CN105975673B - The Nonlinear dynamics parameter identification method of vibrating type energy collector - Google Patents
The Nonlinear dynamics parameter identification method of vibrating type energy collector Download PDFInfo
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- CN105975673B CN105975673B CN201610284491.6A CN201610284491A CN105975673B CN 105975673 B CN105975673 B CN 105975673B CN 201610284491 A CN201610284491 A CN 201610284491A CN 105975673 B CN105975673 B CN 105975673B
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Abstract
The present invention relates to a kind of Nonlinear dynamics parameter identification methods of vibrating type energy collector, belong to energy acquisition field.It solves the problems, such as accurately estimate collector parameter in the case of collector contains unknown nonlinear restoring force.Based on collector restoring force equation, restoring force three-dimensional data point set is constructed using experimental data, the section of restoring force curved surface is constructed by interpolation value method, the identification of stiffness curve and damping curve is realized by ascending order data rearrangement；Using least square method, the fitting of rigidity or amortization data point is realized using polynomial equation.The present invention is suitble to the kinetic parameter of the non-linear collector of various complexity to identify due to not needing anticipation collector resilience model.Compared with prior art, the present invention solves under resilience model unknown situation, the kinetic model identification of vibration energy collector and parameter identification problem, has established theoretical basis for the design and optimization of vibration energy collector.
Description
Technical field
The present invention relates to vibrational energies to acquire field, the nonlinear kinetics ginseng of especially a kind of vibrating type energy collector
Number discrimination method.
Background technique
The low-power dissipation systems such as wireless sensing node and monitoring unit are widely used in monitoring structural health conditions, failure at present
In diagnosis and initial failure early warning system.It is to provide power supply important one of approach for it that vibrational energy is acquired from environment, shape
At research hotspot.Therefore, develop and improve the identification of vibrating type energy collector systems and parameter identification method, to vibrating type energy
The structure Design and optimization parameter and engineer application of collector have important value and significance.
Currently, needing in terms of the dynamic parameters identification of vibrational energy type energy collecting device or identification to restoring force mould
Type itself has certain anticipation, and the accuracy of anticipation largely affects the accuracy of parameter identification；Due to unknown nonlinear
The presence of restoring force, this anticipation are difficult to be consistent with actual conditions.Therefore, for the energy collecting device with nonlinear restoring force
Carrying out parameter identification is a difficult point.
Summary of the invention
In view of the defects existing in the prior art, the object of the present invention is to provide a kind of the non-linear of vibrating type energy collector
Dynamic parameters identification method solves when collector contains unknown nonlinear restoring force, can not accurately identify kinetic parameter
The problem of.
In order to achieve the above objectives, design of the invention is as follows:
Restoring force expression formula are as follows:
Collector arbitrary excitation is given, at the ith sample moment, is obtained if quality m is weighed in advance, electromechanical coupling factor η
It is obtained by piezoelectric material properties, accelerationWith voltage uiAlso (displacement z has been measurediWithIt can be by being obtained to integrated acceleration
To), then the f under each sampling instantiIt is available.Construct three-dimensional numerical value point setThe system resilience can then be drawn
Curved surface.If elastic restoring force and damping restoring force, have:
According to formula (5), by being constructed on restoring force curved surfaceOr the section of z=0, it can be obtained rigidity restoring force
Data sequence or damping restoring force data sequence.
According to above-mentioned design, the present invention adopts the following technical scheme:
A kind of Nonlinear dynamics parameter identification method of vibrating type energy collector is constructed three-dimensional extensive using experimental data
Multiple power curved surface obtains collector rigidity and amortization data sequence using method of section, includes the following steps:
Step 1: traversal point setIt searches and records all work asWhen corresponding data sequence: displacement
(zi,zi+1), speedWith restoring force (fi,fi+1)；
Step 2: by the interpolated value in above data pair, searchingWhen displacement zi' and restoring force fi' data, it obtains
To stiffness curve data sequence (zi’,fi')；
Step 3: to data sequence (zi’,fi') according to zi' ascending order arrangement is carried out, draw stiffness curve z ' → f '；
Step 4: least square method is used, using polynomial equation to stiffness curve z → fsIt is fitted, obtains multinomial
Coefficient completes resilience model identification and parameter identification；
Step 5: when identification damping curve, repeating step 1~4, but need to record and all work as zi×zi+1It is corresponding when < 0
Data sequence, and in ziInterpolation at '=0.
Compared with prior art, the present invention has the advantage that:
This method passes through the means of experiment test first, constructs restoring force data point set；By interpolation method, rigidity is completed
The identification work of curve and damping curve；Polynomial equation is finally utilized, is fitted to obtain each term coefficient using least square method, it is complete
At entire identification and identification work.This method presupposes resilience model due to not needing, to various complex nonlinears
Restoring force form reliably can be recognized and be identified.
Detailed description of the invention
Fig. 1 is vibrating type energy collector equivalent model.
Fig. 2 is vibrating type energy collector dynamics parameter recognition result: (a) being restoring force curved surface；(b) quasi- for rigidity
Close curve and experimental data scatterplot.
Specific embodiment
Embodiments of the present invention is further illustrated with reference to the accompanying drawing.
Vibrating type energy collector equivalent model as shown in Figure 1, model by mass block m, nonlinear spring kn, damped coefficient
The PZT (piezoelectric transducer) that c and electromechanical coupling factor are η forms.zaFor under absolute coordinate, the vibration displacement of collector, zbFor collector
The basic excitation of shell, then relative displacement z can write equation (1)
Z=za-zb (1)
System equation can be written as:
Wherein:For with knUnknown recovery force function related with c, η are electromechanical coupling factor, CpFor piezoelectric material
Equivalent capacity, RLFor external load resistance, u is output voltage.Formula (2) is rewritten as to restore the expression formula (4) of force function:
At the ith sample moment, being obtained if quality m is weighed in advance, electromechanical coupling factor η is obtained by piezoelectric material properties,
AccelerationWith voltage uiAlso (displacement z has been measurediWithCan be by being obtained to integrated acceleration), then under each sampling instant
FiIt is available.Construct three-dimensional numerical value point setThe system resilience curved surface can then be drawn.If elastic restoring force with
Restoring force is damped, then is had:
According to formula (5), by being constructed on restoring force curved surfaceOr the section of z=0, it can be obtained rigidity restoring force
Data sequence or damping restoring force data sequence.
A kind of Nonlinear dynamics parameter identification method of vibrating type energy collector is constructed three-dimensional extensive using experimental data
Multiple power curved surface obtains collector rigidity and amortization data sequence using method of section, includes the following steps:
Step 1: traversal point setIt searches and records all work asWhen corresponding data sequence: displacement
(zi,zi+1), speedWith restoring force (fi,fi+1)；
Step 2: by the interpolated value in above data pair, searchingWhen displacement zi' and restoring force fi' data, it obtains
To stiffness curve data sequence (zi’,fi')；
Step 3: to data sequence (zi’,fi') according to zi' ascending order arrangement is carried out, draw stiffness curve z ' → f '；
Step 4: least square method is used, using polynomial equation to stiffness curve z → fsIt is fitted, obtains multinomial
Coefficient completes resilience model identification and parameter identification；
Step 5: when identification damping curve, repeating step 1~4, but need to record and all work as zi×zi+1It is corresponding when < 0
Data sequence, and in ziInterpolation at '=0.
Test illustration:
Using the above identification and recognition methods, kinetic parameter identification has been carried out to certain rondelle vibration energy collector,
As a result as shown in Figure 2, in which: (a) is 3-d recovery power curved surface；It (b) is rigidity data scatterplot and fitting result.Rigidity fitting is adopted
With 5 order polynomials, as shown in formula (6).Damping recognition result is approximately linear, value 6.28Ns/m.
fs(z)=3.61 × 104z+1.9×107z2-1.08×1011z3-8.1×1012z4+3.5×1017z5 (6)
This method presupposes resilience model due to not needing, to the various equal energy of complex nonlinear restoring force form
Realize identification and identification.
Claims (1)
1. a kind of Nonlinear dynamics parameter identification method of vibrating type energy collector constructs 3-d recovery using experimental data
Power curved surface obtains collector rigidity and amortization data sequence using method of section, which comprises the steps of:
Step 1: traversal point setIt searches and records all work asWhen corresponding data sequence: displacement (zi,
zi+1), speedWith restoring force (fi,fi+1)；
Step 2: by the interpolated value in above data pair, searchingWhen displacement zi' and restoring force fi' data, obtain rigidity
Curve data sequence (zi’,fi')；
Step 3: to data sequence (zi’,fi') according to zi' ascending order arrangement is carried out, draw stiffness curve z ' → f '；
Step 4: using least square method, stiffness curve z ' → f ' is fitted using polynomial equation, obtains system of polynomials
Number completes resilience model identification and parameter identification；
Step 5: when identification damping curve, repeating step 1~4, but need to record and all work as zi×zi+1Corresponding data when < 0
Sequence, and in ziInterpolation at '=0；
Using restoring force expression formula are as follows:
Give collector arbitrary excitationAt the ith sample moment, obtained if quality m is weighed in advance, electromechanical coupling factor η by
Piezoelectric material properties obtain, accelerationWith voltage uiAlso it has measured, has been displaced ziWithBy being obtained to integrated acceleration, then often
F under a sampling instantiIt is available；Construct three-dimensional numerical value point setThen draw the system resilience curved surface；If elastic
Restoring force fs(z) with damping restoring forceIndependently of each other, then have:
According to formula (5), by being constructed on restoring force curved surfaceOr the section of z=0, i.e. acquisition rigidity restore force data sequence
Column or damping restoring force data sequence.
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| CN110083911B (en) * | 2019-04-19 | 2020-10-27 | 西安交通大学 | Modeling optimization method of electromagnetic vibration energy recovery system |
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| CN103812382A (en) * | 2013-11-07 | 2014-05-21 | 西安交通大学 | Nonlinear modeling method of broadband piezoelectric energy capture system |
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Non-Patent Citations (3)
| Title |
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| Past,present and future of nonlinear system identification in structural dynamics;Gaetan Kerschen等;《Mechanical system and signal processing》;20051007;第505-592页 |
| 压电磁耦合振动能量俘获系统的非线性模型研究;周生喜等;《西安交通大学学报》;20140130;第48卷(第1期);第106-110页 |
| 悬臂梁压电振子宽带低频振动能量俘获的随机共振机理研究;陈仲生等;《物理学报》;20110715;第60卷(第7期);第1-7页 |
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