural model and parameter schematic diagram of the embodiment of the present invention.

Fig. 3 is the rotor subject structural finite element model schematic diagram of the embodiment of the present invention.

Fig. 4 is the response curve of four measuring points in the rotor subject structure of the embodiment of the present invention.

The identification curve map of four oil-film forces when Fig. 5, Fig. 6 are embodiment of the present invention uncertain variables midranges.

Fig. 7, Fig. 8 are embodiment of the present invention dynamic loadings in the gradient identification of uncertain variables, four oil-film forces are to injustice The local derviation curve map for the quality that weighs.

Fig. 9, Figure 10 are embodiment of the present invention dynamic loadings in the gradient identification of uncertain variables, four oil-film forces are to bias The local derviation curve map of square.

Figure 11, Figure 12 are embodiment of the present invention dynamic loadings in the gradient identification of uncertain variables, four oil-film forces are not to Balance the local derviation curve map of phase.

Figure 13, Figure 14 are the identification curve maps of the embodiment of the present invention the first oil film bearingses power.

Figure 15, Figure 16 are the identification curve maps of the embodiment of the present invention the second oil film bearingses power.

Embodiment

The present invention is described in further detail with reference to the accompanying drawings and examples.

First, complicated coupling system model

It is the FB(flow block) of the inventive method referring to Fig. 1.It is the sliding bearing-rotor-support-foundation system of the present embodiment referring to Fig. 2 Model, sliding bearing is complicated coupling structure, and rotor is agent structure.Consider to act on second disk in agent structure Unbalance mass, 0.2g, eccentricity 60mm and 0 degree of unbalance phase be uncertain variable, level of uncertainty is 15%. The oil film dynamic characteristic coefficients of sliding bearing are complicated coupling structural dynamic characteristics parameter.The oil film dynamic characteristics system of sliding bearing Number can be converted into oil-film force and act in rotor subject structure.Known rotor agent structure parameter is as shown in Figure 2.

2nd, complicated coupling structural dynamic characteristics parameter is recognized

The limit element artificial module of rotor subject structure is set up as shown in figure 3, obtaining rotor-support-foundation system by transfer matrix method Quality, rigidity and damping matrix.Rotor-support-foundation system is divided into 33 shaft parts, 34 nodes.Coupled structure sliding bearing cloth is the 7th On node and the 24th node, three disks are the 9th, on 17 and 28 shaft parts.Injustice amount is acted on Section 17 point, using true Oil film dynamic characteristic coefficients (being shown in Table 1) by Finite Element Simulation, find and sliding bearing dynamic parameters correlation Strong measuring point is node 3,8,20 and 25.Collect the test response of node 3,8,20 and 25 on rotor structure, and the noise for Jia 5% Simulation, as shown in Figure 4.The deterministic oil-film force of two classes identified with method proposed by the present invention is as shown in Fig. 5 to Figure 12, figure 5th, Fig. 6 is oil-film force recognition result when uncertain variables are midpoint, and Fig. 7 to Figure 12 is that oil-film force is known to the gradient of amount of unbalance Other result.Figure 13 to Figure 16 is the border of 15% uncertain lower Dynamic Load Identification.Table 1 shows complicated coupling structural dynamic characteristic The error of parameter recognition result and the complicated coupling structural dynamic characteristics parameter interval when level of uncertainty is 15%.From table 1 understands that the error of complicated coupling structural dynamic characteristics parameter recognition result below 10%, illustrates the validity and Shandong of the method Rod.

The complicated coupling structural dynamic characteristics parameter that table 1. is recognized based on interval method

The complication system of multi- scenarios method is divided into agent structure and coupled structure by the present invention, between the two with the shape of dynamic loading Formula characterizes the relation that intercouples.The dynamic parameters of the coupled structure acted in agent structure are also converted into dynamic loading shape Formula.So as to which the dynamic parameters of coupled structure identification problem is converted into Dynamic Load Identification.Based on interval method by uncertainty Dynamic Load Identification problem is converted into certainty dynamic state loading identification problem.Directly using complicated coupling structural dynamic characteristics parameter with Mapping relations between test response, only need an agent structure operation and several measuring points just to may recognize that complicated coupling structure is moved Force characteristic parameter, it is to avoid complicated coupling structure, which is layouted, in common method tests difficult.

Claims (2)

1. a kind of complicated coupling structural dynamic characteristics parameter recognition methods based on bounded-but-unknown uncertainty, it is characterised in that：To master The uncertain variable of body structure uses interval method, and based on first order Taylor series expansion by answering with uncertain factor Miscellaneous coupled structure dynamic parameters identification is converted into the deterministic complicated coupling structural dynamic characteristics parameter identification of two classes, i.e., not Determine that the complicated coupling structural dynamic characteristics parameter of variable midpoint is recognized with complicated coupling structural dynamic characteristics parameter for not The identification of the gradient of certainty variable；And the identification of deterministic complicated coupling structural dynamic characteristics parameter is dynamic in agent structure Carried out on the basis of mechanical analysis, i.e., the dynamics of agent structure is set up according to the dynamic (dynamical) basic analyzing method of agent structure Equation, and then the agent structure vibratory response by that can predict, binding kineticses equation, foundation include unknown complex coupled structure and moved The identification equation of force characteristic parameter；Turn complicated coupling structural dynamic characteristics parameter simultaneously is identified as Dynamic Load Identification, linear When constant hypothesis under, time domain internal load is represented by a series of superposition of pulse excitation kernel functions, and the response energy of agent structure Enough got by the response of kernel function and the convolution of dynamic loading；By discretization convolution point, the forward direction of Dynamic Load Identification is set up Model；The pathosis during Dynamic Load Identification is handled with regularization method, complicated coupling structural dynamic characteristics parameter is obtained Coboundary and lower boundary.

2. the complicated coupling structural dynamic characteristics parameter recognition methods based on bounded-but-unknown uncertainty according to claim 1, its It is characterised by comprising the following steps that：

(1) complicated coupling structural dynamic characteristics parameter is converted into dynamic loading form；

(2) uncertain Dynamic Load Identification is made to be converted into certainty Dynamic Load Identification based on interval method；

Dynamic loading is carried out by first order Taylor series expansion at uncertain variables interval midpoint using interval method, t is obtained and moves Load coboundary f^RAnd lower boundary f (t)^L(t) explicit expression：

$f^R\left(t\right)=\underset{\mathrm{\λ}\∈\mathrm{\Γ}}{max}f(t,\mathrm{\λ})=f(t,{\mathrm{\λ}}^c)+\underset{j=1}{\overset{n}{\Σ}}\left|\frac{\∂f(t,{\mathrm{\λ}}^c)}{\∂{\mathrm{\λ}}_j}\right|{\mathrm{\λ}}_j^w;$

$f^L\left(t\right)=\underset{\mathrm{\λ}\∈\mathrm{\Γ}}{min}f(t,\mathrm{\λ})=f(t,{\mathrm{\λ}}^c)-\underset{j=1}{\overset{n}{\Σ}}\left|\frac{\∂f(t,{\mathrm{\λ}}^c)}{\∂{\mathrm{\λ}}_j}\right|{\mathrm{\λ}}_j^w;$

Wherein, λ is uncertain variables；For single order local derviation of the dynamic loading to uncertain variables, utilized with finite difference calculus Partial differential equation are converted into algebraic equation solving by difference scheme；f(t,λ^c) for the dynamic loading at uncertain variables interval midpoint Identification；

(3) for certainty Dynamic Load Identification, first according to the actual conditions of agent structure, select to ring with computer simulation method Answer species, position and the quantity of measuring point；

(4) by testing the dynamic response matrix q at measurement means acquisition each measuring point of agent structure；

(5) kernel function for responding each measuring point with each dynamic load effect point of finite element method to agent structure is responded, and is built Vertical kernel matrix G；In the case of known to transient response matrix q and kernel matrix G, dynamic loading matrix F is calculated：

Or q=GF；

(6) when having error or noise in the response data of measurement, regularization method processing is introduced, filter function f is utilized (α,σ_i) dynamic loading stable estimation：

${\tilde{F}}_{\mathrm{\α}}=G^{\mathrm{\α}}\·q_{\mathrm{\δ}}=\underset{i=1}{\overset{k}{\Σ}}f(\mathrm{\α},{\mathrm{\σ}}_i){\mathrm{\σ}}_i^{-1}\left(U_i^T{q}_{\mathrm{\δ}}\right)V_i;$

In formula, q_δRepresent to include noisy agent structure transient response, U=[u₁,u₂,...,u_k] be G left singular vector and V =[v₁,v₂,...,v_k] be G right singular vector, be two standardization orthogonal matrixes, σ_iFor core letter intrinsic in agent structure The small singular value of matrix number；

(7) according to the coboundary of the corresponding complicated coupling structural dynamic characteristics parameter of the dynamic loading of identification interval acquisition and below Boundary.