In-pipe fluid temperature measurement method, system, electronic device and storage medium

Through the Kalman filter principle and weight coefficient correction, the difficulty of measuring the internal temperature of the pipeline in the existing technology is solved, real-time and continuous internal temperature measurement of the pipeline is achieved, and the measurement range is expanded.

CN116295936BActive Publication Date: 2025-10-24DONGFANG ELECTRIC MACHINERY +1

Patent Information

Application Number
CN202310213722.4
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-03-08
Publication Date
2025-10-24
Estimated Expiration
2043-03-08

AI Technical Summary

Technical Problem

Existing temperature measurement equipment cannot effectively measure the temperature of the fluid inside the pipeline. There are problems such as the equipment disrupting the internal working conditions, the internal temperature of the object being too high to set the equipment, the limited measurement range and the inability to measure continuously, which limit the scope of use of internal temperature measurement.

Method used

The Kalman filter principle is adopted to obtain the internal temperature of the pipeline in real time based on the measured outer wall temperature of the pipeline. By determining the fixed parameters and process parameters, the weight coefficient and covariance are calculated using the Kalman filter to correct the internal temperature model.

Benefits of technology

It realizes real-time and continuous measurement of the internal temperature of the pipeline, expands the measurement range, avoids disturbance of the internal working conditions and measurement difficulties in high temperature environments.

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Abstract

The application discloses a kind of in-pipe fluid temperature measurement method, system, electronic equipment and storage medium, it is related to in-pipe temperature measurement technical field, the method comprises: determining the fixed parameter of target to be measured, the flow rate of fluid, noise variance and observation variance;Fixed parameter includes pipe wall thickness, pipe wall material thermal conductivity, fluid convection heat transfer coefficient and air convection heat transfer coefficient;According to the optimal in-pipe temperature of last time and the flow rate of fluid, determine the predicted temperature of current time;According to the optimal covariance of last time and noise variance, determine the covariance of current time;The optimal covariance of last time is determined according to the weight coefficient of last time, covariance, fixed parameter and observation variance;According to the weight coefficient of current time, determine the covariance of current time, fixed parameter and observation variance;According to the predicted temperature of current time, weight coefficient, outer wall temperature, air temperature, fixed parameter and observation variance, determine the optimal in-pipe temperature of current time.The application expands the use range of in-pipe temperature measurement.
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Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of in-pipe temperature measurement, and in particular to an in-pipe fluid temperature measurement method, system, electronic device and storage medium. BACKGROUND

[0002] Most of the temperature measurement devices on the market directly measure the temperature of the surface of an object. If the temperature of the working medium inside the object (such as the temperature of the water supply in the water supply pipe) is to be measured, such devices cannot achieve this. At present, the method for measuring the temperature of the working medium inside the object is to directly measure the temperature by inserting a temperature measurement device into the object, such as a thermometer on a heating pipe. This has the following effects: first, the insertion of the thermometer increases the local resistance to the flow of fluid and disrupts the original working condition, which is very disadvantageous for conditions that require stable internal working conditions; second, the temperature measurement can only be carried out at fixed points, and if multiple points or continuous temperature values are required, additional instruments must be added, thereby increasing the cost; finally, it is difficult to measure the internal working medium of an already established working condition, and adding a measurement device would require the original structure to be destroyed, which is obviously unrealistic. At the same time, in the case of excessively high internal working medium temperature (such as the high temperature of the fuel inside a rocket injector), it is difficult for the measurement device to be inserted, thereby making measurement difficult. Therefore, the existing methods for measuring internal temperature have the problems of device disturbance to the internal working condition, inability to set up devices in objects with excessively high internal temperature, limited measurement range, and inability to continuously measure, thereby limiting the use range of internal temperature measurement. SUMMARY

[0003] The purpose of the present application is to provide an in-pipe fluid temperature measurement method, system, electronic device and storage medium, which expands the use range of internal temperature measurement.

[0004] To achieve the above-mentioned purpose, the present application provides the following solutions:

[0005] An in-pipe fluid temperature measurement method, the method comprising:

[0006] determining fixed parameters and process parameters of a target to be measured; the target to be measured being a pipe with fluid inside; the fixed parameters including the flow rate of the fluid, the pipe wall thickness of the pipe, the pipe wall material thermal conductivity of the pipe, the convective heat transfer coefficient of the fluid and the air convective heat transfer coefficient; the process parameters including noise variance and observation variance;

[0007] obtaining the outer wall temperature of the pipe and the air temperature at the current time;

[0008] determining the predicted temperature at the current time according to the optimal in-pipe temperature at the previous time and the flow rate of the fluid;

[0009] determine the covariance of the current moment according to the optimal covariance of the last moment and the noise variance; the optimal covariance of the last moment is determined according to the weight coefficient of the last moment, the covariance of the last moment, the fixed parameter and the observation variance; wherein the optimal temperature in the pipe of the initial moment, the weight coefficient and the covariance are obtained by initializing the parameters of the target to be measured;

[0010] determine the weight coefficient of the current moment according to the covariance of the current moment, the fixed parameter and the observation variance;

[0011] determine the optimal temperature in the pipe of the current moment according to the predicted temperature of the current moment, the weight coefficient of the current moment, the outer wall temperature of the pipeline of the current moment, the air temperature of the current moment, the fixed parameter and the observation variance.

[0012] Optionally, the determination process of the fixed parameter specifically includes:

[0013] obtain the inner diameter of the pipeline, the thermal conductivity of the fluid, the flow rate of the fluid, the kinematic viscosity of the fluid, the air thermal conductivity and the length of the pipeline;

[0014] calculate the convective heat transfer coefficient of the fluid according to the Prandtl coefficient, the inner diameter of the pipeline, the thermal conductivity of the fluid, the flow rate of the fluid and the kinematic viscosity of the fluid;

[0015] calculate the air convective heat transfer coefficient according to the Grashof criterion number, the Prandtl coefficient, the air thermal conductivity, the inner diameter of the pipeline and the length of the pipeline.

[0016] Optionally, calculating the air convective heat transfer coefficient according to the Grashof criterion number, the Prandtl coefficient, the air thermal conductivity, the inner diameter of the pipeline and the length of the pipeline specifically includes:

[0017] determine whether the pipeline is a horizontal pipeline or a vertical pipeline;

[0018] when the pipeline is a horizontal pipeline, determine the air convective heat transfer coefficient according to the Grashof criterion number, the Prandtl coefficient, the air thermal conductivity and the inner diameter of the pipeline;

[0019] when the pipeline is a vertical pipeline, determine the air convective heat transfer coefficient according to the Grashof criterion number, the Prandtl coefficient, the air thermal conductivity and the length of the pipeline.

[0020] A pipe fluid temperature measurement system, the system comprises:

[0021] A parameter determination module is configured to determine fixed parameters and process parameters of a target to be measured; the target to be measured is a pipe with a fluid inside; the fixed parameters include: the flow rate of the fluid, the wall thickness of the pipe, the thermal conductivity of the pipe wall material, the convective heat transfer coefficient of the fluid, and the convective heat transfer coefficient of air; the process parameters include: noise variance and observation variance;

[0022] The temperature acquisition module is used to obtain the outer wall temperature and air temperature of the pipeline at the current moment;

[0023] A predicted temperature determination module, configured to determine a predicted temperature at a current moment based on the optimal temperature in the tube at a previous moment and the flow rate of the fluid;

[0024] a covariance determination module, configured to determine the covariance at the current moment based on the optimal covariance at the previous moment and the noise variance; the optimal covariance at the previous moment is determined based on the weight coefficient at the previous moment, the covariance at the previous moment, the fixed parameter, and the observation variance; wherein the optimal in-tube temperature, weight coefficient, and covariance at the initial moment are obtained by initializing the parameters of the target to be measured;

[0025] A weight coefficient determination module, configured to determine the weight coefficient at the current moment based on the covariance at the current moment, the fixed parameter, and the observed variance;

[0026] The optimal in-pipe temperature determination module is used to determine the optimal in-pipe temperature at the current moment based on the predicted temperature at the current moment, the weight coefficient at the current moment, the outer wall temperature of the pipeline at the current moment, the air temperature at the current moment, the fixed parameters and the observation variance.

[0027] An electronic device, comprising:

[0028] one or more processors;

[0029] a storage device having one or more programs stored thereon;

[0030] When the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the above-described method.

[0031] A storage medium stores a computer program thereon, wherein the computer program implements the method described above when executed by a processor.

[0032] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0033] The application discloses a pipe fluid temperature measurement method, system, electronic equipment and storage medium, based on the measured temperature of the outer wall of the pipeline, the principle of Kalman filtering is used to obtain the temperature inside the pipeline in real time, solves the problems of the existing internal temperature measurement method, such as equipment disturbing internal working condition, object internal temperature being too high to set equipment, limited measurement range and unable to continuously measure, and expands the use range of the internal temperature measurement of the pipeline. BRIEF DESCRIPTION OF DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description only represent some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0035] Figure 1 A pipe fluid temperature measurement method flowchart is provided for the embodiment 1 of the present application.

[0036] Figure 2 A pipe fluid temperature measurement flowchart is provided for when the current time is k time (k>1).

[0037] Figure 3 A pipe fluid temperature measurement system structure diagram is provided for the embodiment 2 of the present application. DETAILED DESCRIPTION

[0038] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments only represent some embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without any creative effort belong to the protection scope of the present application.

[0039] The present application aims to provide a pipe fluid temperature measurement method, system, electronic equipment and storage medium, and aims to expand the use range of the internal temperature measurement of the pipeline.

[0040] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail in combination with the drawings and specific embodiments.

[0041] Embodiment 1

[0042] Figure 1 A pipe fluid temperature measurement method flowchart is provided for the embodiment 1 of the present application. Figure 2 A pipe fluid temperature measurement flowchart is provided for when the current time is k time (k>1). For example, Figures 1-2The in-pipe fluid temperature measuring method in the embodiment includes the following steps.

[0043] Step 101: determining the constant parameters and process parameters of the target to be measured; the target to be measured is a pipe with fluid inside; the constant parameters include the flow rate of the fluid, the pipe wall thickness of the pipe, the thermal conductivity coefficient of the pipe wall material of the pipe, the convective heat transfer coefficient of the fluid, and the air convective heat transfer coefficient; and the process parameters include the noise variance and the observation variance.

[0044] Step 102: obtaining the outer wall temperature of the pipe and the air temperature at the current time.

[0045] Specifically, when the current time is the kth time (k>1), the outer wall temperature at the kth time y k is obtained by setting a temperature measuring instrument on the outer wall of the pipe.

[0046] The outer wall temperature at the kth time measured by the temperature measuring instrument and the actual temperature x k of the inside of the pipe at the kth time satisfy the following relationship: y k =Cx k +b (because the outer wall temperature at the kth time measured by the temperature measuring instrument and the actual temperature x k of the inside of the pipe at the kth time satisfy the relationship, the temperature of the inside of the pipe can be determined by calculating the outer wall temperature according to the following formula). Wherein b is the observation noise of the temperature measuring instrument for collecting the outer wall temperature. C is a first intermediate parameter, r is a second intermediate parameter, h' = h1 when the pipe is a horizontal pipe, h' = h2 when the pipe is a vertical pipe, λ3 is the thermal conductivity coefficient of the pipe wall material of the pipe, h is the convective heat transfer coefficient of the fluid, and δ is the pipe wall thickness of the pipe.

[0047] Specifically, when the pipe is a horizontal pipe, the calculation formula of the air convective heat transfer coefficient is: h1 = 0.125 (Gr·Pr) 1 / 3 λ2 / l; when the pipe is a vertical pipe, the calculation formula of the air convective heat transfer coefficient is: h2 = 0.1 (Gr·Pr) 1 / 3 λ2 / H.

[0048] Wherein Gr is the Grashof criterion number, Pr is the Prandtl coefficient, λ2 is the air thermal conductivity coefficient, l is the inner diameter of the pipe, and H is the length of the pipe.

[0049] Step 103: determining the predicted temperature at the current time according to the optimal in-pipe temperature at the last time and the flow rate of the fluid.

[0050] Specifically, when the current time is the kth time (k>1), the calculation formula of the predicted temperature at the kth time is:

[0051] wherein, is the predicted temperature at the kth moment, A is a 1 matrix, is the optimal temperature in the pipe at the (k-1)th moment, B is a zero matrix, and u is the flow rate of the fluid. The optimal temperature in the pipe at the initial moment is initialized to 0.

[0052] Step 104: determining the covariance at the current moment according to the optimal covariance at the previous moment and the noise variance; the optimal covariance at the previous moment is determined according to the weight coefficient at the previous moment, the covariance at the previous moment, the constant parameter and the observation variance; wherein the optimal temperature in the pipe at the initial moment, the weight coefficient and the covariance are obtained by initializing the parameters of the target to be measured.

[0053] Specifically, when the current moment is the kth moment (k>1), the covariance at the kth moment is calculated according to the following formula:

[0054] wherein, is the covariance at the kth moment, P k-1 is the optimal covariance at the (k-1)th moment, and Q is the noise variance, i.e. the variance generated by the noise.

[0055]

[0056] K k-1 is the weight coefficient at the (k-1)th moment, is the covariance at the (k-1)th moment. Wherein the optimal covariance at the initial moment is initialized to 1.

[0057] Step 105: determining the weight coefficient at the current moment according to the covariance at the current moment, the constant parameter and the observation variance.

[0058] Specifically, when the current moment is the kth moment (k>1), the weight coefficient K k at the kth moment is calculated according to the following formula:

[0059] wherein, K k is the weight coefficient at the kth moment, and R is the observation variance, which is determined according to the accuracy of the temperature measuring instrument for collecting the outer wall temperature.

[0060] Step 106: determining the optimal temperature in the pipe at the current moment according to the predicted temperature at the current moment, the weight coefficient at the current moment, the outer wall temperature of the pipeline at the current moment, the air temperature at the current moment, the constant parameter and the observation variance.

[0061] Specifically, when the current moment is the kth moment (k>1), the optimal temperature in the pipe at the kth moment The calculation formula is:

[0062] in, is the optimal temperature inside the tube at the kth moment, D is the third intermediate parameter, z k is the air temperature at the kth moment.

[0063] As an optional implementation, the process of determining the parameters specifically includes:

[0064] Obtain the inner diameter of the pipe, the thermal conductivity of the fluid, the flow rate of the fluid, the kinematic viscosity of the fluid, the thermal conductivity of the air, and the length of the pipe.

[0065] The convective heat transfer coefficient of the fluid is calculated based on the Prandtl coefficient, the inner diameter of the pipe, the thermal conductivity of the fluid, the flow rate of the fluid, and the kinematic viscosity of the fluid.

[0066] The air convection heat transfer coefficient is calculated based on the Grashof criterion number, Prandtl coefficient, air thermal conductivity, inner diameter of the pipe and length of the pipe.

[0067] Specifically, the calculation formula of the fluid convection heat transfer coefficient is: h = 0.023Re 0.8 Pr 0.3 λ1 / l.

[0068] Where Re is the Reynolds number, λ1 is the thermal conductivity of the fluid, and v is the kinematic viscosity of the fluid.

[0069] As an optional implementation, the air convection heat transfer coefficient is calculated based on the Grashof criterion number, the Prandtl coefficient, the air thermal conductivity, the inner diameter of the pipe, and the length of the pipe, specifically including:

[0070] Determine whether the pipeline is horizontal or vertical.

[0071] When the pipeline is horizontal, the air convection heat transfer coefficient is determined based on the Grashof criterion number, Prandtl coefficient, air thermal conductivity and the inner diameter of the pipeline.

[0072] When the pipeline is vertical, the air convection heat transfer coefficient is determined based on the Grashof criterion number, Prandtl coefficient, air thermal conductivity and the length of the pipeline.

[0073] For the problem of temperature measurement in pipe, there are three quantities, which are external temperature, internal temperature and flow rate of fluid. In actual situation, only external temperature can be measured, but internal temperature is expected to be obtained. Therefore, a mathematical model of the three quantities is established through existing relationship. However, neither the model nor the measurement result is accurate, and is noisy. Therefore, the calculation and measurement of external temperature are required to converge to each other to correct the model so as to obtain correct internal temperature. In the above method, the determination of weight K is the key, and the best method for finding K is to use Kalman filter.

[0074] Embodiment 2

[0075] Figure 3 A structure schematic diagram of a fluid temperature measurement system in pipe is provided for Embodiment 2 of the present application. As shown in the figure, the fluid temperature measurement system in pipe in the embodiment comprises: Figure 3

[0076] A parameter determination module 201 is configured to determine fixed parameters and process parameters of a target to be measured. The target to be measured is a pipe with fluid inside. The fixed parameters include flow rate of the fluid, pipe wall thickness of the pipe, pipe wall material thermal conductivity coefficient of the pipe, fluid convective heat transfer coefficient and air convective heat transfer coefficient. The process parameters include noise variance and observation variance.

[0077] A temperature acquisition module 202 is configured to acquire external wall temperature of the pipe and air temperature at a current time.

[0078] A predicted temperature determination module 203 is configured to determine predicted temperature at the current time according to optimal internal temperature at a previous time and flow rate of the fluid.

[0079] A covariance determination module 204 is configured to determine covariance at the current time according to optimal covariance at the previous time and noise variance. The optimal covariance at the previous time is determined according to weight coefficient at the previous time, covariance at the previous time, fixed parameters and observation variance. The optimal internal temperature at the initial time, the weight coefficient and the covariance are obtained by initializing the parameters of the target to be measured.

[0080] A weight coefficient determination module 205 is configured to determine weight coefficient at the current time according to covariance at the current time, fixed parameters and observation variance.

[0081] An optimal internal temperature determination module 206 is configured to determine optimal internal temperature at the current time according to predicted temperature at the current time, weight coefficient at the current time, external wall temperature of the pipe at the current time, air temperature at the current time, fixed parameters and observation variance.

[0082] Embodiment 3

[0083] An electronic device comprises: ​

[0084] one or more processors.

[0085] a memory device having stored thereon one or more programs.

[0086] The one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of measuring temperature of fluid in pipe in the embodiment 1.

[0087] Embodiment 4

[0088] A storage medium having stored thereon a computer program, wherein the computer program, when executed by a processor, implements the method of measuring temperature of fluid in pipe in the embodiment 1.

[0089] The various embodiments described in the specification are presented in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be mutually referred to. For the system disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method part.

[0090] The principles and implementation manners of the present application are described by using specific examples in the present application. The above description of the embodiments is only used to help understand the method of the present application and its core idea. Meanwhile, for the general skilled in the art, the specific implementation manners and application ranges can be changed according to the idea of the present application. In conclusion, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A method of measuring the temperature of a fluid in a pipe, characterized in that, The method comprises: determining fixed parameters and process parameters of a target to be measured; the target to be measured is a pipeline with fluid inside; the fixed parameters comprise flow rate of the fluid, pipe wall thickness of the pipeline, pipe wall material thermal conductivity coefficient of the pipeline, convective heat transfer coefficient of the fluid and air convective heat transfer coefficient; the process parameters comprise noise variance and observation variance; Obtaining the outer wall temperature and air temperature of the pipeline at the current time; the outer wall temperature at the kth time and the actual temperature inside the pipeline at the kth time There is the following relationship: ; The observation noise of the temperature measuring instrument for collecting the outer wall temperature; The first intermediate parameter is , , The second intermediate parameter is when the pipeline is a horizontal pipeline, , The thermal conductivity coefficient of the pipe wall material of the pipeline is The convective heat transfer coefficient of the fluid is The pipe wall thickness of the pipeline is; when the pipeline is a horizontal pipeline, the calculation formula of the air convective heat transfer coefficient is: ; when the pipeline is a vertical pipeline, the calculation formula of the air convective heat transfer coefficient is: ; The Grashof criterion number is The Prandtl coefficient is The air thermal conductivity is The inner diameter of the pipeline is The length of the pipeline is; Determine a predicted temperature at the current time according to the optimal in-pipe temperature at the previous time and the flow rate of the fluid; when the current time is the kth time, the predicted temperature at the kth time The calculation formula is: ; wherein, is the predicted temperature at the kth time instant, k > 1, is a 1 matrix, is the optimal in-pipe temperature at the k-1th time instant, is a zero matrix, is the flow rate of the fluid; the optimal in-pipe temperature at the initial time instant is initialized to 0; Determine the covariance of the current time according to the optimal covariance of the last time and the noise variance; the optimal covariance of the last time is determined according to the weight coefficient of the last time, the covariance of the last time, the fixed parameter and the observation variance; wherein the optimal in-pipe temperature, the weight coefficient and the covariance of the initial time are obtained by initializing the parameters of the target to be measured; when the current time is the kth time, the covariance of the kth time The calculation formula is: ; wherein, is the covariance at the kth time, is the optimal covariance at the k-1th time, is the noise variance, i.e., the variance resulting from the noise; ; is the weight coefficient at the k-1 time, is the covariance at the k-1 time; the optimal covariance at the initial time is initialized as 1; Determine a weight coefficient of the current time according to the covariance of the current time, the parameter and the observation variance; when the current time is the kth time, the weight coefficient of the kth time The calculation formula is: ; wherein, is a weight coefficient at the kth time, is an observation variance, the observation variance being determined according to the accuracy of a temperature measuring instrument for collecting the outer wall temperature; determining the optimal in-pipe temperature at the current time according to the predicted temperature at the current time, the weight coefficient at the current time, the outer wall temperature of the pipeline at the current time, the air temperature at the current time, the parameter and the observation variance; when the current time is the kth time, the optimal in-pipe temperature at the kth time The calculation formula is: ; wherein, Topt(k) is the optimal in-pipe temperature at the kth time instant, Tair(k) is the air temperature at the kth time instant. , Tair(k) is the air temperature at the kth time instant.

2. A temperature measuring system for a fluid in a pipe for implementing the temperature measuring method for a fluid in a pipe as claimed in claim 1, characterized in that The system comprises: a parameter determination module configured to determine fixed parameters and process parameters of a target to be measured; the target to be measured is a pipeline with fluid inside; the fixed parameters comprise flow rate of the fluid, pipe wall thickness of the pipeline, pipe wall material thermal conductivity coefficient of the pipeline, convective heat transfer coefficient of the fluid and air convective heat transfer coefficient; the process parameters comprise noise variance and observation variance; a temperature acquisition module configured to acquire outer wall temperature of the pipeline and air temperature at a current time point; a predicted temperature determination module configured to determine predicted temperature at the current time point according to optimal in-pipe temperature at a previous time point and flow rate of the fluid; a covariance determination module configured to determine covariance at the current time point according to optimal covariance at the previous time point and the noise variance; the optimal covariance at the previous time point is determined according to weight coefficient at the previous time point, covariance at the previous time point, the fixed parameters and the observation variance; wherein optimal in-pipe temperature, weight coefficient and covariance at an initial time point are obtained by performing initialization processing on the parameters of the target to be measured; a weight coefficient determination module configured to determine weight coefficient at the current time point according to covariance at the current time point, the fixed parameters and the observation variance; an optimal in-pipe temperature determination module configured to determine optimal in-pipe temperature at the current time point according to predicted temperature at the current time point, weight coefficient at the current time point, outer wall temperature of the pipeline at the current time point, air temperature at the current time point, the fixed parameters and the observation variance.

3. An electronic device, comprising: comprise: one or more processors; a storage device having one or more programs stored thereon; when the one or more programs are executed by the one or more processors, the one or more processors implement the in-pipe fluid temperature measurement method according to claim 1.

4. A storage medium, characterized by a computer program is stored thereon, wherein the computer program is executed by a processor to implement the in-pipe fluid temperature measurement method according to claim 1.

Citation Information

Patent Citations

  • Method and system for determing thermal state

    CN112031945A

  • Method and system for determining temperature of fluid flowing through tube body

    CN118235028A

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