Noise robust time of flight estimation for acoustic pyrometry
An acoustic signal traversing a hot gas is sampled at a source and a receiver and is represented in overlapping windows that maximize useable signal content. Samples in each window are processed to represented in different sparsified bins in the frequency domain. Determining a signal delay between the source and the receiver from a summation of maximum smoothed coherence transform cross-correlation values of different data windows wherein a sparseness of a mean smoothed coherence transform cross-correlation of windows is maximized. Determining a set of delay times wherein outliers are deleted to estimate a time of flight from which a temperature of the hot gas is calculated.
1. A method for acoustic pyrometry comprising:
recording, by a receiver of an acoustic pyrometer system, an acoustic signal generated by a source included in the acoustic pyrometer system and propagating through a gas medium traveling through a pipe or other channel;
arranging a plurality of samples representing the acoustic signal at the source and the receiver into a plurality of windows based on a physically minimum possible propagation delay from the source to the receiver given a temperature range of interest;
processing, by a processor within the acoustic pyrometer system, the plurality of samples representing the acoustic signal at the source and the receiver to generate data that represent the plurality of samples in a frequency domain;
arranging, by the processor within the acoustic pyrometer system, the data that represent the samples in the frequency domain in a plurality of frequency ranges and selecting one or more frequency ranges with a minimal influence of noise;
correlating, by the processor within the acoustic pyrometer system, the data in each selected frequency range of the source with corresponding data of the receiver to determine a weighted cross-spectral power estimate value for each selected frequency range related to the source corresponding to a delay time;
determining, by the processor within the acoustic pyrometer system, a summation of the maximum weighted cross-spectral power estimate value of each of the selected frequency ranges by using a range of delays wherein the summation has a maximum, such that a sparseness of a mean weighted cross-spectral power estimate of the selected frequency ranges is maximized; and
applying, by the processor within the acoustic pyrometer system, the determined signal delay between the source and the receiver to calculate a temperature of the gas medium.
2. The method of claim 1 , further comprising, the processor arranging the data that represent the plurality of samples in the frequency domain in a plurality of bins and selecting one or more bins with a minimal influence of noise.
3. The method of claim 1 , wherein the plurality of weighted cross-spectral power estimates apply a smoothed coherence transform (SCOT) cross-correlation.
4. The method of claim 1 , wherein a function that maximizes the sparseness is expressed as:
arg
max
t
1
N
∑
n
=
1
N
R
n
,
k
,
m
(
τ
+
t
n
)
1
with
-
d
≤
t
n
≤
d
,
wherein t n is a time variation within a range [−d, d];
N is a number of windows;
τ is a delay time of a signal;
n is an index indicating a window;
k is an index indicating a source;
m is an index indicating a receiver; and
R n,k,m (τ+t n ) represents a smoothed coherence transform cross-correlation for a signal represented in window n, from source k and received at receiver m at a time difference (τ+t n ).
5. The method of claim 1 , wherein a window is based on a physically minimum possible propagation delay from the source to the receiver given a temperature range of interest.
6. The method of claim 1 , further comprising:
determining a plurality of signal delays for a plurality of signals generated by a plurality of sources and received by a plurality of receivers.
7. The method of claim 6 , wherein a preferred signal delay is determined from the plurality of signal delays by applying a physical model based on a distance traversed by the acoustical signal.
8. The method of claim 1 , wherein the method is applied to determine a temperature in a gas turbine.
9. The method of claim 1 , wherein the method is applied to determine a temperature in a nuclear power plant.
10. An acoustic pyrometry system comprising:
an acoustic signal source enabled to generate an acoustic signal in a gas medium with a temperature;
a receiver enabled to record the acoustic signal traveling through the gas medium;
a memory enabled to store data and instructions;
a processor enabled to execute instructions retrieved from the memory to perform the steps:
arranging a plurality of samples representing the acoustic signal at the source and the receivers into a plurality of windows based on a physically minimum possible propagation delay from the source to the receiver given a temperature range of interest;
processing the plurality of samples representing the acoustic signal at the source and the receiver to generate data that represent the plurality of samples in a frequency domain;
arranging the data that represent the samples in the frequency domain in a plurality of frequency ranges and selecting one or more frequency ranges with a minimal influence of noise;
correlating the data in each selected frequency range of the source with corresponding data of the receiver to determine a weighted cross-spectral power estimate value for each selected frequency range related to the source corresponding to a delay time;
determining a summation of the maximum weighted cross-spectral power estimate value of each of the selected frequency ranges by using a range of delays wherein the summation has a maximum, such that a sparseness of a mean weighted cross-spectral power estimate of the selected frequency ranges is maximized; and
applying the determined signal delay between the source and the receiver to calculate a temperature of the gas medium.
11. The system of claim 10 , further comprising, the processor arranging the data that represent the plurality of samples in the frequency domain in a plurality of bins and selecting one or more bins with a minimal influence of noise.
12. The system of claim 10 , wherein the plurality of weighted cross-spectral power estimates apply a smoothed coherence transform (SCOT) cross-correlation.
13. The system of claim 10 , wherein a function that maximizes the sparseness is expressed as:
arg
max
t
1
N
∑
n
=
1
N
R
n
,
k
,
m
(
τ
+
t
n
)
1
with
-
d
≤
t
n
≤
d
,
wherein t n is a time variation within a range [−d, d];
N is a number of windows;
τ is a delay time of a signal;
n is an index indicating a window;
k is an index indicating a source;
m is an index indicating a receiver; and
R n,k,m (τ+t n ) represents a smoothed coherence transform cross-correlation for a signal represented in window n, from source k and received at receiver m at a time difference (τ+t n ).
14. The system of claim 10 , further comprising:
the processor determining a plurality of signal delays for a plurality of signals generated by a plurality of sources and received by a plurality of receivers.
15. The system of claim 14 , wherein a preferred signal delay is determined from the plurality of signal delays by applying a physical model based on a distance traversed by the acoustical signal.
16. The system of claim 10 , wherein the instructions retrieved from the memory further cause the processor to determine a temperature in a gas turbine.
17. The system of claim 10 , wherein the instructions retrieved from the memory further cause the processor to determine a temperature in a nuclear power plant.
18. A method for acoustic pyrometry comprising:
receiving, by a processor, a plurality of samples representing an acoustic signal generated by a source included in the acoustic pyrometer system and recorded by a recorder included in the acoustic pyrometer system, wherein the acoustic signal is recorded after propagating through a medium traveling through a pipe or other channel;
arranging, by the processor, the plurality of samples into a plurality of windows based on a physically minimum possible propagation delay from the source to the receiver given a temperature range of interest;
processing, by the processor, the plurality of samples representing the acoustic signal at the source and the receiver to generate data that represent the plurality of samples in a frequency domain;
arranging, by the processor, the data that represent the samples in the frequency domain in a plurality of frequency ranges and selecting one or more frequency ranges with a minimal influence of noise;
correlating, by the processor, the data in each selected frequency range of the source with corresponding data of the receiver to determine a weighted cross-spectral power estimate value for each selected frequency range related to the source corresponding to a delay time;
determining, by the processor, a summation of the maximum weighted cross-spectral power estimate value of each of the selected frequency ranges by using a range of delays wherein the summation has a maximum, such that a sparseness of a mean weighted cross-spectral power estimate of the selected frequency ranges is maximized; and
applying, by the processor, the determined signal delay between the source and the receiver to calculate a temperature of the medium.