A regularization method and system for multi-parameter collaborative inversion of buried pipe heat exchangers

Abstract

This invention discloses a regularization method and system for multi-parameter collaborative inversion of buried pipe heat exchangers, used for estimating design parameters of buried pipe heat exchangers based on in-situ thermal response tests. By combining a short-time temperature response function and a Tikhonov regularization inversion algorithm, reliable and stable results can be obtained while shortening the in-situ thermal response test time. On the one hand, the short-time heat transfer model allows early, highly sensitive data to be used for parameter inversion; on the other hand, regularization can suppress the influence of data noise, thereby obtaining a smooth and stable inversion solution.

Description

Technical Field

[0001] This invention belongs to the field of ground source heat pump technology application and energy saving, specifically involving a regularization method and system for multi-parameter collaborative inversion of buried pipe heat exchangers. Background Technology

[0002] In-situ thermal response testing of buried pipe heat exchangers is an important method for obtaining the apparent thermal properties of soil and rock. Deducing these properties from the thermal response test is a parameter estimation problem, falling under the category of inverse heat conduction problems. To achieve more reliable results, traditional model parameter estimation requires discarding the first 10 hours of thermal response test data and necessitates at least two days of in-situ testing. Furthermore, parameter estimation using thermal response testing suffers from low identifiability and ill-posed mathematical characteristics, involving issues of solution existence, uniqueness, and stability. These ill-posed problems, especially when testing time decreases or the number of estimated parameters increases, lead to unreliable parameter estimation results.

[0003] To improve testing efficiency and the reliability of parameter estimation, this invention innovatively combines a short-timeline heat source model with Tikhonov regularization. This solves the ill-posedness problem of multi-parameter inversion and makes full use of early, highly sensitive thermal response test data, thereby improving the efficiency of on-site thermal response testing. Summary of the Invention

[0004] In order to solve the technical problems existing in the background art, the present invention aims to provide a regularization method and system for multi-parameter collaborative inversion of buried pipe heat exchangers, which can be used to more accurately estimate multiple parameters such as the thermal properties of soil and backfill materials during thermal response testing.

[0005] To solve the technical problem, the technical solution of the present invention is as follows:

[0006] A regularization method for multi-parameter collaborative inversion of buried pipe heat exchangers, the method comprising the following steps:

[0007] S1: Obtain the pre-set thermal response test circulating fluid temperature data, experimental object characteristic data, and circulating fluid temperature change curve over time;

[0008] S2: Based on the circulating fluid temperature data and the experimental object characteristic data, perform multi-parameter collaborative inversion of the buried pipe heat exchanger to obtain the optimal parameter estimation results;

[0009] S3: Using the optimal parameter estimation results, obtain the relationship curve between circulating fluid temperature and time;

[0010] S4: By comparing the relationship curve with the curve of the circulating fluid temperature changing with time, the multi-parameter collaborative inversion of the buried pipe heat exchanger is realized.

[0011] Furthermore, the characteristic data of the experimental objects include: the initial temperature T0 of the soil and backfill material, and the borehole outer diameter r. b Drilling length L, U-shaped pipe outer diameter r o U-shaped tube inner diameter r i Half the distance between the centers of the U-shaped tube (D), and the thermal conductivity k of the U-shaped tube wall. p Thermal conductivity of soil and rock (k) s Thermal conductivity k of backfill material b Volumetric heat capacity C of the circulating fluid f Volumetric flow rate V of circulating fluid f Average heating rate q of electric heater, volumetric heat capacity of soil and rock C s and the volumetric heat capacity C of the backfill material b .

[0012] Furthermore, step S2 includes:

[0013] S21: Establish an infinitely long linear heat source model for the composite medium circulating fluid temperature;

[0014] S22: Assign values ​​to the model parameters in the experimental object feature data to obtain the assigned model parameters;

[0015] S23: Input the assigned model parameters and the circulating fluid temperature data into the composite medium infinite long line heat source model of the circulating fluid temperature to obtain the assigned composite medium infinite long line heat source model of the circulating fluid.

[0016] S24: Using the system's preset MATLAB calculation unit, perform nonlinear fitting on the composite medium infinite-length linear heat source model of the assigned circulating fluid to obtain the optimal parameter estimation results.

[0017] Furthermore, step S24 specifically includes:

[0018] S241: Determine the objective function for nonlinear fitting of the composite medium infinite linear heat source model of the assigned circulating fluid;

[0019] S242: Determine the range of the regularization parameter in the objective function determined above;

[0020] S243: Perform nonlinear fitting on the objective function corresponding to each regularization parameter within the determined regularization parameter range, solve for the parameter estimation result with the minimum residual, and plot the L curve to determine the optimal regularization parameter and the optimal parameter estimation result;

[0021] Furthermore, the range of the regularization parameter in the objective function determined above is given.

[0022] Furthermore, the objective function is minimized after the given range of regularization parameters to obtain the parameter estimation result corresponding to the minimum residual, which is the optimal parameter estimation result.

[0023] Furthermore, the horizontal axis of the L-curve represents the residual norm of the solution, and its vertical axis represents the norm of the solution.

[0024] Furthermore, the inflection point of the L-curve is the reference range for selecting the optimal regularization parameter.

[0025] Furthermore, the objective function is enhanced with Tikhonov regularization, and the objective function is a modified least squares norm, which is the sum of the least squares norm term and the regularization term.

[0026] A regularization system for multi-parameter collaborative inversion of buried pipe heat exchangers, the system comprising:

[0027] One or more processors;

[0028] Memory, used to store one or more programs;

[0029] When the one or more programs are executed by the one or more processors, the one or more processors perform a regularization method for multi-parameter collaborative inversion of buried pipe heat exchangers as described above.

[0030] It can be understood that combining the short-time temperature response function and the Tikhonov regularization inversion algorithm can shorten the on-site thermal response test time while obtaining reliable and stable results. On the one hand, the composite medium infinite-length heat source model of circulating fluid temperature enables early high-sensitivity data to be used for parameter inversion. On the other hand, regularization can suppress the influence of data noise, thereby obtaining a smooth and stable inversion solution.

[0031] Compared with the prior art, the advantages of the present invention are as follows:

[0032] (1) This invention uses a composite medium infinite long-line heat source model that combines short-time temperature response function, i.e. circulating fluid temperature, and Tikhonov regularization method to solve the ill-posedness of the inversion problem, and obtains reliable and stable results while shortening the on-site thermal response test time;

[0033] (2) This invention utilizes a short-time model to enable short-time, highly sensitive data to be used for parameter inversion, and the regularization method can suppress the influence of data noise, thereby obtaining a smooth and stable approximate solution. Attached Figure Description

[0034] Figure 1 This is the main program flowchart of the regularization method for multi-parameter collaborative inversion of buried pipe heat exchangers of the present invention;

[0035] Figure 2 This is a flowchart for calculating the temperature of circulating fluid.

[0036] Figure 3 This is a flowchart of the parameter estimation iterative calculation;

[0037] Figure 4 The results of estimating the five parameters using zero-order regularization are shown.

[0038] Figure 5 The calculation graph of the L-curve. Detailed Implementation

[0039] The specific implementation of the present invention is described below with reference to embodiments:

[0040] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0041] Furthermore, the terms such as "upper," "lower," "left," "right," "middle," and "one" used in this specification are merely for clarity of description and are not intended to limit the scope of the invention. Any changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0042] Example 1

[0043] A regularization method for multi-parameter collaborative inversion of buried pipe heat exchangers, the method comprising the following steps:

[0044] S1: Obtain the pre-set thermal response test circulating fluid temperature data, experimental object characteristic data, and circulating fluid temperature change curve over time;

[0045] S2: Based on the circulating fluid temperature data and the experimental object characteristic data, perform multi-parameter collaborative inversion of the buried pipe heat exchanger to obtain the optimal parameter estimation results;

[0046] S3: Using the optimal parameter estimation results, obtain the relationship curve between circulating fluid temperature and time;

[0047] S4: By comparing the relationship curve with the curve of the circulating fluid temperature changing with time, the multi-parameter collaborative inversion of the buried pipe heat exchanger is realized.

[0048] like Figure 4As shown, the circle represents the curve of the circulating fluid temperature changing with time in the thermal response test, the solid line represents the curve of the circulating fluid temperature versus time corresponding to the optimal parameter estimation result, the text on the right represents the optimal parameter estimation result, and the quadrilateral represents the residual between the calculated value and the reference value of the circulating fluid temperature.

[0049] Furthermore, the characteristic data of the experimental objects include: the initial temperature T0 of the soil and backfill material, and the borehole outer diameter r. b Drilling length L, U-shaped pipe outer diameter r o U-shaped tube inner diameter r i Half the distance between the centers of the U-shaped tube (D), and the thermal conductivity k of the U-shaped tube wall. p Thermal conductivity of soil and rock (k) s Thermal conductivity k of backfill material b Volumetric heat capacity C of the circulating fluid f Volumetric flow rate V of circulating fluid f Average heating rate q of electric heater, volumetric heat capacity of soil and rock C s and the volumetric heat capacity C of the backfill material b .

[0050] Furthermore, step S2 includes:

[0051] S21: Establish an infinitely long linear heat source model for the composite medium circulating fluid temperature;

[0052] S22: Assign values ​​to the model parameters in the experimental object feature data to obtain the assigned model parameters;

[0053] S23: Input the assigned model parameters and the circulating fluid temperature data into the composite medium infinite long line heat source model of the circulating fluid temperature to obtain the assigned composite medium infinite long line heat source model of the circulating fluid.

[0054] S24: Using the system's preset MATLAB calculation unit, perform nonlinear fitting on the composite medium infinite-length linear heat source model of the assigned circulating fluid to obtain the optimal parameter estimation results.

[0055] Furthermore, step S24 specifically includes:

[0056] S241: Determine the objective function for nonlinear fitting of the composite medium infinite linear heat source model of the assigned circulating fluid;

[0057] S242: Determine the range of the regularization parameter in the objective function determined above;

[0058] S243: Perform nonlinear fitting on the objective function corresponding to each regularization parameter within the determined regularization parameter range, solve for the parameter estimation result with the minimum residual, and plot the L-curve, as shown below. Figure 5 As shown, the optimal regularization parameter and the optimal parameter estimation result are determined;

[0059] Furthermore, the range of the regularization parameter in the objective function determined above is given.

[0060] Furthermore, the objective function is minimized after the given range of regularization parameters to obtain the parameter estimation result corresponding to the minimum residual, which is the optimal parameter estimation result.

[0061] Furthermore, the horizontal axis of the L-curve represents the residual norm of the solution, and its vertical axis represents the norm of the solution.

[0062] Furthermore, the inflection point of the L-curve is the optimal regularization parameter.

[0063] Furthermore, the objective function is processed using the Tikhonov regularization algorithm, and the objective function is the modified least squares norm, that is, the sum of the least squares norm term and the regularization term.

[0064] A regularization system for multi-parameter collaborative inversion of buried pipe heat exchangers, the system comprising:

[0065] One or more processors;

[0066] Memory, used to store one or more programs;

[0067] When the one or more programs are executed by the one or more processors, the one or more processors perform a regularization method for multi-parameter collaborative inversion of buried pipe heat exchangers as described above.

[0068] It can be understood that combining the short-time temperature response function and the Tikhonov regularization inversion algorithm can shorten the on-site thermal response test time while obtaining reliable and stable results. On the one hand, the composite medium infinite-length heat source model of circulating fluid temperature enables early high-sensitivity data to be used for parameter inversion. On the other hand, regularization can suppress the influence of data noise, thereby obtaining a smooth and stable inversion solution.

[0069] Example 2:

[0070] A regularization algorithm for multi-parameter collaborative inversion of buried pipe heat exchangers.

[0071] like Figure 1 As shown, the main program runs:

[0072] Step 1: Collect thermal response test data and record the characteristics of the experimental object;

[0073] Step 2: Determine the types and number of parameters that need to be inverted, i.e., the parameters to be estimated;

[0074] Step 3: Input model conditions and geotechnical thermal property data as initial parameters for the algorithm;

[0075] Step 4: Initialize the heat transfer model of the buried pipe heat exchanger and the relevant parameters of the soil, including the parameters mentioned in the above steps;

[0076] Step 5: Provide initial values ​​for the parameters to be estimated;

[0077] Step 6: Call the fluid temperature subroutine to calculate the circulating fluid temperature at that point;

[0078] Step 7: Call the parameter inversion iterative subroutine to optimize the objective function;

[0079] Step 8: Calculate the fitting residuals and determine if the fitting residuals are minimized. If they are, proceed to step 9; otherwise, return to step 6 and enter the next sub-loop.

[0080] Step 9: Find the optimal regularization parameter and output the parameter estimation results.

[0081] like Figure 3 As shown, the circulating fluid temperature calculation subroutine is called and executed:

[0082] Step 1: Input the parameters for the buried pipe heat exchanger and the soil description. The parameters describing the buried pipe heat exchanger include the borehole radius, borehole height, thermal conductivity and thermal diffusivity of the backfill material, thermal conductivity of the U-tubes, half the U-tube spacing, inner diameter, outer diameter, and type. The parameters describing the soil include the soil's thermal conductivity, thermal diffusivity, and initial temperature.

[0083] Step 2: Set the initial values ​​of the parameters, specify the upper and lower limits, and initialize them;

[0084] Step 3: Initialize the loop pointer time t = 1, and the step size of t is 1;

[0085] Step 4: Determine if t ≤ ts. If yes, proceed to step E; otherwise, proceed to step 8. The value of ts represents the number of sampling times in the experiment, which is determined in step 1.

[0086] Step 5: Input the heat transfer model G function. The composite medium infinite linear heat source model used in this paper can effectively utilize short-time data from thermal response tests to achieve better fitting results. It is currently the most theoretically mature model for fully utilizing thermal response test data. Specifically, it can be obtained through the following formula:

[0087]

[0088]

[0089]

[0090]

[0091] Where G represents the unsteady-state heat transfer process from the outer wall of the U-tube to the semi-infinite medium, and its physical meaning is the unsteady-state thermal resistance; k b Indicates the thermal conductivity of the backfill material; a b The thermal diffusivity of the backfill material is represented by r. A =D-r o and r B =D+r o Let A and B be the x-coordinates of points A and B (with the borehole center as the origin); k and a are dimensionless parameters, k = k s / k b ,a=(a b / a s ) 1 / 2 J n and Y n Let J represent Bessel functions of the first and second kind, respectively, of order n; n 'and Y n 'represents J respectively n and Y n The first derivative; r b Indicates the borehole radius; T f T0 is the temperature of the circulating fluid; T0 is the initial temperature of the soil; q l The heat flux density per unit length of the heat exchanger is expressed as (W / m); N represents the number of U-tubes in the borehole (in this invention, it is a single U-tube, N = 2); R p Indicates the thermal resistance of the tube; k p It is the thermal conductivity of the U-tube; r o and r i These are the inner and outer diameters of the U-shaped tube, respectively; α represents the convective heat transfer coefficient inside the tube.

[0092] Step 6: Calculate the circulating fluid temperature at this point using the heat transfer model, obtain the distribution of the circulating fluid temperature field, and record the calculated circulating fluid temperature at this time point.

[0093] Step 7: Change the time, enter the next sub-loop, calculate the fluid temperature at the next sampling time point, and then go back to step 4;

[0094] Step 8: Transfer the temperature field data back to the main program.

[0095] like Figure 2 As shown, the parameter estimation iterative subroutine is called and executed:

[0096] Step 1: Determine the objective function. The objective function of the regularization method can be considered as the modified least squares norm, which is the sum of the least squares norm term and the regularization term. This paper adopts the Tikhonov regularization term, whose commonly used regularization method is zero-order regularization, which has the following form:

[0097]

[0098] Among them, T f (β) represents the fluid temperature calculated by the model for m observation times, and β represents a vector of estimated parameters, for example, β T =[k s ,k b ,a s ,a b ]; Y = [Y1, Y2, ..., Y m ] T α represents the observation vector of the average temperature of the circulating fluid over m observation periods; α is the regularization parameter; L is the regularization matrix used to control the smoothness of the solution.

[0099] Step 2: Input the range of α values. When α = 0, it means that the regularization term is zero. At this time, it is the objective function of ordinary least squares.

[0100] Step 3: Initialize the loop pointer i = 1, and set the step size of i to 1;

[0101] Step 4: Determine if i ≤ M. If yes, proceed to step e; otherwise, proceed to step g. M is the ordinal number of the regularization parameter α.

[0102] Step 5: Use the nonlinear fitting command built into MATLAB to minimize the objective function, providing the initial values ​​and upper and lower limits of the fitted parameters.

[0103] Step 6: Calculate the fitting residuals to minimize the sum of squared residuals. The iteration ends when a local minimum is obtained, i.e., the sum of squared residuals is minimized.

[0104] Step 7: Plot the L-curve using the inversion iteration results (the horizontal axis is the residual norm of the solution, and the vertical axis is the norm of the solution). The inflection point is the optimal regularization parameter. At this point, the norm of the solution is not large, and the residual norm is also small. The two are well balanced. Therefore, the parameter estimation result at this position is the optimal inversion result.

[0105] Figure 4The results of estimating the five parameters using zero-order regularization are shown. As can be seen from the figure, the calculated values ​​from the model and the measured values ​​from the sandbox data agree very well, with the absolute value of the residuals less than 0.2 K. The estimated soil thermal conductivity ks and backfill material thermal conductivity kb are consistent with the independent measurements from the sandbox experiment (Table 1), with relative errors of 7.1% and 1.4%, respectively. The relative errors for the estimated soil thermal diffusivity as and backfill material thermal diffusivity ab are 68% and 27%, respectively.

[0106] Table 1. Experimental parameters for thermal response testing in the sandbox.

[0107]

[0108] a The heat capacity data for wet sand and backfill material are estimates (not independently measured), which may lead to uncertainty in the estimate of the thermal diffusivity.

[0109] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

[0110] Many other changes and modifications can be made without departing from the concept and scope of this invention. It should be understood that this invention is not limited to the specific embodiments, and the scope of this invention is defined by the appended claims.

Claims

1. A regularization method for multi-parameter collaborative inversion of buried pipe heat exchangers, characterized in that, The method includes the following steps: S1: Obtain the pre-set thermal response test circulating fluid temperature data, experimental object characteristic data, and circulating fluid temperature change curve over time; S2: Based on the circulating fluid temperature data and the experimental object characteristic data, perform multi-parameter collaborative inversion of the buried pipe heat exchanger to obtain the optimal parameter estimation results; S3: Using the optimal parameter estimation results, obtain the relationship curve between circulating fluid temperature and time; S4: By comparing the relationship curve with the curve of circulating fluid temperature changing with time, multi-parameter collaborative inversion of the buried pipe heat exchanger is achieved; Step S2 includes: S21: Establish an infinitely long linear heat source model for the composite medium circulating fluid temperature; S22: Assign values ​​to the model parameters in the experimental object feature data to obtain the assigned model parameters; S23: Input the assigned model parameters and the circulating fluid temperature data into the composite medium infinite long line heat source model of the circulating fluid temperature to obtain the assigned composite medium infinite long line heat source model of the circulating fluid. S24: Using the system's preset MATLAB calculation unit, perform nonlinear fitting on the composite medium infinite linear heat source model of the assigned circulating fluid to obtain the optimal parameter estimation results. Specifically, step S24 includes: S241: Determine the objective function for nonlinear fitting of the composite medium infinite linear heat source model of the assigned circulating fluid; S242: Determine the range of the regularization parameter in the objective function determined above; S243: Perform nonlinear fitting on the objective function corresponding to each regularization parameter within the determined regularization parameter range, solve for the parameter estimation result with the minimum residual, and plot the L curve to determine the optimal regularization parameter and the optimal parameter estimation result.

2. The regularization method for multi-parameter collaborative inversion of a buried pipe heat exchanger according to claim 1, characterized in that, The characteristic data of the experimental objects include: the initial temperature T0 of the soil and backfill material, and the borehole outer diameter r. b Drilling length L, U-shaped pipe outer diameter r o U-shaped tube inner diameter r i Half the distance between the centers of the U-shaped tube (D), and the thermal conductivity k of the U-shaped tube wall. p Thermal conductivity of soil and rock (k) s Thermal conductivity k of backfill material b Volumetric heat capacity C of the circulating fluid f Volumetric flow rate V of circulating fluid f Average heating rate q of electric heater, volumetric heat capacity of soil and rock C s and the volumetric heat capacity C of the backfill material b .

3. The regularization method for multi-parameter collaborative inversion of a buried pipe heat exchanger according to claim 1, characterized in that, The range of the regularization parameter in the objective function determined above is given.

4. The regularization method for multi-parameter collaborative inversion of a buried pipe heat exchanger according to claim 3, characterized in that, Minimize the objective function within the given range of regularization parameters to obtain the parameter estimation result corresponding to the minimum residual, i.e., the optimal parameter estimation result.

5. The regularization method for multi-parameter collaborative inversion of a buried pipe heat exchanger according to claim 1, characterized in that, The horizontal axis of the L-curve represents the residual norm of the solution, and the vertical axis represents the norm of the solution.

6. The regularization method for multi-parameter collaborative inversion of a buried pipe heat exchanger according to claim 5, characterized in that, The inflection point of the L-curve is the reference range for selecting the optimal regularization parameter.

7. The regularization method for multi-parameter collaborative inversion of a buried pipe heat exchanger according to claim 1, characterized in that, The objective function is modified by adding Tikhonov regularization. The objective function is the modified least squares norm, which is the sum of the least squares norm term and the regularization term.

8. A regularization system for multi-parameter collaborative inversion of buried pipe heat exchangers, characterized in that, The system includes: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors perform a regularization method for multi-parameter collaborative inversion of a buried pipe heat exchanger as described in any one of claims 1-7.

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