Transcritical working medium thermophysical property intelligent prediction method suitable for physical property mutation characteristics

Abstract

The invention discloses a transcritical working medium thermophysical property intelligent prediction method suitable for physical property mutation characteristics, and the method comprises the steps: obtaining the physical property-temperature data of a target working medium under a specified working pressure through a standard physical property database, and employing a piecewise linear regression change point detection algorithm based on residual sum of squares and dynamic monitoring; recognition of inflection points of a working medium physical property-temperature curve and self-adaptive division of temperature intervals are achieved, polynomial order optimization is carried out on each segmented interval based on a Bayesian information criterion to balance fitting precision and complexity, continuity constraints at segmented connection points are applied, and a globally continuous segmented polynomial function is constructed. According to the method, the full-process automatic transcritical working medium physical property-temperature function modeling of data acquisition-inflection point identification-order optimization-function generation can be realized, the subjectivity and limitation of artificial experience segmentation are effectively overcome, and the over-fitting risk is avoided while the model precision is ensured; and reliable support is provided for engineering simulation and thermodynamic system design under the transcritical working condition.

Description

Technical Field

[0001] The present invention belongs to the field of thermophysical property modeling and computational fluid dynamics, and specifically relates to an intelligent prediction method for the thermophysical properties of a transcritical working fluid suitable for property mutation characteristics. Background Art

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

[0003] Global high-order polynomial fitting uses a single high-order polynomial to create a unified function model for the entire temperature range. However, the working fluid properties exhibit strong nonlinear mutation characteristics near the critical point, resulting in the following limitations of this method: On the one hand, to capture the local mutation characteristics near the critical point, the polynomial order needs to be increased to enhance the local fitting ability, but the global coupling effect of high-order terms makes the model extremely sensitive to data noise and even produces oscillations in the stable region of physical properties far from the critical point; on the other hand, a single polynomial function cannot simultaneously meet the conflicting requirements of drastic changes near the critical point (which require high-order terms to describe) and slow changes in the stable region (which can be represented by low-order terms), making it difficult for the model to balance local accuracy and global stability.

[0004] Manual empirical piecewise polynomial fitting involves manually dividing the temperature intervals, fitting a low-order polynomial locally within each interval, and then achieving global coverage by splicing the polynomials from each segment. However, this method has the following drawbacks: First, the selection of segmentation points lacks a quantitative standard and is highly subjective, potentially leading to irrational temperature interval divisions due to human misjudgment. Second, no continuity constraints are imposed between temperature intervals, resulting in discontinuities in function values ​​or first-order derivatives at the splicing points, which in turn affects the accuracy of engineering simulations and thermal system calculations. Finally, the segmentation strategy must be redesigned for different working fluids or operating conditions, making it difficult to achieve adaptive function modeling of different working fluid properties, limiting the method's automated application capabilities.

[0005] In summary, the traditional transcritical working fluid property-temperature function modeling method has shortcomings in accuracy, stability and engineering versatility. There is an urgent need for an intelligent modeling method that can adaptively identify the characteristics of physical property mutations, automatically optimize model complexity and ensure global continuity, so as to improve the engineering applicability of transcritical working fluid property models. Summary of the Invention

[0006] The purpose of the present invention is to address the shortcomings in the current modeling of the physical property-temperature function of transcritical working fluids, and to propose an intelligent prediction method for the thermal properties of transcritical working fluids that is suitable for the physical property mutation characteristics, so as to realize the fully automated modeling of the physical property-temperature function of transcritical working fluids and improve the accuracy, stability and engineering versatility of the model.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is:

[0008] An intelligent prediction method for thermal properties of a transcritical working fluid suitable for sudden property changes, comprising the following steps:

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

[0010] Step 2): for the discrete data of working fluid physical property and 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 physical property and temperature curve, and adaptively divide the temperature interval;

[0011] Step 3): Based on the Bayesian Information Criterion (BIC), the polynomial order of each temperature interval is optimized to balance the fitting accuracy and complexity. Continuity constraints are imposed at the connection points of the temperature interval segments, thereby establishing 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 mean absolute percentage error indicators. Using this globally continuous piecewise polynomial function, intelligent prediction of the thermal properties of transcritical working fluids with property mutation characteristics can be performed.

[0013] In one embodiment, in step 2), the physical property-temperature discrete data are traversed based on a sliding window mechanism, and a linear regression model is used in each window to fit the working fluid physical property-temperature relationship. The trend deviation degree of the current physical property data segment is quantified by calculating the residual sum of squares between the actual physical property value and the linear fitting value, where the residual sum of squares is calculated as follows:

[0014]

[0015] Where y i is the actual value of the working fluid’s physical properties, T iis temperature, a and b are the coefficients in the working fluid physical property-temperature linear regression model, i is the data point number, and p is the number of physical property-temperature discrete samples in the sliding window. The larger the residual sum of squares, the greater the trend deviation of the current physical property data segment.

[0016] In one embodiment, in step 2), when the trend of the working fluid's physical property data changes suddenly (e.g., near a critical point), the residual sum of squares increases significantly. As the dynamic sliding window traverses the physical property data, the amount of this change in the residual sum of squares is detected in real time. When the change exceeds a threshold, the current position is marked as an inflection point. Based on the detected inflection point location, the temperature interval is determined according to the minimum interval length constraint. This partitioning method accurately captures the sudden change in the working fluid's physical properties and enables adaptive partitioning of temperature intervals.

[0017] In one embodiment, in step 3), within each temperature interval, candidate polynomial orders (e.g., orders 1 to m) are traversed, a polynomial model is fitted using the least squares method, and the corresponding BIC value is calculated. By comparing the BIC values ​​of the models under different polynomial orders, the order that minimizes the BIC is selected as the optimal polynomial order, where the BIC is calculated as follows:

[0018]

[0019] Where n is the number of discrete property-temperature samples in the temperature range, and m is the order of the polynomial.

[0020] In one embodiment, step 3) applies continuity constraints on the function value and first-order derivative at the temperature interval segment connection points to ensure a smooth transition of the piecewise polynomial function, ultimately constructing a piecewise polynomial function that balances accuracy and global continuity. The kth and k+1th segment functions of the property-temperature piecewise polynomial function must satisfy the following at the segment connection points:

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

[0022] The first-order derivatives are continuous at the piecewise connection points:

[0023] Where, f k and f k+1 are the kth and k+1th segment functions of the property-temperature piecewise polynomial function, respectively, T k is the segment connection point between the kth segment and the k+1th segment function, and T is the temperature.

[0024] In one embodiment, the obtained piecewise polynomial function is verified and evaluated for fitting effect by using the coefficient of determination and mean absolute percentage error indicators. Generally, if the coefficient of determination is higher than 0.99 and the mean absolute percentage error is lower than 2%, it is considered that the fitting effect is good.

[0025] Compared with the existing technology, the present invention can realize the full-process automation of "data collection-inflection point identification-order optimization-function generation" transcritical working fluid physical property-temperature function modeling, effectively overcoming the subjectivity and limitations of traditional manual experience segmentation, while ensuring model accuracy and avoiding overfitting risks, and providing reliable physical property data support for engineering simulation and thermal system design under transcritical working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0027] Figure 2 This is a diagram showing the relationship between the physical properties of CO2 and temperature at 10 MPa. DETAILED DESCRIPTION

[0028] The specific implementation of the present invention is described in detail below with reference to the accompanying drawings and examples.

[0029] In response to the problems of insufficient single polynomial fitting accuracy, strong subjectivity of piecewise polynomial fitting, and poor segmentation rationality caused by the drastic change of physical properties of transcritical working fluids with temperature near the critical point, the present invention proposes an intelligent prediction method for the thermal properties of transcritical working fluids suitable for physical property mutation characteristics. First, the physical property-temperature data of the target working fluid at a specified working pressure are obtained by calling the standard physical property database; secondly, a piecewise linear regression change point detection algorithm based on dynamic monitoring of the residual sum of squares is adopted to realize intelligent identification of inflection points of the working fluid physical property-temperature curve and adaptive division of temperature intervals; finally, the polynomial order of each segmented interval is optimized based on the Bayesian information criterion to balance fitting accuracy and complexity, and continuity constraints are imposed 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 by the coefficient of determination and mean absolute percentage error indicators.

[0030] The present invention is applicable to the prediction of thermal properties of various working fluids such as CO2, N2, and CH4 in transcritical processes. The present invention is described in detail below with reference to the accompanying drawings, taking the modeling of the physical 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 physical property database, the physical property-temperature discrete data of CO2 at 10 MPa were obtained. The physical properties included density, specific heat capacity at constant pressure, thermal conductivity and dynamic viscosity. The sampling interval was 0.1K, covering the temperature range of 250K to 650K, and a total of 4001 sets of discrete data points were obtained.

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

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

[0035]

[0036] Next, within each temperature interval, we traverse the candidate polynomial orders, fit the polynomial model using the least squares method, and calculate the corresponding BIC value. The order that minimizes the BIC is selected as the optimal polynomial order. Continuity constraints are imposed on the function values ​​and first-order derivatives at the connection points of the temperature interval segments 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 function of CO2 at 10 MPa (density, specific heat capacity at constant pressure, thermal conductivity, and dynamic viscosity) is shown below:

[0037]

[0038] Finally, draw a graph showing the relationship between the physical properties of CO2 and temperature at 10 MPa, as shown in the figure: Figure 2 As shown, the error between the true and fitted values ​​of CO2 properties at 10 MPa is observed, and the fitting effect of the piecewise polynomial function model is verified and evaluated using the coefficient of determination and mean absolute percentage error indicators. 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 mutations near the critical point and controlling model complexity in transcritical working fluid property modeling. The property fitting values ​​are highly consistent with the true values, with a coefficient of determination greater than 0.99 and a mean absolute percentage error less than 1%. This method can provide reliable property data support for engineering simulation and thermal system design under transcritical conditions.

[0039] Table 2 Fitting results of CO2 physical properties at 10 MPa

[0040]

[0041] By integrating statistical methods with transcritical fluid property analysis, this paper proposes an intelligent prediction method for the thermal properties of transcritical fluids, suitable for those with sudden changes in physical properties. This method automates the entire process of "data acquisition - inflection point identification - order optimization - function generation" to model transcritical fluid property-temperature functions. This method effectively overcomes the subjectivity and limitations of traditional manual empirical segmentation, ensuring model accuracy while avoiding the risk of overfitting, thereby improving the model's precision, stability, and engineering versatility.

Claims

1. An intelligent prediction method for thermal properties of transcritical working fluids suitable for sudden changes in physical properties, characterized by: The following steps are involved: Step 1): By calling the standard physical property database, the physical property-temperature discrete data of the target working fluid at a specified working pressure is obtained, where the physical property parameters include density, specific heat capacity, thermal conductivity and dynamic viscosity; Step 2): for the discrete data of working fluid physical property and 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 physical property and temperature curve, and adaptively divide the temperature interval; Step 3): Based on the Bayesian Information Criterion (BIC), the polynomial order of each temperature interval is optimized to balance the fitting accuracy and complexity. Continuity constraints are imposed at the connection points of the temperature interval segments to establish a globally continuous piecewise polynomial function with temperature as input and working fluid physical properties as output. Step 4): Utilize the globally continuous piecewise polynomial function to perform intelligent prediction of the thermal properties of a transcritical working fluid with a property mutation characteristic.

2. The intelligent prediction method for thermal properties of transcritical working fluids applicable to sudden changes in physical properties according to claim 1, characterized in that: In step 2), the physical property-temperature discrete data are traversed based on a sliding window mechanism, and a linear regression model is used to fit the working fluid physical property-temperature relationship within each window. The trend deviation degree of the current physical property data segment is quantified by calculating the residual sum of squares between the actual physical property value and the linear fitting value. The calculation of the residual sum of squares is as follows: Where y i is the actual value of the working fluid’s physical properties, T i is the temperature, a and b are the coefficients in the working fluid physical property-temperature linear regression model, i is the data point number, and p is the number of physical property-temperature discrete samples in the sliding window.

3. The intelligent prediction method for thermal properties of transcritical working fluids applicable to sudden changes in physical properties according to claim 1, characterized in that: In step 2), when the trend of the working fluid physical property data suddenly changes, the residual sum of squares will increase significantly. The sudden change in the residual sum of squares is detected in real time during the dynamic sliding window traversal of the physical property data. When the sudden 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.

4. The intelligent prediction method for thermal properties of transcritical working fluids applicable to sudden changes in physical properties according to claim 1, characterized in that: In step 3), within each temperature interval, candidate polynomial orders are traversed, a polynomial model is fitted using the least squares method, and the corresponding BIC value is calculated. By comparing the BIC values ​​of the models under different polynomial orders, the order that minimizes the BIC is selected as the optimal polynomial order, where the BIC is calculated as follows: Where n is the number of discrete property-temperature samples in the temperature range, and m is the order of the polynomial.

5. The intelligent prediction method for thermal properties of transcritical working fluids applicable to sudden changes in physical properties according to claim 1, characterized in that: In the step 3), continuity constraints are imposed on the function values ​​and first-order derivatives at the segmented connection points of the temperature interval to ensure a smooth transition of the piecewise polynomial function, and ultimately a piecewise polynomial function that takes into account both accuracy and global continuity is constructed.

6. The intelligent prediction method for thermal properties of transcritical working fluids applicable to sudden changes in physical properties according to claim 5, characterized in that: The kth and k+1th segment functions of the property-temperature piecewise polynomial function must satisfy the following conditions at the segment connection points: The function value is continuous at the segment connection point: f k (T k )=f k+1 (T k ) The first-order derivatives are continuous at the piecewise connection points: Where, f k and f k+1 are the kth and k+1th segment functions of the property-temperature piecewise polynomial function, respectively, T k is the segment connection point between the kth segment and the k+1th segment function, and T is the temperature.

7. The intelligent prediction method for thermal properties of transcritical working fluids applicable to sudden changes in physical properties according to claim 1, 5 or 6, characterized in that: The obtained piecewise polynomial function was verified and evaluated for fitting effect by using the coefficient of determination and mean absolute percentage error indicators. When the coefficient of determination was higher than 0.99 and the mean absolute percentage error was lower than 2%, the fitting effect was considered to be good.

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