Method for predicting enthalpy of phase change materials

Abstract

The present disclosure relates to a method for predicting the enthalpy of a phase change material, a near-infrared spectrum of a phase change material sample is subjected to a partial least squares regression analysis with a standard enthalpy to establish a first calibration model; then a spectral fitting residual matrix is selected according to the construction process of the first calibration model, the spectral fitting residual matrix and the enthalpy matrix are combined, and are used as input signals and teacher signals of an extreme learning machine respectively to obtain a second calibration model; through the combined application of the first calibration model and the second calibration model, the linear relationship and the nonlinear relationship between the near-infrared spectrum of the phase change material sample and the enthalpy can be comprehensively considered, the enthalpy prediction capability in a wide range is achieved, and the model prediction accuracy is improved.

Description

Technical Field

[0001] This disclosure relates to a method for predicting the enthalpy of phase change materials. Background Technology

[0002] Phase change materials (PCMs) are materials with energy storage and temperature regulation properties, widely used in aerospace, construction, textiles, and other fields. Among them, PCM wax is one of the ideal PCM energy storage materials. It typically refers to special waxes with a phase change temperature of 20–80℃. It is an excellent organic PCM energy storage material with advantages such as good heat storage performance, wide availability of raw materials, low price, and non-toxicity and non-corrosiveness. It can be applied in many industries including building materials, solar energy, industrial waste heat utilization, temperature-regulating textiles, electronics, modern agriculture, and healthcare. The main component of PCM wax is n-alkanes (C6H2O). n H 2n+2 The raw materials for its production mainly come from two categories. One is petroleum wax, which usually requires solvent dewaxing to increase its n-alkanes content in order to avoid affecting the enthalpy value of the product. The other commonly used raw material is Fischer-Tropsch synthetic wax, which is characterized by a relatively simple composition and a n-alkanes content of over 90%, with virtually no cyclic hydrocarbons or aromatics, making it a high-quality raw material for the production of phase change wax.

[0003] Near-infrared spectroscopy offers advantages such as speed and non-destructive analysis, making it one of the most widely studied and deeply researched topics in the petrochemical field for determining the physical properties and composition of chemical products. While a relatively practical analytical model can be established by using partial least squares methods to analyze the near-infrared absorbance and enthalpy of phase change materials, this often comes at the cost of sacrificing predictive accuracy for robustness. Summary of the Invention

[0004] The purpose of this disclosure is to provide a method for predicting the enthalpy of phase change materials, so as to achieve rapid and accurate prediction over a wide range of enthalpy values ​​with both strong robustness and high accuracy.

[0005] To achieve the above objective, this disclosure provides a method for predicting the enthalpy of a phase change material, the method comprising the following steps:

[0006] Near-infrared spectra of multiple phase change material samples and standard enthalpy values ​​of each phase change material sample were obtained;

[0007] The absorbance of the characteristic spectral region in each of the near-infrared spectra is obtained to form a first characteristic spectral matrix; and the standard enthalpy values ​​of all the phase change wax samples are used to form an enthalpy matrix.

[0008] A first correction model is established by performing partial least squares regression analysis on the first characteristic spectral matrix and the enthalpy matrix.

[0009] Based on the first calibration model, select the first spectral fitting residual matrix corresponding to the f-th principal factor, use the first spectral fitting residual matrix as the input signal of the extreme learning machine, and use the enthalpy matrix as the teacher signal of the extreme learning machine to establish the second calibration model.

[0010] Collect the spectrum of the phase change material sample to be tested; obtain the absorbance of the characteristic spectral region of the spectrum of the sample to be tested; determine the predicted value of the first enthalpy value based on the absorbance of the characteristic spectral region of the spectrum of the sample to be tested and the first correction model;

[0011] The second spectral fitting residual matrix corresponding to the f-th principal factor of the phase change material sample to be tested is selected according to the first correction model, and the second enthalpy prediction value is determined according to the second spectral fitting residual matrix and the second correction model.

[0012] Determine the prediction weights of the first and second enthalpy prediction values, and then weight the first and second enthalpy prediction values ​​according to their respective prediction weights to obtain the predicted enthalpy value of the phase change material sample to be tested.

[0013] Optionally, the characteristic spectral region is 5780–7700 cm⁻¹. -1 .

[0014] Optionally, the method further includes:

[0015] The spectral fitting residual matrix Ex is determined according to the following equations (1), (2), or (3):

[0016] Ex = XX(f best (1);

[0017] Where X represents the spectral matrix, X(f best () indicates that the first calibration model takes the optimal principal factor f. best The spectral matrix at time;

[0018] Ex = XX(f best+1～n (2);

[0019] Where X(f) best+1～n () indicates that the first calibration model takes the optimal principal factor f. best The spectral matrix of any one of the 1 to n principal factors, where n is an integer from 2 to 15;

[0020] Ex = X (3);

[0021] Optionally, the number of spectral fitting residual matrices Ex can be one or more.

[0022] Optionally, the method further includes:

[0023] The regression coefficients of the first correction model and the second correction model are obtained respectively, and the regression coefficients are used as the prediction weights corresponding to the first predicted value and the second predicted value.

[0024] Optionally, the method further includes:

[0025] Based on the second spectral fitting residual matrix and the second correction model, multiple predictions are made, and the average value of the multiple prediction results is taken as the predicted value of the second enthalpy.

[0026] Optionally, the method includes:

[0027] Each near-infrared spectrum is subjected to second-order differential processing to obtain the first differential spectrum;

[0028] The first differential absorbance of the characteristic spectral region in each of the first differential spectra is obtained to form the first characteristic spectral matrix.

[0029] Optionally, the method includes:

[0030] The second differential spectrum of the sample to be tested is obtained by performing second-order differential processing.

[0031] Obtain the absorbance of the characteristic spectral region of the second differential spectrum;

[0032] The predicted value of the first enthalpy is determined based on the absorbance in the characteristic spectral region of the second differential spectrum and the first correction model.

[0033] Optionally, the window width for the second-order differential processing is 13 to 25.

[0034] Optionally, the phase change material is a phase change wax.

[0035] Optionally, the standard enthalpy value is determined using differential scanning calorimetry.

[0036] Through the above technical solution, this disclosure performs partial least squares regression analysis on the near-infrared spectrum and standard enthalpy of phase change material samples to establish a first calibration model; then, according to the construction process of the first calibration model, the spectral fitting residual matrix is ​​selected, and the spectral fitting residual matrix and enthalpy matrix are used as the input signal and teacher signal of the extreme learning machine, respectively, to obtain a second calibration model. By combining the first calibration model and the second calibration model, the linear and nonlinear relationships between the near-infrared spectrum and enthalpy of phase change material samples can be comprehensively considered, resulting in a wider range of enthalpy prediction capabilities and improved model prediction accuracy.

[0037] Other features and advantages of this disclosure will be described in detail in the following detailed description section. Attached Figure Description

[0038] The accompanying drawings are provided to further illustrate the present disclosure and form part of the specification. They are used together with the following detailed description to explain the present disclosure, but do not constitute a limitation thereof. In the drawings:

[0039] Figure 1 This is a flowchart illustrating a method for predicting the enthalpy of a phase change material according to one embodiment of this disclosure. Detailed Implementation

[0040] The specific embodiments of this disclosure will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit this disclosure.

[0041] This disclosure provides a method for predicting the enthalpy of phase change materials, such as... Figure 1 As shown, the process includes the following steps S101 to S107:

[0042] S101. Obtain the near-infrared spectra of multiple phase change material samples and the standard enthalpy value of each phase change material sample;

[0043] S102. Obtain the absorbance of the characteristic spectral region in each of the near-infrared spectra to form a first characteristic spectral matrix; and form an enthalpy matrix using the standard enthalpy values ​​of all the phase change wax samples.

[0044] S103. Perform partial least squares regression analysis on the first characteristic spectral matrix and the enthalpy matrix to establish a first correction model;

[0045] S104. Select the first spectral fitting residual matrix corresponding to the f-th principal factor according to the first correction model, use the first spectral fitting residual matrix as the input signal of the extreme learning machine, use the enthalpy matrix as the teacher signal of the extreme learning machine, and establish the second correction model.

[0046] S105. Collect the spectrum of the phase change material sample to be tested; obtain the absorbance of the characteristic spectral region of the spectrum of the sample to be tested; determine the predicted value of the first enthalpy value based on the absorbance of the characteristic spectral region of the spectrum of the sample to be tested and the first correction model.

[0047] S106. Select the second spectral fitting residual matrix corresponding to the f-th principal factor of the phase change material sample to be tested according to the first correction model, and determine the second enthalpy prediction value according to the second spectral fitting residual matrix and the second correction model.

[0048] S107. Determine the prediction weights of the first enthalpy prediction value and the second enthalpy prediction value respectively, and weight the first enthalpy prediction value and the second enthalpy prediction value according to their respective prediction weights to obtain the predicted enthalpy value of the phase change material sample to be tested.

[0049] This disclosure breaks down the relationship between near-infrared spectral absorbance and enthalpy of phase change materials into linear and nonlinear relationships. A correction model is established step by step by combining the two. The linear relationship is fitted and corrected using partial least squares method, and the nonlinear relationship is fitted and corrected using extreme learning machine, which has higher prediction accuracy.

[0050] In this disclosure, partial least squares regression (PLS) analysis can be performed using conventional selection methods and software in the art. Specifically, this disclosure uses an interactive test method to determine the optimal number of principal factors f. best .

[0051] In this disclosure, Extreme Learning Machine (ELM) is a type of machine learning system or method built on Feedforward Neuron Network (FNN).

[0052] This disclosure employs an extreme learning machine (ELM) to correct the nonlinear relationship between absorbance and standard enthalpy in the characteristic spectral region of a phase change material sample. The spectral fitting residuals of partial least squares regression serve as the input signal to the ELM, while the standard enthalpy is used as the teacher signal (i.e., the desired output value, also known as the supervisory signal). Supervised learning (also known as teacher-assisted learning) is performed on the ELM to adjust its parameters so that it meets the performance requirements for predicting the nonlinear relationship between the near-infrared spectrum and enthalpy of the phase change material sample.

[0053] In one embodiment, the characteristic spectral region is 5780–7700 cm⁻¹. -1 In this embodiment, selecting absorbance and standard enthalpy within an appropriate characteristic spectral range to construct the model can improve the correlation between absorbance and standard enthalpy and simplify the computational workload during model construction.

[0054] In one embodiment, the method further includes:

[0055] The spectral fitting residual matrix Ex is determined according to the following equations (1), (2), or (3):

[0056] Ex = XX(f best (1);

[0057] Where X represents the spectral matrix, X(f best () indicates that the first calibration model takes the optimal principal factor f. best The spectral matrix at time;

[0058] Ex = XX(f best+1～n (2);

[0059] Where X(f) best+1～n () indicates that the first calibration model takes the optimal principal factor f. best The spectral matrix of any one of the 1 to n principal factors, where n is an integer from 2 to 15;

[0060] Ex = X (3).

[0061] In this disclosure, three spectral fitting residual matrices are obtained using equations (1), (2), or (3) above, respectively. These three residual matrices are then used to construct a second correction model, resulting in three second correction models. Based on the verification analysis results of the three second correction models, such as dispersion and mean square error, the formula corresponding to the second correction model with better prediction performance is selected.

[0062] In one specific implementation, the number of spectral fitting residual matrices Ex is one or more. Specifically, one or more principal factors f can be selected, resulting in one or more spectral fitting residual matrices Ex. For example, f best When the value is 3, f can be one or more of 1 to 3.

[0063] In one specific implementation, this disclosure uses an interactive testing method to determine the optimal number of principal factors f. best .

[0064] In one specific implementation, the present disclosure selects the f-th principal factor using the following method:

[0065] The residual matrix E corresponding to the spectrum of each principal factor is fitted. x The enthalpy matrix is ​​used as the input signal and teacher signal of the extreme learning machine, respectively, to correct the extreme learning machine and obtain the second correction model corresponding to each principal factor;

[0066] The predicted enthalpy value of the phase change material corresponding to each principal factor is obtained according to the first correction model and the second correction model, and the prediction standard deviation between the predicted enthalpy value and the actual enthalpy value is calculated; the principal factor with the smallest prediction standard deviation or the principal factor with the most stable prediction standard deviation is selected as f in the above formulas (1) to (3).

[0067] Specifically, the grid search method can be used to select f in equations (1) to (3) above. Specifically, the grid search method is used to list all possible principal factors f, and then each one is verified to select the principal factor f with the smallest prediction standard deviation or the principal factor f with the most stable prediction standard deviation.

[0068] In this disclosure, by back-calculating the predicted standard deviation value, an appropriate principal factor is obtained as f in equations (1) to (3) above, which allows for a thorough comparison of the spectral fitting residual matrix E of multiple principal factors. x The model construction results of the enthalpy matrix improve the accuracy of enthalpy prediction.

[0069] In one embodiment, the method further includes:

[0070] The regression coefficients of the first correction model and the second correction model are obtained respectively, and the regression coefficients are used as the prediction weights corresponding to the first predicted value and the second predicted value.

[0071] In one specific embodiment, the enthalpy value y of the sample to be tested un The prediction process includes:

[0072] (1) Determine the first enthalpy prediction value

[0073] x un The absorbance of the characteristic spectral region of the sample to be tested is input into the established first calibration model to obtain the first enthalpy prediction value y1.

[0074] (2) Determine the predicted value of the second enthalpy value

[0075] Based on equations (1), (2), or (3) determined during the establishment of the second model, the spectral fitting residual matrix corresponding to the f-th principal factor of the sample to be tested is obtained; the spectral fitting residual matrix of the sample to be tested is input into the second correction model to obtain the second enthalpy prediction value y2.

[0076] (3) Determine the prediction weights of the first and second enthalpy predictions.

[0077] Perform a multiple regression analysis on the first enthalpy prediction value y1, the second enthalpy prediction value y1, and the enthalpy matrix. That is, substitute y1 and y1 into Y = b1×y1 + b2×y2 + e to solve for the regression coefficients b1 and b2, where e is the residual.

[0078] (4) Solve for the final enthalpy prediction result

[0079] The first and second enthalpy predictions are weighted according to their respective prediction weights to obtain the final enthalpy prediction value y. un , that is, y un= b1×y1+b2×y2+e.

[0080] In one embodiment, the method further includes: performing multiple predictions based on the second spectral fitting residual matrix and the second correction model, and taking the average of the multiple prediction results as the predicted value of the second enthalpy. This avoids errors and improves the accuracy of the prediction results.

[0081] In one embodiment, the method further includes:

[0082] Each near-infrared spectrum is subjected to second-order differential processing to obtain the first differential spectrum;

[0083] Obtain the first differential absorbance of the characteristic spectral region in each of the differential spectra to form the first characteristic spectral matrix;

[0084] The first characteristic spectral matrix and the enthalpy matrix are subjected to partial least squares regression analysis to obtain the first correction model.

[0085] In one embodiment, the method further includes:

[0086] The second differential spectrum of the sample to be tested is obtained by performing second-order differential processing.

[0087] Obtain the absorbance of the characteristic spectral region of the second differential spectrum;

[0088] The predicted value of the first enthalpy is determined based on the absorbance in the characteristic spectral region of the second differential spectrum and the first correction model.

[0089] This disclosure eliminates baseline shift, drift, and background interference in the near-infrared spectrum and / or the spectrum of the sample under test by performing second-order differential processing.

[0090] In one specific embodiment, the window width for the second-order differential processing is 13 to 25. In this disclosure, the second-order differential processing method can be differentiated using the Savitzky-Golay (SG) method.

[0091] In one embodiment, the phase change material sample may be a phase change wax. The method disclosed herein is particularly suitable for predicting the enthalpy of phase change wax samples. The near-infrared spectral absorbance of the phase change wax sample has a good linear relationship with the enthalpy, which is beneficial for achieving rapid and accurate prediction of phase change wax samples with a wide enthalpy range.

[0092] In one specific embodiment, the phase change material sample can be of different types, and the number of samples is at least 100, in order to further improve the accuracy and reliability of the established model.

[0093] In one specific embodiment, the near-infrared spectroscopy detection conditions include: a scanning range of 4000–10000 cm⁻¹. -1 In this disclosure, the resolution can be selected based on the model construction accuracy or instrument accuracy, for example, a resolution of 4cm. -1 8cm -1 The sampling point interval for the near-infrared spectral absorbance is 2 to 16 wavenumbers.

[0094] In this disclosure, the standard enthalpy value is tested using methods conventionally chosen in the art, such as differential scanning calorimetry (DSC).

[0095] In this disclosure, the phase change material samples are divided into a calibration set and a test set. The calibration set is used for model building, and the test set is used to verify the predicted values ​​and actual values ​​of the built model. This disclosure can use a relatively large number of calibration set samples with good representativeness; that is, the enthalpy values ​​of the calibration set samples can cover the enthalpy values ​​of all predicted phase change wax samples, so that the established model has good generalization ability. Preferably, the number of calibration set samples accounts for 2 / 3 to 3 / 4 of the total number of samples, and the remaining 1 / 3 to 1 / 4 is used as the test set. Preferably, the distribution patterns of the calibration set and the test set samples are approximately the same.

[0096] The present disclosure is further illustrated below with examples, but it is not limited thereto.

[0097] In the following examples and comparative examples, the test conditions for near-infrared spectroscopy testing of the calibration set samples and the test set samples are the same.

[0098] The near-infrared spectrometer used was a Thermo Analis II Fourier transform near-infrared spectrometer. Spectral acquisition conditions were: 0.5 mm cuvette, 8 cm⁻¹ resolution. -1 The wavenumber range for acquisition is 4000–10000 cm⁻¹. -1 The cumulative number of scans was 64, using transmission measurement method.

[0099] Example 1

[0100] (1) Determine the enthalpy of phase change wax using DSC method

[0101] One hundred phase change wax samples were collected from a certain factory, and their enthalpy values ​​were determined using the DSC method as standard enthalpy values. Seventy-five representative phase change wax samples were selected to form a calibration set, and the remaining samples were used as the test set.

[0102] (2) Construct the first and second correction models

[0103] Near-infrared spectroscopy was performed on all calibration set samples to obtain their near-infrared spectra. The near-infrared spectra of each calibration set sample were then processed by second-order differentiation with a window width of 25 to obtain the first differential spectrum.

[0104] For each first differential spectrum, select 5780-7700 cm⁻¹ -1 The absorbance in the spectral region will be the 5780-7700 cm⁻¹ of all calibration set samples. -1 The absorbance within the spectral region forms the absorbance matrix X, and the standard enthalpy values ​​of all calibration set samples measured in step (1) form the enthalpy matrix Y.

[0105] Partial least squares regression analysis (PLS regression analysis) was performed on the absorbance matrix X and the enthalpy matrix Y to obtain the first calibration model with linear fit. During the PLS regression analysis, all principal factors were identified, and the optimal number of principal factors f was determined using an interactive test method. best In this embodiment, the number of principal factors selected is 4, f best This is the fourth principal factor.

[0106] The spectral fitting residual matrix (Ex=XX) is calculated according to equation (1). (4) Then, the spectral fitting residual matrix and enthalpy matrix are used as the input signal and teacher signal of the extreme learning machine, respectively. The ELM algorithm is used to perform nonlinear correction on the spectral fitting residual matrix and enthalpy matrix to obtain the second correction model of nonlinear fitting.

[0107] (3) The prediction results of the first and second correction models are validated using test set samples.

[0108] Near-infrared spectroscopy was performed on each sample in the test set to obtain the spectrum of the sample to be tested. After second-order differential processing with a window width of 25, the second differential spectrum was obtained. The wavenumber range of 5780-7700 cm⁻¹ was selected from the second differential spectrum. -1 The absorbance in the spectral region is used as the absorbance to be measured. The absorbance of the characteristic spectral region of the test set sample is input into the established first calibration model to obtain the first enthalpy prediction value y1. According to the first calibration model, the spectral fitting residual matrix corresponding to the fourth principal factor of the test set sample is selected. The spectral fitting residual matrix of the test sample is input into the second calibration model to obtain the second enthalpy prediction value y2. The first enthalpy prediction value y1, the second enthalpy prediction value y1, and the enthalpy matrix are used to perform a multiple regression analysis, that is, y1 and y2 are substituted into Y = b1×y1 + b2×y2 + e to solve for the regression coefficients b1 and b2, where e is the residual. The calculated values ​​are b1 = 0.3481 and b2 = 0.6554.

[0109] The first and second enthalpy predictions are weighted according to their respective prediction weights to obtain the final enthalpy prediction value y. un , that is, y un = b1×y1+b2×y2+e. The comparison results of the predicted enthalpy values ​​of the test set samples with the standard enthalpy values ​​determined by the DSC method are shown in Table 1.

[0110] The formulas for calculating the relevant statistical parameters are as follows:

[0111]

[0112] in, Let y be the predicted value for the i-th sample. i (i = 1, 2, ..., n) represents the true value of the i-th sample, and n is the number of samples in the test set.

[0113] Where, deviation = measured value - predicted value.

[0114] Table 1

[0115]

[0116] Comparative Example 1

[0117] The difference from Example 1 is that only the first step of partial least squares regression analysis (PLS) is performed to construct the first calibration model, without performing the step of constructing the second calibration model, and the optimal principal factor f is not performed. best The model was used for prediction under the condition of = 4. The comparison results of the predicted enthalpy values ​​of the test set samples with the standard enthalpy values ​​determined by the DSC method are shown in Table 2.

[0118] Table 2

[0119]

[0120] Comparative Example 2

[0121] The difference from Example 1 is that the Extreme Learning Machine (ELM) algorithm is used alone to build the calibration model. In this example, the ELM algorithm used is a pre-trained ELM algorithm, and the model is used for prediction under optimal parameter conditions. The comparison results of the predicted enthalpy values ​​of the test set samples with the standard enthalpy values ​​determined by the DSC method are shown in Table 3.

[0122] Table 3

[0123]

[0124]

[0125] Based on the above embodiments and comparative data, it can be seen that the SEP of the phase change material enthalpy prediction model obtained by the method provided in this disclosure is smaller, indicating that compared with the standalone linear partial least squares phase change material enthalpy prediction method (Comparative Example 1) and the standalone nonlinear limit learning machine phase change material enthalpy prediction method (Comparative Example 2), the method provided in this disclosure has better prediction accuracy for phase change material enthalpy.

[0126] The preferred embodiments of this disclosure have been described in detail above with reference to the accompanying drawings. However, this disclosure is not limited to the specific details of the above embodiments. Within the scope of the technical concept of this disclosure, various simple modifications can be made to the technical solutions of this disclosure, and these simple modifications all fall within the protection scope of this disclosure.

[0127] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, this disclosure will not describe the various possible combinations separately.

[0128] Furthermore, various different embodiments of this disclosure can be combined in any way, as long as they do not violate the spirit of this disclosure, they should also be regarded as the content disclosed in this disclosure.

Claims

1. A method for predicting the enthalpy of a phase change material, characterized in that, The method includes the following steps: Near-infrared spectra of multiple phase change material samples and standard enthalpy values ​​of each phase change material sample were obtained; The absorbance of the characteristic spectral region in each of the near-infrared spectra is obtained to form a first characteristic spectral matrix; and the standard enthalpy values ​​of all the phase change wax samples are used to form an enthalpy matrix. A first correction model is established by performing partial least squares regression analysis on the first characteristic spectral matrix and the enthalpy matrix. Based on the first calibration model, select the first spectral fitting residual matrix corresponding to the f-th principal factor, use the first spectral fitting residual matrix as the input signal of the extreme learning machine, and use the enthalpy matrix as the teacher signal of the extreme learning machine to establish the second calibration model. Collect the spectrum of the phase change material sample to be tested; obtain the absorbance of the characteristic spectral region of the spectrum of the sample to be tested; determine the predicted value of the first enthalpy value based on the absorbance of the characteristic spectral region of the spectrum of the sample to be tested and the first correction model; The second spectral fitting residual matrix corresponding to the f-th principal factor of the phase change material sample to be tested is selected according to the first correction model, and the second enthalpy prediction value is determined according to the second spectral fitting residual matrix and the second correction model. The regression coefficients of the first correction model and the second correction model are obtained respectively. The regression coefficients are used as the prediction weights corresponding to the first enthalpy prediction value and the second enthalpy prediction value. The first enthalpy prediction value and the second enthalpy prediction value are weighted according to their respective prediction weights to obtain the predicted enthalpy value of the phase change material sample to be tested. The phase change material is a phase change wax.

2. The method according to claim 1, wherein, The characteristic spectral region is 5780~7700 cm⁻¹. -1 .

3. The method according to claim 1, wherein, The method also includes: The spectral fitting residual matrix is ​​determined according to the following equations (1), (2), or (3). Ex : Ex = X - X ( f best ) （1）； in X Represents the spectral matrix, X ( f best () indicates that the first calibration model takes the optimal principal factors. f best The spectral matrix at that time; Ex = X - X ( f best+1~n ) （2）； in X ( f best+1~n () indicates that the first calibration model takes the optimal principal factors. f best The spectral matrix of any one of the 1 to n principal factors, where n is an integer from 2 to 15; Ex = X （3）； Optionally, the spectral fitting residual matrix Ex The number of elements can be one or more.

4. The method according to claim 1, wherein, The method also includes: Based on the second spectral fitting residual matrix and the second correction model, multiple predictions are made, and the average value of the multiple prediction results is taken as the predicted value of the second enthalpy.

5. The method according to claim 1, wherein, The method includes: Each near-infrared spectrum is subjected to second-order differential processing to obtain the first differential spectrum; The first differential absorbance of the characteristic spectral region in each of the first differential spectra is obtained to form the first characteristic spectral matrix.

6. The method according to claim 5, wherein, The method includes: The second differential spectrum of the sample to be tested is obtained by performing second-order differential processing. Obtain the absorbance of the characteristic spectral region of the second differential spectrum; The predicted value of the first enthalpy is determined based on the absorbance in the characteristic spectral region of the second differential spectrum and the first correction model.

7. The method according to claim 5 or 6, wherein, The window width for the second-order differential processing is 13~25.

8. The method according to claim 1, wherein, The standard enthalpy value was determined using the differential scanning calorimetry method.

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