Method for determining concentration of nitric acid and plutonium in P350 solution

By establishing a model between the concentrations and spectral data of plutonium and nitric acid, the problem that the prior art cannot simultaneously determine the concentrations of nitric acid and plutonium in P350 solution is solved, and efficient concentration determination is achieved.

CN119935949APending Publication Date: 2025-05-06CHINA INSTITUTE OF ATOMIC ENERGY
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Patent Information

Application Number
CN202510120703.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-01-24
Publication Date
2025-05-06

AI Technical Summary

Technical Problem

The existing analytical methods cannot simultaneously determine the concentration of nitric acid and plutonium in P350 solution, resulting in difficulty in evaluating the process operation status.

Method used

By acquiring spectral data of multiple modeled samples, a model is established between the concentrations and spectral data of plutonium and nitric acid, and the concentration prediction of the samples to be measured is used.

Benefits of technology

The simultaneous measurement of nitric acid and plutonium concentrations in P350 solution is achieved, which is simple and convenient to operate and improves the analysis efficiency.

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Abstract

The invention provides a method for determining the concentration of nitric acid and plutonium in a P350 solution, and the method comprises the following steps: obtaining first spectral data of plutonium and second spectral data of nitric acid in a plurality of modeling samples, the plurality of modeling samples being a plurality of P350 solutions of nitric acid and plutonium with different concentrations; a first determination model and a second determination model are established based on the modeling sample, the first determination model comprises a corresponding relation between the plutonium concentration and the first spectral data, and the second determination model comprises a corresponding relation between the nitric acid concentration and the second spectral data; acquiring sample spectrum data of plutonium and sample spectrum data of nitric acid in a sample to be detected; acquiring a predicted value of the concentration of plutonium in the to-be-detected sample based on the first determination model and the sample spectral data of plutonium, and acquiring a predicted value of the concentration of nitric acid in the to-be-detected sample based on the second determination model and the sample spectral data of nitric acid; the method is used for simultaneously measuring the concentration of nitric acid and the concentration of plutonium in the P350 solution.
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Description

Technical Field

[0001] The present application relates to the technical field of chemical analysis, and in particular to a method for determining the concentrations of nitric acid and plutonium in a P350 solution. Background Art

[0002] This section is intended to provide a background or context for the embodiments of the present application. No description herein is admitted to be prior art by virtue of its inclusion in this section.

[0003] P350, i.e. dimethylheptyl methylphosphonate, is widely used in related extraction processes due to its good extraction performance. Plutonium can be separated and purified by using P350 in nitric acid solution to extract plutonium. Therefore, in the study of related process flow, it is necessary to measure the concentrations of plutonium and nitric acid in a timely manner to evaluate the operating status of the process. At present, the main analysis methods for plutonium are X-ray fluorescence, redox titration, L absorption edge density method, etc., but the above methods cannot measure the concentration of nitric acid. The concentration of nitric acid and the concentration of plutonium in P350 solution need to be measured separately. With the increase in demand, it is of great significance to carry out research on the simultaneous analysis technology of nitric acid and plutonium in P350 and establish a method for the simultaneous determination of nitric acid and plutonium concentrations in P350 solution. Summary of the invention

[0004] In view of this, an embodiment of the present application hopes to provide a method for measuring the concentrations of nitric acid and plutonium in a P350 solution, which can simultaneously measure the concentrations of nitric acid and plutonium in a P350 solution.

[0005] The present application embodiment provides a method for determining the concentration of nitric acid and plutonium in a P350 solution, comprising:

[0006] Acquiring first spectral data of plutonium and second spectral data of nitric acid in a plurality of modeling samples, wherein the plurality of modeling samples are P350 solutions of nitric acid and plutonium with a plurality of different concentrations;

[0007] Establishing a first measurement model and a second measurement model based on the modeling sample, wherein the first measurement model includes a correspondence between the concentration of plutonium and the first spectrum data, and the second measurement model includes a correspondence between the concentration of nitric acid and the second spectrum data;

[0008] Obtaining sample spectrum data of plutonium and sample spectrum data of nitric acid in the sample to be tested;

[0009] Based on the first measurement model and the sample spectrum data of plutonium, a predicted value of the concentration of plutonium in the sample to be tested is obtained; based on the second measurement model and the sample spectrum data of nitric acid, a predicted value of the concentration of nitric acid in the sample to be tested is obtained.

[0010] In some embodiments, the concentration of plutonium in the modeling sample is between 0.5 g / L and 20 g / L.

[0011] In some embodiments, the concentration of nitric acid in the modeling sample is between 0.01 mol / L and 0.2 mol / L.

[0012] In some embodiments, first spectral data of plutonium and second spectral data of nitric acid in a plurality of the modeling samples are acquired by a near-infrared spectrometer.

[0013] In some embodiments, sample spectrum data of plutonium and sample spectrum data of nitric acid in the sample to be tested are obtained by a near-infrared spectrometer.

[0014] In some embodiments, the first spectral data is the absorbance of plutonium in the modeled sample; the second spectral data is the absorbance of nitric acid in the modeled sample; the sample spectral data of plutonium is the absorbance of plutonium in the sample to be tested; and the sample spectral data of nitric acid is the absorbance of nitric acid in the sample to be tested.

[0015] In some embodiments, the wavelength range of the nitric acid is between 1800 nm and 2100 nm.

[0016] In some embodiments, the wavelength range of the plutonium is between 800 nm and 1100 nm.

[0017] In some embodiments, the first determination model and the second determination model are both partial least squares models.

[0018] In some embodiments, the concentration determination method comprises:

[0019] Acquiring third spectrum data of plutonium and fourth spectrum data of nitric acid in a plurality of verification samples, wherein known concentrations of nitric acid and plutonium in the plurality of verification samples are reference values;

[0020] Obtaining a predicted value of the concentration of plutonium in the verification sample based on the first measurement model and the third spectral data, and obtaining a predicted value of the concentration of nitric acid in the verification sample based on the second measurement model and the fourth spectral data;

[0021] The first measurement model is verified based on the reference value of the plutonium concentration and the predicted value of the plutonium concentration, and the second measurement model is verified based on the reference value of the nitric acid concentration and the predicted value of the nitric acid concentration.

[0022] The method for determining the concentration of nitric acid and plutonium in a P350 solution provided in an embodiment of the present application establishes a first determination model based on the correspondence between the concentration of plutonium and the first spectral data, and establishes a second determination model based on the correspondence between the concentration of nitric acid and the second spectral data. After the first determination model and the second determination model are established, it is only necessary to collect the sample spectral data of plutonium and the sample spectral data of nitric acid in the sample to be tested of unknown concentration each time, and substitute the sample spectral data of plutonium into the first determination model and the sample spectral data of nitric acid into the second determination model, so as to obtain the predicted values ​​of the concentrations of nitric acid and plutonium in the sample to be tested. In this way, the simultaneous measurement of the concentrations of nitric acid and plutonium in the P350 solution can be achieved, which is simple and convenient to operate and improves the analysis efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Schematic diagram of a method for determining the concentration of nitric acid and plutonium in a P350 solution in some embodiments of the present application;

[0024] Figure 2 A correlation diagram between the reference value and the predicted value for verifying the concentration of nitric acid in the sample;

[0025] Figure 3 Correlation diagram between the reference value and the predicted value for verifying the plutonium concentration in the sample. DETAILED DESCRIPTION

[0026] The following is a further detailed description of the implementation of the present application in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present application but cannot be used to limit the scope of the present application.

[0027] The various specific technical features and embodiments described in the specific implementation methods can be combined in any suitable manner without contradiction. For example, different implementation methods can be formed by combining different specific technical features / embodiments. In order to avoid unnecessary repetition, the various possible combinations of the specific technical features / embodiments in this application are no longer described separately. In addition, the terms "first" and "second" are used for descriptive purposes only and cannot be understood as indicating or implying relative importance. The application is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0028] It should be noted that, in the embodiments of the present application, “multiple” includes two and more than two.

[0029] See also Figure 1 The present application embodiment provides a method for determining the concentration of nitric acid and plutonium in a P350 solution, the concentration determination method comprising:

[0030] S10, obtaining first spectrum data of plutonium and second spectrum data of nitric acid in a plurality of modeling samples, wherein the plurality of modeling samples are P350 solutions of nitric acid and plutonium with a plurality of different concentrations;

[0031] P350 solution refers to dimethylheptyl methylphosphonate solution. P350 solution can be used as an extractant to extract plutonium. Specifically, plutonium exists in the form of tetravalent plutonium ions in P350 solution.

[0032] Exemplarily, multiple modeling samples can be prepared by dilution through extraction.

[0033] The water liquid used in the embodiments of the present application is all deionized water.

[0034] The multiple modeling samples are P350 solutions of nitric acid and plutonium with different concentrations. In other words, in each modeling sample, P350 is used as a solvent, and the concentrations of nitric acid and plutonium are different.

[0035] Different concentrations of plutonium correspond to different first spectrum data, that is, the first spectrum data of plutonium is correlated with the concentration of plutonium.

[0036] Different concentrations of nitric acid correspond to different second spectrum data, that is, the second spectrum data of nitric acid is correlated with the concentration of nitric acid.

[0037] S20, establishing a first measurement model and a second measurement model based on the modeled sample, wherein the first measurement model includes a correspondence between the concentration of plutonium and the first spectral data, and the second measurement model includes a correspondence between the concentration of nitric acid and the second spectral data;

[0038] The chemometric method was used to select the optimal spectral wavelength and spectral preprocessing method, and the correlation between the concentration of plutonium in the modeling sample and its absorption spectrum, and the correlation between the concentration of nitric acid and its absorption spectrum were established.

[0039] The spectrum preprocessing method includes but is not limited to smoothing, first-order derivative, second-order derivative and normalization of both the first spectrum data and the second spectrum data.

[0040] S30, obtaining sample spectrum data of plutonium and sample spectrum data of nitric acid in the sample to be tested;

[0041] The sample to be tested is a P350 solution containing nitric acid and plutonium. The concentration of plutonium and the concentration of nitric acid in the sample to be tested may be unknown.

[0042] S40. Based on the first measurement model and the sample spectrum data of plutonium, obtain a predicted value of the concentration of plutonium in the sample to be tested; based on the second measurement model and the sample spectrum data of nitric acid, obtain a predicted value of the concentration of nitric acid in the sample to be tested.

[0043] Exemplarily, the sample spectrum data of plutonium may be substituted into the first measurement model, and the plutonium concentration corresponding to the first spectrum data identical to the sample spectrum data of plutonium is the predicted value of the plutonium concentration in the sample to be measured.

[0044] Exemplarily, the sample spectrum data of nitric acid may be substituted into the second measurement model, and the concentration of nitric acid corresponding to the second spectrum data identical to the sample spectrum data of nitric acid is the predicted value of the concentration of nitric acid in the sample to be measured.

[0045] A determination model is established through steps S10 and S20, and the concentrations of plutonium and nitric acid in the sample to be tested are determined through steps S30 and S40.

[0046] It will be appreciated that the concentration of nitric acid may be a molar concentration and the concentration of plutonium may be a mass concentration.

[0047] The method for determining the concentration of nitric acid and plutonium in a P350 solution provided in an embodiment of the present application establishes a first determination model based on the correspondence between the concentration of plutonium and the first spectral data, and establishes a second determination model based on the correspondence between the concentration of nitric acid and the second spectral data. After the first determination model and the second determination model are established, it is only necessary to collect the sample spectral data of plutonium and the sample spectral data of nitric acid in the sample to be tested of unknown concentration each time, and substitute the sample spectral data of plutonium into the first determination model and the sample spectral data of nitric acid into the second determination model, so as to obtain the predicted values ​​of the concentrations of nitric acid and plutonium in the sample to be tested. In this way, the simultaneous measurement of the concentrations of nitric acid and plutonium in the P350 solution can be achieved, which is simple and convenient to operate and improves the analysis efficiency.

[0048] In some embodiments, the concentration of plutonium in the modeling sample is between 0.5 g / L and 20 g / L. For example, the concentration of plutonium in the modeling sample can be 0.5 g / L, 1.0 g / L, 5.0 g / L, 10.0 g / L, 15.0 g / L, 18.0 g / L or 20.0 g / L, etc. In this way, the concentration of plutonium in the modeling sample is moderate, and the first spectrum data of plutonium is easy to collect, and the concentration of plutonium and the first spectrum data have a good correlation.

[0049] In some embodiments, the concentration of nitric acid in the modeling sample is between 0.01 mol / L and 0.2 mol / L. For example, the concentration of nitric acid in the modeling sample can be 0.01 mol / L, 0.05 mol / L, 0.1 mol / L, 0.12 mol / L, 0.15 mol / L or 0.2 mol / L, etc. In this way, the concentration of nitric acid in the modeling sample is moderate, and it is easy to collect the second spectrum data of plutonium, and the concentration of nitric acid and the second spectrum data have a good correlation.

[0050] In some embodiments, first spectral data of plutonium and second spectral data of nitric acid in a plurality of the modeling samples are acquired by a near-infrared spectrometer.

[0051] Near-infrared spectrometers use near-infrared light, which is a cell wave between visible light and mid-infrared light. The wavelength of near-infrared light is between 780nm-2500nm.

[0052] In this embodiment, the probe of the near infrared spectrometer can be inserted into multiple modeling samples to measure the first spectrum data of plutonium and the second spectrum data of nitric acid. The near infrared spectrometer has relatively high measurement accuracy, which is conducive to quickly obtaining the corresponding relationship between the concentration of plutonium and the first spectrum data, and the corresponding relationship between the concentration of nitric acid and the second spectrum data, so as to quickly establish the first measurement model and the second measurement model.

[0053] In some embodiments, the sample spectrum data of plutonium and the sample spectrum data of nitric acid in the sample to be tested are obtained by a near-infrared spectrometer.

[0054] In some embodiments, during the measurement using an infrared spectrometer, air is used as a reference, and a quartz cuvette is used as a measuring cell. The best measuring optical path is selected to collect the near-infrared absorption spectra of nitric acid and plutonium in the P350 solution.

[0055] Illustratively, by establishing a first measurement model and a second measurement model, the concentrations of nitric acid and plutonium in the sample to be tested can be obtained by measuring the sample spectral data of plutonium and the sample spectral data of nitric acid in the sample to be tested each time. Each measurement takes about a few minutes, with a fast measurement speed and a wide measurement range.

[0056] In this embodiment, the probe of the near infrared spectrometer can be inserted into the sample to be tested to measure the sample spectrum data of plutonium and the sample spectrum data of nitric acid. The near infrared spectrometer has relatively high measurement accuracy and can realize online in-situ analysis.

[0057] It is understandable that the spectrum collection conditions of the infrared spectrometer can be selected according to needs. For example, the resolution, spectrum collection range, spectrum collection times and optical path length of the probe of the infrared spectrometer can be selected according to needs.

[0058] In some embodiments, the first spectral data is the absorbance of plutonium in the modeled sample; the second spectral data is the absorbance of nitric acid in the modeled sample; the sample spectral data of plutonium is the absorbance of plutonium in the sample to be tested; and the sample spectral data of nitric acid is the absorbance of nitric acid in the sample to be tested.

[0059] The first spectral data may be the absorbance of near-infrared light of plutonium in the modeling sample.

[0060] The second spectral data may be the absorbance of near-infrared light of nitric acid in the modeling sample.

[0061] The sample spectrum data of plutonium may be the absorbance of near-infrared light of plutonium in the sample to be tested.

[0062] The sample spectrum data of nitric acid may be the absorbance of near-infrared light of nitric acid in the sample to be tested.

[0063] In some embodiments, the wavelength range of the nitric acid is between 1800 nm and 2100 nm.

[0064] Since the information of near-infrared spectrum is relatively complex, and the information of some bands is useless, it is possible to select a better band for the measurement of plutonium and nitric acid. In the wavelength range of 1800nm ​​to 2100nm, the absorption peak intensity of nitric acid increases with the increase of nitric acid concentration, and the absorbance tends to increase gradually. The concentration and absorbance of nitric acid are correlated and can be used for quantitative analysis. Therefore, nitric acid is measured at a wavelength of 1800nm ​​to 2100nm to avoid the spectral area with severe interference and avoid interference from other components.

[0065] In some embodiments, the wavelength range of the plutonium is between 800 nm and 1100 nm.

[0066] In the wavelength range of 800nm ​​to 1100nm, the absorption peak intensity of tetravalent plutonium increases with the increase of plutonium concentration, and the absorbance tends to gradually increase. The concentration of plutonium and the absorbance are correlated and can be used for quantitative analysis. Therefore, plutonium is measured at a wavelength of 800nm ​​to 1100nm to avoid spectral regions with more serious interference and avoid interference from other components.

[0067] In some embodiments, the first determination model and the second determination model are both partial least squares models.

[0068] Exemplarily, partial least squares regression software may be used for data processing, and partial least squares regression analysis may be used to establish the first measurement model and the second measurement model.

[0069] The Partial Least Squares (PLS) model is a statistical method used to process multivariate data, especially for the problem of multicollinearity between independent variables. The PLS model performs regression analysis by projecting the independent and dependent variables into a new space and finding the best linear relationship between them.

[0070] In some embodiments, the concentration determination method comprises:

[0071] S50, obtaining third spectrum data of plutonium and fourth spectrum data of nitric acid in a plurality of verification samples, wherein known concentrations of nitric acid and plutonium in the plurality of verification samples are reference values;

[0072] S60, obtaining a predicted value of the concentration of plutonium in the verification sample based on the first measurement model and the third spectral data, and obtaining a predicted value of the concentration of nitric acid in the verification sample based on the second measurement model and the fourth spectral data;

[0073] S70. Verify the first measurement model based on the reference value of the plutonium concentration and the predicted value of the plutonium concentration, and verify the second measurement model based on the reference value of the nitric acid concentration and the predicted value of the nitric acid concentration.

[0074] Steps S10 and S20 may be performed first, and then steps S50, S60 and S70 may be performed in sequence. That is, after the first measurement model and the second measurement model are established, the prediction accuracy of the first measurement model and the prediction accuracy of the second measurement model may be verified.

[0075] It is understood that the verification sample is a P350 solution containing nitric acid and plutonium. The concentrations of plutonium and nitric acid in each verification sample may be different.

[0076] Exemplarily, multiple verification samples can be prepared by dilution using an extraction method.

[0077] The configuration method of the verification sample can be the same as the configuration method of the modeling sample.

[0078] The reference value is a known value, which may be a value that has been confirmed during the process of configuring the verification sample.

[0079] The verification sample can be prepared at the same time as the modeling sample, and a part of all the prepared P350 solutions containing nitric acid and plutonium is used as the modeling sample, and the other part of the solution is used as the verification sample.

[0080] The first measurement model is verified based on a deviation between a reference value of plutonium concentration and a predicted value of the plutonium concentration, and the second measurement model is verified based on a deviation between a reference value of nitric acid concentration and a predicted value of the nitric acid concentration.

[0081] The deviation includes but is not limited to at least one of the parameters such as the root mean square error of calibration (RMSEC, Root Mean Square Error of Calibration and its correlation coefficient, the root mean square error of prediction (RMSEP, Root Mean Square Error of Prediction and its correlation coefficient).

[0082] Using chemometric software such as partial least squares regression software, using near-infrared absorption spectra obtained under the best optical measurement path, selecting the wavelength range of nitric acid between 1800nm ​​and 2100nm and the wavelength range of plutonium between 800nm ​​and 1100nm, we can obtain reference values ​​and predicted values ​​for multiple verification samples. For details, please refer to Figure 2 and Figure 3 , Figure 2 To verify the correlation diagram between the reference value and the predicted value of the concentration of nitric acid in the sample, Figure 3 To verify the correlation diagram between the reference value and the predicted value of the plutonium concentration in the sample, Figure 2 It can be seen that the RMSEC of the second determination model of nitric acid is 0.0015 mol / L and the correlation coefficient is 0.9998, which shows that the prediction accuracy of the second determination model is relatively high; Figure 3 It can be seen that the RMSEC of the first measurement model for tetravalent plutonium is 0.0317 g / L and the correlation coefficient is 0.9999, which shows that the prediction accuracy of the first measurement model is relatively high.

[0083] In an exemplary embodiment, a certain amount of P350 solution is taken as a verification sample and placed in a cuvette, and air is used as a reference. The spectrum acquisition conditions for establishing the first measurement model and the second measurement model are consistent, and the third spectrum data and the fourth spectrum data of the verification sample are obtained. The predicted value of the concentration of plutonium in the verification sample is obtained based on the first measurement model and the third spectrum data. The predicted value of the concentration of nitric acid in the verification sample is obtained based on the second measurement model and the fourth spectrum data. The measurement results of the verification sample are shown in Table 1:

[0084] Table 1

[0085]

[0086] It can be seen from the analysis results in Table 1 that the first measurement model and the second measurement model can more accurately measure the concentrations of acid and plutonium in the verification sample.

[0087] In the description of this specification, the description with reference to the terms "an embodiment", "some embodiments" and "exemplary" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the embodiments of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification and the features of different embodiments or examples, unless they are contradictory.

[0088] The various embodiments / implementations provided in this application can be combined with each other without causing any contradiction. The above description is only a preferred embodiment of this application and is not intended to limit this application. For those skilled in the art, this application may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of this application shall be included in the protection scope of this application.

Claims

1. A method for determining the concentration of nitric acid and plutonium in a P350 solution, characterized in that: include: Acquiring first spectral data of plutonium and second spectral data of nitric acid in a plurality of modeling samples, wherein the plurality of modeling samples are P350 solutions of nitric acid and plutonium with a plurality of different concentrations; Establishing a first measurement model and a second measurement model based on the modeling sample, wherein the first measurement model includes a correspondence between the concentration of plutonium and the first spectrum data, and the second measurement model includes a correspondence between the concentration of nitric acid and the second spectrum data; Obtaining sample spectrum data of plutonium and sample spectrum data of nitric acid in the sample to be tested; Based on the first measurement model and the sample spectrum data of plutonium, a predicted value of the concentration of plutonium in the sample to be tested is obtained; based on the second measurement model and the sample spectrum data of nitric acid, a predicted value of the concentration of nitric acid in the sample to be tested is obtained.

2. The concentration determination method according to claim 1, characterized in that: The concentration of plutonium in the modeling sample is between 0.5 g / L and 20 g / L.

3. The concentration determination method according to claim 1, characterized in that: The concentration of nitric acid in the modeling sample is between 0.01 mol / L and 0.2 mol / L.

4. The concentration determination method according to claim 1, characterized in that: The first spectrum data of plutonium in the plurality of modeling samples and the second spectrum data of nitric acid are obtained by a near infrared spectrometer.

5. The concentration determination method according to claim 4, characterized in that: The sample spectrum data of plutonium and the sample spectrum data of nitric acid in the sample to be tested are obtained by a near-infrared spectrometer.

6. The concentration determination method according to claim 4, characterized in that: The first spectral data is the absorbance of plutonium in the modeled sample; the second spectral data is the absorbance of nitric acid in the modeled sample; the sample spectral data of plutonium is the absorbance of plutonium in the sample to be tested; the sample spectral data of nitric acid is the absorbance of nitric acid in the sample to be tested.

7. The concentration determination method according to claim 4, characterized in that: The wavelength range of the nitric acid is between 1800nm ​​and 2100nm.

8. The concentration determination method according to claim 4, characterized in that: The wavelength range of the plutonium is between 800nm ​​and 1100nm.

9. The concentration determination method according to claim 1, characterized in that: The first measurement model and the second measurement model are both partial least squares models.

10. The concentration determination method according to claim 1, characterized in that: The concentration determination method comprises: Acquiring third spectrum data of plutonium and fourth spectrum data of nitric acid in a plurality of verification samples, wherein known concentrations of nitric acid and plutonium in the plurality of verification samples are reference values; Obtaining a predicted value of the concentration of plutonium in the verification sample based on the first measurement model and the third spectral data, and obtaining a predicted value of the concentration of nitric acid in the verification sample based on the second measurement model and the fourth spectral data; The first measurement model is verified based on the reference value of the plutonium concentration and the predicted value of the plutonium concentration, and the second measurement model is verified based on the reference value of the nitric acid concentration and the predicted value of the nitric acid concentration.