Acoustic vector sensor

Abstract

An acoustic vector sensor (“AVS”) includes one or more sensitive elements arranged in an orthogonal configuration to provide high-sensitivity directional performance. The one more sensitive elements may be seismometers arranged in a pendulum-type configuration. The AVS further includes a hydrophone.

Claims

1. An acoustic vector sensor system comprising: a housing including therein at least three acoustically sensitive elements arranged in a 3-axis orthogonal configuration; a pendulum assembly including the at least three acoustically sensitive elements connected to an interior portion of the housing via a pendulum mount; and at least one omni-directional hydrophone.

2. The acoustic vector sensor system of claim 1, further comprising: a set of electronics for receiving analog signals from the at least three acoustically sensitive elements and for pre-amplifying the analog signals therefrom.

3. The acoustic vector sensor system of claim 1, wherein the housing is filled with a fluid.

4. The acoustic vector sensor system of claim 1, wherein the at least three acoustically sensitive elements are seismometers.

5. The acoustic vector sensor system of claim 1, wherein the at least three acoustically sensitive elements includes six seismometers, wherein three pairs of the six seismometers are arranged in a different direction of the 3 axis.

6. The acoustic vector sensor system of claim 1, wherein the system further includes a flotation mechanism.

7. An acoustic vector sensor system comprising: a waterproof housing containing therein a pendulum assembly, the pendulum assembly being attached to an interior portion of the waterproof housing via a pendulum mount and including therein an arrangement of seismometers; a flotation mechanism, wherein the waterproof housing is secured to the flotation mechanism; and at least one omni-directional hydrophone.

8. The acoustic vector sensor system of claim 7, wherein the arrangement of seismometers includes multiple seismometers, wherein at least one of the multiple seismometers is arranged in each of three orthogonal axis configurations.

9. The acoustic vector sensor system of claim 7, further comprising: a set of electronics for receiving analog signals from each of the seismometers and for pre-amplifying the analog signals from the seismometers.

10. The acoustic vector sensor system of claim 7, wherein the waterproof housing is filled with a fluid.

11. The acoustic vector sensor system of claim 8, wherein the multiple seismometers include three seismometers.

12. The acoustic vector sensor system of claim 8, wherein the multiple seismometers include six seismometers, where two of the six seismometers are arranged in each of the three orthogonal axes.

13. The acoustic vector sensor system of claim 7, wherein the system has an outside diameter in the range of approximately 4 to 5 inches and a length in the range of approximately 7 to 17 inches.

14. The acoustic vector system of claim 2, wherein the set of electronics includes an A/D converter and a packetizer.

15. The acoustic vector system of claim 9, wherein the set of electronics includes an A/D converter and a packetizer.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) The following figures are intended to be considered in conjunction with the description below.

(2) FIG. 1 is an exemplary acoustic vector sensor (“AVS”) in accordance with an embodiment described herein;

(3) FIGS. 2a to 2c illustrate acoustic vector sensor (“AVS”) using a pendulum assembly of in accordance with certain embodiments described herein;

(4) FIG. 3 is a vector sensor self-noise comparison of an (“AVS”) in accordance with an embodiment described herein;

(5) FIG. 4 illustrates a simple physical model of a suspension system in accordance with an embodiment described herein;

(6) FIG. 5 graphs dependence of seismometer-element motion relative to housing on viscosity of fluid in housing in accordance with an embodiment described herein;

(7) FIG. 6 provides a graphical representation of equation (5);

(8) FIG. 7 plots orientation of the sensitive elements as a function of time where the initial orientation is 20 degrees relative to the required orientation;

(9) FIG. 8 plots measured and expected data for sensitivity of an AVS as a function of frequency; and

(10) FIG. 9 plots measured and expected data for AVS beam-pattern defined as the response of the AVS as a function of azimuth.

DETAILED DESCRIPTION

(11) Referring to FIG. 1, in a first particular exemplary embodiment, an acoustic vector sensor (“AVS”) 10 includes three (3) seismometers or geophones (hereafter “sensors” or “seismometers” but not so limited) 15a, 15b, 15c, in an orthogonal, 3-axis configuration, to provide high-sensitivity directional performance. The embodiment of FIG. 1 is referred to as a pendulum-type and, as shown, is in a single sensor per axis configuration (1s Config). The second exemplary embodiment shown in FIGS. 2a and 2b is a dual sensor per axis, i.e., six (6) sensor 15a-15f (1.5f not shown, but opposite 15e), configuration (2s Config) pendulum-type. One skilled in the art will appreciate that the present embodiments may use fewer than three (3) seismometers

(12) As shown in the first and second exemplary embodiments, the seismometers are enclosed in a pendulum assembly 45 within a housing 20 and held in place by retainer plates 55 (see FIG. 2a), along with a first set of electronics 25 for pre-amplifying the analog signal from the seismometers. The first set of electronics 25 provides a low-noise preamplifier to preserve the inherent performance of the seismometers 15a-15f. The output of the preamplifier is typically routed to an A/D (Analog-to-Digital) converter.

(13) The housing 20 may be filled with an appropriate fluid 35, such as a silicone-based fluid like Polydimethylsiloxane (PDMS) Silicone. In the configuration shown in FIGS. 1,2a and 2b, the pendulum assembly 45 is attached to housing 20 via a pendulum mount 40.

(14) The AVS is coupled with a hydrophone 50 and a second set of electronics 30 to form a complete AVS system that is far less expensive than existing commercial-off-the-shelf (COTS) designs and is competitive with prior art omni-directional hydrophones. The second of electronics 30, independent of the first set 25, digitizes the analog data and packetizes the data. The second set of electronics 30 also contains a 3-axis compass for heading and tilt. Although shown as separate sets of electronics, one skilled in the art recognizes that the components and functionality of the first and second electronics may be combined on a single board. Exemplary and non-limiting dimensional ranges for the AVS system include: 4″ to 5″ OD (outside diameter) and 7″ to 17″ length.

(15) FIG. 2e illustrates the AVS fitted with a flotation mechanism 90. The flotation is needed to adjust the specific gravity of the sensor to reduce sensitivity loss due to the density mismatch to water.

(16) The embodiments describe multiple embodiments of a precision, high-performance AVS using robust and inexpensive seismometers. These sensors are very rugged and suitable for deployment in the most demanding locations and using the most abusive deployment techniques.

(17) A key performance metric for a sensor of this type is self-noise. The graph at FIG. 3 shows self-noise in equivalent acoustic-pressure units. For perspective, self-noises of two prior-art sensors are plotted along with Sea-State-Zero ocean noise. While the self-noise of the prior-art #1 sensor is better than the present embodiment, the self-noise advantage is typically not useful since the Sea-State-Zero noise dominates. More importantly, the size and cost of prior-art #1 sensor are nearly an order of magnitude too high to accommodate the principle requirements being addressed. Self-noise of the prior-art #2 sensor is prohibitively high relative to Sea State Zero. The graph in FIG. 3 shows the AVS of the present embodiments (“Simple 1s Config”) is quiet compared to Sea State zero, and thus sufficient to meet current needs. Additionally, a fairly simple modification, incorporating two sensitive elements per axis for a total of six (6) sensitive elements, improves the performance (“2s Config”). Increasing the number sensitive elements beyond two allows further improvements in self-noise. This property of the general embodiments presents the opportunity to create a family of vector sensors at different price points and self-noises.

(18) The theory of operation of the pendulum-type AVS described herein is discussed below with reference to FIGS. 4-7. The AVS provides a unique suspension system that meets two fundamental requirements. The first is to autonomously and passively orient the sensitive elements to within an acceptable tolerance (±1 degree for example) of the optimum operating geometry. The second is to provide an acceptable motion transfer function (0 dB±0.5 dB from 0.1 Hz to 100 Hz for example) while maintaining fidelity of the signal (−30 dB harmonic distortion for example). In this case, the motion transfer-function is defined as the frequency-dependent relationship of the sensitive-element motion relative to the motion of the physical body housing the sensitive elements. These requirements are met by using a damped mechanical pendulum to support the sensitive elements, Gravity enables the suspension system to meet the geometric alignment requirement whereas viscous-fluid damping enables the suspension system to meet the motion transfer-function requirement.

(19) The following sections present a simple physical model of the suspension system—along with a mathematical analysis to quantify its performance. The analysis treats the X (east direction). Dynamics of the Y (north) direction is identical. The Z (up) direction is trivial since there is a rigid mechanical wire or rope (see FIG. 4) connecting the sensitive elements to the physical-body housing.

(20) The math model assumes a general polynomial expression for the viscous coupling effect (F.sub.1):

(21) Note: m=1 meter of distance and s=1 second of time.

(22) $\begin{array}{cc}{F}_1=K_d\left(a_1\frac{\stackrel{.}{R}}{q}+{a_2\left(\frac{\stackrel{.}{R}}{q}\right)}^2\mathrm{sgn}\left(\stackrel{.}{R}\right)\right)\mathrm{where}\stackrel{.}{R}\stackrel{\Delta }{=}\frac{d}{\mathrm{dt}}\left[p\left(t\right)-x\left(t\right)\right]q=1m/s\begin{array}{c}\mathrm{sgn}\left(\stackrel{.}{R}\right)=+1\mathrm{for}\stackrel{.}{R}\ge 0\\ =-1\mathrm{otherwise}\end{array}& \mathrm{eq}\left(1\right)\end{array}$
Wherein α.sub.1, α.sub.2, are dimensionless scaling constants and K.sub.d has units of force (Newtons). Sum forces in the x-direction:

(23) $F_x={\mathrm{MA}}_x=M\frac{d^2}{{\mathrm{dt}}^2}x=M\stackrel{.Math.}{x}$
Where we include x-direction force due to the force of gravity on the sensitive-element represented by the lumped mass M:

(24) $M\stackrel{.Math.}{x}=F_1-\mathrm{Mg}\tan \left(\Phi \right)\mathrm{where}g\stackrel{\Delta }{=}\mathrm{gravity}\mathrm{constant}=9.8\frac{m}{s^2}$

(25) And substituting the expression for Fi results in the second-order non-linear differential equation (1) below:

(26) $\begin{array}{cc}M\stackrel{.Math.}{x}=K_d\left(a_1\frac{\stackrel{.}{R}}{q}+{a_2\left(\frac{\stackrel{.}{R}}{q}\right)}^2\mathrm{sgn}\left(\stackrel{.}{R}\right)\right)-\mathrm{Mg}\tan \left(\Phi \right)& \mathrm{eq}\left(2\right)\end{array}$

(27) The trig expression tan(t) can be eliminated by recognizing (from FIG. 4) that

(28) $\tan \left(\Phi \right)=\frac{x-p}{h}\mathrm{and}h=\sqrt{L^2-{\left(x-p\right)}^2}.$

(29) So, equation (2) can be rewritten as:

(30) $M\stackrel{.Math.}{x}=K_d\left(a_1\frac{R}{q}+a_2\left(\frac{R^{\mathrm{\prime 2}}}{q}\right)\mathrm{sgn}\left(R\right)\right)-\mathrm{Mg}\frac{x-p}{\sqrt{L^2-{\left(x-p\right)}^2}}$

(31) The analysis that follows linearizes the math model and develops closed-form solutions for the motion transfer function and homogeneous transient response.

(32) Equation (2) can be simplified by recognizing

(33) $\tan \left(\Phi \right)=\frac{x-p}{h}$

(34) and h≈L for all

(35) cases of interest. Therefore tan(ϕ) of equation (2) can be replaced by

(36) $\frac{x-p}{L}$

(37) provide.

(38) $\begin{array}{cc}M\stackrel{.Math.}{x}=K_d\left(a_1\frac{\stackrel{.}{R}}{q}+{a_2\left(\frac{\stackrel{.}{R}}{q}\right)}^2\mathrm{sgn}\left(\stackrel{.}{R}\right)\right)-\mathrm{Mg}\frac{x-p}{L}& \mathrm{eq}\left(2^{\prime }\right)\end{array}$

(39) And, the equation can be further simplified by recognizing that a.sub.2 is virtually zero for cases of interest. This simplification results in the linear 2.sup.nd order equation:

(40) 0$\begin{array}{cc}M\stackrel{.Math.}{x}=K_d\left(a_1\frac{\stackrel{.}{R}}{q}\right)-\mathrm{Mg}\frac{x-p}{L}& \mathrm{eq}\left(2^{″}\right)\end{array}$

(41) where q is simply a units-normalizing factor,

(42) $q=1\frac{m}{s}.$
In this simpler form, the shorthand parameter R can easily be replaced by its definition:

(43) $R=\frac{d}{\mathrm{dt}}\left[p\left(t\right)-x\left(t\right)\right]=\frac{d}{\mathrm{dt}}p\left(t\right)-\frac{d}{\mathrm{dt}}x\left(t\right)$

(44) where (see FIG. 4)

(45) p(t)=x—direction motion of the outside physical housing relative to the inertial coordinate system, and

(46) x(t)=x—direction motion of the sensitive element relative to the inertial coordinate system. Substituting into eq(2″) and replacing the “dot” notation with the more explicit derivative notation results in:

(47) $M\frac{d^2}{{\mathrm{dt}}^2}x\left(t\right)=K_d\frac{a_1}{q}\frac{d}{\mathrm{dt}}p\left(t\right)-K_d\frac{a_1}{q}\frac{d}{\mathrm{dt}}x\left(t\right)-\mathrm{Mg}\frac{x\left(t\right)-p\left(t\right)}{L}$

(48) dividing through by the M and rearranging terms:

(49) $\begin{array}{cc}\frac{d^2}{{\mathrm{dt}}^2}x\left(t\right)+\frac{K_d}{M}\frac{a_1}{q}\frac{d}{\mathrm{dt}}x\left(t\right)+\frac{g}{L}\left[x\left(t\right)-p\left(t\right)\right]=\frac{K_d}{M}\frac{a_1}{q}\frac{d}{\mathrm{dt}}p\left(t\right)& \mathrm{eq}\left(3\right)\end{array}$

(50) At this point, it is convenient to solve for the steady-state response to a sinusoidal input p(t) by taking the Laplace transform of equation (3). In doing so the derivative operators

(51) $\frac{d}{\mathrm{dt}}$

(52) are replaced by the Laplace parameter “s” and x(t) and p(t) are replaced by X(s) and P(s) resulting in the algebraic form of the differential equation:

(53) $s^{2}X\left(s\right)+s\frac{K_d}{M}\frac{a_1}{q}X\left(s\right)+\frac{g}{L}\left[X\left(s\right)-P\left(s\right)\right]=\frac{K_d}{M}\frac{a_1}{q}\mathrm{sP}\left(s\right)$

(54) From here, we can solve the transfer function H(s):

(55) $\begin{array}{cc}H\left(s\right)\stackrel{△}{=}\frac{X\left(s\right)}{P\left(s\right)}=\frac{\frac{K_d}{M}\frac{a_1}{q}s+\frac{g}{L}}{s^2+\frac{K_d}{M}\frac{a_1}{q}s+\frac{g}{L}}& \mathrm{eq}\left(4\right)\end{array}$

(56) By substituting s=jω(where j=√−1and ω=2πf and f=frequency (Hz))we obtain the motion transfer function for a steady-state sinusoidal excitation p(t).

(57) The magnitude-part of eq(4) is graphically illustrated in FIG. 5. For small values of Kd (<100), the motion transfer function is unfavorable with respect to typical requirements (0 dB±0.5 dB). For larger values (Kd>10,000 for example), the motion transfer function is much better than typical requirements.

(58) The parameter Kd is related to viscosity of the fluid filling the housing of FIG. 4. From FIG. 5, it is clear that a value of Kd=10,000 or greater is satisfactory to achieve the desired motion transfer function. It is important to relate this parameter to mechanical considerations such as time required for the suspension system to orient the sensitive elements to the required geometry. The following analysis provides this relationship by computing the homogeneous transient response of the suspension system for the case where a.sub.2=0 in eq(1) (same as for the motion-transfer-function analysis). FIG. 7 provides a practical example by plotting orientation of the sensitive elements as a function of time where the initial orientation is 20 degrees relative to the required orientation. FIG. 7 shows that the suspension system requires about 55 seconds to achieve the typically-required 1-degree alignment for the case where Kd=10,000. This amount of time is quite acceptable for the intended operation of the device. The next section derives an expression for the homogeneous response with arbitrary initial conditions. This is the expression used to compute the graph of FIG. 7.

(59) For the homogeneous case, we set the forcing function, p(t), in equation (3) to zero, resulting in:

(60) $\begin{array}{cc}\frac{d^2}{{\mathrm{dt}}^2}x\left(t\right)+\frac{K_d}{M}\frac{a_1}{q}\frac{d}{\mathrm{dt}}x\left(t\right)+\frac{g}{L}x\left(t\right)=0& \mathrm{eq}\left(3H\right)\end{array}$

(61) It is now convenient to express the

(62) $\frac{d^2}{d{t}^2}x\left(t\right)$

(63) in terms of

(64) 0$\frac{d}{\mathrm{dt}}x\left(t\right)$

(65) x(t)

(66) $\begin{array}{cc}\frac{d^2}{{\mathrm{dt}}^2}x\left(t\right)=\frac{-K_d}{M}\frac{a_1}{q}\frac{d}{\mathrm{dt}}x\left(t\right)-\frac{g}{L}x\left(t\right)& \mathrm{eq}\left(5\right)\end{array}$

(67) We can now use equation(5) to draw a signal-flow graph and define a state-variable vector X.

(68) FIG. 6 provides a graphical representation of eq(5). The state-variable vector defines the “state” of the second-order system. One element (x.sub.0) accounts for the displacement (x) of the mass M. The other element, (x.sub.1) accounts for the velocity

(69) $\frac{\mathrm{dx}}{\mathrm{dt}}$

(70) So, the state vector is defined by:

(71) And the derivative

(72) $\frac{d}{\mathrm{dt}}X=\left[\begin{array}{c}\frac{d}{\mathrm{dt}}{x}_0\\ \frac{d}{\mathrm{dt}}{x}_1\end{array}\right]=\underset{\underset{A}{︸}}{\left[\begin{array}{cc}0& 1\\ \frac{-g}{L}& -\frac{K_d}{M}\frac{a_1}{q}\end{array}\right]}\underset{\underset{X}{︸}}{\left[\begin{array}{c}{x}_0\\ x_1\end{array}\right]}$

(73) Where the derivation of matrix A is more-clearly presented in FIG. 6. So then

(74) $\frac{d^{}X}{\mathrm{dt}}=\mathrm{AX}$

(75) represents a matrix-version of eq(5), which has the solution:
X(t)=e.sup.AtX(t=0)  eq(6)

(76) Where the two elements of X(t) represent the displacement and velocity of the mass M (representing the sensitive element). And, X(t=0) is simply the displacement and velocity of the mass M at time=0. Computing the 2×2 matrix e.sup.At is easily accomplished with a computer implementing the numerical series expansion:

(77) $e^{\mathrm{At}}=\mathrm{ID}+\mathrm{At}+\frac{1}{2}{\left(\mathrm{At}\right)}^2+\frac{1}{6}{\left(\mathrm{At}\right)}^3+.$

(78) FIG. 7 shows an example transient response computed from eq(6). FIG. 7 shows that the suspension system requires about 55 seconds to achieve the typically-required 1 degree alignment for the case where Kd=10,000 This amount of time is quite acceptable for the intended operation of the device.

(79) Underwater tests were performed at a US Government facility located on Seneca Lake, New York. The tests served to verify operation of the AVS and validate the math model described above. The validation was done by comparing the AVS response to that of a calibrated reference hydrophone. FIG. 8 provides a sample of the results. The solid curve represents measured sensitivity of the AVS as a function of frequency. The dashed curve represents the sensitivity predicted from the above-presented suspension-system model in conjunction with a math model of the internal sensitive elements. The agreement between the measured data and the math model from 30 Hz to 150 Hz indicate the math model is accurately accounting for the physical processes. The systematic-like divergence between the two curves from 30 Hz to 10 Hz is caused by near-field effects of the measurement setup. The near-field-effects change the relationship between acoustic pressure and particle velocity. In doing so, it alters the comparison between the pressure-sensitive calibrated reference hydrophone and particle-velocity-sensitive AVS. In summary, the measured data indicate that the math models accurately account for the physical processes and that the AVS performs as designed.

(80) The AVS beam-pattern was also measured at the US Government facility located on Seneca Lake. In this case, beam-pattern is defined as the response of the AVS as a function of azimuth. A sample of these data is shown in FIG. 9. The solid curve represents the measured data whereas the dashed curve represents a standard cosine math model. These data are further evidence that the math models accurately account for the physical processes and that the AVS performs as designed.

(81) As discussed above, AVS systems provide more sensor degrees of freedom than conventional omni-based systems and result in the ability to provide bearing ambiguity elimination, effective background noise isolation or shading, and steering of beams to place nulls where desired. To date, the cost of prior art systems, i.e., the typically-used force-feedback implementation, has been a large deterrent to larger scale use. The technology described herein significantly reduces cost and makes it feasible to produce AVS for use in single-point, array, and networked array systems.

(82) One skilled in the art recognizes that the AVS embodiments described herein maybe used in numerous applications including, but not limited to: Anti-Submarine Warfare; Ocean Noise Measurement; Marine Mammal Monitoring; Ocean Observation; Environmental Monitoring; Offshore Energy Operations; Marine Renewable Energy; Tidal Energy; Wave Energy; Offshore; Wind Farms; Ocean Observatories; Earthquake & Tsunami Monitoring; Subsea Volcano Detection; ROV's & AUV's; Harbor Security; Pipeline Leak Detection; Fisheries Research; and Arctic Ice Monitoring.

(83) The exemplary embodiments described herein are not intended to be limiting. Certain variations to one or more aspects will be readily recognized by those skilled in the art and are intended to be considered as being within the scope of the embodiments.