CN104777054B - A kind of parameter identification method of the resonant mode fatigue crack propagation test vibrational system based on soft-measuring technique - Google Patents

Abstract

A kind of parameter identification method of the resonant mode fatigue crack propagation test vibrational system based on soft-measuring technique, comprises the following steps：1) system Three Degree Of Freedom vibration mechanical model is set up, kinetics equation is obtained, the system frequency equation on system frequency, spring rate and point mass relation is derived by；2) rigidity of test specimen under different crack lengths is calculated according to finite element method, Crack Extension is measured to the resonant frequency of system during different length；3) system resonance frequencies value during different crack lengths and corresponding specimen stiffness are updated in system frequency equation, obtained on over-determined systems that quality to be identified and rigidity are unknown number；4) by least square solution over-determined systems, the Nonlinear System of Equations on quality and rigidity is obtained；5) Newton Raphson formula are utilized, Nonlinear System of Equations is solved, identifies Vibration Parameters quality and rigidity.Operability of the present invention is good, cost is relatively low, accuracy is good.

Description

A kind of resonant mode fatigue crack propagation test vibrational system based on soft-measuring technique Parameter identification method

Technical field

The present invention relates to Vibration Parameters identification technology field, more particularly to a kind of resonant mode based on soft-measuring technique The parameter identification method of fatigue crack propagation test vibrational system.

Background technology

The service behaviour of electromagnetic resonance HF fatigue testing machine directly affects the accuracy of result of the test, i.e., in crackle The stability of the intrinsic frequency of strict tracking system and Control experiment load in expansion process, to reach this purpose, needs to set up The kinetic model of system, and the dynamic characteristic of system is accurately analyzed, so firstly the need of the matter to vibrational system Point mass and spring rate are measured and calculated, but the particle of vibrational system is by multiple different shapes, the parts group of material Into carrying out direct measurement to point mass has significant limitation, although the rigidity of system can typically pass through finite element method meter Calculate, but the spring shapes of some vibrational systems, stress, constrain complex, had during the foundation of model many cumbersome Work.

The content of the invention

In order to overcome existing resonant mode fatigue crack propagation test vibrational system parameter identification method operability compared with Difference, the deficiency that cost is higher, accuracy is poor, the present invention provides that a kind of operability is good, cost is relatively low, accuracy is good The parameter identification method of resonant mode fatigue crack propagation test vibrational system based on soft-measuring technique.

The technical solution adopted for the present invention to solve the technical problems is：

A kind of parameter identification method of the resonant mode fatigue crack propagation test vibrational system based on soft-measuring technique, including Following steps：

1) structural analysis is carried out to vibrational system, sets up system Three Degree Of Freedom vibration mechanical model, and to the mechanical model Force analysis is carried out, kinetics equation is obtained, is derived by by kinetics equation on system frequency, spring rate and matter The system frequency equation of point mass relation；

2) rigidity of test specimen under different crack lengths is calculated according to finite element method, passes through intrinsic frequency measurement experiment side Method measures Crack Extension to the resonant frequency of system during different length；

3) system resonance frequencies value during different crack lengths and corresponding specimen stiffness are updated in system frequency equation, obtained To on over-determined systems that quality to be identified and rigidity are unknown number；

4) by least square solution over-determined systems, it is drawn on quality and the least square solution of rigidity, so that To one on quality and the Nonlinear System of Equations of rigidity；

5) Newton-Raphson formula are finally utilized, one are solved on quality and the Nonlinear System of Equations of rigidity, from And identify the Vibration Parameters quality and rigidity.

Further, the parameter identification method is further comprising the steps of：6) method accuracy checking is carried out：On testing stand Increase counterweight, the master for changing system shakes quality, identify the quality of added counterweight using proposed method, and with true counterweight Quality compare, if relative error within a preset range, verifies the reasonability of the parameter identification method.

The beneficial effects of the invention are as follows：Resonant mode fatigue crack propagation test vibration system of the invention based on soft-measuring technique After the parameter identification method of system is by simplifying vibration system model, the kinetics equation of system is set up, its system frequency is derived Rate equation, the rigidity of test specimen under different crack lengths is calculated using finite element method, utilizes intrinsic frequency measurement experiment method Crack Extension is measured to the resonant frequency of system during different length, corresponding specimen stiffness and resonant frequency are substituted into system frequency Equation solution can carry out Vibration Parameters identification.Experiment is workable, and single experiment expense is relatively low.By this method The quality and rigidity of vibrational system can be identified exactly.

Brief description of the drawings

Fig. 1 is that the parameter identification method of the resonant mode fatigue crack propagation test vibrational system based on soft-measuring technique is basic Schematic flow sheet；

Fig. 2 be the resonant mode fatigue crack propagation test vibrational system based on soft-measuring technique parameter identification method in electricity Magnetic resonance fatigue tester (PLG-100) structure chart；

Fig. 3 is The vibration mechanical model of system；

Fig. 4 be the resonant mode fatigue crack propagation test vibrational system based on soft-measuring technique parameter identification method in three Free degree linear vibrating system mechanical model；

Fig. 5 is the parameter identification method acceptance of the bid of the resonant mode fatigue crack propagation test vibrational system based on soft-measuring technique Quasi- CT sample dimensions figure.

Embodiment

The invention will be further described below in conjunction with the accompanying drawings.

1~Fig. 5 of reference picture, a kind of parameter of the resonant mode fatigue crack propagation test vibrational system based on soft-measuring technique Recognition methods, comprises the following steps：

1) structural analysis is carried out to vibrational system, sets up system Three Degree Of Freedom vibration mechanical model, and to the mechanical model Force analysis is carried out, kinetics equation is obtained, is derived by by kinetics equation on system frequency, spring rate and matter The system frequency equation of point mass relation；

2) rigidity of test specimen under different crack lengths is calculated according to finite element method, passes through intrinsic frequency measurement experiment side Method measures Crack Extension to the resonant frequency of system during different length；

3) system resonance frequencies value during different crack lengths and corresponding specimen stiffness are updated in system frequency equation, obtained To on over-determined systems that quality to be identified and rigidity are unknown number；

4) by least square solution over-determined systems, it is drawn on quality and the least square solution of rigidity, so that To one on quality and the Nonlinear System of Equations of rigidity；

5) Newton-Raphson formula are finally utilized, one are solved on quality and the Nonlinear System of Equations of rigidity, from And identify the Vibration Parameters quality and rigidity.

Further, the parameter identification method is further comprising the steps of：6) method accuracy checking is carried out：On testing stand Increase counterweight, the master for changing system shakes quality, identify the quality of added counterweight using proposed method, and with true counterweight Quality compare, if relative error within a preset range, verifies the reasonability of the parameter identification method.

Illustrated by taking electromagnetic resonance fatigue tester as an example, a kind of resonant mode fatigue crack based on soft-measuring technique The parameter identification method of expanding test vibrational system, comprises the following steps：

1) structure first to the electromagnetic resonance fatigue tester shown in Fig. 2 is analyzed.Servomotor, turbine snail Bar transmission mechanism m₆With moving beam m₄Pass through guide upright post and type rack m₅It is connected, frame passes through four damping spring k₅ It is connected with the earth.Balance Iron and electromagnet coil pass through exciting vibration spring k₃It is connected with workbench, electromagnet armature, lower clamp and work Platform passes through main vibration spring k₄It is connected with moving beam.Upper fixture and flange m₁Pass through force snesor k₁It is connected with frame, test specimen k₂It is logical Pin is crossed respectively with upper fixture and lower clamp to be connected.It is main shake quality and exciting quality be influence main frame resonance performance it is key because Element, wherein the main quality m that shakes₂Including the flange and the quality of lower clamp on electromagnet armature, workbench and workbench, exciting quality m₃Including Balance Iron and electromagnet coil.By studying the connection and interaction of each mechanical part of system, system is established Vibration mechanical model, as a result refering to Fig. 3.Due to the quality m of support₄、m₅And m₆The master for being far longer than system shakes quality m₂With swash Quality of shaking m₃, and the rigidity of the other springs of the rigidity of damping spring far smaller than system, therefore system can be reduced to three certainly By degree linear vibrating system mechanical model, as a result refering to Fig. 4.It is fixed according to newton second for being positive direction under this model orientation Restrain and Three Degree Of Freedom quality --- spring system free vibration model sets up Equation of Motion and is：

Wherein F_e=F₀Sin (ω t), F₀For electro-magnetic exciting force amplitude, x_i(i=1,2,3) it is respectively upper fixture and flange matter Measure m₁Vibration displacement, the main quality m that shakes₂Vibration displacement and exciting quality m₃Vibration displacement, k_i(i=1,2,3,4) it is respectively The rigidity of force snesor, the rigidity of test specimen, the rigidity of exciting vibration spring and the rigidity of main vibration spring, ω are electro-magnetic exciting force frequency, Carry it into above formula and equivalently represented with matrix and column vector be：

The intrinsic frequency for solving vibrational system is the characteristic value for solving the system dynamic matrix, and the exciting force for making system is Zero, obtain the system free vibration differential equation：

For a Three Degree Of Freedom undamped system, it has three intrinsic frequencies, when system is intrinsic by any one When frequency makees free vibration, the motion of system be all one kind be synchronized with the movement change with time system on each coordinate except fortune Dynamic amplitude differs outer, and other characteristics of motion all identicals are moved, referred to as principal oscillation, makes the principal oscillation be：

(3) formula is carried it into obtain：

It is zero to make the determinant of coefficient in (5) formula, you can obtaining system frequency equation is：

I.e.：

2) test specimen used in the embodiment of the present invention is standard compact tension specimen as shown in Figure 5.Choose ten pieces of differences The CT test specimens of crack length, are modeled, mesh generation, by the upper half disc in hole on CT test specimens in FEM-software ANSYS respectively Stationary state is set to, the lower half disc of test specimen lower opening is set to stress surface.After the external force addition for constraining and applying is finished, Its deflection is calculated, Rigidity Calculation is carried out according to Rigidity Calculation formula.Rigidity Calculation formula is：

K is rigidity in formula, and P is the constant force acted on component, and δ is the deformation quantity produced by the constant force.

The CT test specimens of ten pieces of selection different crack lengths are respectively installed on HF fatigue testing machine the system that carries out humorous Vibration frequency is measured, and is to eliminate experimental error as far as possible, and the measurement of system resonance frequencies is used repeatedly surveys under each crack length Measure the method averaged.System resonance frequencies test specimen and rigidity data are as shown in table 1 when crack length and corresponding crack length.

Table 1

3) deformation process is carried out to obtained system frequency equation (7) formula first, makes intermediate quantity X₁、X₂、X₃、X₄、X₅、X₆ For:

Wherein, upper fixture and flange quality m₁, the main quality m that shakes₂, exciting quality m₃, force snesor rigidity k₁, exciting vibration spring Rigidity k₃With main vibration spring rigidity k₄For amount to be identified, specimen stiffness k₂For known quantity, then frequency equation (7) formula of system is variable For：

X₁ω⁶+X₂k₂ω⁴+X₃ω⁴+X₄k₂ω²+X₅ω²+X₆=k₂ (10)

The form for being write as matrix is：

That is ω X=k₂, by system resonance frequencies value during different crack lengths and corresponding specimen stiffness, substitute into (11) formula and build Overdetermined linear system：

Wherein ω₁、ω₂...ω₁₀Resonant frequency during for ten crack lengths, k_2-1、k_2-2...k_2-10Split for corresponding ten Specimen stiffness during line length.

4) undetermined coefficient vector is solved using least square method：

Wherein (ω^Tω)^-1ω^TFor ω pseudo inverse matrix, intermediate quantity X is obtained by calculating₁、X₂、X₃、X₄、X₅、X₆Solution, (9) formula structure Nonlinear System of Equations is carried it into again to obtain：

Wherein m₁、m₂、m₃、k₁、k₃、k₄For amount to be identified, X₁、X₂、X₃、X₄、X₅、X₆For known quantity.

5) Newton-Raphson equations, order are utilized：

Then：

Wherein L_iFor the value initially set,

Set initial value L₁=[m₁ m₂ m₃ k₁ k₃ k₄]^T=[20 300 500 10⁹ 10⁶ 10⁷]^T, obtain upper fixture With flange quality m₁=21.118Kg, the main quality m that shakes₂=280.417Kg, exciting quality m₃=520.296Kg, force snesor are firm Spend k₁=6.824 × 10⁹N/m, exciting rigidity k₃=4.481 × 10⁶N/m, the main rigidity k that shakes₄=0.969 × 10⁷N/m；

6) change its master and shake increasing quality m=5Kg counterweight on the table and repeat the above steps by way of quality. The vibration parameters of measurement are compared with the vibration parameters not plus before counterweight, concrete outcome is as shown in table 2.

Table 2

From Table 2, it can be seen that after workbench adds counterweight, the upper fixture and flange quality m identified₁', exciting matter Measure m₃', force snesor rigidity k₁', exciting vibration spring rigidity k₃' and main vibration spring rigidity k₄' with not recognized when workbench adds counterweight It is almost equal twice before and after result out.And the main quality m that shakes₂'=285.079Kg, obtained master is recognized with not adding during counterweight Quality of shaking m₂It is poor that=280.417Kg makees, and obtains the counterbalance mass m'=m measured using this paper institutes extracting method₂'-m₂=4.662Kg, It is compared with the quality m=5Kg of counterweight, it is known that the absolute error of counterbalance mass is Δ m=m-m'=0.338Kg, relative to miss Difference is δ=Δ m/m=6.76%.This is for 5Kg counterweight, and this error is acceptable.

Finally illustrate, above example is only for patent of the present invention spirit explanation for example.Patent of the present invention Person of ordinary skill in the field can make various modifications or supplement to described specific embodiment or use class As method substitute, but spirit without departing from patent of the present invention or surmount scope defined in appended claims.

Claims (2)

1. a kind of parameter identification method of the resonant mode fatigue crack propagation test vibrational system based on soft-measuring technique, its feature It is：Comprise the following steps：

1) structural analysis is carried out to vibrational system, sets up system Three Degree Of Freedom vibration mechanical model, and the mechanical model is carried out Force analysis, obtains kinetics equation, is derived by by kinetics equation on system frequency, spring rate and particle matter The system frequency equation of magnitude relation；

In electromagnetic resonance fatigue tester, servomotor, turbine and worm transmission mechanism m₆With moving beam m₄Pass through guide upright post With type rack m₅It is connected, frame passes through four damping spring k₅It is connected with the earth；Balance Iron and electromagnet coil pass through exciting Spring k₃It is connected with workbench, electromagnet armature, lower clamp and workbench pass through main vibration spring k₄It is connected with moving beam；Upper fixture With flange m₁Pass through force snesor k₁It is connected with frame, test specimen k₂It is connected respectively with upper fixture and lower clamp by pin；Main matter of shaking Amount and exciting quality are to influence the key factor of main frame resonance performance, wherein, the main quality m that shakes₂Including electromagnet armature, workbench And flange and the quality of lower clamp on workbench, exciting quality m₃Including Balance Iron and electromagnet coil, it is by studying Unite the connection and interaction of each mechanical part, establish system vibration mechanical model；Due to the quality m of support₄、m₅And m₆ The master for being far longer than system shakes quality m₂With exciting quality m₃, and the other springs of the rigidity of damping spring far smaller than system Rigidity, therefore vibrational system is reduced to Three Degree Of Freedom linear vibrating system mechanical model, for being square under this model orientation To setting up Equation of Motion according to Newton's second law and Three Degree Of Freedom quality-spring system free vibration model and be：

$\left\{\begin{array}{c}{m}_1{\stackrel{\·\·}{x}}_1=k_2(x_2-x_1)-k_1{x}_1\\ m_2{\stackrel{\·\·}{x}}_2=2k_3(x_3-x_2)-2k_4{x}_2-k_2(x_2-x_1)-F_e\\ m_3{\stackrel{\·\·}{x}}_3=F_e-2k_3(x_3-x_2)\end{array}\right.---\left(1\right)$

Wherein F_e=F₀Sin (ω t), F₀For electro-magnetic exciting force amplitude, x_iRespectively upper fixture and flange quality m₁Vibration displacement, The main quality m that shakes₂Vibration displacement and exciting quality m₃Vibration displacement, i=1,2,3；k_iRespectively the rigidity of force snesor, is tried The rigidity of part, the rigidity of exciting vibration spring and the rigidity of main vibration spring, i=1,2,3,4；ω is electro-magnetic exciting force frequency, by its band Enter above formula and equivalently represented with matrix and column vector be：

$\left[\begin{array}{ccc}{m}_1& 0& 0\\ 0& m_2& 0\\ 0& 0& m_3\end{array}\right]\left[\begin{array}{c}{\stackrel{\·\·}{x}}_1\\ {\stackrel{\·\·}{x}}_2\\ {\stackrel{\·\·}{x}}_3\end{array}\right]+\left[\begin{array}{ccc}{k}_1+k_2& -k_2& 0\\ -k_2& k_2+2k_3+2k_4& -2k_3\\ 0& -2k_3& 2k_3\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]=\left[\begin{array}{c}0\\ -F_e\\ F_e\end{array}\right]---\left(2\right)$

The intrinsic frequency for solving vibrational system is the characteristic value for solving the system dynamic matrix, and the exciting force for making system is zero, is obtained To the system free vibration differential equation：

$\left[\begin{array}{ccc}{m}_1& 0& 0\\ 0& m_2& 0\\ 0& 0& m_3\end{array}\right]\left[\begin{array}{c}{\stackrel{\·\·}{x}}_1\\ {\stackrel{\·\·}{x}}_2\\ {\stackrel{\·\·}{x}}_3\end{array}\right]+\left[\begin{array}{ccc}{k}_1+k_2& -k_2& 0\\ -k_2& k_2+2k_3+2k_4& -2k_3\\ 0& -2k_3& 2k_3\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right]---\left(3\right)$

For a Three Degree Of Freedom undamped system, it has three intrinsic frequencies, when system presses any one intrinsic frequency When making free vibration, the motion of system be all one kind be synchronized with the movement change with time system on each coordinate except motion is shaken Width differs outer, and other characteristics of motion all identicals are moved, referred to as principal oscillation, makes the principal oscillation be：

$\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]=\left[\begin{array}{c}{X}_a\\ X_b\\ X_c\end{array}\right]sin\left(\mathrm{\ω}t\right)---\left(4\right)$

(3) formula is carried it into obtain：

$\left[\begin{array}{ccc}-{\mathrm{\ω}}^2{m}_1+k_1+k_2& -k_2& 0\\ -k_2& -{\mathrm{\ω}}^2{m}_2+k_2+2k_3+2k_4& -2k_3\\ 0& -2k_3& -{\mathrm{\ω}}^2{m}_3+2k_3\end{array}\right]\left[\begin{array}{c}{X}_a\\ X_b\\ X_c\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right]---\left(5\right)$

It is zero to make the determinant of coefficient in (5) formula, you can obtaining system frequency equation is：

$\mathrm{\Δ}\left(\mathrm{\ω}\right)=\left|\begin{array}{ccc}-{\mathrm{\ω}}^2{m}_1+k_1+k_2& -k_2& 0\\ -k_2& -{\mathrm{\ω}}^2{m}_2+k_2+2k_3+2k_4& -2k_3\\ 0& -2k_3& -{\mathrm{\ω}}^2{m}_3+2k_3\end{array}\right|=0---\left(6\right)$

I.e.：

$\begin{array}{c}\frac{m_1{m}_2{m}_3}{2k_1{k}_3+4k_3{k}_4}{\mathrm{\ω}}^6-\frac{m_1{m}_3+m_2{m}_3}{2k_1{k}_3+4k_3{k}_4}{k}_2{\mathrm{\ω}}^4-\frac{2m_1{m}_3{k}_3+2m_1{m}_3{k}_4+m_2{m}_3{k}_1+2m_1{m}_2{k}_3}{2k_1{k}_3+4k_3{k}_4}{\mathrm{\ω}}^4+\\ \frac{m_3{k}_1+2m_3{k}_3+2m_3{k}_4+2m_1{k}_3+2m_2{k}_3}{2k_1{k}_3+4k_3{k}_4}{k}_2{\mathrm{\ω}}^2+\frac{2m_3{k}_1{k}_3+2m_3{k}_1{k}_4+4m_1{k}_3{k}_4+2m_2{k}_1{k}_3}{2k_1{k}_3+4k_3{k}_4}{\mathrm{\ω}}^2-\\ \frac{4k_1{k}_3{k}_4}{2k_1{k}_3+4k_3{k}_4}=k_2\end{array}---\left(7\right);$

2) rigidity of test specimen under different crack lengths is calculated according to finite element method, is surveyed by intrinsic frequency measurement experiment method Go out Crack Extension to the resonant frequency of system during different length；

The CT test specimens of ten pieces of different crack lengths are chosen, are modeled respectively in FEM-software ANSYS, mesh generation tries CT The upper half disc in hole is set to stationary state on part, and the lower half disc of test specimen lower opening is set into stress surface, by constraint and application External force addition finish after, calculate its deflection, Rigidity Calculation carried out according to Rigidity Calculation formula, Rigidity Calculation formula is：

$k=\frac{P}{\mathrm{\δ}}---\left(8\right)$

K is rigidity in formula, and P is the constant force acted on component, and δ is the deformation quantity produced by the constant force；

The CT test specimens of ten pieces of selection different crack lengths are respectively installed on HF fatigue testing machine and carry out system resonance frequency Rate is measured, and the measurement of system resonance frequencies is used repeatedly measures the method averaged under each crack length；

3) system resonance frequencies value during different crack lengths and corresponding specimen stiffness are updated in system frequency equation, closed In the over-determined systems that quality to be identified and rigidity are unknown number；

Deformation process is carried out to obtained system frequency equation (7) formula first, intermediate quantity X is made₁、X₂、X₃、X₄、X₅、X₆For:

$\left\{\begin{array}{c}{X}_1=\frac{m_1{m}_2{m}_3}{2k_1{k}_3+4k_3{k}_4}\\ X_2=-\frac{m_1{m}_3+m_2{m}_3}{2k_1{k}_3+4k_3{k}_4}\\ X_3=-\frac{2m_1{m}_3{k}_3+2m_1{m}_3{k}_4+m_2{m}_3{k}_1+2m_1{m}_2{k}_3}{2k_1{k}_3+4k_3{k}_4}\\ X_4=\frac{m_3{k}_1+2m_3{k}_3+2m_3{k}_4+2m_1{k}_3+2m_2{k}_3}{2k_1{k}_3+4k_3{k}_4}\\ X_5=\frac{2m_3{k}_1{k}_3+2m_3{k}_1{k}_4+4m_1{k}_3{k}_4+2m_2{k}_1{k}_3}{2k_1{k}_3+4k_3{k}_4}\\ X_6=-\frac{4k_1{k}_3{k}_4}{2k_1{k}_3+4k_3{k}_4}\end{array}\right.---\left(9\right)$

Wherein, upper fixture and flange quality m₁, the main quality m that shakes₂, exciting quality m₃, force snesor rigidity k₁, exciting vibration spring rigidity k₃ With main vibration spring rigidity k₄For amount to be identified, specimen stiffness k₂For known quantity, then frequency equation (7) formula of system can be changed into：

X₁ω⁶+X₂k₂ω⁴+X₃ω⁴+X₄k₂ω²+X₅ω²+X₆=k₂ (10)

The form for being write as matrix is：

$\left[\begin{array}{cccccc}{\mathrm{\ω}}^6& k_2{\mathrm{\ω}}^4& {\mathrm{\ω}}^4& k_2{\mathrm{\ω}}^2& {\mathrm{\ω}}^2& 1\end{array}\right]\left[\begin{array}{c}{X}_1\\ X_2\\ X_3\\ X_4\\ X_5\\ X_6\end{array}\right]=k_2---\left(11\right)$

That is ω X=k₂, by system resonance frequencies value during different crack lengths and corresponding specimen stiffness, substitute into (11) formula and build overdetermination System of linear equations：

$\left[\begin{array}{cccccc}{\mathrm{\ω}}_1^6& k_{2-1}{\mathrm{\ω}}_1^4& {\mathrm{\ω}}_1^4& k_{2-1}{\mathrm{\ω}}_1^2& {\mathrm{\ω}}_1^2& 1\\ {\mathrm{\ω}}_2^6& k_{2-2}{\mathrm{\ω}}_2^4& {\mathrm{\ω}}_2^4& k_{2-2}{\mathrm{\ω}}_2^2& {\mathrm{\ω}}_2^2& 1\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ {\mathrm{\ω}}_5^6& k_{2-5}{\mathrm{\ω}}_5^4& {\mathrm{\ω}}_5^4& k_{2-5}{\mathrm{\ω}}_5^2& {\mathrm{\ω}}_5^2& 1\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ {\mathrm{\ω}}_{10}^6& k_{2-10}{\mathrm{\ω}}_{10}^4& {\mathrm{\ω}}_{10}^4& k_{2-10}{\mathrm{\ω}}_{10}^2& {\mathrm{\ω}}_{10}^2& 1\end{array}\right]\left[\begin{array}{c}{X}_1\\ X_2\\ X_3\\ X_4\\ X_5\\ X_6\end{array}\right]=\left[\begin{array}{c}{k}_{2-1}\\ k_{2-2}\\ .\\ .\\ .\\ k_{2-5}\\ .\\ .\\ .\\ k_{2-10}\end{array}\right]---\left(12\right)$

Wherein ω₁、ω₂…ω₁₀Resonant frequency during for ten crack lengths, k_2-1、k_2-2…k_2-10For corresponding ten crack lengths When specimen stiffness；

4) by least square solution over-determined systems, it is drawn on quality and the least square solution of rigidity, so as to obtain one It is individual on quality and the Nonlinear System of Equations of rigidity；

Undetermined coefficient vector is solved using least square method：

$\left[\begin{array}{c}{X}_1\\ X_2\\ X_3\\ X_4\\ X_5\\ X_6\end{array}\right]={\left({\mathrm{\ω}}^T\mathrm{\ω}\right)}^{-1}{\mathrm{\ω}}^T{k}_2---\left(13\right)$

Wherein (ω^Tω)^-1ω^TFor ω pseudo inverse matrix, intermediate quantity X is obtained by calculating₁、X₂、X₃、X₄、X₅、X₆Solution, then by its (9) formula structure Nonlinear System of Equations is brought into obtain：

$\left\{\begin{array}{c}{f}_1=m_1{m}_2{m}_3-(2k_1{k}_3+4k_3{k}_4)X_1=0\\ f_2=m_1{m}_3+m_2{m}_3+(2k_1{k}_3+4k_3{k}_4)X_2=0\\ f_3=2m_1{m}_3{k}_3+2m_1{m}_3{k}_4+m_2{m}_3{k}_1+2m_1{m}_2{k}_3+(2k_1{k}_3+4k_3{k}_4)X_3=0\\ f_4=m_3{k}_1+2m_3{k}_3+2m_3{k}_4+2m_1{k}_3+2m_2{k}_3-(2k_1{k}_3+4k_3{k}_4)X_4=0\\ f_5=2m_3{k}_1{k}_3+2m_3{k}_1{k}_4+4m_1{k}_3{k}_4+2m_2{k}_1{k}_3-(2k_1{k}_3+4k_3{k}_4)X_5=0\\ f_6=4k_1{k}_3{k}_4+(2k_1{k}_3+4k_3{k}_4)X_6=0\end{array}\right.---\left(14\right)$

Wherein m₁、m₂、m₃、k₁、k₃、k₄For amount to be identified, X₁、X₂、X₃、X₄、X₅、X₆For known quantity；

5) Newton-Raphson formula are finally utilized, one are solved on quality and the Nonlinear System of Equations of rigidity, so as to know Do not go out the Vibration Parameters quality and rigidity；

Utilize Newton-Raphson equations, order：

$L=\left[\begin{array}{c}{m}_1\\ m_2\\ m_3\\ k_1\\ k_3\\ k_4\end{array}\right],F\left(L\right)=\left[\begin{array}{c}{f}_1(m_1,m_2,m_3,k_1,k_3,k_4)=0\\ f_2(m_1,m_2,m_3,k_1,k_3,k_4)=0\\ f_3(m_1,m_2,m_3,k_1,k_3,k_4)=0\\ f_4(m_1,m_2,m_3,k_1,k_3,k_4)=0\\ f_5(m_1,m_2,m_3,k_1,k_3,k_4)=0\\ f_6(m_1,m_2,m_3,k_1,k_3,k_4)=0\end{array}\right]=\left[\begin{array}{c}{f}_1\left(L\right)=0\\ f_2\left(L\right)=0\\ f_3\left(L\right)=0\\ f_4\left(L\right)=0\\ f_5\left(L\right)=0\\ f_6\left(L\right)=0\end{array}\right]$

Then：

$L_{i+1}=L_i-{\[\frac{\∂F\left(L_i\right)}{\∂L}\]}^{-1}\·F\left(L_i\right)---\left(15\right)$

Wherein L_iFor the value initially set,

$\frac{\∂F\left(L_i\right)}{\∂L}=\left[\begin{array}{cccccc}\frac{\∂f_1\left(L_i\right)}{\∂m_1}& \frac{\∂f_1\left(L_i\right)}{\∂m_2}& \frac{\∂f_1\left(L_i\right)}{\∂m_3}& \frac{\∂f_1\left(L_i\right)}{\∂k_1}& \frac{\∂f_1\left(L_i\right)}{\∂k_3}& \frac{\∂f_1\left(L_i\right)}{\∂k_4}\\ \frac{\∂f_2\left(L_i\right)}{\∂m_1}& \frac{\∂f_2\left(L_i\right)}{\∂m_2}& \frac{\∂f_2\left(L_i\right)}{\∂m_3}& \frac{\∂f_2\left(L_i\right)}{\∂k_1}& \frac{\∂f_2\left(L_i\right)}{\∂k_3}& \frac{\∂f_2\left(L_i\right)}{\∂k_4}\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ \frac{\∂f_6\left(L_i\right)}{\∂m_1}& \frac{\∂f_6\left(L_i\right)}{\∂m_2}& \frac{\∂f_6\left(L_i\right)}{\∂m_3}& \frac{\∂f_6\left(L_i\right)}{\∂k_1}& \frac{\∂f_6\left(L_i\right)}{\∂k_3}& \frac{\∂f_6\left(L_i\right)}{\∂k_4}\end{array}\right]$

Set initial value L₁=[m₁ m₂ m₃ k₁ k₃ k₄]^T, obtain upper fixture and flange quality m₁, the main quality m that shakes₂, exciting quality m₃, force snesor rigidity k₁, exciting rigidity k₃With the main rigidity k that shakes₄。

2. the parameter of the resonant mode fatigue crack propagation test vibrational system as claimed in claim 1 based on soft-measuring technique is known Other method, it is characterised in that：The parameter identification method is further comprising the steps of：6) method accuracy checking is carried out：In work Increase counterweight on platform, the master for changing system shakes quality, identify the quality of added counterweight using proposed method, and with it is true The quality of counterweight is compared, if relative error within a preset range, verifies the reasonability of the parameter identification method.