Method for determining uncertainty of silicate concentration in water based on chemiluminescence method

Abstract

The invention relates to an uncertainty evaluation method for determining the silicate concentration in water based on a chemiluminescence method. The method comprises the following steps: S1, determining the silicate concentration based on the chemiluminescence method; s2, establishing a mathematical model for silicate measurement; and S3, based on the mathematical model of silicate measurement, determining synthesis relative uncertainty and expansion relative uncertainty. The main source of the measurement uncertainty of the silicate concentration in the water can be accurately determined, and control measures are taken aiming at the main source, so that the measurement precision of the silicate is further improved. Meanwhile, the method is verified through the Monte Carlo method, it is determined that the non-obvious nonlinear model used in the method is suitable for a first-order approximate uncertainty propagation law formula in the GUM method, and reference is provided for uncertainty evaluation of similar nonlinear models.

Description

Technical Field

[0001] This invention relates to the field of analytical instrument calibration technology, and in particular to a method for evaluating the uncertainty of determining silicate concentration in water based on chemiluminescence method. Background Technology

[0002] The treatment and monitoring of boiler water in thermal power plants is a crucial aspect, directly impacting boiler safety, energy efficiency, and the overall economic benefits of the power plant. The silicate content in boiler water, as a key indicator of boiler water quality, is of profound significance. Currently, methods for detecting silicate content in water mainly include spectrophotometry, electrochemical methods, gravimetric methods, chemical precipitation methods, ion chromatography, continuous flow analysis, and chemiluminescence. At present, most thermal power plants and the semiconductor industry primarily use silicate analyzers based on the molybdenum blue colorimetric principle (spectrophotometry) as the main detection method for silicate ion concentration. The detection process requires manual addition of a certain amount of reagent; after a chemical colorimetric reaction, the silicate ion concentration is measured using the silicate analyzer. To ensure the accuracy and repeatability of silicate measurement, the State Administration for Quality Supervision, Inspection and Quarantine issued JJF 1539-2015 "Calibration Specification for Silicate Analyzers" in 2015. Appendix D provides an example of measurement uncertainty assessment, which is applicable to silicate analyzers based on spectrophotometry.

[0003] Chemiluminescence (silicomolybdate heteropolyacid spectrophotometry) is a rapid and effective method for measuring trace amounts of silicate ions. It involves the reaction of silicon and molybdate under specific conditions to produce silicomolybdate heteropolyacids, which, upon reaction with luminol, generate strong chemiluminescence. The concentration of the reactants can be directly determined by detecting the intensity of the chemiluminescence. The luminescence reaction is completed within tens of seconds. Uncertainty reflects the reasonable dispersion of the measured value and is a parameter related to the measurement result. It is an important indicator in contemporary error theory for quantitatively describing the quality of measurement results. Currently, there are no methods for evaluating the uncertainty of silicate ion measurement using chemiluminescence methods, either domestically or internationally. Due to differences in measurement principles, the measurement models and uncertainty sources of chemiluminescence and spectrophotometry differ, making the uncertainty evaluation method proposed in JJF1539-2015 "Calibration Specification for Silicate Analyzers" inapplicable. Therefore, this invention patent establishes a chemiluminescence measurement method for silicate concentration in water, builds a mathematical model, analyzes the sources of uncertainty, and calculates the uncertainty of silicate ions within the actual operating condition concentration range, providing methodological support for improving the silicate concentration traceability system.

[0004] The drawback of existing technologies is that they lack a method for assessing the uncertainty of chemiluminescence immunoassay for silicate determination. The reasons for this drawback include:

[0005] 1. Existing uncertainty analysis methods are designed for spectrophotometry and cannot be directly applied to chemiluminescence. Therefore, it is necessary to establish an uncertainty analysis method suitable for chemiluminescence.

[0006] 2. The measurement model for silicate ion determination by chemiluminescence is a nonlinear model, and it is unclear whether higher-order Taylor series expansions should be considered in the uncertainty propagation formula.

[0007] 3. Analysis of sources of uncertainty in the measurement of silicate without chemiluminescence.

[0008] Therefore, there is a technical need to design new methods for assessing the uncertainty of determining silicate concentration in water. Summary of the Invention

[0009] The purpose of this invention is to provide an uncertainty assessment method for determining silicate concentration in water based on chemiluminescence immunoassay. This method can accurately identify the main sources of uncertainty in silicate concentration measurement and implement control measures targeting these main sources, thereby further improving the measurement accuracy of silicate. Simultaneously, the method is verified using the Monte Carlo method, confirming that the non-obvious nonlinear model used in this invention is applicable to the first-order approximate uncertainty propagation law formula in the GUM method, providing a reference for uncertainty assessment of similar nonlinear models.

[0010] This invention provides a method for evaluating the uncertainty of determining silicate concentration in water based on chemiluminescence immunoassay, comprising:

[0011] S1, Silicate concentration was determined based on chemiluminescence method;

[0012] S2, Establish a mathematical model for silicate measurement;

[0013] S3, Based on the mathematical model of the silicate measurement, determine the combined relative uncertainty and the expanded relative uncertainty.

[0014] Preferably, S1 includes:

[0015] S11, the actual sample is introduced into the measurement system through the injection cup (1);

[0016] S12, after the actual sample is heated at a constant temperature in the heater (2), it is placed into the luminescent dish (6);

[0017] S13, add ammonium molybdate solution A from the first reagent bottle (3) and sulfuric acid solution B from the second reagent bottle (4) into the luminescent dish (6) to react with silicate in the actual sample to generate silicomolybdenum heteropoly acid. This process takes tens of seconds.

[0018] S14, after the reaction is completed, the luminol luminescent agent C in the third reagent addition bottle (5) is added to the luminescent dish (6), and the reaction of the silicomolybdenum heteropolyacid oxidizing luminol produces a chemiluminescent effect;

[0019] S15, the chemiluminescence effect is detected and received by the photomultiplier tube (7), amplified and converted into an electrical signal, and then transmitted to the data acquisition and analysis system (8) to calculate the silicate concentration value; wherein the calculated silicate concentration value includes:

[0020] Collect the standard signal corresponding to the silicate concentration, obtain the voltage signal, and establish a standard curve based on the standard signal and the voltage signal;

[0021] The silicate concentration in the actual sample was calculated based on the standard curve.

[0022] Preferably, S2 includes:

[0023] Based on the relationship between silicate concentration and the measured signal value, the following mathematical model is established:

[0024] y = ax 2 +bx+c (1)

[0025] In the formula: x represents the silicate concentration (ug / L); y represents the peak value of the measurement kinetic curve (mV); a represents the quadratic coefficient; b represents the linear coefficient; c represents the intercept;

[0026] According to equation (1), the measured concentration must be positive and within the calibration range. The mathematical model for silicate measurement is established as equation (2):

[0027]

[0028] The combined uncertainty u(C) of the measured quantity C of silicate concentration is expressed as:

[0029]

[0030] Since the measurement model is not a standard linear relationship and the input quantities are uncorrelated, the expression for the combined standard uncertainty considers higher-order terms in the Taylor series expansion. The expression for the combined standard relative uncertainty u(C) considering higher-order terms in the Taylor series expansion is as follows:

[0031]

[0032] Note: u(x1)=u(y); u(x2)=u(a); u(x3)=u(b); u(x4)=u(c);

[0033] in:

[0034]

[0035] Preferably, let t = b 2 +4a(yc), then the formulas for calculating the sensitivity coefficients required in equations (3) and (4) are as follows:

[0036]

[0037]

[0038] Preferably, S3 includes:

[0039] S31, Analyze the sources of uncertainty;

[0040] S32, Calculate the uncertainty components based on the uncertainty sources obtained from the analysis;

[0041] S33, Calculate the combined standard relative uncertainty based on uncertainty components;

[0042] The combined uncertainty u(C) of the measured quantity C based on the silicate concentration is expressed as follows:

[0043]

[0044] And considering the combined standard relative uncertainty u(C) of higher-order terms in the Taylor series expansion, the expression is as follows:

[0045]

[0046] By combining the calculation results of each uncertainty component, the combined standard relative uncertainty u(C) is obtained;

[0047] S34, Calculate the expanded standard relative uncertainty based on the combined standard relative uncertainty u(C);

[0048] The expanded standard relative uncertainty U is obtained based on the combined standard relative uncertainty u(C):

[0049] U = ku(C), k = 2 (20).

[0050] Preferably, the sources of uncertainty are classified as either Type A or Type B:

[0051] Type A uncertainty: assessed through statistical analysis of repeated observations, including:

[0052] Measurement repeatability: When the same sample is measured repeatedly under the same conditions, the standard deviation of the result or its variants is directly an important component of the Type A uncertainty;

[0053] Intercept, first-order coefficient, and second-order coefficient: When performing linear or polynomial regression on calibration data, the regression algorithm calculates the standard uncertainty of the slope as the first-order coefficient, the intercept, and possible higher-order coefficients as the second-order coefficient; the statistically calculated value of the standard uncertainty belongs to Type A evaluation.

[0054] Type B uncertainty: Uncertainty obtained using non-statistical methods based on experience, scientific judgment, and existing information, including:

[0055] Pipettes, volumetric flasks and / or metering pumps: their maximum permissible error (MPE) or uncertainty information on the calibration certificate, converted into standard uncertainty based on their error distribution, wherein the error distribution is assumed to be rectangular, triangular or normal;

[0056] High-voltage power supplies and / or photomultiplier tubes: stability specifications, accuracy parameters, or uncertainty information provided in their technical manuals or calibration certificates;

[0057] Calibration solutions and / or national standard solutions: the standard values ​​and uncertainties of the reference materials given on the certificates provided by the suppliers;

[0058] Instrument measurement: The overall uncertainty given in the instrument manual or on the calibration certificate, which includes multiple Type B components;

[0059] This also includes: uncertainties about equipment that may be used but is not listed; and uncertainties about the volume caused by the effect of ambient temperature.

[0060] Preferably, all identified and categorized sources are listed in the form of standard uncertainty of their contribution, with each source corresponding to an uncertainty component;

[0061] For Type A uncertainty: the component values ​​are directly derived from the statistical results, including the standard deviation of repeatability and / or the standard error of the regression coefficients;

[0062] For Type B uncertainty: the component values ​​need to be converted based on existing information and assumed distributions, including MPE and / or certificate values.

[0063] Preferably, based on uncertainty source analysis, the uncertainty components affecting the measurement of silicate concentration in water by chemiluminescence are as follows:

[0064] ⑨u(R): ​​Standard uncertainty introduced by measurement repeatability (including uncertainty introduced by environmental factor fluctuations);

[0065] ⑩u(y1): Standard uncertainty introduced by polynomial regression;

[0066] u(y2): Standard uncertainty introduced by calibration liquid (including standard uncertainty introduced by standard liquid, pipette, and volumetric flask);

[0067] u(y3): Standard uncertainty introduced by instrument measurement (including standard uncertainty introduced by metering pump, photomultiplier tube, and high voltage module);

[0068] u(c): Standard uncertainty introduced by the intercept;

[0069] u(b): Standard uncertainty introduced by the first-order coefficient;

[0070] u(a): Standard uncertainty introduced by the quadratic coefficient.

[0071] Preferably, the evaluation of each standard uncertainty component is as follows:

[0072] ③ Standard uncertainty introduced by measurement repeatability: u(R)

[0073] Measurement repeatability is affected by inconsistencies in the sample liquid, ambient temperature, pressure, and human operational factors. Under repeatability conditions, the same gas sample is measured six times according to the established measurement method to examine measurement repeatability. The standard deviation is calculated using the Bessel formula:

[0074]

[0075] The standard uncertainty of the average silicate concentration from the six measurements is:

[0076]

[0077] ④ Standard uncertainty introduced by polynomial regression: u(y1)

[0078] In actual measurement, the concentration of silica in the sample liquid is measured using the calibration curve obtained by linear regression using the least squares method. The standard deviation introduced during polynomial regression, i.e., the polynomial regression standard uncertainty, is as follows:

[0079]

[0080] Note: Matrix X, estimator See equations (11) and (13); n is the dilution factor;

[0081] ③ Standard uncertainty introduced by the calibration liquid: u(y2)

[0082] The calibration solution was prepared by diluting the GBW(E)081219 standard reference material for silicate composition analysis in water with laboratory ultrapure water. The uncertainty of the calibration solution comes from the standard reference material, pipette, and volumetric flask. Therefore, the standard uncertainty introduced by the calibration solution is:

[0083]

[0084] In the formula: U(y4) is the expanded relative uncertainty of the standard substance; k = 2; The average value of the peak value of the kinetic curve is used to measure the kinetic curve.

[0085] ④ Standard uncertainty introduced by instrument measurement: u(y3)

[0086] The maximum permissible error of the chemiluminescence analyzer used for measuring silicate concentration in water is 1%. Assuming a uniform distribution, the relative standard uncertainty of the instrument is:

[0087]

[0088] The corresponding standard uncertainty is:

[0089]

[0090] The formulas for calculating the standard uncertainty introduced by the intercept, first-order coefficient, and second-order coefficient are as follows. Based on the theory of multiple linear regression, matrix X is designed:

[0091]

[0092] Where, x ij Let β represent the value of the j-th independent variable in the i-th sample, where j = 1, 2, 3 correspond to 1, X, X2 respectively. Construct the parameter vector β:

[0093]

[0094] The following is obtained from the least squares estimation:

[0095]

[0096] Estimated quantity The covariance matrix is:

[0097]

[0098] Then, ⑤ the standard uncertainty introduced by the intercept: u(c)

[0099]

[0100] ⑥ Standard uncertainty introduced by the first-order coefficient: u(b)

[0101]

[0102] The standard uncertainty introduced by the quadratic coefficient: u(a)

[0103]

[0104] Preferably, the evaluation method further includes:

[0105] Based on the consideration of correlation and propagation analysis, it is determined whether there is a correlation between different uncertainty components, which will affect the synthesis method; according to the mathematical model of the measurement results, the uncertainty propagation law is applied to calculate how each component "propagates" and is synthesized into the uncertainty of the final result.

[0106] The uncertainty assessment method for determining silicate concentration in water based on chemiluminescence immunoassay of the present invention has the following beneficial effects:

[0107] This invention proposes an uncertainty assessment method for determining silicate concentration in water based on chemiluminescence immunoassay. It analyzes in detail the sources of uncertainty in this method and compares the impact of considering higher-order Taylor series terms on uncertainty assessment in non-significantly nonlinear models. Therefore, it has the following beneficial effects:

[0108] (1) Provide detailed uncertainty assessment methods;

[0109] (2) Analyzing the sources of uncertainty helps improve measurement accuracy;

[0110] (3) Provides a basis for uncertainty assessment of non-obvious nonlinear models. Attached Figure Description

[0111] To more clearly illustrate the technical solutions in the specific embodiments or related technologies of the present invention, the drawings used in the description of the specific embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0112] Figure 1 This is a block diagram illustrating the uncertainty assessment principle provided in the embodiments of the present invention;

[0113] Figure 2 A schematic diagram of the principle of a chemiluminescence analyzer provided in an embodiment of the present invention;

[0114] Figure 3 Uncertainty source analysis diagram provided for embodiments of the present invention;

[0115] Figure 4The flowchart below shows the process for calculating uncertainty using the Monte Carlo method, as provided in an embodiment of the present invention. Detailed Implementation

[0116] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0117] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0118] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0119] like Figure 1 As shown, this invention provides, in one aspect, a method for evaluating the uncertainty of determining silicate concentration in water based on chemiluminescence immunoassay, comprising:

[0120] like Figure 2 As shown, S1, the silicate concentration was determined based on chemiluminescence immunoassay;

[0121] In a preferred embodiment, S1 includes:

[0122] S11, the actual sample is introduced into the measurement system through the injection cup (1);

[0123] S12, after the actual sample is heated at a constant temperature in the heater (2), it is placed into the luminescent dish (6);

[0124] S13, add ammonium molybdate solution A from the first reagent bottle (3) and sulfuric acid solution B from the second reagent bottle (4) into the luminescent dish (6) to react with silicate in the actual sample to generate silicomolybdenum heteropoly acid. This process takes tens of seconds.

[0125] S14, after the reaction is completed, the luminol luminescent agent C in the third reagent addition bottle (5) is added to the luminescent dish (6), and the reaction of the silicomolybdenum heteropolyacid oxidizing luminol produces a chemiluminescent effect;

[0126] S15, the chemiluminescence effect is detected and received by the photomultiplier tube (7), amplified and converted into an electrical signal, and then transmitted to the data acquisition and analysis system (8) to calculate the silicate concentration value; wherein the calculated silicate concentration value includes:

[0127] Collect the standard signal corresponding to the silicate concentration, obtain the voltage signal, and establish a standard curve based on the standard signal and the voltage signal;

[0128] The silicate concentration in the actual sample was calculated based on the standard curve.

[0129] S2, Establish a mathematical model for silicate measurement;

[0130] In a preferred embodiment, S2 includes:

[0131] Based on the relationship between silicate concentration and the measured signal value, the following mathematical model is established:

[0132] y = ax 2 +bx+c (1)

[0133] In the formula: x represents the silicate concentration (ug / L); y represents the peak value of the measurement kinetic curve (mV); a represents the quadratic coefficient; b represents the linear coefficient; and c represents the intercept.

[0134] According to equation (1) and combined with actual measurement experience, the measured concentration must be positive and within the calibration range. Therefore, the mathematical model for silicate measurement is established as equation (2):

[0135]

[0136] The combined uncertainty u(C) of the measured quantity C of silicate concentration is expressed as:

[0137]

[0138] However, since the measurement model is not a standard linear relationship and the input quantities are uncorrelated, the expression for the combined standard uncertainty needs to consider the higher-order terms in the Taylor series expansion. Therefore, the expression for the combined standard relative uncertainty u(C) considering the higher-order terms in the Taylor series expansion is:

[0139]

[0140] Note: u(x1)=u(y); u(x2)=u(a); u(x3)=u(b); u(x4)=u(c);

[0141] in:

[0142]

[0143] To simplify the expression of the sensitivity coefficient, let t = b 2 +4a(yc), then the formulas for calculating the sensitivity coefficients required in equations (3) and (4) are as follows:

[0144]

[0145]

[0146] S3, Based on the mathematical model of the silicate measurement, determine the combined relative uncertainty and the expanded relative uncertainty.

[0147] Preferably, S3 includes:

[0148] S31, Analyze the sources of uncertainty;

[0149] like Figure 3 As shown, understanding the measurement principles and models is fundamental to the analysis. It is necessary to clarify what is being measured (e.g., concentration, temperature, length), what measurement method is used (e.g., titration, spectrophotometry, gravimetric method), and how the results are calculated (mathematical model).

[0150] Figure 3 The terms "linear regression," "standard fitting curve," and "instrument measurement" suggest that the measurement results may be calculated based on calibration curves (such as the relationship curve between standard solution concentration and instrument response signal).

[0151] Systematically identify sources:

[0152] Along the entire measurement chain, consider each factor that may introduce error at each stage.

[0153] The analysis of error sources includes:

[0154] The object being tested: whether the sample itself is uniform and stable, and whether the sampling is representative. Figure 3 The keyword association is: Measurement repeatability reflects the local non-uniformity of the sample or sampling differences.

[0155] Measuring equipment / instruments:

[0156] The accuracy and error of the equipment itself ( Figure 3 Related keywords: volumetric error of pipettes, volumetric flasks, and metering pumps; gain stability and dark current of photomultiplier tubes; stability of high-voltage power supplies.

[0157] The device's resolution (minimum readable scale).

[0158] The calibration status of the equipment and the uncertainty introduced by calibration ( Figure 3 Keyword association: Uncertainty in calibration solutions and national standard solutions will be passed on to instrument calibration; metering pumps, pipettes, and volumetric flasks all require calibration.

[0159] Standard substance / reference material: the uncertainty of the standard solution used and the standard substance itself ( Figure 3 (Keywords related to calibration solution, national standard solution).

[0160] Environmental conditions: the effects of temperature, humidity, pressure, vibration, etc. on measuring equipment or samples (e.g., the effect of temperature on the volumetric flask volume).

[0161] Operator consistency: such as reading parallax, timing error, and minor differences in operating procedures. Figure 3 Keyword association: Measurement repeatability typically includes random fluctuations introduced by human operation.

[0162] Measurement method principle:

[0163] The inherent limitations or assumptions of the method (such as the applicability of linear models) Figure 3 The keywords related to linear regression, intercept, first-order coefficient, and second-order coefficient suggest the importance of evaluating the goodness of fit of the calibration curve and model bias.

[0164] The degree of incompleteness of a chemical reaction, side reactions, etc.

[0165] Data processing:

[0166] Data rounding rules.

[0167] Uncertainty of constants or parameters used in the calculation.

[0168] Selection of fitting algorithm ( Figure 3 The keywords related to linear regression, intercept, first-order coefficient, and second-order coefficient are directly derived from the curve fitting process in data processing.

[0169] Classify the source as either Category A or Category B:

[0170] Type A uncertainty: assessed through statistical analysis of repeated observations.

[0171] Figure 3 Chinese keyword association:

[0172] Measurement repeatability: When the same sample is measured repeatedly under the same conditions, the standard deviation (or a variant thereof) of the result is directly an important component of Type A uncertainty.

[0173] Intercept, first-order coefficient, second-order coefficient: when performing linear or polynomial regression on calibration data ( Figure 3 When using keywords related to linear regression and standard fitting curves, the regression algorithm calculates the standard uncertainty of the slope (first-order coefficient), intercept, and possible higher-order coefficients (second-order coefficients). These statistically calculated standard uncertainties fall under Type A assessment.

[0174] Type B uncertainty: assessed using non-statistical methods. Based on experience, scientific judgment, and existing information (such as certificates, manuals, and literature).

[0175] Figure 3 Chinese keyword association:

[0176] Pipettes, volumetric flasks, and metering pumps: their maximum permissible error (MPE) or uncertainty information on the calibration certificate. This needs to be converted to standard uncertainty based on their error distribution (usually assumed to be rectangular, triangular, or normal).

[0177] High voltage (power supply), photomultiplier tube: stability indicators, accuracy parameters or uncertainty information provided in their technical manuals or calibration certificates.

[0178] Calibration solutions and national standard solutions: The standard values ​​and uncertainties of the standard substances given on the certificates provided by the suppliers.

[0179] Instrument measurement: The overall uncertainty (usually containing multiple Type B components) given in the instrument manual, the resolution and accuracy specifications, or the calibration certificate.

[0180] Other implicit uncertainties include: uncertainties related to thermometers, balances, and other unlisted but potentially used equipment; and the uncertainty of the correction factor for the effect of ambient temperature on volume.

[0181] Construct a list of uncertainty components:

[0182] List all identified and categorized sources according to their contribution in the form of standard uncertainty. Each source corresponds to one uncertainty component.

[0183] For category A: component values ​​come directly from statistical results (such as repeatability standard deviation, standard error of regression coefficient).

[0184] For type B: Component values ​​need to be converted based on existing information (such as MPE, certificate value) and the assumed distribution (e.g., u = MPE / √3 for a rectangular distribution).

[0185] Consider relevance and propagation (usually in subsequent steps):

[0186] Analyze whether there is a correlation between different uncertainty components (e.g., the volume errors of standard solutions of different concentrations prepared using the same pipette will be correlated). Correlation can affect the synthesis method.

[0187] Based on the mathematical model (calculation process) of the measurement results, the uncertainty propagation law (such as the GUM method) is applied to calculate how each component "propagates" and is combined into the uncertainty of the final result. This step is usually performed after source analysis.

[0188] See Figure 3 Key points of analysis reflected in the content:

[0189] Category A sources were highlighted: Figure 3 The study specifically emphasizes the Type A uncertainty introduced by measurement repeatability (random effects) and calibration curve fitting (intercept, coefficients). This indicates that the measurement results are highly dependent on the statistical properties of repeated observations and fitted data.

[0190] Key Class B hardware / standards sources: Figure 3 The document lists common laboratory hardware (pipettes, volumetric flasks, metering pumps, photomultiplier tubes, high-voltage power supplies) and standard substances (calibration solutions, national standard solutions), which are typical sources of Type B uncertainty. Their error or uncertainty information usually comes from manufacturer specifications or calibration certificates.

[0191] Calibration is key: keywords such as "calibration solution," "instrument measurement," "standard fitting curve," and "linear regression" all point to the fact that the instrument calibration process is a crucial step in determining measurement results and uncertainties. The uncertainty introduced by calibration (from standard substances, fitting, and repeatability) is one of the main contributors to the total uncertainty.

[0192] Therefore, the process of "uncertainty source analysis" includes:

[0193] (1) Understanding measurement: Knowing what to measure, how to measure, and how to calculate.

[0194] (2) Comprehensive identification: Along the measurement process, identify all possible sources of error.

[0195] (3) Scientific classification: Determine whether each source should be evaluated using statistical observation (Category A) or other information (Category B).

[0196] (4) Quantification of components: Calculate the standard uncertainty (u) of the contribution of each source.

[0197] (Subsequent) Composite evaluation: Considering the correlation, all u components are synthesized according to the mathematical model to obtain the total standard uncertainty of the measurement results, and then the expanded uncertainty (U) is calculated.

[0198] In this embodiment, based on the uncertainty source analysis, the uncertainty components affecting the measurement of silicate concentration in water by chemiluminescence are as follows:

[0199] u(R): ​​Standard uncertainty introduced by measurement repeatability (including uncertainty introduced by environmental factor fluctuations);

[0200] u(y1): Standard uncertainty introduced by polynomial regression;

[0201] u(y2): Standard uncertainty introduced by calibration liquid (including standard uncertainty introduced by standard liquid, pipette, and volumetric flask);

[0202] u(y3): Standard uncertainty introduced by instrument measurement (including standard uncertainty introduced by metering pump, photomultiplier tube, and high voltage module);

[0203] u(c): Standard uncertainty introduced by the intercept;

[0204] u(b): Standard uncertainty introduced by the first-order coefficient;

[0205] u(a): Standard uncertainty introduced by the quadratic coefficient.

[0206] S32, Calculate the uncertainty components based on the uncertainty sources obtained from the analysis;

[0207] In this embodiment, the standard uncertainty components are evaluated as follows:

[0208] ⑤ Standard uncertainty introduced by measurement repeatability: u(R)

[0209] Measurement repeatability is mainly affected by factors such as inconsistencies in the sample liquid, ambient temperature, pressure, and human operation. Under repeatability conditions, the same gas sample is measured six times according to the established measurement method to examine measurement repeatability. The standard deviation is calculated using the Bessel formula.

[0210]

[0211] The standard uncertainty of the average silicate concentration from the six measurements is:

[0212]

[0213] ⑥ Standard uncertainty introduced by polynomial regression: u(y1)

[0214] In actual measurement, the concentration of silica in the sample liquid is measured using the calibration curve obtained by linear regression using the least squares method. The standard deviation introduced during polynomial regression, i.e., the polynomial regression standard uncertainty, is as follows:

[0215]

[0216] Note: Matrix X, estimator See equations (11) and (13); n is the dilution factor.

[0217] ③ Standard uncertainty introduced by the calibration liquid: u(y2)

[0218] The calibration solution was prepared by diluting the GBW(E)081219 standard reference material for silicate composition analysis in water with laboratory ultrapure water. Therefore, the uncertainty of the calibration solution mainly comes from the standard reference material, pipette, and volumetric flask. Because the pipette and volumetric flask used in the experiment have high precision, the uncertainty components introduced by them are very small and can be ignored. Therefore, the standard uncertainty introduced by the calibration solution is:

[0219]

[0220] In the formula: U(y4) is the expanded relative uncertainty of the standard substance; k = 2; This is used to measure the average value of the peak value of the kinetic curve.

[0221] ④ Standard uncertainty introduced by instrument measurement: u(y3)

[0222] The maximum permissible error of the chemiluminescence analyzer used for measuring silicate concentration in water is 1%. Assuming a uniform distribution, the relative standard uncertainty of the instrument is:

[0223]

[0224] The corresponding standard uncertainty is:

[0225]

[0226] The formulas for calculating the standard uncertainty introduced by the intercept, first-order coefficient, and second-order coefficient are as follows. Based on the theory of multiple linear regression, matrix X is designed:

[0227]

[0228] Where, x ij Let β represent the value of the j-th independent variable in the i-th sample, where j = 1, 2, 3 correspond to 1, X, X2 respectively. Construct the parameter vector β:

[0229]

[0230] The following is obtained from the least squares estimation:

[0231]

[0232] Estimated quantity The covariance matrix is:

[0233]

[0234] Then, ⑤ the standard uncertainty introduced by the intercept: u(c)

[0235]

[0236] ⑥ Standard uncertainty introduced by the first-order coefficient: u(b)

[0237]

[0238] ⑦ Standard uncertainty introduced by the quadratic coefficient: u(a)

[0239]

[0240] S33, Calculate the combined standard relative uncertainty based on uncertainty components;

[0241] In this embodiment, the combined uncertainty u(C) of the measured quantity C based on the silicate concentration is expressed as follows:

[0242]

[0243] And considering the combined standard relative uncertainty u(C) of higher-order terms in the Taylor series expansion, the expression is as follows:

[0244]

[0245] By combining the calculation results of each uncertainty component, the combined standard relative uncertainty u(C) is obtained;

[0246] S34, Calculate the expanded standard relative uncertainty based on the combined standard relative uncertainty u(C).

[0247] The expanded standard relative uncertainty U is obtained based on the combined standard relative uncertainty u(C):

[0248] U = ku(C), k = 2 (20).

[0249] Application examples: as shown in Table 1 (Uncertainty Component Analysis Table) and Table 2 (Comparison Table of Uncertainty Evaluation Methods).

[0250] Table 1 Uncertainty Component Analysis Table

[0251]

[0252]

[0253] Note: This table shows the measurement uncertainties for nominal concentrations of 5 ug / L, 10 ug / L, 20 ug / L, and 40 ug / L, calculated according to the uncertainty assessment method proposed in this invention. The dimension of the uncertainty component u(y) is mV; u(a), u(b), and u(c) are dimensionless.

[0254] Table 2 Comparison of Uncertainty Assessment Methods

[0255]

[0256] like Figure 4 As shown, although two formulas for calculating the combined standard uncertainty are given in this embodiment, the calculation formula without considering higher-order terms of Taylor expansion is highly consistent with the calculation results of the Monte Carlo method (sampling times of 10,000) when compared with the results of the Monte Carlo method. This is because after considering higher-order terms, the higher-order terms will change more with the fluctuation of the input, resulting in an increased range of variation in the calculated output. The measurement model described in this invention is not an obvious nonlinear model and is more suitable for evaluation using the first-order approximate uncertainty propagation law formula. Therefore, in the uncertainty evaluation of the determination of silicate concentration in water based on chemiluminescence method, when reporting the expanded standard uncertainty U, the combined standard uncertainty u(C) measured by the Monte Carlo method should be used, either formula (3) or the combined standard uncertainty u(C) measured by the Monte Carlo method.

[0257] Through the above description of the embodiments, those skilled in the art can clearly understand that the above embodiments can be implemented by software, or by using software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solutions of the above embodiments can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.), including several instructions to cause a computer device (such as a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0258] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for evaluating uncertainty in determining the concentration of silicate in water based on chemiluminescence, characterized by, Comprise: S1, determine the concentration of silicate based on chemiluminescence method; S2, establish a mathematical model of silicate measurement; S3, determine the combined relative uncertainty and expanded relative uncertainty based on the mathematical model of silicate measurement.

2. The method for evaluating uncertainty in the determination of the concentration of silicate in water based on chemiluminescence according to claim 1, characterized in that, The S1 comprises: S11, the actual sample is put into the measuring system through the sample cup (1); S12, after constant temperature heating in the heater (2), the actual sample enters the luminescence dish (6); S13, the ammonium molybdate solution A in the first added reagent bottle (3) and the sulfuric acid solution B in the second added reagent bottle (4) are added into the luminescence dish (6) to react with the silicate in the actual sample to generate silicomolybdate, which needs tens of seconds; S14, after the reaction is completed, the luminol luminescent agent C in the third added reagent bottle (5) is added into the luminescence dish (6), and the reaction of silicomolybdate oxidizing luminol produces chemiluminescence effect; S15, the chemiluminescence effect is detected and received by the photomultiplier tube (7), and after being amplified and converted into an electrical signal, it is transmitted to the data acquisition and analysis system (8) to calculate the silicate concentration value; wherein the calculation of the silicate concentration value comprises: Collect the standard signal corresponding to the silicate concentration, obtain the voltage signal, and establish a standard curve based on the standard signal and the voltage signal; Based on the standard curve, the silicate concentration in the actual sample is calculated.

3. The method for evaluating uncertainty in the determination of the concentration of silicate in water based on chemiluminescence according to claim 2, characterized in that, The S2 comprises: According to the relationship between the silicate concentration and the measurement signal value, a mathematical model is established as follows: y = ax 2 + bx + c (1) In the formula, x represents the silicate concentration (ug / L); y represents the peak value of the measurement kinetics curve (mV); a represents the quadratic coefficient; b represents the linear coefficient; c represents the intercept; According to formula (1), the measured concentration is a positive value and within the calibration interval, the mathematical model of silicate measurement is established as formula (2): The combined uncertainty u(C) of the measured value C of the silicate concentration is expressed as: Based on the measurement model which is not a standard linear relationship and the input quantities are not related, the high-order term in the Taylor series expansion is considered in the expression of the combined standard uncertainty, and the combined standard relative uncertainty u(C) considering the high-order term in the Taylor series expansion is: Note: u(x1) = u(y); u(x2) = u(a); u(x3) = u(b); u(x4) = u(c); Wherein:

4. The method for evaluating uncertainty in the determination of the concentration of silicate in water based on chemiluminescence according to claim 3, characterized in that, Let t = b 2 + 4a(y - c), then the required sensitivity coefficient calculation formula in formula (3) (4) is as follows:

5. The method for evaluating uncertainty in the determination of the concentration of silicate in water based on chemiluminescence according to claim 4, characterized in that, The S3 comprises: S31, analyze the uncertainty sources; S32, calculate the uncertainty components based on the uncertainty sources obtained by analysis; S33, calculate the combined standard relative uncertainty based on the uncertainty components; According to the combined uncertainty u(C) of the measured value C of the silicate concentration: And the combined standard relative uncertainty u(C) considering the high-order term in the Taylor series expansion is: Combined with the calculation results of each uncertainty component, the combined standard relative uncertainty u(C) is obtained; S34, calculate the expanded standard relative uncertainty based on the combined standard relative uncertainty u(C); Based on the combined standard relative uncertainty u(C), the expanded standard relative uncertainty U is obtained: U=ku(C), k=2 (20).

6. The method for evaluating uncertainty in the determination of the concentration of silicate in water based on chemiluminescence according to claim 5, characterized in that, The uncertainty sources are classified as A or B: Class A uncertainty: evaluated by statistical analysis of repeated observations, including: Measurement repeatability: the standard deviation of the results or its variants of the same sample repeatedly measured under the same conditions is an important component of the type A uncertainty; Intercept, linear coefficient, quadratic coefficient: when linear or polynomial regression is performed on the calibration data, the regression algorithm calculates the slope as the linear coefficient, the intercept and possibly the higher order coefficients as the standard uncertainty of the quadratic coefficient; the statistical calculation of the standard uncertainty belongs to the type A evaluation; Type B uncertainty: the uncertainty obtained by non-statistical methods based on experience, scientific judgment and existing information, including: Pipette, volumetric flask and / or metering pump: the maximum permissible error MPE or the uncertainty information on the calibration certificate, which is converted into the standard uncertainty according to the error distribution, wherein the error distribution is assumed to be rectangular distribution, triangular distribution or normal distribution; High-voltage power supply and / or photomultiplier tube: the stability index, precision parameter or uncertainty information provided in the technical manual or calibration certificate of the high-voltage power supply and / or photomultiplier tube; Calibration solution and / or national standard solution: the standard value of the standard substance and its uncertainty given on the certificate provided by the supplier; Instrument measurement: the resolution, precision index given in the instrument manual or the overall uncertainty on the calibration certificate, which contains multiple type B components; Also including: the uncertainty of equipment not listed but possibly used; and the correction factor uncertainty of the environmental temperature effect volume.

7. The method for evaluating uncertainty in the determination of the concentration of silicate in water based on chemiluminescence according to claim 6, characterized in that, List all identified and classified sources in the form of their contribution to the standard uncertainty, with each source corresponding to an uncertainty component; For type A uncertainty: the component value directly comes from the statistical result, including the standard deviation of repeatability and / or the standard error of regression coefficient; For type B uncertainty: the component value needs to be converted according to the existing information and the assumed distribution, and the existing information includes MPE and / or certificate value.

8. The method for evaluating uncertainty of a determination of a concentration of silicate in water based on a chemiluminescence method according to claim 7, characterized by, From the uncertainty source analysis, the uncertainty components affecting the measurement of silicon dioxide concentration in water by chemiluminescence method are: ① u(R): the standard uncertainty introduced by measurement repeatability (including environmental factor fluctuation and uncertainty); ② u(y1): the standard uncertainty introduced by polynomial regression; ③ u(y2): the standard uncertainty introduced by calibration liquid (including the standard uncertainty introduced by standard liquid, pipette and volumetric flask); ④ u(y3): the standard uncertainty introduced by instrument measurement (including the standard uncertainty introduced by metering pump, photomultiplier tube and high-voltage module); ⑤ u(c): the standard uncertainty introduced by intercept; ⑥ u(b): the standard uncertainty introduced by linear coefficient; ⑦ u(a): the standard uncertainty introduced by quadratic coefficient.

9. The method for evaluating uncertainty in the determination of the concentration of silicate in water based on chemiluminescence according to claim 8, characterized in that, Each standard uncertainty component is evaluated as follows: ① The standard uncertainty introduced by measurement repeatability: u(R) The measurement repeatability is caused by the inconsistency of sample liquid, environmental temperature, pressure and personnel operation factors; under the repeatability condition, the same gas sample is repeatedly measured 6 times according to the determined measurement method to investigate the measurement repeatability, and the standard deviation is calculated by the Bessel formula: The standard uncertainty of the average value of 6 times of determination of silicon dioxide concentration is: ② The standard uncertainty introduced by polynomial regression: u(y1) In the actual measurement process, the calibration curve obtained by linear regression by least square method is used to measure the concentration of silica in sample liquid, the standard uncertainty introduced in the process of polynomial regression, i.e. the polynomial regression standard uncertainty: Note: Matrix X, estimator See equation (11), equation (13); n is the dilution factor; ③The standard uncertainty introduced by calibration liquid: u(y2) The calibration liquid is obtained by diluting GBW(E)081219 water-soluble silicate component analysis standard substance with laboratory ultrapure water, and the uncertainty of the calibration liquid is derived from the standard substance, the pipette and the volumetric flask. Therefore, the standard uncertainty introduced by the calibration solution is: where: U(y4) is the expanded relative uncertainty of the standard; k = 2; to measure the average of the peak values of the kinetic curves; ④The standard uncertainty introduced by instrument measurement: u(y3) The maximum allowable error of the chemiluminescence instrument used for measuring the concentration of water-soluble silicate is 1%, and the relative standard uncertainty of the instrument is considered to be uniformly distributed: The corresponding standard uncertainty is: The calculation formula of the standard uncertainty introduced by the intercept, the first-order coefficient and the second-order coefficient is as follows: according to the theory of multiple linear regression, the design matrix X is: where x ij represents the value of the jth independent variable of the ith sample, where j = 1, 2, 3 correspond to 1, X, X2, respectively, and the parameter vector β is constructed: The least square estimation is obtained as follows: estimator The covariance matrix of the estimates is: Therefore, ⑤the standard uncertainty introduced by the intercept: u(c) ⑥the standard uncertainty introduced by the first-order coefficient: u(b) ⑧the standard uncertainty introduced by the second-order coefficient: u(a) 10. The method for evaluating uncertainty of a determination of a concentration of silicate in water based on a chemiluminescence method according to claim 9, characterized by, The evaluation method further comprises: Based on considering the correlation and whether there is a correlation between different uncertainty components according to the propagation analysis, the correlation will affect the synthesis method; according to the mathematical model of the measurement result, the uncertainty propagation law is applied to calculate how each component "propagates" and is synthesized into the uncertainty of the final result.

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