Method for determining gas concentration by sensor group

Abstract

A method for determining a measured value of a gas concentration from a group of at least two non-dispersive infrared (NDIR) gas sensors (S1-SN) is described. The method comprises the following steps: at a processing unit (1), the measured value of the gas concentration from each NDIR gas sensor (S1-SN) is obtained as a trust function Pi(x), the trust function Pi(x) providing a probability as a function of the intensity of light detected at a specific wavelength; in the processing unit, the trust functions Pi(x) are combined into a combined trust function P(x). A computer program for executing the method is also described.

Description

Technical Field

[0001] The present invention relates to determining gas concentration by a set of at least two non-dispersive infrared (NDIR) gas sensors. Background Art

[0002] Gas sensors are devices used to measure the presence or concentration of gas in an area and play an important role in many applications. Non-dispersive infrared sensors (NDIR sensors) are simple spectral sensors in which non-dispersive elements are used to filter broadband light into a narrow spectrum suitable for detecting specific gases. However, NDIR sensors have been found to be sensitive to changes in ambient temperature, atmospheric pressure, humidity, and some other environmental factors. In addition, aging of sensor components can also lead to inaccuracy in the sensor. Therefore, regular calibration is required to ensure the long-term accuracy of the sensor.

[0003] Today, the state-of-the-art for self-calibration of infrared gas sensors is the well-established ABC technique (Automatic Baseline Correction), where the sensor is calibrated to a fixed value assumed to be the fresh air gas concentration. However, this approach does not work well in megacities where the sensor is never exposed to fresh air. Therefore, it becomes increasingly important to design more robust and intelligent self-calibration algorithms that can be widely applied in different environments. Summary of the invention

[0004] It is an object of the present invention to provide a method for determining gas concentration by a set of at least two non-dispersive infrared NDIR gas sensors which provides more reliable results than methods according to the prior art.

[0005] Another object of the present invention is to provide a method for determining gas concentration from a set of at least two non-dispersive infrared NDIR gas sensors which handles the aging of the NDIR gas sensors in a better way than methods according to the prior art.

[0006] Another object of the present invention is to provide a computer program for determining gas concentration by a set of at least two non-dispersive infrared NDIR gas sensors, which provides more reliable results than methods according to the prior art.

[0007] At least one of these objects is achieved by a method and a computer program according to the independent claims.

[0008] Further advantages are achieved by the features of the dependent claims.

[0009] According to a first aspect of the invention, there is provided a method for determining a measure of a gas concentration by a group of at least two non-dispersive infrared (NDIR) gas sensors, wherein the method comprises the steps of obtaining at a processing unit the measured value of the gas concentration from each NDIR gas sensor as a belief function, which is a probability as a function of the measured value of the gas concentration at a specific wavelength, and incorporating the belief function P in the processing unit. i (x) is the combined trust function P(x).

[0010] The measured value of the gas concentration may be an intensity value of the light penetrating the gas. The gas sensor may also be configured to convert the intensity value into a gas concentration. In this case, the measured value of the gas concentration is the gas concentration. If the processing unit performing the method knows the conversion from light intensity to gas concentration, the light intensity may be used. However, if the processing unit does not know the conversion from light intensity to gas concentration, the trust function is preferably a probability as a function of the gas concentration. The gas sensor measures the light intensity and includes self-awareness of the sensor uncertainty in the measurement. The measurement result from the gas sensor may then be sent as a probability as a function of the light intensity. Alternatively, the light intensity may be converted into a gas concentration, and the trust function from the gas sensor may be sent as a gas concentration as a function of the gas concentration.

[0011] By using an NDIR sensor that provides gas concentration measurements as a trust function that provides probability as a function of the gas concentration detected at a specific wavelength, i.e. measuring at a specific wavelength, the uncertainty in the actual gas concentration can be reduced, which will then result in better gas measurements.

[0012] An NDIR sensor providing a trust function can be configured in many different ways. An alternative to such an NDIR sensor is to use oversampling, i.e. the sensor outputs sensor readings at a lower frequency than the frequency at which measurements of gas concentration are obtained. The variation in the measurements can be provided as a trust function.

[0013] Alternatively, an NDIR sensor providing a trust function may be configured to obtain measurements of gas concentration and output the measurements as a Gaussian distribution around the obtained measurements of gas concentration.

[0014] Alternatively, the NDIR sensor can be configured to use a model that includes physical knowledge about the NDIR gas sensor. Using the Lambert-Beer law as the basis for the model, we can use supervised or unsupervised machine learning algorithms to learn the statistical behavior of the sensor. In particular, such a model can compensate for environmental factors such as temperature.

[0015] The method may further include the step of calibrating each NDIR gas sensor using the combined trust function P(x). By calibrating each NDIR gas sensor using the combined trust function P(x), the self-awareness of each NDIR sensor will be improved, and further measurements using the NDIR gas sensor will be more accurate.

[0016] The processing unit may be a central processing unit in communication with each NDIR gas sensor. By having a central processing unit, measurements of gas concentration measurements may be performed using different NDIR gas sensors in different measurements, wherein the selection of the NDIR sensor is done by the central processing unit.

[0017] The incorporation of the belief function Pi(x) can be performed using the Dempster-Shafer theory. The Dempster-Shafer theory itself is known but has not been used for the present purpose.

[0018] The combination of the trust function Pi(x) can include the trust function P i The weighted average P(x) of (x) is calculated, where the weight of each trust function depends on the i (x) and other trust functions P j,j≠i (x) The distance between i (x),P j (x)), so that the trust function P i (x) and other trust functions P j,j≠i (x) increases the distance W2(P i (x),P j (x)) leads to the trust function P i The weight of (x) is reduced.

[0019] Trust function P i The calculation of the weighted average P(x) of the sum ...

[0020] In the trust function Pi The two trust functions P used in the weighting of (x) i (x), P j The distance between (x) is determined as the Wasserstein distance W p , where for two probability measurements P defined over the gas concentration range i and P j W p (p≥1) is given by

[0021]

[0022] where Γ(Pi,Pj) represents the joint probability measurement value P defined over the gas concentration range ij The set of , with margins Pi and Pj, and d represents the distance of the gas concentration value to the corresponding random variable of the gas concentration range. It is advantageous to use the Wasserstein distance in the calculation because this distinguishes trust functions that are different from most trust functions that measure similarity well.

[0023] The support of the given trust function can be calculated as

[0024]

[0025] in

[0026]

[0027] And among them

[0028]

[0029] Then, the corresponding weight factor of the trust function Pi obtained after normalization, where the weight factor α i is represented as

[0030]

[0031] The weighted average of all N trust functions can be expressed as

[0032]

[0033] It is used to compute the final trust function for each sensor. There are alternatives to using a weighted average to compute the combined trust, for example, a weighted average trust function applied to itself N-1 times using the Dempster-Shafer rule can be used.

[0034] The method may further comprise the step of selecting an NDIR gas sensor in the group from a plurality of NDIR gas sensors, wherein each of the plurality of NDIR gas sensors is associated with a current location, and wherein the NDIR gas sensors are selected based on their current location. The NDIR gas sensors preferably have a positioning sensor such as, for example, a GPS sensor to determine their location. By selecting an NDIR gas sensor in the group from a plurality of NDIR gas sensors, a gas sensor close to the location where the measurement is to be performed may be selected. The NDIR gas sensor may, for example, be placed in a car that is moved around.

[0035] NDIR gas sensors may also be associated with historical locations, and wherein NDIR gas sensors are selected based on their historical locations as well. By having NDIR gas sensors also associated with historical locations, such gas sensors that have recently been in an environment with known gas concentrations or have recently been calibrated may be selected.

[0036] The historical location correlation of the NDIR gas sensor may be implemented by storing information about the locations and corresponding points in time in the processing unit.

[0037] For a car with a gas sensor measuring CO2 concentration, in the case of CO2, the environment with known gas concentration may be in the countryside. If the sensors have calibrated themselves in the countryside, they will be more reliable. Regarding the most recent calibration, the NDIR gas sensor may store information about when it was last calibrated.

[0038] It is also possible to select NDIR gas sensors based on their gas concentration measurement results. If one gas sensor provides a very different gas concentration compared to the remaining gas sensors, the gas sensor providing the very different gas concentration can be deselected before the next measurement. In this way the quality of the measurement can be improved.

[0039] The selection of the NDIR gas sensor can be performed repeatedly over time. If the purpose of the measurement is to measure the gas concentration at a specific location, the gas sensor selected for each measurement is a gas sensor close to the specific location.

[0040] According to a second aspect of the invention, there is provided a computer program for determining gas concentration by a group of at least two non-dispersive infrared gas NDIR sensors, the program comprising instructions which, when executed by a processor in a processing unit, cause the processor unit to control the processing unit to perform a method according to the first aspect of the invention or any of the embodiments described above.

[0041] According to a third aspect of the present invention, there is provided a processing unit configured to determine a gas concentration from a group of at least two non-dispersive infrared gas NDIR sensors, wherein the processing unit is configured to

[0042] - obtain the measured value of the gas concentration from each NDIR gas sensor as a confidence function, which is the probability as a function of the measured value of the gas concentration at a specific wavelength, i.e., measuring at a specific wavelength,

[0043] - In the processing unit, the trust function P i (x) are merged into the combined trust function P(x). BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A system is shown having a set of gas sensors communicating with a processing unit configured to perform the method according to the invention.

[0045] Figure 2 A gas sensor according to an embodiment of the present invention is schematically shown.

[0046] Figure 3 Shown by Figure 1 Different trust functions provided by the gas sensors in the system.

[0047] Figure 4 a and Figure 4 b shows the merging by using the Dempster-Shafer rule for merging and the weighted average, respectively. Figure 3 The merged trust function generated by the trust function in .

[0048] Figure 5 Shown by Figure 1 Five different trust functions P1(x)-P5(x) provided by the gas sensors S1-SN in the system.

[0049] Figure 6 a and Figure 6 b shows the merging by using the Dempster-Shafer rule for merging and the weighted average, respectively. Figure 5 The merged trust function generated by the trust function in .

[0050] Figure 7 A number of cars, each of which includes a gas sensor, are shown. DETAILED DESCRIPTION

[0051] In the following detailed description of the present invention, similar features in different drawings will be denoted by the same reference numerals.

[0052] Figure 1A system is shown having a group of N gas sensors S1-SN communicating with a processing unit configured to perform a method according to the invention. All gas sensors preferably communicate wirelessly with the processing unit. According to an alternative embodiment, the processing unit 1 can be integrated in at least one gas sensor. According to another alternative, the processing unit 1 can be integrated in all gas sensors S1-SN. According to this alternative embodiment, all gas sensors communicate with each other and each processing unit performs a method according to an embodiment of the invention.

[0053] According to an embodiment with a separate processing unit 1, the processing unit obtains the measured value of the gas concentration from each NDIR gas sensor as a trust function, which provides a probability as a function of the detected light intensity measured at a specific wavelength, provides the trust function from each NDIR gas sensor to the processing unit, and transmits the trust function P in the processing unit 1. i (x) is combined into a combined trust function P(x). The combined trust function P(x) provides a more reliable measurement of the gas concentration. In order to further improve future measurements of gas concentration, the processing unit 1 can provide the combined trust function to each gas sensor S1-SN for calibration of the gas sensors S1-SN.

[0054] Figure 2 A gas sensor S1-SN according to an embodiment of the present invention is schematically shown. The gas sensor S1-SN comprises an NDIR detection unit 2, a processing unit 1 and a communication interface 3. The processing unit 1 obtains the measured value of the gas concentration from the NDIR detection unit 2 and controls the transmission of the measured value of the gas concentration from the gas sensor S1-SN to other gas sensors S1-SN. The gas sensor S1-SN also comprises a positioning sensor 4, such as, for example, a GPS sensor, which enables the gas sensor S1-SN to determine its position.

[0055] Figure 3 Shown by Figure 1 The gas sensors S1-SN in the system provide five different trust functions P1(x)-P5(x). Each trust function P1(x)-P5(x) shows the probability as a function of CO2 concentration. Figure 3 It can be seen that the trust functions P1(x)-P5(x) extend over a larger concentration range.

[0056] Figure 4 a and Figure 4 b shows the merging by using the Dempster-Shafer rule for merging and the weighted average, respectively. Figure 3The combined confidence function generated by the confidence function in . The two different merging techniques lead to similar resulting combined confidence functions P(x). Both merging techniques lead to a probability peak at 482 ppm CO2.

[0057] Figure 5 Shown by Figure 1 Another example of different confidence functions P1(x)-P5(x) provided by the gas sensors in the system. Each confidence function P1(x)-P5(x) shows the probability as a function of CO2 concentration. Figure 3 It can be seen from Figure 2 that the trust functions P1(x)-P5(x) extend over a larger concentration range. Figure 5 It can be seen that the fifth trust function P5(x) obviously moves to a lower CO2 concentration than the other trust functions P1(x)-P4(x).

[0058] Figure 6 a and Figure 6 b shows the merging by using the Dempster-Shafer rule for merging and the weighted average, respectively. Figure 5 The combined trust function generated by the trust function in . Figure 6 As can be seen in , merging the trust functions P1(x)-P5(x) using the Dempster-Shafer rule results in a merged trust function P(x) with a significant probability peak at a CO2 concentration of 479ppm. Merging the trust functions P1(x)-P5(x) using a weighted average results in a merged trust function P(x) with a significant probability peak at a CO2 concentration of 482ppm. Therefore, the effect of the fifth trust function P5(x) is reduced when merging using a weighted average. The fifth gas sensor may have drifted and provided erroneous results. Therefore, it is advantageous to reduce the influence of the fifth gas sensor, i.e., Sensor 5 (Sensor5).

[0059] In the following, it will be described in more detail how the combined trust function P(x) may be implemented and calculated.

[0060] In the trust function P i The two trust functions P used in the weighting of (x) i (x), P j The distance between (x) is determined as the Wasserstein distance W p , where for two probability measurements P defined over the gas concentration range i and P j W p (p≥1) is given by

[0061]

[0062] Where Γ(Pi,Pj) represents the joint probability measurement value P defined over the gas concentration range. ij The set of , with margins Pi and Pj, and d represents the distance of the gas concentration value from the corresponding random variable. It is advantageous to use the Wasserstein distance in the calculation because this distinguishes trust functions that are different from most trust functions that measure similarity well.

[0063] The support of a given belief function can be calculated as

[0064]

[0065] in

[0066]

[0067] And among them

[0068]

[0069] Then, the corresponding weight factor of the trust function Pi obtained after normalization, where the weight factor α i is represented as

[0070]

[0071] The weighted average of all N trust functions can be expressed as

[0072]

[0073] Used to compute the final trust function for each sensor. There are alternatives to using a weighted average to compute the combined trust, for example, a weighted average trust function applied to itself N-1 times using the Dempster-Shafer rule can be used.

[0074] Figure 7 A plurality of vehicles 5 are shown at an intersection between two streets 6, 7, each vehicle including a gas sensor S1-SN ( Figure 2 ).exist Figure 7 In the illustrated embodiment, a processing unit 1 including a processor 10 is arranged at a fixed position that may be away from the intersection. The processing unit 1 is connected to a communication interface 3 that communicates with the communication interfaces of the gas sensors S1-SN in the vehicle 5. The processing unit 1 selects the vehicle 5 that is located in the middle of the intersection within the dashed rectangle 8. The location is determined using the positioning sensor 4 in each gas sensor S1-SN. After having received the trust function P from each gas sensor S1-SN, the processing unit 1 selects the vehicle 5 that is located in the middle of the intersection within the dashed rectangle 8. i (x), processing unit 1 may then calculate the combined trust function P(x) as described above.

[0075] The embodiments described above may be modified in many ways without departing from the scope of the present invention which is limited only by the accompanying claims.

Claims

1. A method for determining a measured value of a gas concentration by a group of at least two non-dispersive infrared (NDIR) gas sensors (S1 ... SN), wherein: The method comprises the following steps: - selecting at least two of said NDIR gas sensors (S1 ... SN) of said group from a plurality of NDIR gas sensors, wherein each NDIR gas sensor (S1 ... SN) of said plurality of NDIR gas sensors is associated with a current position, and wherein said NDIR gas sensors (S1 ... SN) are selected based on their current positions, - At the processing unit (1), the measured value of the gas concentration from each NDIR gas sensor (S1..SN) in the group is obtained as a trust function P i (x), the trust function P i (x) is a probability as a function of a measurement of the gas concentration at a particular wavelength, wherein each NDIR gas sensor (S1..SN) is configured to oversample the measurement of the gas concentration and the variation in the measurement is provided as the confidence function, - In the processing unit, the trust function P i (x) are merged into the combined trust function P(x).

2. The method of claim 1, further comprising the step of calibrating each NDIR gas sensor using the combined trust function P(x).

3. The method according to claim 1 or 2, wherein: The processing unit (1) is a central processing unit that communicates with each of the NDIR gas sensors (S1..SN).

4. The method according to claim 1 or 2, wherein: The merging of the belief functions Pi(x) is performed using the Dempster-Shafer rule for merging.

5. The method according to claim 1 or 2, wherein: The combination of the trust function Pi(x) includes the trust function P i The weighted average P(x) of (x) is calculated, where the weight of each trust function depends on the weight of each trust function P i (x) and other trust functions P j,j≠i (x) The distance between i (x),P j (x)), so that the trust function P i (x) and the other trust function P j,j≠i (x) increases the distance W2(P i (x),P j (x)) leads to the trust function P i The weight of (x) is reduced.

6. The method according to claim 5, wherein: In the trust function P i The two trust functions P used in the weighting of (x) i (x), P j The distance between (x) is determined as the Wasserstein distance W p , where for two probability measurements P defined over the gas concentration range i and P j W p , p ≥ 1, is given by Where Γ(Pi,Pj) represents the joint probability measurement value P defined over the gas concentration range. ij The marginals are Pi and Pj, and d represents the distance between the gas concentration value and the corresponding random variable.

7. The method according to claim 6, wherein: Given the trust function P i The support degree of (x) Supp(P i (x)) is calculated as in in Among them, the weight factor α i is represented as And wherein the weight factor α i is used for the trust function P i (x) Merger.

8. The method according to claim 1 or 2, wherein: The NDIR gas sensors (S1 ... SN) are also associated with historical locations, and wherein the NDIR gas sensors (S1 ... SN) are also selected based on their historical locations.

9. The method according to claim 8, wherein: The NDIR gas sensors are also selected based on the gas concentration measurement results of the NDIR gas sensors (S1....SN).

10. The method according to claim 1, wherein: The selection of the NDIR gas sensors (S1 ...SN) is repeatedly performed over time.

11. A computer-readable storage medium storing a computer program for determining gas concentration by a group of at least two non-dispersive infrared (NDIR) gas sensors (S1....SN), the computer program comprising instructions which, when executed by a processor (10) in a processing unit (1), cause the processing unit (1) to control the processing unit (1) to perform a method according to any one of claims 1 to 10.

12. A processing unit (1) configured to determine a gas concentration from a group of at least two non-dispersive infrared (NDIR) gas sensors (S1 . . . SN), wherein: The processing unit (1) is configured to - select at least two of the NDIR gas sensors (S1....SN) in the group from a plurality of NDIR gas sensors, wherein each NDIR gas sensor (S1....SN) of the plurality of NDIR gas sensors is associated with a current position, and wherein the NDIR gas sensors (S1....SN) are selected based on their current positions, - obtaining a measurement of the gas concentration from each NDIR gas sensor (S1 ....SN) as a trust function, the trust function being a probability as a function of the measurement of the gas concentration at a particular wavelength, wherein each NDIR gas sensor (S1 ....SN) is configured to oversample the measurement of the gas concentration and the variation in the measurement is provided as the trust function, - In the processing unit (1), the trust function P i (x) are merged into the combined trust function P(x).

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