Fully automated calibration for acoustic pyrometry

1. A computer implemented method of calibrating transceiver positions inside an acoustic pyrometry measuring vessel that contains a plurality of transceivers, the method executed by the computer comprising the steps of:

placing the acoustic pyrometry measuring vessel in a space of a known constant temperature containing a gas of known composition and allowing the acoustic pyrometry measuring vessel to equilibrate;

determining a speed of sound in said acoustic pyrometry measuring vessel from the known constant temperature and the known gas composition of the gas inside said acoustic pyrometry measuring vessel;

acquiring time-of-flight (TOFs) Δti ,j measurements from a plurality of pairs i,j of transceivers inside said acoustic pyrometry measuring vessel;

estimating a radius of said acoustic pyrometry measuring vessel from an average of the acquired TOF measurements; and

using the estimated radius of said acoustic pyrometry measuring vessel to estimate errors Δθj of displacement angles of the transceivers,

wherein the errors Δθj of displacement angles of the transceivers from the calibration are utilized to accurately determine a temperature within the acoustic pyrometry measuring vessel when the temperature inside the acoustic pyrometry measuring vessel is not known, and

wherein the determined temperature within the acoustic pyrometry measuring vessel is displayed on a display.

2. The method of claim 1 , further comprising repeating said steps of estimating a radius of said acoustic pyrometry measuring vessel and using said estimated radius to estimate errors Δθj of displacement angles until convergence.

3. The method of claim 1 , wherein the radius r i of each transceiver of said acoustic pyrometry measuring vessel is estimated from the average over all TOF measurements:

C

0

(

N

-

1

)

⁢

∑

i

=

1

,

i

≠

j

N

⁢

⁢

Δ

⁢

⁢

t

i

,

j

2

⁢

⁢

sin

(



θ

^

i

-

θ

^

j



2

)

+

(

Δθ

i

-

Δθ

j

)

⁢

cos

(

θ

^

i

-

θ

^

j

2

)

,

wherein C 0 is a speed of sound, N is a number of transceivers, and θ i is a displacement angle of transceiver i.

4. The method of claim 1 , wherein the speed of sound C in said acoustic pyrometry measuring vessel is determined from

C

=

γ

⁢

⁢

RT

m

,

where T is the temperature T in degrees Kelvin, γ is a ratio between specific heats of the gas at constant pressure and constant volume, R is the gas constant, and m is a molecular weight of the gas.

5. The method of claim 1 , wherein errors Δθj of displacement angles of the transceivers are estimated from

(

Δθ

i

-

Δθ

j

)

⁢

cos

(

θ

^

i

-

θ

^

j

2

)

=

Δ

⁢

⁢

t

i

,

j

⁢

C

0

r

-

2

⁢

⁢

sin

⁢

(

θ

^

i

-

θ

^

j

2

)

,

wherein C 0 is a speed of sound, r is the estimated radius, and {circumflex over (θ)} i is an intended angle of transceiver i.

6. The method of claim 5 , wherein the errors Δθj of displacement angles of the transceivers are estimated using a least squares fit.

7. A system for calibrating transceiver positions for acoustic pyrometry, comprising:

an acoustic pyrometry measuring vessel;

a plurality of transceivers disposed about a perimeter of said measuring vessel, said transceivers configured to transmit an acoustic wave signal upon receipt of an electric signal and to receive acoustic wave signals and convert a received acoustic wave signal into an electric signal; and

a computer processor configured to automatically perform the calibration by transmitting and receiving the electric signals sent to and received from the transceivers, determining time-of-flight (TOFs) Δti ,j measurements from each pair i,j of transceivers inside said acoustic pyrometry measuring vessel, to estimate a radius of said acoustic pyrometry measuring vessel from an average of the acquired TOF measurements, and to using the estimated radius of said acoustic pyrometry measuring vessel to estimate errors Δθj of displacement angles of the transceivers,

wherein said computer processor is configured to determine a speed of sound in said acoustic pyrometry measuring vessel from placement of the acoustic pyrometry measuring vessel in a known constant temperature and a known gas composition of a gas inside said acoustic pyrometry measuring vessel,

wherein the errors Δθj of displacement angles of the transceivers from the calibration are utilized to accurately determine a temperature within the acoustic pyrometry measuring vessel when the temperature inside the acoustic pyrometry measuring vessel is not known, and

wherein the determined temperature within the acoustic pyrometry measuring vessel is displayed on a display.

8. A non-transitory program storage device readable by a computer, tangibly embodying a program of instructions executed by the computer to perform the method steps for calibrating transceiver positions inside an acoustic pyrometry measuring vessel that contains a plurality of transceivers, the method comprising the steps of:

placing the acoustic pyrometry measuring vessel in a space of a known constant temperature containing a gas of known composition and allowing the acoustic pyrometry measuring vessel to equilibrate

determining a speed of sound in said acoustic pyrometry measuring vessel from the known constant temperature and the constant gas composition of the gas inside said acoustic pyrometry measuring vessel;

acquiring time-of-flight (TOFs) Δti ,j measurements from a plurality of pairs i,j of transceivers inside said acoustic pyrometry measuring vessel;

estimating a radius of said acoustic pyrometry measuring vessel from an average of the acquired TOF measurements;

using the estimated radius of said acoustic pyrometry measuring vessel to estimate errors Δθj of displacement angles of the transceivers; and

utilizing errors Δθj of displacement angles of the transceivers during the calibration to accurately determine a temperature within the acoustic pyrometry measuring vessel when the temperature inside the acoustic pyrometry measuring vessel is not known,

wherein the determined temperature within the acoustic pyrometry measuring vessel is displayed on a display.

9. The computer readable program storage device of claim 8 , the method further comprising repeating said steps of estimating a radius of said acoustic pyrometry measuring vessel and using said estimated radius to estimate errors Δθj of displacement angles until convergence.

10. The computer readable program storage device of claim 8 , wherein the radius r i of each transceiver said acoustic pyrometry measuring vessel is estimated from the average over all TOF measurements:

C

0

(

N

-

1

)

⁢

∑

i

=

1

,

i

≠

j

N

⁢

⁢

Δ

⁢

⁢

t

i

,

j

2

⁢

⁢

sin

(



θ

^

i

-

θ

^

j



2

)

+

(

Δθ

i

-

Δθ

j

)

⁢

cos

(

θ

^

i

-

θ

^

j

2

)

,

wherein C 0 is a speed of sound, N is a number of transceivers, and θ i is a displacement angle of transceiver i.

11. The computer readable program storage device of claim 8 , wherein the speed of sound C in said acoustic pyrometry measuring vessel is determined from

C

=

γ

⁢

⁢

RT

m

,

where T is the temperature T in degrees Kelvin, γ is a ratio between specific heats of the gas at constant pressure and constant volume, R is the gas constant, and m is a molecular weight of the gas.

12. The computer readable program storage device of claim 8 , wherein errors Δθj of displacement angles of the transceivers are estimated from

(

Δθ

i

-

Δθ

j

)

⁢

cos

(

θ

^

i

-

θ

^

j

2

)

=

Δ

⁢

⁢

t

i

,

j

⁢

C

0

r

-

2

⁢

⁢

sin

⁢

(

θ

^

i

-

θ

^

j

2

)

,

wherein C 0 is a speed of sound, r is the estimated radius, and {circumflex over (θ)} i is an intended angle of transceiver i.

13. The computer readable program storage device of claim 12 , wherein the errors Δθj of displacement angles of the transceivers are estimated using a least squares fit.