An intelligent prediction method for thermophysical properties of transcritical working fluids suitable for property jump characteristics

Abstract

The application discloses a kind of intelligent prediction methods for trans-critical working medium thermophysical property suitable for property mutation characteristics, obtain the property-temperature data of target working medium under specified working pressure by standard property database, using piecewise linear regression variable point detection algorithm based on residual sum of squares dynamic monitoring, realize the identification of working medium property-temperature curve inflection point and the adaptive division of temperature interval, based on bayesian information criterion, the polynomial order optimization of each segmented interval is carried out to balance fitting accuracy and complexity, and continuity constraint is applied at the connection point of segmentation, to build globally continuous segmented polynomial function.The application can realize the whole process automation of trans-critical working medium property-temperature function modeling of "data acquisition-inflexion point identification-order optimization-function generation", effectively overcome the subjectivity and limitation of artificial experience segmentation, while ensuring the accuracy of model, avoid overfitting risk, provide reliable support for engineering simulation and thermodynamic system design under trans-critical condition.

Description

Technical Field

[0001] This invention belongs to the field of thermophysical property modeling and computational fluid dynamics, specifically involving an intelligent prediction method for the thermophysical properties of transcritical working fluids with abrupt property changes. Background Technology

[0002] In engineering simulation and thermodynamic system design involving transcritical processes, the physical properties of the working fluid (such as density, specific heat capacity, thermal conductivity, dynamic viscosity, etc.) exhibit significant nonlinear changes with temperature, especially near the critical point where there are drastic abrupt changes in physical properties. This abrupt change characteristic places extremely high demands on the reliability of engineering simulation and thermodynamic system design. Traditional physical property-temperature function modeling methods mainly include global high-order polynomial fitting or piecewise polynomial fitting based on human experience.

[0003] Global high-order polynomial fitting models the entire temperature range using a single high-order polynomial. However, the working fluid properties exhibit strong nonlinear abrupt changes near the critical point, leading to the following limitations of this method: On the one hand, to capture the local abrupt changes near the critical point, the polynomial order needs to be increased to enhance the local fitting ability. However, the global coupling effect of high-order terms makes the model extremely sensitive to data noise, and may even cause oscillations in the stable property region far from the critical point. On the other hand, a single polynomial function cannot simultaneously satisfy the contradictory requirements of drastic changes near the critical point (requiring high-order terms to describe) and slow changes in the stable region (which can be characterized by low-order terms), making it difficult for the model to balance local accuracy and global stability.

[0004] Piecewise polynomial fitting based on human experience involves manually dividing temperature ranges and using low-order polynomials for local fitting within each range, achieving global coverage by concatenating the polynomials from each range. However, this method has the following drawbacks: First, the selection of segmentation points lacks quantitative standards and is highly subjective, potentially leading to unreasonable temperature range divisions due to human error. Second, the lack of continuity constraints between temperature ranges can result in discontinuities in function values ​​or first derivatives at concatenation points, affecting the accuracy of engineering simulations and thermodynamic system calculations. Finally, when dealing with different working fluids or conditions, a redesigned segmentation strategy is required, making it difficult to achieve adaptive function modeling for different working fluid properties and limiting the method's ability to be automated.

[0005] In summary, traditional transcritical working fluid property-temperature function modeling methods have shortcomings in terms of accuracy, stability, and engineering versatility. There is an urgent need for an intelligent modeling method that can adaptively identify property mutation characteristics, automatically optimize model complexity, and ensure global continuity, thereby improving the engineering applicability of transcritical working fluid property models. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of current transcritical working fluid property-temperature function modeling by proposing an intelligent prediction method for transcritical working fluid thermophysical properties with abrupt property changes. This method aims to achieve fully automated transcritical working fluid property-temperature function modeling, thereby improving the accuracy, stability, and engineering versatility of the model.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A smart prediction method for the thermophysical properties of transcritical working fluids with abrupt property changes includes the following steps:

[0009] Step 1): By calling the standard property database, obtain the discrete property-temperature data of the target working fluid under the specified working pressure. The standard property database can be the REFPROP standard property database, which is suitable for property modeling of various working fluids such as CO2, N2, and CH4 involved in transcritical processes. The property parameters include density, specific heat capacity, thermal conductivity, and dynamic viscosity.

[0010] Step 2): For the discrete data of working fluid properties-temperature, a piecewise linear regression change point detection algorithm based on dynamic monitoring of residual sum of squares is used to identify the inflection point of the working fluid property-temperature curve and adaptively divide the temperature range.

[0011] Step 3): Based on the Bayesian Information Criterion (BIC), the polynomial order of each temperature range is optimized to balance the fitting accuracy and complexity. Continuity constraints are applied at the connection points of the temperature range segments to establish a globally continuous piecewise polynomial function with temperature as input and working fluid physical properties as output.

[0012] Step 4): The fitting effect of the piecewise polynomial function model is verified and evaluated by the coefficient of determination and the mean absolute percentage error index. Using this globally continuous piecewise polynomial function, intelligent prediction of the thermophysical properties of transcritical working fluids with abrupt property changes can be carried out.

[0013] In one embodiment, step 2) involves iterating through the discrete material property-temperature data using a sliding window mechanism. Within each window, a linear regression model is used to fit the material property-temperature relationship of the working fluid. The degree of trend deviation of the current material property data segment is quantified by calculating the sum of squared residuals between the actual material property values ​​and the linearly fitted values. The calculation of the sum of squared residuals is as follows:

[0014]

[0015] In the formula, y i T represents the true physical properties of the working fluid. iLet be temperature, a and b be the coefficients in the linear regression model of working fluid property-temperature, i be the data point number, and p be the number of discrete samples of property-temperature within the sliding window. The larger the sum of squared residuals, the greater the deviation of the trend in the current property data segment.

[0016] In one embodiment, in step 2), when the trend of the working fluid's physical properties changes abruptly (e.g., near a critical point), the sum of squared residuals will increase significantly. During the dynamic sliding window traversal of the physical property data, the abrupt change in the sum of squared residuals is detected in real time. When the abrupt change exceeds a threshold, the current position is marked as an inflection point. Based on the detected inflection point position, the temperature range is determined according to the minimum interval length constraint. Through this division method, the abrupt change characteristics of the working fluid's physical properties can be accurately captured, achieving adaptive division of the temperature range.

[0017] In one embodiment, step 3) involves iterating through candidate polynomial orders (e.g., from 1 to m) within each temperature range, fitting the polynomial model using the least squares method, and calculating the corresponding BIC value. By comparing the BIC values ​​of the model under different polynomial orders, the order that minimizes the BIC is selected as the optimal polynomial order. The calculation of BIC is as follows:

[0018]

[0019] In the formula, n is the number of discrete samples of physical properties and temperature within the temperature range, and m is the order of the polynomial.

[0020] In one embodiment, step 3) applies continuity constraints on the function values ​​and first derivatives at the piecewise connection points of the temperature range to ensure a smooth transition of the piecewise polynomial function, ultimately constructing a piecewise polynomial function that balances accuracy and global continuity. Specifically, the k-th and (k+1)-th segments of the property-temperature piecewise polynomial function must satisfy the following at the piecewise connection points:

[0021] The function value is continuous at the piecewise connection point: f k (T k )=f k+1 (T k )

[0022] The first derivative is continuous at the piecewise connection point:

[0023] In the formula, f k and f k+1 These are the k-th and (k+1)-th segments of the piecewise polynomial function of the property-temperature relationship, respectively. k Let T be the point where the function connects the k-th and (k+1)-th segments, and let T be the temperature.

[0024] In one embodiment, the obtained piecewise polynomial function is validated and evaluated for its fitting effect using the coefficient of determination and mean absolute percentage error (MASE). Typically, a coefficient of determination higher than 0.99 and a MASE lower than 2% are considered to indicate a good fitting effect.

[0025] Compared with existing technologies, this invention can realize fully automated modeling of transcritical working fluid property-temperature functions, from "data acquisition to inflection point identification to order optimization to function generation". It effectively overcomes the subjectivity and limitations of traditional manual experience-based segmentation, and avoids the risk of overfitting while ensuring model accuracy. It provides reliable property data support for engineering simulation and thermodynamic system design under transcritical conditions. Attached Figure Description

[0026] Figure 1 This is a flowchart of the transcritical working fluid property-temperature function modeling method of the present invention;

[0027] Figure 2 The graph shows the relationship between the physical properties of CO2 and temperature at 10 MPa. Detailed Implementation

[0028] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings and examples.

[0029] To address the problems of insufficient accuracy in single polynomial fitting, strong subjectivity, and poor segmentation rationality in transcritical working fluids due to drastic temperature changes in physical properties near the critical point, this invention proposes an intelligent prediction method for the thermophysical properties of transcritical working fluids with abrupt property changes. First, the method obtains the physical property-temperature data of the target working fluid at a specified working pressure by calling a standard physical property database. Second, a piecewise linear regression change point detection algorithm based on dynamic monitoring of the residual sum of squares is used to intelligently identify the inflection points of the working fluid's physical property-temperature curve and adaptively divide the temperature range. Finally, based on the Bayesian information criterion, the polynomial order of each segment interval is optimized to balance fitting accuracy and complexity, and continuity constraints are applied at the segment connection points to construct a globally continuous piecewise polynomial function. The fitting effect of the piecewise polynomial function model is verified and evaluated using the coefficient of determination and the mean absolute percentage error index.

[0030] This invention is applicable to the prediction of thermophysical properties of various working fluids, such as CO2, N2, and CH4, involving transcritical processes. The following detailed description, with reference to the accompanying drawings, uses the modeling of the property-temperature function of CO2 at 10 MPa as an example:

[0031] like Figure 1 As shown, the transcritical working fluid property-temperature function modeling method of the present invention is as follows:

[0032] First, by calling the REFPROP standard property database, discrete data of CO2 properties at 10 MPa were obtained. The properties included density, specific heat capacity at constant pressure, thermal conductivity and dynamic viscosity. The sampling interval was 0.1 K, covering a temperature range of 250 K to 650 K, and a total of 4001 discrete data points were obtained.

[0033] Secondly, a piecewise linear regression change point detection algorithm based on dynamic monitoring of residual sum of squares is adopted. This algorithm uses a dynamic sliding window to traverse discrete data points of physical properties and temperature, detecting abrupt changes in the residual sum of squares. When the abrupt change exceeds a threshold, the current position is marked as an inflection point. Based on the detected inflection point positions, temperature intervals are divided according to the minimum interval length constraint (3K). Table 1 shows the number of inflection points and temperature interval divisions for CO2 physical properties at 10MPa.

[0034] Table 1. Number of inflection points and temperature range division of CO2 properties at 10 MPa

[0035]

[0036] Next, within each temperature range, the candidate polynomial orders are traversed, and the polynomial model is fitted using the least squares method. The corresponding BIC value is calculated, and the order that minimizes the BIC is selected as the optimal polynomial order. Continuity constraints on the function values ​​and first derivatives at the piecewise connection points of the temperature ranges are applied to ensure a smooth transition of the piecewise polynomial function. This constructs a piecewise polynomial function that balances accuracy and global continuity. The physical property-temperature functions (density, specific heat capacity at isobaric pressure, thermal conductivity, and dynamic viscosity) of CO2 at 10 MPa are shown below:

[0037]

[0038] Finally, a graph showing the relationship between the physical properties of CO2 and temperature at 10 MPa was plotted, as follows: Figure 2 As shown, the error between the true and fitted values ​​of CO2 properties at 10 MPa was observed, and the fitting effect of the piecewise polynomial function model was verified and evaluated through the coefficient of determination and mean absolute percentage error index. Table 2 shows the fitting effect of CO2 properties at 10 MPa. It can be seen that the transcritical working fluid property-temperature function modeling method proposed in this invention can effectively solve the problems of characterizing abrupt changes near the critical point and controlling model complexity in transcritical working fluid property modeling. The property fitting values ​​have a high degree of agreement with the true values, with a coefficient of determination higher than 0.99 and a mean absolute percentage error lower than 1%, which can provide reliable property data support for engineering simulation and thermodynamic system design under transcritical conditions.

[0039] Table 2. Fitting effect of CO2 properties at 10 MPa

[0040]

[0041] This invention proposes an intelligent prediction method for the thermophysical properties of transcritical working fluids, applicable to characteristics of abrupt property changes, by integrating statistical methods with transcritical working fluid property analysis. This invention enables fully automated modeling of the transcritical working fluid property-temperature function, encompassing the entire process of "data acquisition - inflection point identification - order optimization - function generation." It effectively overcomes the subjectivity and limitations of traditional manual, experience-based segmentation, ensuring model accuracy while avoiding overfitting risks, thus improving the model's precision, stability, and engineering versatility.

Claims

1. A method for intelligent prediction of the thermophysical properties of transcritical working fluids with abrupt property changes, characterized in that, Includes the following steps: Step 1): By calling the standard physical property database, obtain the discrete physical property-temperature data of the target working fluid under the specified working pressure, where the physical property parameters include density, specific heat capacity, thermal conductivity and dynamic viscosity; Step 2): For the aforementioned discrete material property-temperature data, a piecewise linear regression change point detection algorithm based on dynamic monitoring of residual sum of squares is used to identify the inflection points of the working fluid's material property-temperature curve and adaptively divide the temperature range. The implementation method is as follows: The discrete material property-temperature data is traversed using a sliding window mechanism. Within each window, a linear regression model is used to fit the material property-temperature relationship of the working fluid. The degree of trend deviation of the current material property data segment is quantified by calculating the sum of squared residuals between the actual material property values ​​and the linearly fitted values. The calculation of the sum of squared residuals is shown below: In the formula, y i T represents the true physical properties of the working fluid. i Let be temperature, a and b be the coefficients in the linear regression model of working fluid property-temperature, i be the data point number, and p be the number of discrete samples of property-temperature within the sliding window; When the trend of the working fluid property data changes abruptly, the sum of squared residuals will increase significantly. During the process of traversing the property data in a dynamic sliding window, the abrupt change in the sum of squared residuals is detected in real time. When the abrupt change exceeds the threshold, the current position is marked as an inflection point. Based on the detected inflection point position, the temperature range is determined according to the minimum interval length constraint. Step 3): Based on the Bayesian Information Criterion (BIC), the polynomial order of each temperature range is optimized to balance the fitting accuracy and complexity. Continuity constraints are applied at the connection points of the temperature range segments to establish a globally continuous piecewise polynomial function with temperature as input and working fluid properties as output. Step 4): Utilize the globally continuous piecewise polynomial function to perform intelligent prediction of the thermophysical properties of transcritical working fluids with abrupt property changes.

2. The intelligent prediction method for the thermophysical properties of transcritical working fluids with abrupt property changes, as described in claim 1, is characterized in that, In step 3), within each temperature range, candidate polynomial orders are traversed, the polynomial model is fitted using the least squares method, and the corresponding BIC value is calculated. By comparing the BIC values ​​of the model under different polynomial orders, the order that minimizes BIC is selected as the optimal polynomial order. The calculation of BIC is as follows: In the formula, n is the number of discrete samples of physical properties and temperature within the temperature range, and m is the order of the polynomial.

3. The intelligent prediction method for the thermophysical properties of transcritical working fluids with abrupt property changes, as described in claim 1, is characterized in that... In step 3), continuity constraints are applied to the function values ​​and first derivatives at the point where the temperature range is segmented, ensuring a smooth transition of the piecewise polynomial function and ultimately constructing a piecewise polynomial function that balances accuracy and global continuity.

4. The intelligent prediction method for transcritical working fluid thermophysical properties applicable to abrupt changes in physical properties as described in claim 3, characterized in that, The k-th and (k+1)-th segments of the piecewise polynomial function of property-temperature must satisfy the following at the junctions: The function value is continuous at the piecewise connection point: f k (T k )=f k+1 (T k ) The first derivative is continuous at the piecewise connection point: In the formula, f k and f k+1 These are the k-th and (k+1)-th segments of the piecewise polynomial function of the property-temperature relationship, respectively. k Let T be the point where the function connects the k-th and (k+1)-th segments, and let T be the temperature.

5. The intelligent prediction method for transcritical working fluid thermophysical properties applicable to abrupt changes in physical properties, as described in claim 1, 3, or 4, is characterized in that... The obtained piecewise polynomial function is used to verify and evaluate the fitting effect through the coefficient of determination and the mean absolute percentage error index. When the coefficient of determination is higher than 0.99 and the mean absolute percentage error is lower than 2%, the fitting effect is considered to be good.

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