CN1472514A - Sound field reconfiguration method for rapid noise diagnosis - Google Patents

Abstract

The method divides sound field into a numbers of regions and to present sound field at each region as linear superposition of region node sound pressure according to sound pressure at several known measuring points in certain sound field of known sound source shape. The regional node sound pressure can be obtained according to sound pressure of measuring point through least square method and singular value decomposition, and then sound pressure for the complete sound field can be rebuilt through sound pressure of regional node. The method is more accurate and efficient than HELS method in describing sound field.

Description

The sound field reconstructing method of quick noise diagnostics

Affiliated technical field

What the present invention relates to is a kind of sound field reconstructing method, particularly a kind ofly can come the sound field reconstructing method of the quick noise diagnostics of other dot informations of reconstruct accurately according to the information of the less point of measuring in the sound field, belongs to the noise diagnostics technical field.

Background technology

In the noise failure diagnosis, may can only measure noise signal seldom, how in a short period of time, be similar to unknown signaling in the sound field, cause many scholars' attention according to these less known signals.

Adopt computing method such as near-field holography, boundary element to carry out noise diagnostics, generally expend time in more or cost higher.1997, people such as Wang proposed to use the HELS method, and used analog computation and experimental study that the HELS method is verified respectively 1998,2000, calendar year 2001 etc.HELS method reconstruct sound field efficient is very high, and simple, flexible, does not have Element BEM in the not unique shortcoming of feature wave number.Therefore, the HELS method is extremely suitable is applied to quick noise diagnostics.In the prior art, the patent No. is 5,712,805 United States Patent (USP) " noise diagnostics system " is to adopt the HELS method, acoustic pressure in the sound field is converted into the stack of spheric wave function, uses least square method then, come the acoustic pressure on reconstruct sound source surface according to known noise signal.The problem that this method exists is: when independent function is selected improper or selected the measurement point of different radii is arranged, use the sound field of HELS method reconstruct pulsation ball also to produce than mistake.Require the point of reconstruct very approaching from the point of measuring, and, use the HELS method to be difficult to the sound field of the common spherical sound source of reconstruct, for non-ball sound source, the error of calculating is very big.This method is inapplicable for high frequency, and very low to the efficient of non-ball sound source sound field reconstruct.

Summary of the invention

Be deficiency and the defective that overcomes prior art, expand the scope of application of traditional HELS method, and keep the high-level efficiency of traditional HELS method.The present invention has proposed a kind of sound field reconstructing method that is used for quick noise diagnostics on the basis of traditional HELS method and Infinite Element Method.This new sound field reconstructing method, wider than the scope of application of traditional HELS method, efficient is higher.

This method is that the acoustic pressure of known some spots (being called measurement point) is divided into several zones to sound field according in known certain sound field of sound source shape, and each regional sound field is expressed as the linear superposition of Area Node acoustic pressure.According to the acoustic pressure of measurement point,, can obtain the acoustic pressure of Area Node by least square method and svd.By the acoustic pressure of Area Node, can obtain the acoustic pressure of each regional every bit then.Concrete grammar is as follows:

1, sets up ellipsoidal coordinates

The sound source near surface draw an ellipsoid more approaching with the sound source shape (also can be drawn in the sound source by fraction, in a word will with the roughly similar ellipsoid of sound source shape), set up ellipsoidal coordinates.

2, zoning and node

According to the number and the distribution situation of measurement point in the sound field, sound field is divided into several zones along the change in coordinate axis direction of ellipsoidal coordinates.If outside sound field, just the radial direction along ellipsoidal coordinates is divided into several infinite regions, and each infinite region extends along radial direction is outwards unlimited; If internal acoustic field just is divided into limited area.

If the number of measurement point is more in the sound field, the number of regions in the sound field needs more; The dense place of measurement point distribution also needs more zone in the sound field.There is plurality of nodes in each zone.For the purpose of convenience of calculation was accurate, the node in zone was next to measurement point as much as possible.

3, calculate the interpolating function of each measurement point

Utilize the interpolating function formula in infinite element method zone: $\mathrm{\ψ}={\mathrm{\ψ}}_{\mathrm{\μ}}^{\left(r\right)}{\mathrm{\ψ}}_v^{\left(\mathrm{\φ}\right)}{\mathrm{\ψ}}_w^{\left(\mathrm{\θ}\right)}......\left(1\right)$ Wherein (r, φ θ) are ellipsoidal coordinates, ψ _v ^(φ), ψ _w ^(θ)Be respectively along φ, traditional finite element interpolating function of θ direction is chosen as the Lagrange interpolation polynomial here, if the sound field of limited area, ψ _μ ^(r)Be the interpolation polynomial of r direction, also can be chosen as the Lagrange interpolation polynomial here.Because for the sound field of infinite region, must consider the infinite distance radiation boundary condition, be chosen as here: ${\mathrm{\ψ}}_{\mathrm{\μ}}^r\left(r_{\mathrm{\μ}}\right)=e^{-\mathrm{ik}(r-r_{\mathrm{\μ}})}\underset{\stackrel{.}{\mathrm{\μ}}=1}{\overset{n}{\mathrm{\Σ}}}\frac{h_{\mathrm{\μ}\stackrel{.}{\mathrm{\μ}}}}{(\mathrm{kr}{)}^{\stackrel{.}{\mathrm{\μ}}}}\mathrm{\μ}=\mathrm{1,2},\mathrm{\Λ},n(n\≥2)......\left(2\right)$ H=S wherein ^-1, S _1m=(kr _m) ^-1, r _μThe radial coordinate of representing μ node, k represents wave number.(2) formula also may be thought of as shifted Legendre polynomial expression and shifted Chebyshev polynomial expression simultaneously, and its ultimate principle is identical, and (2) formula is simple a little but use both calculation procedures of writing of back.

4, calculate the node acoustic pressure

Come the computing node acoustic pressure according to the sound pressure level of measurement point and the interpolating function of measurement point:

{C}＝[ζ] ^u{ξ} (3)

Wherein, can calculate by interpolating function and measurement point acoustic pressure respectively in matrix [ζ] and the vector { ξ }.Matrix element wherein is respectively ${\mathrm{\ζ}}_{\mathrm{mn}}={\mathrm{\ψ}}_{\mathrm{jm}}^{*}{\mathrm{\ψ}}_{\mathrm{nj}}^{*},$ ${\mathrm{\ξ}}_1=P_{\mathrm{oi}}{\mathrm{\ψ}}_{\mathrm{ji}}^{*},$ [ζ] ^uBe the pseudoinverse of trying to achieve by svd, P _{() i}Expression measurement point acoustic pressure.

In particular cases, can be chosen as node to measurement point, calculating can be omitted this process 3 and 4 like this, and the calculated amount of this moment will sharply descend, and counting yield will be greatly improved.

5, calculate the interpolating function of reconstruction point

The computing method of reconstruction point interpolating function are as 3, and computing formula still is (1) (2).

6, reconstruct in the sound field acoustic pressure of any arbitrarily

The acoustic pressure of reconstruction point can be calculated according to following acoustic pressure equation: $P\left(x\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{C}_i{\mathrm{\ψ}}_i\left(x\right)......\left(4\right)$

What N wherein represented is the number of this zone interior nodes, C _I(x) acoustic pressure of i node of expression, ψ _iInterpolating function for reconstruction point.

Because the acoustic pressure of use node is described the information in the sound field, be equivalent to use rational interpolating function to come the sound field of approximate region, do not attempt to find the solution the simple function that to describe whole sound field, therefore sound field can be described more accurate than HELS method, more efficiently, sound source, each frequency range sound field reconstruct problem that can the approximate solution different shape.Again because be quick noise diagnostics, and do not require the acoustic pressure of accurately describing each point, so the zone can be seldom.The present invention has avoided using the loaded down with trivial details equation integration of the unlimited unit of ellipsoid sound, thereby has significantly reduced the calculating time spent.This method had both kept the high-level efficiency of traditional HELS method, had widened the calculating suitable application area of this method again widely.This method can be generalized to unbounded fields such as magnetic field, wave stroke equally easily.

Description of drawings

Fig. 1 is dividing region and a node synoptic diagram in certain long rotation ellipsoid sound source sound field.Contain 20 infinite regions, 40 nodes among the figure altogether, each 4 node in zone, for example 1,20,21,40 4 node is contained in zone one, and 1,2,21,22 4 node is contained in zone two, or the like.Among the figure from inside to outside the radius of ellipsoid be respectively 1,2,10, infinity, represent the radius of sound source, the radius of node 1～20 place ellipsoid, the radius of node 21～40 place ellipsoids, infinite distant place successively.

The sound pressure amplitude of the reconstruct of the long rotation ellipsoid sound source of Fig. 2 is with the variation of θ, and solid line representation theory value, * add dotted line and represent reconstruction value of the present invention, and adds the reconstruction value that dotted line represents to use the HELS method of 6 independent functions.Wherein the longitudinal axis represent sound pressure amplitude (unit is: handkerchief), transverse axis denotation coordination θ.

Embodiment

Below in conjunction with accompanying drawing concrete enforcement of the present invention is further described.

As shown in Figure 1, one long rotation ellipsoid sound source, its major axis and minor axis are respectively 1 and 0.5 meter, radius is on 3 and 9 (coordinate the is ellipsoidal coordinates) ellipsoid far away in the sound field, select a measurement point along angular direction θ from 4.5 degree every 9 degree, have 80 measurement points, the acoustic pressure of 80 measurement points is known.

According to these 80 measurement point acoustic pressures, the process that reconstructs whole sound field acoustic pressure is as follows:

1, sets up ellipsoidal coordinates

Set up ellipsoidal coordinates (only having used two-dimensional coordinate here), its major axis is 1 meter, and minor axis is 0.5 meter.Wherein ellipsoidal coordinates (r, θ) and Cartesian coordinates (x, corresponding relation y) is:

2, zoning and node

By the distribution situation of measurement point, whole sound field is divided into 20 zones along unlimited direction, there are 4 nodes in each zone.Each node is all on radius is 10 and 2 ellipsoid.4 nodes are contained in each zone.

3, calculate the interpolating function of each measurement point

Here set: ${\mathrm{\ψ}}_1^{\left(\mathrm{\θ}\right)}\left(\mathrm{\ξ}\right)=\frac{1}{2}(\mathrm{\ξ}-1)$ ${\mathrm{\ψ}}_2^{\left(\mathrm{\θ}\right)}\left(\mathrm{\ξ}\right)=\frac{1}{2}(\mathrm{\ξ}+1)$ $\mathrm{\θ}\left(\mathrm{\ξ}\right)=\underset{v=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\ψ}}_v^{\left(\mathrm{\φ}\right)}\left(\mathrm{\ξ}\right){\mathrm{\θ}}_v......\left(6\right)$

Coordinate figure by measurement point can calculate: ${\mathrm{\ψ}}_1^r\left(r\right)=e^{-i\×11.088\×(r-2)}[-\frac{1}{2r}+\frac{5}{r^2}]$ ${\mathrm{\ψ}}_2^r\left(r\right)=e^{-i\×11.088\×(r-10)}[\frac{25}{2r}-\frac{25}{r^2}]......\left(7\right)$

According to formula (1), can calculate the interpolating function of measurement point.

4, calculate the node acoustic pressure

According to formula (3), the acoustic pressure that can calculate each node is planted.

5, calculate the interpolating function of reconstruction point

The interpolating function computing method of reconstruction point are identical with 3.

6, reconstruct in the sound field acoustic pressure of any arbitrarily

According to the interpolating function value of reconstruction point and the sound pressure level of node,, can calculate the acoustic pressure of reconstruction point by formula (4).Because the position of reconstruction point can be selected arbitrarily, thus sound pressure level that can the whole sound field of reconstruct.

Reconstruction point is that result of calculation is shown in * among Fig. 2 on 5 the ellipsoid at radius, and the * with dashed lines among the figure links up.

Adopt Element BEM to calculate theoretical approximate value, represent with solid line in the drawings.

For superiority of the present invention is described, use 6 independent functions of HELS method to calculate same example, result of calculation is shown in among Fig. 2, and the with dashed lines among the figure links up.

As can be seen, reconstruction result of the present invention overlaps with theoretical solution is approximate from the figure.

Superiority of the present invention can also display by following reconstruction result.

(1) computing time

The 0.04 second used time of the present invention, and the HELS method surpasses 0.15 second (not comprising the orthogonalized time of its independent function).

(2) computational accuracy

Reconstructed error of the present invention is less than 1%, and the reconstructed error of HELS method nearly 200%.

Therefore, the new sound field reconstructing method of the present invention's proposition is superior to the HELS method far away.

Claims (1)

1, a kind of sound field reconstructing method of quick noise diagnostics, it is characterized in that: this method is according in known certain sound field of sound source shape, the acoustic pressure of known some spots (being called measurement point), sound field is divided into several zones, each regional sound field is expressed as the linear superposition of Area Node acoustic pressure, acoustic pressure according to measurement point, by least square method and svd, can obtain the acoustic pressure of Area Node, acoustic pressure by Area Node then, can reconstruct the acoustic pressure of whole sound field, concrete grammar is:

(1) sets up ellipsoidal coordinates

Draw an ellipsoid more approaching at the sound source near surface, set up ellipsoidal coordinates based on this with the sound source shape;

(2) zoning and node

Number and distribution situation according to measurement point in the sound field, change in coordinate axis direction along ellipsoidal coordinates is divided into several zones to sound field, if outside sound field, just the radial direction along ellipsoidal coordinates is divided into several infinite regions, and each infinite region extends along radial direction is outwards unlimited; If internal acoustic field just is divided into limited area;

(3) calculate the interpolating function of each measurement point

Utilize the interpolating function formula in infinite element method zone to calculate: $\mathrm{\ψ}={\mathrm{\ψ}}_{\mathrm{\μ}}^{\left(r\right)}{\mathrm{\ψ}}_v^{\left(\mathrm{\φ}\right)}{\mathrm{\ψ}}_w^{\left(\mathrm{\θ}\right)};$

(4) calculate the node acoustic pressure

According to the sound pressure level of measurement point and the interpolating function of measurement point, come the computing node acoustic pressure by least square method and svd:

{C}＝[ζ] ^u{ξ}；

(5) calculate the interpolating function of reconstruction point

The computing method of reconstruction point interpolating function are the same with 3;

(6) reconstruct in the sound field acoustic pressure of any arbitrarily

According to the acoustic pressure of the interpolating function and the node of reconstruction point, calculate by following acoustic pressure equation: $P\left(x\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{C}_i{\mathrm{\ψ}}_i\left(x\right).$

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