A hierarchical lightweight calibration method for cross-sensitivity of electrochemical gas sensors

Abstract

This invention provides a hierarchical lightweight calibration method for cross-sensitivity in electrochemical gas sensors, including primary, secondary, and tertiary cross-sensitivity calibration. This progressive and complementary calibration system reliably identifies and handles cross-sensitivity effects throughout the sensor's entire lifecycle. The invention employs a lightweight model design, based on the response mechanism of electrochemical sensors—that is, the sensor response has an approximately linear relationship with gas concentrations within a certain range. The polynomial used is no higher than second order, satisfying the need to capture slight nonlinearities in the response while preventing overfitting, thus improving model generalization ability and making it highly suitable for implementation on resource-constrained edge devices. This invention can quickly determine the model form at each level according to industry requirements, enabling high-precision, low-latency, and low-power real-time cross-sensitivity calibration on resource-constrained edge devices.

Description

Technical Field

[0001] This invention relates to the field of measurement and testing technology, and specifically to a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors. Background Technology

[0002] Electrochemical gas sensors are characterized by low cost and power consumption, high sensitivity, and fast response. They can effectively detect specific target gases (such as CO, H2S, SO2, NO2, O3, and Cl2) and have been widely used in various fields of gas detection, such as ambient air quality monitoring, industrial process control, safety protection, and medical diagnosis.

[0003] When an electrochemical sensor comes into contact with an analyte, an electrochemical reaction occurs at the electrode, producing changes in current and charge. By detecting these changes in electrical quantities during the electrochemical reaction, the composition and content of the substance can be measured. However, electrochemical gas sensors do not only respond to the target gas; they also produce changes in electrical quantities for non-target gases through electrochemical reactions—a property known as cross-sensitivity. Cross-sensitivity causes the sensor's output signal to not reflect the concentration information of the target gas in a simple linear fashion, affecting the accuracy of target gas concentration detection and potentially leading to false alarms. In complex scenarios involving multiple coexisting gases, the impact of cross-sensitivity on electrochemical sensors is even more severe. Therefore, to improve the reliability, measurement accuracy, and applicability of electrochemical sensors, the effects of cross-sensitivity must be overcome.

[0004] To address the issue of cross-sensitivity, the industry has proposed numerous solutions for both the sensing and processing ends of electrochemical sensors. These solutions primarily fall into three categories: hardware improvement and optimization, algorithm recognition, and concentration inversion. Solutions at the sensing end involve hardware improvement and optimization, including adding physical or chemical filters at the sensor-analyte contact point, or optimizing electrode materials and electrolytes to improve selectivity for the target analyte. Solutions at the processing end focus on algorithm recognition and concentration inversion. For example, arrays of sensors detecting different target gases can be used, employing traditional algorithms (including principal component analysis, partial least squares regression, and support vector machines) to achieve target gas concentration inversion with a certain degree of anti-interference capability. Alternatively, intelligent algorithms such as deep neural networks, convolutional neural networks, and recurrent neural networks can be used to achieve accurate target gas concentration inversion. Another approach involves uploading sensor detection results to a cloud server, processing them using complex algorithms in the background, and then transmitting the results back.

[0005] The above methods have limitations and are applicable only to certain scenarios. For example, solutions at the sensing end have limited effectiveness in eliminating cross-sensitivity, may reduce sensor response speed or sensitivity, and increase hardware complexity and cost. Solutions at the processing end also increase system cost and power consumption. Algorithm optimization requires a large amount of calibration data, is complex, and costly. Traditional algorithms also suffer from insufficient accuracy and robustness, while intelligent algorithms, due to model complexity, require high computing power and are unsuitable for embedded devices and applications with high real-time requirements. Uploading data to a server for backend computation and then transmitting it back requires a reliable network connection, increasing operating and maintenance costs, and is not applicable in situations with poor network conditions or sensitive data security.

[0006] In summary, the core contradiction facing existing cross-sensitivity calibration methods for electrochemical gas sensors lies in the fact that high-precision calibration algorithms (such as deep learning) often have high computational complexity and resource consumption, making them unsuitable for real-time operation on resource-constrained edge devices. Meanwhile, lightweight algorithms (such as simple filtering or traditional models) struggle to effectively handle complex cross-interference, leading to false alarms. Therefore, significantly reducing the computational complexity, memory requirements, and power consumption of algorithms while ensuring calibration accuracy and eliminating false alarms, enabling them to run efficiently and in real-time on embedded systems or portable devices with limited computing power, storage space, and battery life, has become a critical technical challenge that urgently needs to be addressed in the field of electrochemical gas sensor technology.

[0007] Therefore, there is an urgent need for a cross-sensitivity calibration method for electrochemical gas sensors that can resolve the contradiction between the difficulty of deploying complex models at the edge and the requirements for real-time performance and lightweight design. Summary of the Invention

[0008] This invention addresses the problem of effective cross-sensitivity correction of electrochemical gas sensors in resource-sensitive environments and for rapid applications. It provides a hierarchical and lightweight correction method for cross-sensitivity of electrochemical gas sensors. Through hierarchical processing and lightweight model design, it achieves high-precision, low-latency, and low-power real-time cross-sensitivity correction on resource-constrained edge devices, effectively improving the reliability and practicality of electrochemical gas sensors in complex environments and meeting the reliable measurement requirements of electrochemical gas sensors in edge applications.

[0009] This invention provides a graded lightweight calibration method for cross-sensitivity electrochemical gas sensors, comprising the following steps:

[0010] S1. Obtaining electrochemical sensors under standard conditions For target gas The output voltage at different concentration points, where, ;

[0011] S2, Calculate the values ​​for each electrochemical sensor First-order polynomials for output voltage and concentration for all gases;

[0012] S3. Extract the coefficients of the first-order polynomials for output voltage and concentration, respectively. ,intercept Obtain the coefficient matrix and intercept matrix Intercept matrix Each element value is from an electrochemical sensor. Zero-point voltage ( ) and intercept sum;

[0013] S4. Calculate the coefficient matrix The inverse matrix yields the concentration coefficient matrix. Calculate the values ​​of each electrochemical sensor Output voltage and intercept matrix The concentration intercept matrix is ​​obtained by the difference between corresponding element values. ;

[0014] S5. Concentration coefficient matrix and concentration intercept matrix By constructing a new first-order polynomial, the individual electrochemical sensors can be calculated. The initial concentration was obtained by measuring the concentration. ;

[0015] S6. Extracting electrochemical sensors at different concentrations of non-target gases. With a non-zero initial concentration, an electrochemical sensor is constructed using a polynomial of order no higher than second order. Corrected concentration With electrochemical sensors Initial concentration of non-target gas Relationship;

[0016] S7, according to and The quadratic correction concentration polynomial of the false alarm sensor is obtained and the quadratic correction concentration is obtained. ;

[0017] S8. Determine the secondary correction concentration based on the false alarm threshold. If there is a false alarm, proceed to step S9; otherwise, proceed to step S11.

[0018] S9. Construct a polynomial of order no higher than first order to establish the relationship between the secondary correction concentration of the false alarm sensor for non-target gases and the secondary correction concentration of other sensors, thus obtaining the relationship between the non-target gas and the second-order correction concentration of ... third-order correction concentration of the second The correction amount of the secondary correction concentration of the support sensor ;

[0019] S10. Based on the secondary correction concentration of the false alarm sensor. and Three corrected concentrations were obtained polynomials;

[0020] S11, Based on the secondary correction concentration Or three-fold correction concentration To obtain the final concentration .

[0021] The present invention provides a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors. In a preferred embodiment, steps S1 to S5 constitute the first level of the algorithm, namely, cross-sensitivity primary calibration; steps S6 to S7 constitute the second level of the algorithm, namely, secondary calibration; and steps S8 to S10 constitute the third level of the algorithm, namely, tertiary calibration.

[0022] In step S1, the target gas For electrochemical sensors The gas to be measured should be a single type, and the standard environment should be a standard atmospheric pressure, standard temperature, and standard humidity environment, with corresponding values ​​of 101.325 kPa, 25℃, and 60%RH, respectively. There should be at least three different concentration points, and one of the concentration points should be zero, which is the sensor response caused by pure nitrogen or synthetic air.

[0023] The present invention provides a graded lightweight calibration method for cross-sensitivity electrochemical gas sensors. In a preferred embodiment, step S2, the first-order polynomial of the output voltage and concentration can be expressed as:

[0024] ;

[0025] in, For the number The electrochemical sensor detection number is The output voltage of the sensor is measured in volts (V). When the target gas is used, the output voltage remains unchanged. For other gases, the output voltage of each sensor needs to be reduced by the zero-point voltage. ; The number used for calibration is The standard gas concentration is expressed in ppm.

[0026] The present invention provides a graded lightweight calibration method for cross-sensitivity electrochemical gas sensors. In a preferred embodiment, step S3 includes...

[0027] ;

[0028] ;

[0029] in, For sensors Zero-point voltage, symbol This is a transpose.

[0030] The present invention provides a graded lightweight calibration method for cross-sensitivity electrochemical gas sensors. As a preferred embodiment, in step S4, if the coefficient matrix... If the coefficient matrix is ​​a singular matrix, first optimize the first-order polynomial of output voltage and concentration in step S2, and repeat step S3. If the coefficient matrix in step S3 is still a singular matrix, return to step S1, reselect points, and repeat steps S2 and S3. If the coefficient matrix in step S3 is still a singular matrix, then use numerical methods to approximate its inverse matrix. Numerical methods include Moore-Penrose pseudo-inverse, singular value decomposition, least squares method, and regularization method.

[0031] In step S4,

[0032] ;

[0033] in, For sensors ; output voltage; These are the elements in the intercept matrix obtained in step S3.

[0034] The present invention provides a graded lightweight calibration method for cross-sensitivity electrochemical gas sensors. As a preferred embodiment, the initial concentration in step S5... for:

[0035] ;

[0036] in, For column arrangement The initial concentration of the sensor, .

[0037] The present invention provides a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors. In a preferred embodiment, in step S6, sensors that have non-zero measurement concentration results for gases other than the target gas are sensors that need further de-cross-sensitivity resolution.

[0038] Polynomials of order no higher than 2 are:

[0039] ;

[0040] in, , , The coefficients are, in order, the coefficients of the quadratic term, the linear term, and the constant term, and their values ​​are real numbers.

[0041] The polynomial for the calibration concentration of the sensor and the concentration of other gases can be constructed by using mathematical calculation software to perform multiple fittings, including first-order fitting and second-order fitting, with the minimum average deviation serving as the basis for the final selection of a certain polynomial.

[0042] Sensors that produce non-zero measured concentrations for gases other than the target gas require further de-cross-sensitivity analysis. The goal is to construct the relationship using polynomials of order no higher than second, achieving a balance between cross-sensitivity compensation and the needs of resource-sensitive and rapid application scenarios.

[0043] The polynomial for constructing the sensor's calibration concentration and other gas concentrations, as described in step S6, can be achieved through multiple fitting operations using mathematical calculation software. Multiple fitting operations include first-order fitting and second-order fitting, with the minimum average deviation serving as the basis for finally selecting a particular polynomial.

[0044] In step S7,

[0045] .

[0046] The present invention provides a graded lightweight calibration method for cross-sensitivity electrochemical gas sensors. In a preferred embodiment, in step S8, the standard for determining whether the calculated concentration has a false alarm needs to be determined according to specific industry standards. When the electrochemical sensor is a portable consumer-grade air detection device, the false alarm threshold is 10% to 20% of the measurement range.

[0047] When it is determined that there are no false alarms in the secondary correction concentration.

[0048]

[0049] The present invention provides a graded lightweight calibration method for cross-sensitivity electrochemical gas sensors. In a preferred embodiment, in step S9, the relationship between the secondary calibration concentration correction of the false alarm sensor for non-target gases and the secondary calibration concentrations of other sensors is as follows:

[0050] ;

[0051] in, and The coefficients of the first term and constant term of the secondary correction concentration of the false alarm sensor and the secondary correction gas concentration of other sensors are real numbers.

[0052] Multiple fitting can be performed using mathematical calculation software to construct the relationship between the secondary correction concentration of the false alarm sensor for non-target gases and the secondary correction concentration of other sensors. Multiple fitting is mainly based on the first fitting, and the minimum average deviation is used as the basis for the final selection of a certain polynomial.

[0053] In step S10,

[0054] ;

[0055] In step S11,

[0056] .

[0057] The present invention provides a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors, which, as a preferred embodiment, further includes step S12.

[0058] S12, Calculate the first The sensor is for the first Relative deviation of calculated concentration results for each gas Determine the relative deviation based on the false alarm threshold. Has the target been achieved? If yes, the correction method is complete; if no, return to step S1 to recalibrate.

[0059] ;

[0060] in, For the first The true concentration of the gas For the first The full-scale concentration of a gas.

[0061] This invention provides a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors, which mainly consists of a three-level algorithm. The first-level algorithm, called cross-sensitivity primary calibration, determines the cross-sensitivity coefficient of each gas sensor to non-target gases through experiments, and obtains a first-order polynomial for calculating the initial concentration of each sensor. This method includes five steps: First, obtain the output voltage of the electrochemical sensor at different concentration points of the target gas under standard conditions; second, calculate the first-order polynomial of the output voltage and concentration of each sensor for all gases; then, extract the coefficients and intercepts of the first-order polynomial obtained in the previous step, and construct a coefficient matrix and an intercept matrix, where each element in the intercept matrix is ​​the sum of the zero-point voltage of the sensor and the intercept of the first-order polynomial; then, calculate the inverse matrix of the coefficient matrix from the previous step, denoted as the concentration coefficient matrix, and calculate the difference between the output voltage of each sensor and the corresponding element value in the intercept matrix from the previous step, denoted as the concentration intercept matrix; finally, combine the concentration coefficient matrix and the concentration intercept matrix from the previous step to form a new first-order polynomial, and substitute the output voltage of each sensor into it to obtain the corresponding measured concentration, denoted as the initial concentration. The second-level algorithm, called cross-sensitivity secondary correction, further corrects cross-sensitivity by establishing a concentration correction formula. It includes two steps: first, extracting the non-zero initial concentrations of each sensor at different concentrations of non-target gases, and constructing a relationship between the corrected concentration of the sensor and the concentration of the non-target gas using a polynomial of order no higher than second order; then, fusing the polynomial of order no higher than second order from the previous step with the first-order polynomial of the initial concentration obtained from the first-level algorithm to construct a polynomial for the secondary correction concentration of the false alarm sensor. The third level determines whether the sensor's secondary correction concentration is falsely reported. If so, it constructs a relationship between the secondary correction concentration of the false alarm sensor and the secondary correction gas concentrations of other sensors using a polynomial of order no higher than first order; then, it constructs a polynomial for the cubic correction concentration of the false alarm sensor; finally, it constructs the final concentration calculation formula for the false alarm sensor; if the above secondary correction concentrations are not falsely reported, the final concentration of the sensor is the secondary correction concentration; finally, it calculates the relative deviation and evaluates the algorithm's performance. This invention aims to solve the problem of effective correction of cross-sensitivity in electrochemical gas sensors in resource-sensitive applications and rapid application requirements, providing a hierarchical lightweight correction method for cross-sensitivity in electrochemical gas sensors, meeting the reliable measurement requirements of electrochemical gas sensors.

[0062] This invention proposes a hierarchical lightweight calibration method for cross-sensitivity of electrochemical gas sensors. It aims to achieve high-precision, low-latency, and low-power real-time cross-sensitivity calibration on resource-constrained edge devices by using the core ideas of hierarchical processing and lightweight model design, thereby effectively improving the reliability and practicality of electrochemical gas sensors in complex environments.

[0063] The present invention has the following advantages:

[0064] The advantages of this invention compared to the prior art are:

[0065] The hierarchical processing method proposed in this invention, namely cross-sensitivity primary correction, secondary correction and tertiary correction, is a progressive and complementary correction system that can reliably identify and process cross-sensitivity effects throughout the entire life cycle of the sensor.

[0066] The cross-sensitive three-level calibration method proposed in this invention adopts a lightweight model design concept. Based on the response mechanism of electrochemical sensors, namely, the sensor response and the gas concentration within a certain range are approximately linearly related, the polynomial used is no higher than the second order, which satisfies the slight nonlinearity requirement of capturing the response and prevents the introduction of overfitting risk. It is beneficial to improve the generalization ability of the model and is very suitable for implementation on resource-constrained edge devices.

[0067] The cross-sensitivity correction method proposed in this invention, which uses hierarchical processing and lightweight model design, can quickly determine the form of each level of the model according to industry needs, and can achieve high-precision, low-latency, and low-power real-time cross-sensitivity correction on resource-constrained edge devices. Attached Figure Description

[0068] Figure 1 A flowchart of a graded lightweight calibration method for cross-sensitivity electrochemical gas sensors;

[0069] Figure 2 This is a graded lightweight calibration method for the cross-sensitivity of electrochemical gas sensors—the cross-sensitivity calibration result of an NH3 sensor for NH3.

[0070] Figure 3 This is a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors—the cross-sensitivity calibration result of an SO2 sensor for SO2.

[0071] Figure 4 This is a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors—the cross-sensitivity calibration result of an H2S sensor for H2S.

[0072] Figure 5 This is a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors—the cross-sensitivity calibration result of the H2 sensor for H2;

[0073] Figure 6 This is a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors—the cross-sensitivity calibration result of a C2H4 sensor for C2H4;

[0074] Figure 7 This is a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors—the cross-sensitivity calibration result of a CO sensor for CO.

[0075] Figure 8 This is a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors—the cross-sensitivity calibration results of an H2S sensor for H2S and CO.

[0076] Figure 9 This is a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors—the cross-sensitivity calibration results of a CO sensor for H2S and CO. Detailed Implementation

[0077] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Example 1

[0078] like Figure 1 As shown, a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors includes the following steps:

[0079] S1. Obtain the output voltage of the electrochemical sensor at different concentration points of the target gas under standard conditions;

[0080] S2. Calculate the first-order polynomial of the output voltage and concentration of each sensor for all gases;

[0081] S3. Extract the coefficients and intercepts of the first-order polynomial obtained in the previous step, and construct the coefficient matrix and intercept matrix. The value of each element in the intercept matrix is ​​the sum of the zero-point voltage of the sensor and the intercept of the first-order polynomial.

[0082] S4. Calculate the inverse matrix of the coefficient matrix in the previous step, denoted as the concentration coefficient matrix, and calculate the difference between the output voltage of each sensor and the corresponding element value in the intercept matrix in the previous step, denoted as the concentration intercept matrix.

[0083] S5. Combine the concentration coefficient matrix and concentration intercept matrix from the previous step to form a new first-order polynomial, and calculate the measured concentration of each sensor, which is recorded as the initial concentration.

[0084] S6. Extract the non-zero initial concentration of each sensor at different concentrations of non-target gas, and construct the relationship between the sensor's calibration concentration and the concentration of non-target gas using a polynomial of no higher than second order.

[0085] S7. Construct polynomials for the output voltage of each sensor and the correction concentration;

[0086] S8. Determine if there is a false alarm for the calibration concentration. If there is a false alarm, proceed to step S9; otherwise, proceed to step S11.

[0087] S9. Construct the relationship between the correction concentration of the false alarm sensor and the correction concentration of other sensors using a polynomial of no higher than first order.

[0088] S10. Construct the polynomial for the third correction concentration of the false alarm sensor;

[0089] S11. Construct the final concentration calculation formula;

[0090] S12. Calculate the relative deviation and evaluate the algorithm performance. Example 2

[0091] like Figure 1 As shown, a graded lightweight calibration method for cross-sensitivity of electrochemical gas sensors includes the following steps:

[0092] S1. Build an experimental platform and obtain the output voltage of several electrochemical sensors at at least three different concentration points of their respective target gases when the atmospheric pressure is 101.325 kPa, the temperature is 25℃, and the humidity is 60%RH. One of the concentration points is zero (the sensor response caused by pure nitrogen or synthetic air).

[0093] S2. Calculate the first-order polynomial for the output voltage and concentration of each sensor for all gases. The first-order polynomial is expressed as:

[0094] ;

[0095] In the formula, Number the electrochemical gas sensors (1 to ); Number the gases to be tested (1 to...) ,generally and equal); For the number The electrochemical sensor detection number is The output voltage (in volts (V)) of the sensor is given when the target gas is used. The output voltage remains unchanged when the target gas is used; for other gases, the output voltage of each sensor needs to be reduced by the zero-point voltage. ( ); The coefficients to be determined; The intercept is to be determined; The number used for calibration is Standard gas concentration (unit: ppm, i.e., parts per million).

[0096] S3. Extract the coefficients of the first-order polynomial obtained in the previous step. and intercept Construct the coefficient matrix and intercept matrix Each element in the intercept matrix represents the zero-point voltage of the sensor. ( Intercept of the first-order polynomial sum;

[0097] coefficient matrix Represented as:

[0098] ;

[0099] Intercept matrix Represented as:

[0100] ;

[0101] S4. Calculate the coefficient matrix from the previous step. The inverse matrix is ​​denoted as the concentration coefficient matrix. And calculate the output voltage of each sensor and the intercept matrix from the previous step. The difference between corresponding element values ​​is denoted as the concentration intercept matrix. ;

[0102] Find the coefficient matrix When calculating the inverse matrix, the coefficient matrix must first be determined. If the matrix is ​​singular, find its inverse directly. That's sufficient; otherwise, new experimental data or repeated experiments are needed to reconstruct the coefficient matrix. If it is still a singular matrix, then methods such as Moore-Penrose pseudoinverse, singular value decomposition, least squares method, or regularization should be used to approximate its inverse matrix.

[0103] Concentration intercept matrix Represented as:

[0104] ;

[0105] S5. The concentration coefficient matrix from the previous step... and concentration intercept matrix A new first-order polynomial is constructed, and the measured concentration of each sensor is calculated and denoted as the initial concentration. ;

[0106] The method for determining the initial concentration is as follows:

[0107] ;

[0108] S6. Extract the non-zero initial concentration of each sensor under different concentrations of non-target gas, and construct the relationship between the sensor's calibration concentration and the concentration of non-target gas using a polynomial of no higher than second order.

[0109] This is achieved through multiple fitting operations using mathematical calculation software. Multiple fitting operations include single-step and double-step fitting, with the minimum average deviation used as the criterion for selecting a specific polynomial. Polynomials of order no higher than two take the form:

[0110] ;

[0111] In the formula, For non-target gas to the first The correction amount of the calibration concentration of the support sensor. For the first The initial concentration of the sensor in response to non-target gases. , , The coefficients are, in order, the quadratic term, the linear term, and the constant term, and their values ​​are real numbers.

[0112] S7. Construct the polynomial for the quadratic correction concentration of the false alarm sensor;

[0113] In the form of:

[0114] ;

[0115] In the formula, For the first Secondary calibration concentration of the support sensor For the first The initial concentration of the sensor, For non-target gas to the first The correction amount of the calibration concentration of the support sensor.

[0116] S8. Determine if there is a false alarm for the calibration concentration. If there is a false alarm, proceed to step S9; otherwise, proceed to step S11.

[0117] In portable consumer-grade air quality monitoring devices, a false alarm is considered to occur when the false alarm value exceeds 10% to 20% of the measurement range.

[0118] Determine if there are any false alarms in the secondary calibration concentration. If there are no false alarms, then the sensor's final concentration... The calculation formula is in the form of:

[0119] ;

[0120] If there is a false alarm, proceed to step S9.

[0121] S9. Construct a formula relating the secondary correction concentration of the false alarm sensor to the secondary correction gas concentration of other sensors using a polynomial of order no higher than first order.

[0122] This is achieved through multiple fitting operations using mathematical calculation software. The multiple fitting primarily uses the first-order fitting, with the minimum average deviation serving as the criterion for selecting a specific polynomial. The relational expression is as follows:

[0123] ;

[0124] In the formula, For non-target gas to the first The correction amount of the secondary correction concentration of the sensor. For the first The secondary correction concentration of the sensor for gases other than the target gas. and The coefficients of the primary term and constant term of the secondary correction concentration of the false alarm sensor and the secondary correction gas concentration of other sensors are real numbers.

[0125] S10. Constructing the three-stage calibration concentration for the false alarm sensor. A polynomial of the form:

[0126] ;

[0127] S11, Constructing the final concentration A polynomial of the form:

[0128] ;

[0129] S12, Calculate the first The sensor is for the first The relative deviation of the calculated concentration results for each gas is used to evaluate the algorithm's performance.

[0130] ;

[0131] In the formula, For the first The sensor is for the first The relative deviation of the calculated concentration results for the gas. For the first The sensor is for the first The final concentration of the gas, For the first The true concentration of the gas For the first The full-scale concentration of a gas.

[0132] Example 3

[0133] like Figure 1-9 As shown, a hierarchical lightweight calibration method for cross-sensitivity of electrochemical gas sensors is implemented through the following steps:

[0134] S1. Obtain the output voltage of the electrochemical sensor at different concentration points of the target gas under standard conditions;

[0135] At atmospheric pressure of 101.325 kPa, temperature of 25°C, and humidity of 60%RH, the output voltage of NH3, SO2, H2S, H2, C2H4, and CO electrochemical sensors (a total of 6 types) was acquired for at least 3 different concentration points of their respective target gases, one of which was the sensor response caused by zero point (pure nitrogen or synthetic air).

[0136] Table 1 shows the correspondence between various sensor types and symbols.

[0137] Table 1. Correspondence between sensor types and symbols

[0138]

[0139] The concentration points measured by each sensor for its respective target gas are summarized below:

[0140] (1) The NH3 sensor measures the NH3 concentration at zero point (pure nitrogen), 5.0197 ppm, 10.0397 ppm, and 20.0808 ppm;

[0141] (2) The SO2 sensor measures SO2 concentration at zero point (synthetic air), 4.9990 ppm, 9.9995 ppm, and 20.0000 ppm;

[0142] (3) The H2S sensor measured the H2S concentration at zero point (pure nitrogen), 1.4897 ppm, 2.9798 ppm, and 11.9202 ppm;

[0143] (4) The H2 sensor measured the H2 concentration at zero point (pure nitrogen), 994.7726 ppm, and 3979.7891 ppm;

[0144] (5) The C2H4 sensor measured the C2H4 concentration at zero point (synthetic air), 25.2500 ppm, 50.5000 ppm, and 100.8155 ppm;

[0145] (6) The CO sensor measures CO concentration at zero point (synthetic air), 4.9990ppm, 9.9982ppm, 19.9990ppm, and 100ppm.

[0146] S2. Calculate the first-order polynomial of the output voltage and concentration of each sensor for all gases;

[0147] Taking the relationship between the output voltage and concentration of an NH3 sensor for NH3, SO2, H2S, H2, C2H4, and CO gases as an example, the following is an example:

[0148] ;

[0149] The zero-point voltage is 0.020561V.

[0150] S3. Extract the coefficients and intercepts of the first-order polynomial obtained in the previous step, and construct the coefficient matrix and intercept matrix. The value of each element in the intercept matrix is ​​the sum of the zero-point voltage of the sensor and the intercept of the first-order polynomial.

[0151] coefficient matrix for:

[0152] ;

[0153] Intercept matrix Represented as:

[0154] ;

[0155] S4. Calculate the inverse matrix of the coefficient matrix in the previous step, denoted as the concentration coefficient matrix, and calculate the difference between the output voltage of each sensor and the corresponding element value in the intercept matrix in the previous step, denoted as the concentration intercept matrix.

[0156] coefficient matrix inverse matrix —The concentration coefficient matrix is ​​as follows:

[0157] ;

[0158] Concentration intercept matrix for:

[0159] ;

[0160] S5. Combine the concentration coefficient matrix and concentration intercept matrix from the previous step to form a new first-order polynomial, and calculate the measured concentration for each sensor.

[0161] This is recorded as the initial concentration;

[0162] initial concentration The solution method is as follows:

[0163] ;

[0164] Taking the initial concentration calculation results of NH3, SO2, H2S, H2, C2H4 and CO gases of a certain concentration by each sensor as an example, the results are shown in Tables 2 to 7.

[0165] Table 2 Calculation results of initial concentration of NH3 sensor

[0166]

[0167] Table 3 Calculation results of initial concentration of SO2 sensor

[0168]

[0169] Table 4 Calculation results of initial concentration of H2S sensor

[0170]

[0171] Table 5 Calculation results of initial concentration of H2 sensor

[0172]

[0173] Table 6 Calculation results of initial concentration of C2H4 sensor

[0174]

[0175] Table 7 Initial concentration calculation results from CO sensor

[0176]

[0177] S6. Extract the non-zero initial concentration of each sensor under different concentrations of non-target gas, and construct the relationship between the sensor's calibration concentration and the concentration of non-target gas using a polynomial of no higher than second order.

[0178] The constructed relation is as follows:

[0179] ;

[0180] S7. Construct the polynomial for the quadratic correction concentration of the false alarm sensor;

[0181] The constructed polynomial is:

[0182] ;

[0183] S8. Determine if there is a false alarm for the secondary correction concentration. If there is a false alarm, proceed to step S9; otherwise, proceed to step S11.

[0184] Based on the examples in Tables 2-7, the secondary correction concentration was calculated to determine whether there were any false alarms. The results are shown in Tables 8-13.

[0185] Table 8 Calculation results of secondary calibration concentration of NH3 sensor

[0186]

[0187] Table 9 Calculation results of SO2 sensor secondary calibration concentration

[0188]

[0189] Table 10 Calculation results of H2S sensor secondary calibration concentration

[0190]

[0191] Table 11 Calculation results of H2 sensor secondary calibration concentration

[0192]

[0193] Table 12 Calculation results of secondary calibration concentration of C2H4 sensor

[0194]

[0195] Table 13 Calculation results of CO sensor secondary calibration concentration

[0196]

[0197] The NH3 sensor is the one that has false alarms and positive values. Therefore, S9 performs a third correction on the secondary correction concentration of the NH3 sensor. The gases that have residual cross-sensitivity with it are SO2 and H2S.

[0198] S9. Construct a formula relating the secondary correction concentration of the false alarm sensor to the secondary correction concentration of other sensors using a polynomial of order no higher than first order.

[0199] The relationship between the secondary correction concentration of the NH3 sensor and the secondary correction concentrations of the SO2 and H2S sensors is constructed as follows:

[0200] ;

[0201] S10. Construct the polynomial for the third correction concentration of the false alarm sensor;

[0202] The polynomial for constructing the cubic correction concentration of the NH3 sensor is as follows:

[0203] ;

[0204] S11. Construct the final concentration calculation formula;

[0205] The constructed relation is as follows:

[0206] ;

[0207] S12. Calculate the relative deviation and evaluate the algorithm performance.

[0208] The formula for calculating relative deviation is:

[0209] ;

[0210] In the formula, For the first The sensor is for the first The relative deviation of the calculated concentration results for the gas. For the first The sensor is for the first The final concentration of the gas, For the first The true concentration of the gas For the first The full-scale concentration of a gas.

[0211] Calculate the output concentrations and relative deviations of the electrochemical sensors for NH3, SO2, H2S, H2, C2H4, and CO when their respective target gases are introduced, as well as when a mixture of H2S and CO is introduced. Figures 2-9 As shown, the maximum relative deviation occurred when the SO2 sensor measured 20 ppm of pure SO2 gas, at -6.94%.

[0212] Based on the examples in Tables 8-13, the final correction concentration was calculated to determine whether there were any false alarms. The results are shown in Tables 14-19.

[0213] Table 14 Calculation results of the final calibration concentration of the NH3 sensor

[0214]

[0215] Table 15 Calculation results of final calibration concentration of SO2 sensor

[0216]

[0217] Table 16 Calculation results of final calibration concentration of H2S sensor

[0218]

[0219] Table 17 Calculation results of the final calibration concentration of the H2 sensor

[0220]

[0221] Table 18 Calculation results of the final calibration concentration of the C2H4 sensor

[0222]

[0223] Table 19 Calculation results of final calibration concentration of CO sensor

[0224]

[0225] In the above measurements, none of the sensors gave false alarms for gases other than their target gases, and there was no cross-interference. At the same time, the maximum absolute value of the relative deviation for each target gas was 5.16%, which meets the requirements for false alarm values ​​in portable consumer-grade air detection devices (a false alarm is considered to occur when the value exceeds 10% to 20% of the measurement range). Therefore, there were no false alarms.

[0226] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A hierarchical light-weight correction method for cross-sensitivity of an electrochemical gas sensor, characterized by: Includes the following steps: S1, obtaining an electrochemical sensor under a standard environment to a target gas Output voltage at different concentration points, wherein ; S2, calculate the output voltage of each electrochemical sensor The output voltage of all gases is a first-order polynomial with concentration. S3, extracting coefficients of the first order polynomial of the output voltage and the concentration, respectively , intercept , obtaining a coefficient matrix , and an intercept matrix , each element value of the intercept matrix is the zero point voltage of the electrochemical sensor , the sum of the zero point voltage and the intercept​​ S4. Calculate the coefficient matrix. The inverse matrix yields the concentration coefficient matrix. Calculate the values ​​of each electrochemical sensor Output voltage and the intercept matrix The concentration intercept matrix is ​​obtained by the difference between corresponding element values. ; S5. The concentration coefficient matrix is... and the concentration intercept matrix By constructing a new first-order polynomial, the individual electrochemical sensors can be calculated. The initial concentration was obtained by measuring the concentration. ; S6. Extracting electrochemical sensors at different concentrations of non-target gases. With a non-zero initial concentration, an electrochemical sensor is constructed using a polynomial of order no higher than second order. Corrected concentration With electrochemical sensors Initial concentration of non-target gas Relationship; S7, according to and The quadratic correction concentration polynomial of the false alarm sensor is obtained and the quadratic correction concentration is obtained. ; S8. Determine the secondary correction concentration based on the false alarm threshold. If there is a false alarm, proceed to step S9; otherwise, proceed to step S11. S9. Construct a polynomial of order no higher than first order to establish the relationship between the secondary correction concentration of the false alarm sensor for non-target gases and the secondary correction concentration of other sensors, thus obtaining the relationship between the non-target gas and the second-order correction concentration of ... third-order correction concentration of the second The correction amount of the secondary correction concentration of the support sensor ; S10. Based on the secondary correction concentration of the false alarm sensor. and Three corrected concentrations were obtained polynomials; S11, Based on the secondary correction concentration Or three-fold correction concentration To obtain the final concentration .

2. The hierarchical lightweight calibration method for cross-sensitivity of electrochemical gas sensors according to claim 1, characterized in that: Steps S1 to S5 are the first cross-sensitivity correction, steps S6 to S7 are the second correction, and steps S8 to S10 are the third correction. In step S1, the target gas For electrochemical sensors The gas to be measured is a single type, and the standard environment is a standard atmospheric pressure, standard temperature, and standard humidity environment, with corresponding values ​​of 101.325 kPa, 25°C, and 60% RH, respectively; there are at least three different concentration points, and one of the concentration points is zero, which is the sensor response caused by pure nitrogen or synthetic air.

3. The hierarchical lightweight calibration method for cross-sensitivity of electrochemical gas sensors according to claim 1, characterized in that: In step S2, the first-order polynomial of the output voltage and concentration can be expressed as: ； in, For the number The electrochemical sensor detection number is The output voltage of the sensor is measured in volts (V). When the target gas is used, the output voltage remains unchanged. For other gases, the output voltage of each sensor needs to be reduced by the zero-point voltage. ; The number used for calibration is The standard gas concentration is expressed in ppm.

4. The hierarchical lightweight calibration method for cross-sensitivity electrochemical gas sensors according to claim 1, characterized in that: In step S3, ； ； in, For sensors Zero-point voltage, symbol This is a transpose.

5. A graded lightweight calibration method for cross-sensitivity electrochemical gas sensors according to claim 1, characterized in that: In step S4, if the coefficient matrix If the coefficient matrix is ​​a singular matrix, first optimize the first-order polynomial of output voltage and concentration in step S2, and repeat step S3. If the coefficient matrix in step S3 is still a singular matrix, return to step S1, reselect points, and repeat steps S2 and S3. If the coefficient matrix in step S3 is still a singular matrix, then use numerical methods to approximate its inverse matrix. The numerical methods include Moore-Penrose pseudo-inverse, singular value decomposition, least squares method, and regularization method. In step S4, ； in, For sensors ; output voltage; These are the elements in the intercept matrix obtained in step S3.

6. A graded lightweight calibration method for cross-sensitivity electrochemical gas sensors according to claim 1, characterized in that: The initial concentration mentioned in step S5 for: ； in, For column arrangement The initial concentration of the sensor, .

7. A graded lightweight calibration method for cross-sensitivity electrochemical gas sensors according to claim 1, characterized in that: In step S6, sensors that have non-zero measured concentration results for gases other than the target gas are sensors that need further de-cross-sensitivity analysis. Polynomials of order no higher than 2 are: ； in, , , The coefficients are, in order, the coefficients of the quadratic term, the linear term, and the constant term, and their values ​​are real numbers. The polynomial for the calibration concentration of the sensor and the concentration of other gases can be constructed by using mathematical calculation software to perform multiple fittings, including first-order fitting and second-order fitting, with the minimum average deviation serving as the basis for the final selection of a certain polynomial. In step S7, 。 8. A graded lightweight calibration method for cross-sensitivity electrochemical gas sensors according to claim 1, characterized in that: In step S8, when the electrochemical sensor is a portable consumer-grade air detection device, the false alarm threshold is 10% to 20% of the measurement range; When it is determined that the secondary correction concentration does not produce a false alarm. 。 9. A graded lightweight calibration method for cross-sensitivity electrochemical gas sensors according to claim 1, characterized in that: In step S9, the relationship between the secondary correction concentration of the false alarm sensor for non-target gases and the secondary correction concentration of other sensors is as follows: ； in, and The coefficients of the first term and constant term of the secondary correction concentration of the false alarm sensor and the secondary correction gas concentration of other sensors are real numbers. The relationship between the secondary correction concentration of the false alarm sensor for non-target gases and the secondary correction concentration of other sensors is constructed by a single fitting, and the minimum average deviation is used as the basis for the final selection of a certain polynomial. In step S10, ； In step S11, 。 10. A graded lightweight calibration method for cross-sensitivity electrochemical gas sensors according to claim 1, characterized in that: It also includes step S12; S12, Calculate the first The sensor is for the first Relative deviation of calculated concentration results for each gas Determine the relative deviation based on the false alarm threshold. Has the target been achieved? If yes, the correction method is complete; if no, return to step S1 to recalibrate. ； in, For the first The true concentration of the gas For the first The full-scale concentration of a gas.

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