Claims
- 1. A method for determining whether a pressure sensor being tested is properly responding to a pressure field comprising the steps of:
- providing a shell filled with a liquid and having impedance heads attached to a first end and a second end of said shell and a number of pressure sensors positioned between said first and second ends within said liquid filled shell;
- developing a model of the pressure field within said liquid-filled shell by modeling an extensional wave contribution and by modeling a breathing wave contribution; and
- comparing the response of at least one of said pressure sensors to said pressure field described by said model.
- 2. The method of claim 1 further comprising determining the total pressure in said shell by summing the extensional wave contribution and the breathing wave contribution using the following
- P(x,.omega.)=P.sub.b (x,.omega.)+P.sub.e (x,.omega.)=A(.omega.)e.sup.ik.sbsp.b.sup.x +B(.omega.)e.sup.-ik.sbsp.b.sup.x +C(.omega.)e.sup.ik.sbsp.e.sup.x +D(.omega.)e.sup.-ik.sbsp.e.sup.x,
- where P(x,.alpha.) is the temporal Fourier transform of the pressure that is generated by both the extensional and breathing waves; i is the square root of -1; and A(.omega.), B(.omega.), C(.omega.), D(.omega.), k.sub.b and k.sub.e are wave propagation coefficients determined by the boundary conditions.
- 3. The method of claim 2 further comprising:
- dividing the pressure field at position x by the temporal Fourier transform of an acceleration at the forward end of the shell and arriving at the following equation: ##EQU33## where P(x,.omega.) is the temporal Fourier transform of the pressure generated by both extensional and breathing waves; U is the temporal Fourier transform of the acceleration at the forward end of the shell; and A(.omega.), B(.omega.), C(.omega.), and D(.omega.) are the wave propagation coefficients; and
- determining said wave propagation coefficients, a breathing wavenumber and an extensional wavenumber.
- 4. The method of claim 3 wherein said wave propagation coefficient determining step comprises estimating the extensional wavenumber and thereafter estimating the breathing wavenumber.
- 5. The method of claim 4 wherein said extensional wavenumber estimating step comprises:
- determining the extensional wavenumber using data measurements in the form of transfer functions from forward and aft impedance heads attached to said ends of said shell for a number of frequencies; and
- determining a complex valued extensional wave speed at each frequency.
- 6. The method of claim 5 wherein said breathing wavenumber estimating step comprises determining a breathing wave speed for each said frequency using measurements of the spatial field by five independent equally spaced pressure sensors within said shell to eliminate the wave propagation coefficients.
- 7. The method of claim 6 further comprising the step of estimating said wave propagation coefficients using a direct inverse method.
- 8. The method of claim 7 wherein said estimating step comprises using four pressure sensor measurements to produce an exact solution for the coefficients.
- 9. The method of claim 6 further comprising the step of estimating said wave propagation coefficients using a number of hydrophone measurements and a Gauss linearization scheme with an ordinary least squares constraint to solve for said coefficients.
STATEMENT OF GOVERNMENT INTEREST
The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.
US Referenced Citations (3)