CN105975673A - Nonlinear dynamical parameter identification method of vibration type energy collector - Google Patents

Abstract

The invention relates to a nonlinear dynamical parameter identification method of a vibration type energy harvester, and belongs to the field of energy harvesting. According to the method, the problem that the parameters of the harvester cannot be accurately evaluated when the harvester contains unknown linear restoring force is solved. On the basis of a harvester restoring force equation, a restoring force three-dimensional data set is established by use of experimental data; the cross section of a restoring force curved surface is established through an interpolation method; a rigidity curve and a damping curve are identified through rearranging data in ascending sequence; through adoption of a least square method, and rigidity or damping data points are fitted by use of a polynomial equation. According to the method, a harvester restoring force model is unnecessarily pre-judged, and therefore, the method is suitable for dynamical parameter identification of various complex nonlinear harvesters. Compared with the prior art, the method has the advantages that the dynamical model identification and parameter identification problems of the vibration type energy harvester are solved under the condition that the restoring force model is unknown, and the theoretical basis is established for design and optimization of the vibration type energy harvester.

Description

The Nonlinear dynamics parameter identification method of vibrating type energy harvester

Technical field

The present invention relates to vibrational energy and gather field, the nonlinear kinetics ginseng of a kind of vibrating type energy harvester Number discrimination method.

Background technology

The low-power dissipation system such as wireless sensing node and monitoring means is widely used in monitoring structural health conditions, fault at present In diagnosis and initial failure early warning system.Gathering vibrational energy from environment is to provide one of important approach of power supply, shape for it Become study hotspot.Therefore, develop and improve vibrating type energy collector systems identification and parameter identification method, to vibrating type energy The structure Design and optimization parameter of harvester and engineer applied have important value and significance.

At present, in terms of the dynamic parameters identification or identification of vibrational energy type energy collecting device, need restoring force mould Type itself has certain anticipation, and the accuracy of anticipation largely have impact on the accuracy of parameter identification；Due to unknown nonlinear The existence of restoring force, this anticipation is difficult to be consistent with practical situation.Therefore, for having the energy collecting device of nonlinear restoring force Carrying out parameter identification is a difficult point.

Summary of the invention

The defect existed for prior art, it is an object of the invention to provide the non-linear of a kind of vibrating type energy harvester Dynamic parameters identification method, solves when harvester contains unknown nonlinear restoring force, it is impossible to accurately identify kinetic parameter Problem.

For reaching above-mentioned purpose, the design of the present invention is as follows:

Restoring force expression formula is:

$f(z,\stackrel{\·}{z})=-m{\stackrel{\·\·}{z}}_b-m\stackrel{\·\·}{z}-\mathrm{\η}u---\left(4\right)$

Give harvester arbitrary excitation, in the ith sample moment, obtain if quality m weighs in advance, electromechanical coupling factor η Obtained by piezoelectric material properties, accelerationWith voltage u_iThe most measure (displacement z_iWithCan be by integrated acceleration be obtained Arrive), the f under the most each sampling instant_iThe most available.Structure three-dimensional numerical value point setThen can draw this system resilience Curved surface.If elastic restoring force and damping restoring force, then have:

$f(z,\stackrel{\·}{z})=f_d\left(\stackrel{\·}{z}\right)+f_s\left(z\right)---\left(5\right)$

According to formula (5), by constructing on restoring force curved surfaceOr the cross section of z=0, rigidity restoring force can be obtained Data sequence or damping restoring force data sequence.

According to above-mentioned design, the present invention adopts the following technical scheme that

A kind of Nonlinear dynamics parameter identification method of vibrating type energy harvester, utilizes experimental data structure three-dimensional extensive Multiple Massa Medicata Fermentata face, utilizes method of section to obtain harvester rigidity and amortization data sequence, comprises the steps:

Step 1: traversal point setSearch and record all working asTime corresponding data sequence: displacement (z_i,z_i+1), speedWith restoring force (f_i,f_i+1)；

Step 2: by data above centering interpolated value, searchTime displacement z_i' and restoring force f_i' data, To stiffness curve data sequence (z_i’,f_i’)；

Step 3: to data sequence (z_i’,f_i') according to z_i' carry out ascending order arrangement, draw stiffness curve z ' → f '；

Step 4: use method of least square, utilize polynomial equation to stiffness curve z → f_sIt is fitted, obtains multinomial Coefficient, completes resilience model identification and parameter identification；

Step 5: when identifying damping curve, repeats step 1～4, but needs to record and all work as z_i×z_i+1< corresponding when 0 Data sequence, and at z_iInterpolation at '=0.

Compared with prior art, present invention have the advantage that:

This method first passes through the means of experiment test, constructs restoring force data point set；By interpolation method, complete rigidity The identification work of curve and damping curve；Finally utilize polynomial equation, utilize least square fitting to obtain each term coefficient, complete Become whole identification and identify work.The method presupposes resilience model, therefore to various complex nonlinears owing to need not Restoring force form all can reliable identification and identification.

Accompanying drawing explanation

Fig. 1 is vibrating type energy harvester equivalent model.

Fig. 2 is vibrating type energy harvester kinetics parameter recognition result: (a) is restoring force curved surface；B () is that rigidity is intended Close curve and experimental data scatterplot.

Detailed description of the invention

Embodiments of the present invention is further illustrated below in conjunction with the accompanying drawings.

Vibrating type energy harvester equivalent model is as it is shown in figure 1, model is by mass m, nonlinear spring k_n, damped coefficient C and the piezoelectric transducer composition that electromechanical coupling factor is η.z_aFor under absolute coordinate, the vibration displacement of harvester, z_bFor harvester The basic excitation of shell, then relative displacement z can write equation (1)

Z=z_a-z_b (1)

System equation can be written as:

$m\stackrel{\&CenterDot;\&CenterDot;}{z}+f(z,\stackrel{\&CenterDot;}{z})+\mathrm{\&eta;}u=-m{\stackrel{\&CenterDot;\&CenterDot;}{z}}_b---\left(2\right)$

$-\mathrm{\&eta;}\stackrel{\&CenterDot;}{z}+C_p\stackrel{\&CenterDot;}{u}+u/R_L=0---\left(3\right)$

Wherein:For with k_nThe unknown restoring force function relevant with c, η is electromechanical coupling factor, C_pFor piezoelectric Equivalent capacity, R_LFor external load resistance, u is output voltage.Formula (2) is rewritten as the expression formula (4) of restoring force function:

$f(z,\stackrel{\&CenterDot;}{z})=-m{\stackrel{\&CenterDot;\&CenterDot;}{z}}_b-m\stackrel{\&CenterDot;\&CenterDot;}{z}-\mathrm{\&eta;}u---\left(4\right)$

In the ith sample moment, obtaining if quality m weighs in advance, electromechanical coupling factor η is obtained by piezoelectric material properties, AccelerationWith voltage u_iThe most measure (displacement z_iWithCan be by integrated acceleration be obtained), under the most each sampling instant f_iThe most available.Structure three-dimensional numerical value point setThen can draw this system resilience curved surface.If elastic restoring force and resistance Buddhist nun's restoring force, then have:

$f(z,\stackrel{\&CenterDot;}{z})=f_d\left(\stackrel{\&CenterDot;}{z}\right)+f_s\left(z\right)---\left(5\right)$

According to formula (5), by constructing on restoring force curved surfaceOr the cross section of z=0, rigidity restoring force can be obtained Data sequence or damping restoring force data sequence.

A kind of Nonlinear dynamics parameter identification method of vibrating type energy harvester, utilizes experimental data structure three-dimensional extensive Multiple Massa Medicata Fermentata face, utilizes method of section to obtain harvester rigidity and amortization data sequence, comprises the steps:

Step 1: traversal point setSearch and record all working asTime corresponding data sequence: displacement (z_i,z_i+1), speedWith restoring force (f_i,f_i+1)；

Step 2: by data above centering interpolated value, searchTime displacement z_i' and restoring force f_i' data, obtain Stiffness curve data sequence (z_i’,f_i’)；

Step 3: to data sequence (z_i’,f_i') according to z_i' carry out ascending order arrangement, draw stiffness curve z ' → f '；

Step 4: use method of least square, utilize polynomial equation to stiffness curve z → f_sIt is fitted, obtains multinomial Coefficient, completes resilience model identification and parameter identification；

Step 5: when identifying damping curve, repeats step 1～4, but needs to record and all work as z_i×z_i+1< corresponding when 0 Data sequence, and at z_iInterpolation at '=0.

Experiment illustration:

Utilize above identification and recognition methods, certain rondelle vibration energy collector carried out kinetic parameter identification, Result is as in figure 2 it is shown, wherein: (a) is 3-d recovery Massa Medicata Fermentata face；B () is rigidity data scatterplot and fitting result.Rigidity matching is adopted With 5 order polynomials, as shown in formula (6).Damping recognition result is approximately linear, and its value is 6.28Ns/m.

f_s(z)=3.61 × 10⁴z+1.9×10⁷z²-1.08×10¹¹z³-8.1×10¹²z⁴+3.5×10¹⁷z⁵ (6)

The method presupposes resilience model, therefore to the various complex nonlinear equal energy of restoring force form owing to need not Realize identification and identification.

Claims (1)

1. a Nonlinear dynamics parameter identification method for vibrating type energy harvester, utilizes experimental data to construct 3-d recovery Massa Medicata Fermentata face, utilizes method of section to obtain harvester rigidity and amortization data sequence, it is characterised in that to comprise the steps:

Step 1: traversal point setSearch and record all working asTime corresponding data sequence: displacement (z_i, z_i+1), speedWith restoring force (f_i,f_i+1)；

Step 2: by data above centering interpolated value, searchTime displacement z_i' and restoring force f_i' data, obtain rigidity Curve data sequence (z_i’,f_i’)；

Step 3: to data sequence (z_i’,f_i') according to z_i' carry out ascending order arrangement, draw stiffness curve z ' → f '；

Step 4: use method of least square, utilize polynomial equation to stiffness curve z → f_sIt is fitted, obtains multinomial coefficient, Complete resilience model identification and parameter identification；

Step 5: when identifying damping curve, repeats step 1～4, but needs to record and all work as z_i×z_i+1< data corresponding when 0 Sequence, and at z_iInterpolation at '=0.