CN104915570A - Analyzing method of dynamic characteristics of biomimetic seal whisker sensor - Google Patents

Abstract

The present invention provides an analyzing method of the dynamic characteristics of a biomimetic seal whisker sensor. The analyzing method comprises the following steps of : dividing a biomimetic seal whisker into a plurality of continuous Timoshenko beam sections; according to the kinematical equation and the dynamic balance equation of the Timoshenko beam sections, calculating the frequency-response function H00 of the linear displacement in accordance with shear force, the frequency-response function N00 of the angular displacement in accordance with the shear force, the frequency-response function L00 of the linear displacement in accordance with the bending moment, and the frequency-response function P00 of the angular displacement in accordance with the bending moment, of any point on the biomimetic seal tentacle. The analyzing method of the dynamic characteristics of the biomimetic seal whisker sensor adopts a multi-section Timoshenko beam theory and a transfer matrix method to analyze the dynamic characteristics of the biomimetic seal whisker in the free state, and reveals the influence rules of elasticity modulus, shear coefficients, damping ratios, sectional dimensions and the like on structural natural vibration characteristics, so that the analyzing method disclosed by the present invention has an important significance in the development of the biomimetic seal whisker sensor.

Description

The analytical approach of the dynamics of bionical sea dog Whisker Sensor

Technical field

The present invention relates to bionical Whisker Sensor technical field, particularly relate to a kind of analytical approach of dynamics of bionical sea dog Whisker Sensor.

Background technology

Marine oil and gas resource and deep sea mineral resources exploitation are the emerging fields with strategic importance, have huge potentiality to be exploited.In exploration of ocean resources performance history, autonomous underwater robot is absolutely necessary one of instrument, and it uses camera or sonar technique perceptually system usually, wherein, camera is not suitable for the water body of muddiness or dark, and sonar and sound system are very expensive, battery performance is also limited.Compare with the underwater sensor of the sense of hearing with dependence vision, the imitative sea dog Whisker Sensor of Recent study perceives surrounding objects by water flow variation, is more suitable for the sensory perceptual system of underwater robot.

The sea dog of blindfoldness can only have 0.7 μm of turbulent water caused because of small prey by beard perception, realizes prey and follows the tracks of.2010, B.Stocking etc. are subject to the inspiration of sea dog antenna perceptional function, based on electric capacity, have developed the artificial Whisker Sensor in energy perception water velocity and direction, artificial for rigidity antenna is installed on the parallel capacitance matrix of cone-in-cone type, and provides necessary damping and restoring force by PDMS film.2013, Robyn Grant etc. are the technique study method of sea dog identification article size by experiment, and result shows, sea dog determines article size fast by the antenna quantity of contact object, is generally no more than 400ms.W.C.Eberhardt etc. improve sensor: adjust antenna deformation test pattern, increase female cone size, with silver epoxy plating, shielded signal circuit, reduce electric capacity to suppress voltage output range.Sensor gain after improvement has been up to 300 times before improving.Mohsen Asadnia etc., and to be encapsulated into interconnected for 10 Whisker Sensors on flexible liquid crystal polymkeric substance nutrient culture media by gold thread.

The research of current bionical Whisker Sensor stresses the extraction of its contacting mechanism and object features mostly, and understands in depth for the dynamics shortage affecting its identification precision and reliability.Imitative sea dog antenna has that quality is light, slenderness ratio large, the feature of hollow, variable cross section and high flexibility, and its vibration characteristics is easily subject to hydrodynamic impact, proposes requirements at the higher level to the stability of sensor and precision controlling.Given this, be the identification precision of sea dog Whisker Sensor imitative under guarantee streamflow regime, the dynamics of imitative sea dog Whisker Sensor under needing to understand streamflow regime in depth.Fluid-wall interaction dynamics problem is the difficult point of academia always, the difficulty of imitative sea dog Whisker Sensor dynamics research under adding streamflow regime, have researchist by acceleration transducer and laser unique sensor the dynamics to bionical sea dog Whisker Sensor study, but because acceleration transducer is difficult to be fixed on antenna, and its relative mass is excessive, the vibration performance of antenna can be had a strong impact on, and laser displacement sensor testing range is fixed, the real-time vibration performance of imitative sea dog Whisker Sensor under accurately can not catching flow state.

Summary of the invention

The technical problem to be solved in the present invention is: for the current analysis Shortcomings for bionical sea dog Whisker Sensor, and the analytical approach that the invention provides a kind of dynamics of bionical sea dog Whisker Sensor solves the problems referred to above.

The technical solution adopted for the present invention to solve the technical problems is: a kind of analytical approach of dynamics of bionical sea dog Whisker Sensor, comprises the following steps:

A1, a bionical sea dog antenna is divided into continuous multiple Timoshenko beam section, makes the moment of flexure of the left side of described Timoshenko beam section and shearing force be respectively M _i-1, Q _i-1, moment of flexure and the shearing force of right side are respectively M _i, Q _i, the kinematical equation setting up described Timoshenko beam section is as follows:

$\frac{\∂}{\∂x^2}\left(EI\frac{{\∂}^{2}y}{\∂x^2}\right)+m\frac{{\∂}^{2}y}{\∂t^2}-\frac{mI}{A}\frac{{\∂}^{4}y}{\∂x^2\∂t^2}-\frac{mEIk}{GA}\frac{{\∂}^{4}y}{\∂x^2\∂t^2}-\frac{m^{2}Ik}{{\mathrm{GA}}^2}\frac{{\∂}^{4}y}{\∂t^4}=0;$

Wherein, y (x, t) is the straight-line displacement of any point in described Timoshenko beam section; A is Timoshenko beam section cross-sectional area; M is the Timoshenko beam section quality of unit length; E is Young's modulus of elasticity; G is modulus of shearing; K is shearing factor; I is second-order section moment of inertia; L is beam segment length;

The dynamic balance equation setting up described Timoshenko beam section is as follows:

$\frac{GA}{k}(\frac{{\∂}^{2}y}{\∂x^2}-\frac{\∂\mathrm{\θ}}{\∂x})-m\frac{{\∂}^{2}y}{\∂t^2}=0;$

Wherein, θ is the angular displacement of any point in described Timoshenko beam section;

A2, the state vector expression formula obtaining described Timoshenko beam section left side according to the kinematical equation of described Timoshenko beam section and dynamic balance equation are as follows:

$\begin{array}{c}{\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_{i-1}=\left[\begin{array}{cc}0& 1\\ \frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\δ}}^2}{GA\mathrm{\δ}}& 0\\ 0& -\frac{EI\left({\mathrm{mk\ω}}^2-{\mathrm{GA\δ}}^2\right)}{GA}\\ \frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}& 0\end{array}\right.\\ \left.\begin{array}{cc}0& 1\\ \frac{{\mathrm{mk\ω}}^2+{\mathrm{GA\ϵ}}^2}{GA\mathrm{\ϵ}}& 0\\ 0& -\frac{EI\left({\mathrm{mk\ω}}^2-{\mathrm{GA\ϵ}}^2\right)}{GA}\\ \frac{{\mathrm{m\ω}}^2}{\mathrm{\ϵ}}& 0\end{array}\right]\left\{\begin{array}{c}{C}_1\\ C_2\\ C_3\\ C_4\end{array}\right\}\end{array};$

And the state vector expression formula of described Timoshenko beam section right side is as follows:

$\begin{array}{c}{\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_i=\left[\begin{array}{cc}\sin l\mathrm{\δ}& \cos l\mathrm{\δ}\\ -\frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\δ}}^2}{GA\mathrm{\δ}}\cos l\mathrm{\δ}& \frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\δ}}^2}{GA\mathrm{\δ}}\sin l\mathrm{\δ}\\ \frac{EI({\mathrm{GA\δ}}^2-{\mathrm{mk\ω}}^2)}{GA}\sin l\mathrm{\δ}& \frac{EI({\mathrm{GA\δ}}^2-{\mathrm{mk\ω}}^2)}{GA}\cos l\mathrm{\δ}\\ \frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}\cos l\mathrm{\δ}& -\frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}\sin l\mathrm{\δ}\end{array}\right.\\ \left.\begin{array}{cc}shl\mathrm{\ϵ}& chl\mathrm{\δ}\\ \frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\ϵ}}^2}{GA\mathrm{\ϵ}}chl\mathrm{\ϵ}& \frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\ϵ}}^2}{GA\mathrm{\ϵ}}shl\mathrm{\δ}\\ -\frac{EI({\mathrm{GA\ϵ}}^2+{\mathrm{mk\ω}}^2)}{GA}shl\mathrm{\ϵ}& -\frac{EI({\mathrm{GA\ϵ}}^2+{\mathrm{mk\ω}}^2)}{GA}chl\mathrm{\ϵ}\\ -\frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}chl\mathrm{\ϵ}& -\frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}shl\mathrm{\ϵ}\end{array}\right]\left\{\begin{array}{c}{C}_1\\ C_2\\ C_3\\ C_4\end{array}\right\}\end{array};$

A3, order ${\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_{i-1}=T_{i-1}\left\{\begin{array}{c}{C}_1\\ C_2\\ C_3\\ C_4\end{array}\right\}$ With ${\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_i=T_i\left\{\begin{array}{c}{C}_1\\ C_2\\ C_3\\ C_4\end{array}\right\},$ Then the pass of described Timoshenko beam section left side and right side state vector is:

${\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_i=T_i{T}_{i-1}^{-1}{\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_{i-1};$

Then the transfer matrix of described Timoshenko beam section left side and right side is:

$D_i=T_i{T}_{i-1}^{-1};$

Then the transitive relation of described bionical sea dog antenna entirety is:

{z} _i＝[D _i][D _i-1][D _i-2]…[D ₂][D ₁]{z} ₀＝[H]{z} ₀；

A4, the transitive relation of described bionical sea dog antenna entirety to be revised as:

{z} _i＝[H]({z} ₀-{Δz}) ₀-{Δz} _i；

And by the transfer matrix of described bionical sea dog antenna entirety be:

${\left\{\begin{array}{c}y\\ \mathrm{\θ}\\ 0\\ 0\end{array}\right\}}_i=\left[\begin{array}{cccc}\×& \×& \×& \×\\ \×& \×& \×& \×\\ t_{4i-13}& t_{4i-12}& \×& t_{4i-10}\\ t_{4i-3}& t_{4i-2}& \×& t_{4i}\end{array}\right]{\left\{\begin{array}{c}y\\ \mathrm{\θ}\\ 0\\ -P\end{array}\right\}}_0$

The wherein shearing force of P suffered by described bionical sea dog antenna entirety, to calculate on described bionical sea dog antenna any point straight-line displacement for the frequency response function H of shearing force ₀₀with the frequency response function N of angular displacement for shearing force ₀₀:

$H_{00}=\frac{y_0}{P_0}=\frac{t_{4i-10}{t}_{4i-2}-t_{4i-12}{t}_{4i}}{t_{4i-13}{t}_{4i-2}-t_{4i-3}{t}_{4i-12}};$

$N_{00}=\frac{{\mathrm{\θ}}_0}{P_0}=\frac{t_{4i-3}{t}_{4i-10}-t_{4i-13}{t}_{4i}}{t_{4i-3}{t}_{4i-12}-t_{4i-13}{t}_{4i-2}};$

In like manner can to obtain on described bionical sea dog antenna any point straight-line displacement for the frequency response function L of moment of flexure ₀₀with the frequency response function P of angular displacement for moment of flexure ₀₀.

2, the analytical approach of the dynamics of bionical sea dog Whisker Sensor as claimed in claim 1, is characterized in that: the further comprising the steps of current that obtain distribute to the dynamic force of bionical sea dog antenna:

Set up General Hidden Markov Model (GHMM):

λ＝(N,M,π,A,B)；

Wherein, N represents hidden state number, and hidden state can be expressed as S={S ₁, S ₂..., S _n, in t, hidden state variable is q _t; What M represented each state may observe number, and the observed result of each state can be expressed as V={v ₁, v ₂..., v _n, be o in the observed reading of t _t; Observation sequence is designated as O={o ₁, o ₂..., o _n, the observation sequence upper bound is observation sequence lower bound is o= o ₁, o ₂..., o _n;

By Baum-Welch algorithm, General Hidden Markov Model training formula can be obtained as follows:

$\log p\left(\underset{\‾}{O},Q|\mathrm{\λ}\right)=\log \left(p\left(Q|\mathrm{\λ}\right).p\left(\underset{\‾}{O},|Q,\mathrm{\λ}\right)\right)={\mathrm{log\π}}_{q_1}^l+\underset{t=1}{\overset{T-1}{\Σ}}{\mathrm{loga}}_{q_t{q}_{t+1}}^l+\underset{t=1}{\overset{T}{\Σ}}{\mathrm{loga}}_{q_t}^l\left({\underset{\‾}{O}}_t\right);$

Thus obtain the bound revaluation formula of GHMM parameter, as obtain maximal value, GHMM parameter upper bound revaluation formula can be obtained as follows:

$a_{ij}^l=c_{ij}^l/dual\underset{j}{\Σ}{c}_{ij}^l=\underset{t=1}{\overset{T-1}{\Σ}}{\mathrm{\ξ}}_t^l(i,j)/dual\underset{t=1}{\overset{T-1}{\Σ}}{\mathrm{\γ}}_t^l\left(i\right);$

$b_{j\left(k\right)}^l=d_{jk}^l/dual\underset{k}{\Σ}{d}_{jk}^l=\underset{t=1,{\underset{\‾}{o}}_t=v_k}{\overset{T}{\Σ}}{\mathrm{\γ}}_t^l\left(j\right)/dual\underset{t=1}{\overset{T}{\Σ}}{\mathrm{\γ}}_t^l\left(j\right);$

${\mathrm{\π}}_i^l=e_1^l/dual\underset{i}{\Σ}{e}_1^l={\mathrm{\γ}}_1^l\left(i\right);$

Wherein, represent the lower bound of the state transfer interval probability being transferred to state j by state i; represent under state j prerequisite, observed reading is the lower bound of the observation interval probability of k; the lower bound of expression state i original state interval probability; represent that t is i state, the t+1 moment is the interval probability lower bound of j state; represent that t state is the interval probability lower bound of j;

Finally derive the dynamic force distribution of current to described bionical sea dog antenna as follows:

$\frac{\∂u}{\∂t}+(u\·\▿)u=g-\frac{1}{\mathrm{\ρ}}\▿P+\mathrm{\ν}{\▿}^{2}u;$

Wherein, Hamiltonian operator u is velocity, and g is gravitational vector, and ▽ P is pressure differential, and ρ is density, ν ▽ ²u is diffusion term.

The invention has the beneficial effects as follows, the analytical approach of the dynamics of this bionical sea dog Whisker Sensor adopts multistage Timoshenko beam theory and passes the dynamics of the bionical sea dog antenna of matrix analysis method free state, disclose the parameters such as elastic modulus, shearing factor, damping ratio and sectional dimension to the affecting laws of Structural Natural Vibration Characteristic, the progress for bionical sea dog Whisker Sensor is significant.

Accompanying drawing explanation

Below in conjunction with drawings and Examples, the present invention is further described.

Fig. 1 be the optimum embodiment of the analytical approach of the dynamics of the present invention bionical sea dog Whisker Sensor based on the schematic diagram of the kinetic model of the bionical sea dog antenna under free state.

Fig. 2 is that the optimum embodiment of the analytical approach of the dynamics of the present invention bionical sea dog Whisker Sensor is to the stepwise schematic views of complete bionical sea dog antenna.

Fig. 3 is the collection of illustrative plates of the frequency response function of bionical sea dog antenna free end.

Fig. 4 is the collection of illustrative plates of the frequency response function of bionical sea dog antenna junction.

Fig. 5 is the schematic diagram of the kinetic model of imitative sea dog Whisker Sensor.

Fig. 6 is the schematic diagram of General Hidden Markov Model.

Fig. 7 is the structural response collection of illustrative plates of bionical sea dog antenna.

Embodiment

Be described below in detail embodiments of the invention, the example of described embodiment is shown in the drawings, and wherein same or similar label represents same or similar element or has element that is identical or similar functions from start to finish.Being exemplary below by the embodiment be described with reference to the drawings, only for explaining the present invention, and can not limitation of the present invention being interpreted as.On the contrary, embodiments of the invention comprise fall into attached claims spirit and intension within the scope of all changes, amendment and equivalent.

In describing the invention, it will be appreciated that, term " " center ", " longitudinal direction ", " transverse direction ", " length ", " width ", " thickness ", " on ", D score, " front ", " afterwards ", " left side ", " right side ", " vertically ", " level ", " top ", " end " " interior ", " outward ", " axis ", " radial direction ", orientation or the position relationship of the instruction such as " circumference " are based on orientation shown in the drawings or position relationship, only the present invention for convenience of description and simplified characterization, instead of indicate or imply that the device of indication or element must have specific orientation, with specific azimuth configuration and operation, therefore limitation of the present invention can not be interpreted as.

In addition, term " first ", " second " etc. only for describing object, and can not be interpreted as instruction or hint relative importance.In describing the invention, it should be noted that, unless otherwise clearly defined and limited, term " is connected ", " connection " should be interpreted broadly, such as, can be fixedly connected with, also can be removably connect, or connect integratedly; Can be mechanical connection, also can be electrical connection; Can be directly be connected, also indirectly can be connected by intermediary.For the ordinary skill in the art, concrete condition above-mentioned term concrete meaning in the present invention can be understood.In addition, in describing the invention, except as otherwise noted, the implication of " multiple " is two or more.

The invention provides a kind of analytical approach of dynamics of bionical sea dog Whisker Sensor, comprise the following steps:

A1, a bionical sea dog antenna is divided into continuous multiple Timoshenko beam section, as shown in Figure 1, this is the kinetic model of the bionical sea dog antenna under free state, makes the moment of flexure of the left side of Timoshenko beam section and shearing force be respectively M _i-1, Q _i-1, moment of flexure and the shearing force of right side are respectively M _i, Q _i, the kinematical equation setting up Timoshenko beam section is as follows:

$\frac{\∂}{\∂x^2}\left(EI\frac{{\∂}^{2}y}{\∂x^2}\right)+m\frac{{\∂}^{2}y}{\∂t^2}-\frac{mI}{A}\frac{{\∂}^{4}y}{\∂x^2\∂t^2}-\frac{mEIk}{GA}\frac{{\∂}^{4}y}{\∂x^2\∂t^2}-\frac{m^{2}Ik}{{\mathrm{GA}}^2}\frac{{\∂}^{4}y}{\∂t^4}=0;$

Wherein, y (x, t) is the straight-line displacement of any point in Timoshenko beam section; A is Timoshenko beam section cross-sectional area; M is the Timoshenko beam section quality of unit length; E is Young's modulus of elasticity; G is modulus of shearing; K is shearing factor; I is second-order section moment of inertia; L is beam segment length;

The dynamic balance equation setting up Timoshenko beam section is as follows:

$\frac{GA}{k}(\frac{{\∂}^{2}y}{\∂x^2}-\frac{\∂\mathrm{\θ}}{\∂x})-m\frac{{\∂}^{2}y}{\∂t^2}=0;$

Wherein, θ is the angular displacement of any point in Timoshenko beam section;

A2, the state vector expression formula obtaining Timoshenko beam section left side according to the kinematical equation of Timoshenko beam section and dynamic balance equation are as follows:

$\begin{array}{c}{\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_{i-1}=\left[\begin{array}{cc}0& 1\\ \frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\δ}}^2}{GA\mathrm{\δ}}& 0\\ 0& -\frac{EI\left({\mathrm{mk\ω}}^2-{\mathrm{GA\δ}}^2\right)}{GA}\\ \frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}& 0\end{array}\right.\\ \left.\begin{array}{cc}0& 1\\ \frac{{\mathrm{mk\ω}}^2+{\mathrm{GA\ϵ}}^2}{GA\mathrm{\ϵ}}& 0\\ 0& -\frac{EI\left({\mathrm{mk\ω}}^2-{\mathrm{GA\ϵ}}^2\right)}{GA}\\ \frac{{\mathrm{m\ω}}^2}{\mathrm{\ϵ}}& 0\end{array}\right]\left\{\begin{array}{c}{C}_1\\ C_2\\ C_3\\ C_4\end{array}\right\}\end{array};$

And the state vector expression formula of Timoshenko beam section right side is as follows:

$\begin{array}{c}{\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_i=\left[\begin{array}{cc}\sin l\mathrm{\δ}& \cos l\mathrm{\δ}\\ -\frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\δ}}^2}{GA\mathrm{\δ}}\cos l\mathrm{\δ}& \frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\δ}}^2}{GA\mathrm{\δ}}\sin l\mathrm{\δ}\\ \frac{EI({\mathrm{GA\δ}}^2-{\mathrm{mk\ω}}^2)}{GA}\sin l\mathrm{\δ}& \frac{EI({\mathrm{GA\δ}}^2-{\mathrm{mk\ω}}^2)}{GA}\cos l\mathrm{\δ}\\ \frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}\cos l\mathrm{\δ}& -\frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}\sin l\mathrm{\δ}\end{array}\right.\\ \left.\begin{array}{cc}shl\mathrm{\ϵ}& chl\mathrm{\δ}\\ \frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\ϵ}}^2}{GA\mathrm{\ϵ}}chl\mathrm{\ϵ}& \frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\ϵ}}^2}{GA\mathrm{\ϵ}}shl\mathrm{\δ}\\ -\frac{EI({\mathrm{GA\ϵ}}^2+{\mathrm{mk\ω}}^2)}{GA}shl\mathrm{\ϵ}& -\frac{EI({\mathrm{GA\ϵ}}^2+{\mathrm{mk\ω}}^2)}{GA}chl\mathrm{\ϵ}\\ -\frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}chl\mathrm{\ϵ}& -\frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}shl\mathrm{\ϵ}\end{array}\right]\left\{\begin{array}{c}{C}_1\\ C_2\\ C_3\\ C_4\end{array}\right\}\end{array};$

A3, order ${\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_{i-1}=T_{i-1}\left\{\begin{array}{c}{C}_1\\ C_2\\ C_3\\ C_4\end{array}\right\}$ With ${\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_i=T_i\left\{\begin{array}{c}{C}_1\\ C_2\\ C_3\\ C_4\end{array}\right\},$ Then the pass of Timoshenko beam section left side and right side state vector is:

${\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_i=T_i{T}_{i-1}^{-1}{\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_{i-1};$

Then the transfer matrix of Timoshenko beam section left side and right side is:

$D_i=T_i{T}_{i-1}^{-1};$

As Fig. 2, complete bionical sea dog antenna is divided into 11 sections, then the transitive relation of bionical sea dog antenna entirety is:

{z} _i＝[D ₁₁][D ₁₀][D ₉]…[D ₂][D ₁]{z} ₀＝[H]{z} ₀；

A4, the transitive relation of bionical sea dog antenna entirety to be revised as:

{z} _i＝[H]({z} ₀-{Δz}) ₀-{Δz} _i；

And by the transfer matrix of bionical sea dog antenna entirety be:

${\left\{\begin{array}{c}y\\ \mathrm{\θ}\\ 0\\ 0\end{array}\right\}}_{11}=\left[\begin{array}{cccc}\×& \×& \×& \×\\ \×& \×& \×& \×\\ t_{31}& t_{32}& \×& t_{34}\\ t_{41}& t_{42}& \×& t_{44}\end{array}\right]{\left\{\begin{array}{c}y\\ \mathrm{\θ}\\ 0\\ -P\end{array}\right\}}_0$

The wherein shearing force of P suffered by bionical sea dog antenna entirety, to calculate on bionical sea dog antenna any point straight-line displacement for the frequency response function H of shearing force ₀₀with the frequency response function N of angular displacement for shearing force ₀₀:

$H_{00}=\frac{y_0}{P_0}=\frac{t_{34}{t}_{42}-t_{32}{t}_{44}}{t_{31}{t}_{42}-t_{41}{t}_{32}}$

$N_{00}=\frac{{\mathrm{\θ}}_0}{P_0}=\frac{t_{41}{t}_{34}-t_{31}{t}_{44}}{t_{41}{t}_{32}-t_{31}{t}_{42}}$

In like manner can to obtain on bionical sea dog antenna any point straight-line displacement for the frequency response function L of moment of flexure ₀₀with the frequency response function P of angular displacement for moment of flexure ₀₀; As shown in Figure 3 and Figure 4, the frequency response function of bionical sea dog antenna free end and the frequency response function of bionical sea dog antenna junction can be found out very intuitively.

The further comprising the steps of current that obtain distribute to the dynamic force of bionical sea dog antenna:

The faying face of bionical sea dog antenna and sensor body is simulated by straight line, main spring and damping unit, utilize DYNAMIC DISTRIBUTION load F (z, t) simulated flow is to the radial forces of imitative sea dog antenna, the kinetic model of imitative sea dog Whisker Sensor under setting up streamflow regime, as shown in Figure 5.Assuming that fluid is continuous print, and all fields related to, such as pressure field, temperature field etc. all can be micro-;

Due to randomness and the pulsating nature of Particles flow under streamflow regime, the present invention passes through General Hidden Markov Model, as shown in Figure 6, prediction current are to the dynamic force of imitative sea dog antenna structure, using the DYNAMIC DISTRIBUTION load as structure that predicts the outcome, General Hidden Markov Model is exactly utilize the exact probability in generalized interval probability replacement Hidden Markov Model (HMM), effectively can solve the impact that initial probability distribution predicts the outcome on acting force, significantly improve the precision of prediction of dynamic force, be specially:

Set up General Hidden Markov Model (GHMM):

λ＝(N,M,π,A,B)；

Wherein, N represents hidden state number, and hidden state can be expressed as S={S ₁, S ₂..., S _n, in t, hidden state variable is q _t; What M represented each state may observe number, and the observed result of each state can be expressed as V={v ₁, v ₂..., v _n, be o in the observed reading of t _t; Observation sequence is designated as O={o ₁, o ₂..., o _n, the observation sequence upper bound is observation sequence lower bound is o= o ₁, o ₂..., o _n;

By Baum-Welch algorithm, General Hidden Markov Model training formula can be obtained as follows:

$\log p(\underset{\‾}{O},Q|\mathrm{\λ})=log\left(p\right(Q\left|\mathrm{\λ}\right).p\left(\underset{\‾}{O}\right|Q,\mathrm{\λ}))={\mathrm{log\π}}_{q_1}^l+\underset{t=1}{\overset{T-1}{\Σ}}{\mathrm{loga}}_{q_t{q}_{t+1}}^l+\underset{t=1}{\overset{T}{\Σ}}{\mathrm{loga}}_{q_t}^l\left({\underset{\‾}{O}}_t\right);$

Thus obtain the bound revaluation formula of GHMM parameter, as obtain maximal value, GHMM parameter upper bound revaluation formula can be obtained as follows:

$a_{ij}^l=c_{ij}^l/dual\underset{j}{\Σ}{c}_{ij}^l=\underset{t=1}{\overset{T-1}{\Σ}}{\mathrm{\ξ}}_t^l(i,j)/dual\underset{t=1}{\overset{T-1}{\Σ}}{y}_t^l\left(i\right);$

$b_{j\left(k\right)}^l=d_{jk}^l/dual\underset{k}{\Σ}{d}_{jk}^l=\underset{t=1,{\underset{\‾}{o}}_t=v_k}{\overset{T}{\Σ}}{\mathrm{\γ}}_t^l\left(j\right)/dual\underset{t=1}{\overset{T}{\Σ}}{\mathrm{\γ}}_t^l\left(j\right);$

${\mathrm{\π}}_i^l=e_1^l/dual\underset{i}{\Σ}{e}_1^l={\mathrm{\γ}}_1^l\left(i\right);$

Wherein, represent the lower bound of the state transfer interval probability being transferred to state j by state i; represent under state j prerequisite, observed reading is the lower bound of the observation interval probability of k; the lower bound of expression state i original state interval probability; represent that t is i state, the t+1 moment is the interval probability lower bound of j state; represent that t state is the interval probability lower bound of j;

Finally derive the dynamic force distribution of current to bionical sea dog antenna as follows:

$\frac{\∂u}{\∂t}+(u\·\▿)u=g-\frac{1}{\mathrm{\ρ}}\▿P+\mathrm{\ν}{\▿}^{2}u;$

Wherein, Hamiltonian operator u is velocity, and g is gravitational vector, and ▽ P is pressure differential, and ρ is density, ν ▽ ²u is diffusion term;

As shown in Figure 7, according to the end points frequency response function of bionical sea dog antenna with act on bionical sea dog antenna structure dynamics distribution of forces situation, the dynamic response of bionical sea dog antenna structure free end, intermediate point and stiff end can be obtained by the method for integration.

In the description of this instructions, specific features, structure, material or feature that the description of reference term " embodiment ", " some embodiments ", " example ", " concrete example " or " some examples " etc. means to describe in conjunction with this embodiment or example are contained at least one embodiment of the present invention or example.In this manual, identical embodiment or example are not necessarily referred to the schematic representation of described term.And the specific features of description, structure, material or feature can combine in an appropriate manner in any one or more embodiment or example.

With above-mentioned according to desirable embodiment of the present invention for enlightenment, by above-mentioned description, relevant staff in the scope not departing from this invention technological thought, can carry out various change and amendment completely.The technical scope of this invention is not limited to the content on instructions, must determine its technical scope according to right.

Claims (2)

1. an analytical approach for the dynamics of bionical sea dog Whisker Sensor, is characterized in that: comprise the following steps:

A1, a bionical sea dog antenna is divided into continuous multiple Timoshenko beam section, makes the moment of flexure of the left side of described Timoshenko beam section and shearing force be respectively M _i-1, Q _i-1, moment of flexure and the shearing force of right side are respectively M _i, Q _i, the kinematical equation setting up described Timoshenko beam section is as follows:

$\frac{\∂}{\∂x^2}\left(EI\frac{{\∂}^{2}y}{\∂x^2}\right)+m\frac{{\∂}^{2}y}{\∂t^2}-\frac{mI}{A}\frac{{\∂}^{4}y}{\∂x^2\∂t^2}-\frac{mEIk}{GA}\frac{\∂4y}{\∂x^2\∂t^2}-\frac{m^{2}Ik}{{\mathrm{GA}}^2}\frac{\∂4y}{\∂t^4}=0;$

Wherein, y (x, t) is the straight-line displacement of any point in described Timoshenko beam section; A is Timoshenko beam section cross-sectional area; M is the Timoshenko beam section quality of unit length; E is Young's modulus of elasticity; G is modulus of shearing; K is shearing factor; I is second-order section moment of inertia; L is beam segment length;

The dynamic balance equation setting up described Timoshenko beam section is as follows:

$\frac{GA}{k}(\frac{{\∂}^{2}y}{\∂x^2}-\frac{\∂\mathrm{\θ}}{\∂x})-m\frac{{\∂}^{2}y}{\∂t^2}=0;$

Wherein, θ is the angular displacement of any point in described Timoshenko beam section;

A2, the state vector expression formula obtaining described Timoshenko beam section left side according to the kinematical equation of described Timoshenko beam section and dynamic balance equation are as follows:

$\begin{array}{c}{\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_{i-1}=\left[\begin{array}{cc}0& 1\\ \frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\δ}}^2}{GA\mathrm{\δ}}& 0\\ 0& -\frac{EI({\mathrm{mk\ω}}^2-{\mathrm{GA\δ}}^2)}{GA}\\ \frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}& 0\end{array}\right.\\ \left.\begin{array}{cc}0& 1\\ \frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\ϵ}}^2}{GA\mathrm{\ϵ}}& 0\\ 0& -\frac{EI({\mathrm{mk\ω}}^2-{\mathrm{GA\ϵ}}^2)}{GA}\\ \frac{{\mathrm{m\ω}}^2}{\mathrm{\ϵ}}& 0\end{array}\right]\left\{\begin{array}{c}{C}_I\\ C_2\\ C_3\\ C_4\end{array}\right\}\end{array};$

And the state vector expression formula of described Timoshenko beam section right side is as follows:

$\begin{array}{c}{\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_i=\left[\begin{array}{cc}\sin l\mathrm{\δ}& \cos l\mathrm{\δ}\\ -\frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\δ}}^2}{GA\mathrm{\δ}}\cos l\mathrm{\δ}& \frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\δ}}^2}{GA\mathrm{\δ}}\sin l\mathrm{\δ}\\ \frac{EI({\mathrm{GA\δ}}^2-{\mathrm{mk\ω}}^2)}{GA}\sin l\mathrm{\δ}& \frac{EI({\mathrm{GA\δ}}^2-{\mathrm{mk\ω}}^2)}{GA}\cos l\mathrm{\δ}\\ \frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}\cos l\mathrm{\δ}& -\frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}\sin l\mathrm{\δ}\end{array}\right.\\ \left.\begin{array}{cc}shl\mathrm{\ϵ}& chl\mathrm{\ϵ}\\ \frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\ϵ}}^2}{GA\mathrm{\ϵ}}chl\mathrm{\ϵ}& \frac{{\mathrm{mk\ω}}^2-{\mathrm{GA\ϵ}}^2}{GA\mathrm{\ϵ}}shl\mathrm{\δ}\\ -\frac{EI({\mathrm{GA\φ}}^2-{\mathrm{mk\ω}}^2)}{GA}shl\mathrm{\ϵ}& -\frac{EI({\mathrm{GA\ϵ}}^2-{\mathrm{mk\ω}}^2)}{GA}chl\mathrm{\ϵ}\\ -\frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}chl\mathrm{\ϵ}& -\frac{{\mathrm{m\ω}}^2}{\mathrm{\δ}}shl\mathrm{\ϵ}\end{array}\right]\left\{\begin{array}{c}{C}_1\\ C_2\\ C_3\\ C_4\end{array}\right\}\end{array};$

A3, order ${\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_{i-1}=T_{i-1}\left\{\begin{array}{c}{C}_1\\ C_2\\ C_3\\ C_4\end{array}\right\}$ With ${\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_i=T_i\left\{\begin{array}{c}{C}_1\\ C_2\\ C_3\\ C_4\end{array}\right\},$ Then the pass of described Timoshenko beam section left side and right side state vector is:

${\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_i=T_i{T}_{i-1}^{-1}{\left[\begin{array}{c}y\\ \mathrm{\θ}\\ M\\ Q\end{array}\right]}_{i-1};$

Then the transfer matrix of described Timoshenko beam section left side and right side is:

$D_i=T_i{T}_{i-1}^{-1};$

Then the transitive relation of described bionical sea dog antenna entirety is:

{z} _i＝[D _i][D _i-1][D _i-2]…[D ₂][D ₁]{z} ₀＝[H]{z} ₀；

A4, the transitive relation of described bionical sea dog antenna entirety to be revised as:

{z} _i＝[H]({z} ₀-{Δz}) ₀-{Δz} _i；

And by the transfer matrix of described bionical sea dog antenna entirety be:

${\left\{\begin{array}{c}y\\ \mathrm{\θ}\\ 0\\ 0\end{array}\right\}}_i=\left[\begin{array}{cccc}\×& \×& \×& \×\\ \×& \×& \×& \×\\ t_{4i-13}& t_{4i-12}& \×& t_{4i-10}\\ t_{4i-3}& t_{4i-2}& \×& t_{4i}\end{array}\right]{\left\{\begin{array}{c}y\\ \mathrm{\θ}\\ 0\\ -P\end{array}\right\}}_0$

The wherein shearing force of P suffered by described bionical sea dog antenna entirety, to calculate on described bionical sea dog antenna any point straight-line displacement for the frequency response function H of shearing force ₀₀with the frequency response function N of angular displacement for shearing force ₀₀:

$H_{00}=\frac{y_0}{P_0}=\frac{t_{4i-10}{t}_{4i-2}-t_{4i-12}{t}_{4i}}{t_{4i-13}{t}_{4i-2}-t_{4i-3}{t}_{4i-12}};$

$N_{00}=\frac{{\mathrm{\θ}}_0}{P_0}=\frac{t_{4i-3}{t}_{4i-10}-t_{4i-13}{t}_{4i}}{t_{4i-3}{t}_{4i-12}-t_{4i-13}{t}_{4i-2}};$

In like manner can to obtain on described bionical sea dog antenna any point straight-line displacement for the frequency response function L of moment of flexure ₀₀with the frequency response function P of angular displacement for moment of flexure ₀₀.

2. the analytical approach of the dynamics of bionical sea dog Whisker Sensor as claimed in claim 1, is characterized in that: the further comprising the steps of current that obtain distribute to the dynamic force of bionical sea dog antenna:

Set up General Hidden Markov Model (GHMM):

λ＝(N,M,π,A,B)；

Wherein, N represents hidden state number, and hidden state can be expressed as S={S ₁, S ₂..., S _n, in t, hidden state variable is q _t; What M represented each state may observe number, and the observed result of each state can be expressed as V={v ₁, v ₂..., v _n, be o in the observed reading of t _t; Observation sequence is designated as O={o ₁, o ₂..., o _n, the observation sequence upper bound is $\stackrel{\‾}{O}=\{{\stackrel{\‾}{o}}_1,{\stackrel{\‾}{o}}_2,...,{\stackrel{\‾}{o}}_N\},$ Observation sequence lower bound is o= o ₁, o ₂..., o _n}

By Baum-Welch algorithm, General Hidden Markov Model training formula can be obtained as follows:

$\log p(\underset{\‾}{\text{O}},Q|\mathrm{\λ})=\log (p\left(Q\right|\mathrm{\λ}).p\left(\underset{\‾}{\text{O}}\right|Q,\mathrm{\λ}))={\mathrm{log\π}}_{q_1}^l+\underset{t=1}{\overset{T-1}{\mathrm{\Σ}}}{\mathrm{loga}}_{q_t{q}_{t+1}}^l+\underset{t=1}{\overset{T}{\mathrm{\Σ}}}{\mathrm{loga}}_{q_t}^l\left({\underset{\‾}{\text{O}}}_t\right);$

Thus obtain the bound revaluation formula of GHMM parameter, as obtain maximal value, GHMM parameter upper bound revaluation formula can be obtained as follows:

$a_{ij}^l=c_{ij}^l/dual\underset{j}{\Σ}{c}_{ij}^l=\underset{t=1}{\overset{T-1}{\Σ}}{\mathrm{\ξ}}_t^l(i,j)/dual\underset{t=1}{\overset{T-1}{\Σ}}{y}_t^l\left(i\right);$

$b_{j\left(k\right)}^l=d_{jk}^l/dual\underset{k}{\Σ}{d}_{jk}^l=\underset{t=1,{\underset{\‾}{o}}_t=v_k}{\overset{T}{\Σ}}{y}_t^l\left(j\right)/dual\underset{t=1}{\overset{T}{\Σ}}{y}_t^l\left(j\right);$

${\mathrm{\π}}_i^l=e_1^l/dual\underset{i}{\Σ}{e}_1^l={\mathrm{\γ}}_1^l\left(i\right);$

Wherein, represent the lower bound of the state transfer interval probability being transferred to state j by state i; represent under state j prerequisite, observed reading is the lower bound of the observation interval probability of k; the lower bound of expression state i original state interval probability; represent that t is i state, the t+1 moment is the interval probability lower bound of j state; represent that t state is the interval probability lower bound of j;

Finally derive the dynamic force distribution of current to described bionical sea dog antenna as follows:

$\frac{\∂u}{\∂t}+(u\·\▿)u=g-\frac{1}{\mathrm{\ρ}}\▿P+v{\▿}^{2}u;$

Wherein, Hamiltonian operator u is velocity, and g is gravitational vector, and ▽ P is pressure differential, and ρ is density, ν ▽ ²u is diffusion term.