Method for estimating fouling thermal resistance of direct air-cooling condenser in combination with scaling mechanism

Abstract

The invention relates to the technical field of thermal power generation, in particular to a direct air cooling condenser fouling thermal resistance estimation method combined with a scaling mechanism, and aims to realize stable and accurate real-time estimation of the fouling thermal resistance of a condenser. The method includes the steps that operation parameters of the direct air cooling unit are collected and preprocessed to form a continuous time sequence; calculating multiple groups of cleaning total heat transfer coefficients based on the cleaning period operation parameters, training a machine learning model based on the cleaning total heat transfer coefficients, and establishing a cleaning heat transfer coefficient reference model; calculating an actual total heat transfer coefficient based on the current operation parameters, inputting the reference model to obtain a corresponding cleaning coefficient, and calculating initial fouling thermal resistance according to the cleaning coefficient; and establishing a discrete linear recursion physical filtering model based on a dirt deposition-denudation mechanism, identifying model parameters on line by taking the initial dirt thermal resistance as an observed quantity, performing physical constraint filtering on the model parameters, and outputting a final dirt thermal resistance online estimated value.

Description

Technical Field

[0001] This invention relates to the field of thermal power generation technology, and in particular to a method for estimating the fouling thermal resistance of a direct air-cooled condenser by incorporating fouling mechanisms. Background Technology

[0002] Direct air-cooled condensers are key cold-end equipment in large-scale thermal power generating units in coal-rich but water-scarce regions of my country. They directly cool the turbine exhaust steam within the finned tube bundles by using axial flow fans to drive ambient air, saving significant amounts of circulating cooling water. Therefore, they are widely used in water-scarce areas of northern China. However, the finned tube bundles are constantly exposed to the natural environment, making them susceptible to fouling from atmospheric dust, fly ash, and other pollutants, leading to a buildup of fouling. This results in decreased heat transfer performance, increased back pressure, and higher coal consumption. Therefore, accurate and reliable online monitoring of the fouling thermal resistance of air-cooled condensers is a crucial technical requirement for guiding scientific cleaning and ensuring the economical operation of the unit.

[0003] Currently, there are two main technical approaches for monitoring fouling conditions in direct-air condensers. One approach is the engineering estimation method based on performance back-calculation. This method uses unit operating parameters and a heat transfer model to calculate the overall heat transfer coefficient in real time, thereby inferring the fouling thermal resistance. While this method can achieve online estimation, its results are significantly affected by measurement noise, environmental disturbances, and changes in operating conditions, exhibiting drastic high-frequency fluctuations that often mask the true long-term trend of slow fouling growth, thus limiting its practicality. The other approach is purely data-driven or mathematical filtering methods, such as offline training of neural network models or using techniques like exponential smoothing and Kalman filtering to smooth the engineering estimation results. Although these methods can suppress noise to some extent, they lack consideration of the physical mechanisms of fouling in the condenser itself, resulting in a lack of physical interpretability of the model parameters. This makes them prone to estimation drift during long-term operation, making it difficult to guarantee the long-term stability and physical rationality of the results. Summary of the Invention

[0004] The purpose of this invention is to provide a method for estimating the fouling thermal resistance of a direct air-cooled condenser by incorporating the fouling mechanism. The aim is to achieve a stable, accurate, and physically interpretable real-time estimate of the fouling thermal resistance of the condenser by combining the actual fouling mechanism of the condenser.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides a method for estimating the fouling thermal resistance of a direct air-cooled condenser based on fouling mechanisms, comprising: S1. Real-time acquisition of operating parameters of the direct air-cooled unit, including at least ambient air temperature, fan speed, number of operating fans, unit power, steam parameters, and condenser back pressure; and preprocessing the operating parameters to form a continuous time series; S2. Based on the operating parameters during the clean period of the condenser in the continuous time series, calculating multiple sets of overall clean heat transfer coefficients using the number of heat transfer units method; using the operating parameters during the clean period and their corresponding overall clean heat transfer coefficients as training samples to train a machine learning model and establish a benchmark model for the clean heat transfer coefficient; S3. Based on... The operating parameters at the current moment in the continuous time series are used to calculate the current actual overall heat transfer coefficient using the number of heat transfer units method. The current operating parameters are input into the clean heat transfer coefficient benchmark model to obtain the corresponding clean overall heat transfer coefficient. Based on the clean overall heat transfer coefficient and the current actual overall heat transfer coefficient, the preliminary fouling thermal resistance is calculated. S4. Based on the deposition-erosion kinetic mechanism of the condenser fouling accumulation process, a discrete linear recursive physical filtering model for fouling thermal resistance is established. The preliminary fouling thermal resistance is used as an observation, and the parameters of the physical filtering model are identified in real time using an online parameter identification method. The identified parameters are used to perform physical constraint filtering on the preliminary fouling thermal resistance, and the final online estimate of the fouling thermal resistance is output.

[0006] In steps S2 and S3, the process of calculating the overall heat transfer coefficient using the number of heat transfer units method includes: calculating the exhaust steam flow rate and exhaust steam enthalpy based on the turbine variable operating condition model and current steam parameters; determining the corresponding saturated water enthalpy based on the condenser back pressure; calculating the total heat transfer of the condenser based on the exhaust steam flow rate, exhaust steam enthalpy, and saturated water enthalpy; calculating the number of heat transfer units in the condenser based on the heat transfer relationship between the air side and the steam side, combined with the face velocity, face area, and ambient air properties; and calculating the overall heat transfer coefficient based on the total heat transfer, the number of heat transfer units, and the total heat transfer area of ​​the condenser.

[0007] The oncoming wind speed is calculated based on the similarity theorem of the wind turbine. The input parameters of the similarity theorem include the design volume flow rate of the wind turbine, the wind turbine cluster factor, the actual average operating speed of the wind turbine, the actual number of wind turbines in operation, and the design speed of the wind turbine.

[0008] In step S2, the clean heat transfer coefficient benchmark model is a machine learning model based on an improved gradient boosting decision tree; the input features of the training samples include at least the unit load, ambient air temperature, fan speed, face wind speed and condenser back pressure, and the output of the clean heat transfer coefficient benchmark model is the overall clean heat transfer coefficient under the corresponding operating conditions.

[0009] In step S3, the difference between the reciprocal of the clean overall heat transfer coefficient output by the clean heat transfer coefficient benchmark model and the reciprocal of the current actual overall heat transfer coefficient is the preliminary fouling thermal resistance.

[0010] In step S4, the discrete linear recursive physical filter model is a mass balance model of fouling deposition and erosion based on Kern-Seaton theory, and the change in fouling thermal resistance per unit time is modeled as a recursive form that is linearly related to the current fouling thermal resistance value.

[0011] The online parameter identification method is the sliding window online robust least squares method, which is used to estimate the deposition coefficient and erosion coefficient in the discrete linear recursive physical filter model in real time.

[0012] Step S5 is included after step S4: Based on the online estimated value of fouling thermal resistance output in step S4 and the overall clean heat transfer coefficient output by the clean heat transfer coefficient benchmark model, the cleaning factor of the condenser is calculated; when the cleaning factor is continuously lower than the preset threshold, the condenser is determined to be in poor clean condition and needs to be cleaned.

[0013] The cleaning factor is obtained by calculating the ratio of the reciprocal of the overall cleaning heat transfer coefficient to the online estimated value of the fouling thermal resistance, using the sum of the reciprocal of the overall cleaning heat transfer coefficient as the denominator and the numerator as the denominator.

[0014] After each condenser cleaning is completed, the online estimate of the fouling thermal resistance is reset to the initial value of the clean state, and step S2 is re-executed using the operating data within the predetermined time window after cleaning to update and calibrate the clean heat transfer coefficient benchmark model.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. The method provided in this invention employs a two-stage processing mechanism combining preliminary estimation with physical constraint filtering. First, it obtains basic data based on the number of heat transfer units method. Then, it optimizes the data using a physical filtering model constructed based on the deposition-erosion kinetic mechanism, effectively filtering out interference signals and ensuring a smooth and continuous final estimate that accurately reflects the physical evolution of the fouling. A benchmark model for the clean heat transfer coefficient is constructed using a model based on an improved gradient boosting decision tree. Cleaning state data before and after cleaning are used as training samples. Input features cover key influencing factors such as unit load, ambient temperature, and fan operating parameters. This model accurately maps the clean heat transfer performance under different operating conditions, providing a reliable benchmark for calculating fouling thermal resistance and avoiding estimation errors caused by benchmark deviations.

[0016] 2. By employing a sliding window online robust least squares method to identify the deposition and erosion coefficients of the physical filtering model in real time, it can dynamically respond to dynamic scenarios such as seasonal changes, environmental wind speed fluctuations, and unit load adjustments. This solves the problem of traditional mechanistic models having fixed parameters and being difficult to adapt to complex actual operating conditions, ensuring the reliability of estimations during long-term operation. Finally, by calculating cleaning factors and setting clear judgment thresholds, the abstract fouling thermal resistance is transformed into an intuitive cleanliness indicator, providing maintenance personnel with clear cleaning trigger signals. This avoids the problems of blind cleaning (causing resource waste) or delayed cleaning (leading to decreased unit efficiency), achieving precise control of cleaning operations. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating a method for estimating the fouling thermal resistance of a direct air-cooled condenser based on a fouling mechanism, as provided in an embodiment of this application. Figure 2 This is a calculation diagram of a method for estimating the fouling thermal resistance of a direct air-cooled condenser based on the fouling mechanism, provided in an embodiment of this application. Figure 3 This is a typical growth curve of fouling thermal resistance provided in the embodiments of this application; Figure 4 This is a comparison chart of experimental results provided in an embodiment of this application. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0019] Reference Figure 1 and Figure 2 This application provides a method for estimating the fouling thermal resistance of a direct air-cooled condenser based on the fouling mechanism, including: S1. Real-time acquisition of operating parameters of the direct air-cooled unit, including at least ambient air temperature, fan speed, number of operating fans, unit power, steam parameters, and condenser back pressure; and preprocessing of the operating parameters to form a continuous time series.

[0020] For example, by removing outliers and filling in missing data to form a continuous and valid time series, a reliable input is provided for calculating the heat transfer coefficient and estimating the fouling thermal resistance. Furthermore, to ensure data continuity and stability, the outlier removal and missing data completion in step S1 employs the adjacent sample average substitution method.

[0021] S2. Based on the operating parameters of the condenser during the clean state period in the continuous time series, the overall clean heat transfer coefficient of multiple sets is calculated using the number of heat transfer units (η-NTU) method. Using the operating parameters during the clean state period and their corresponding overall clean heat transfer coefficient as training samples, a machine learning model is trained to establish a benchmark model for the clean heat transfer coefficient.

[0022] For example, in step S2, the clean heat transfer coefficient benchmark model is a machine learning model based on an improved gradient boosting decision tree (XGBoost machine learning model); the input features of the training samples include at least unit load, ambient air temperature, fan speed, face wind speed, and condenser back pressure, and the output of the clean heat transfer coefficient benchmark model is the overall clean heat transfer coefficient under the corresponding operating conditions. The clean heat transfer coefficient benchmark model can reflect the mapping relationship between the clean heat transfer coefficient and the operating conditions, and is used for comparison and evaluation of heat transfer performance in actual operation.

[0023] S3. Based on the operating parameters at the current moment in the continuous time series, calculate the current actual overall heat transfer coefficient using the number of heat transfer units method. Input the current operating parameters into the clean heat transfer coefficient benchmark model to obtain the corresponding overall clean heat transfer coefficient; calculate the preliminary fouling thermal resistance based on the overall clean heat transfer coefficient and the current actual overall heat transfer coefficient. .

[0024] For example, in steps S2 and S3, the process of calculating the overall heat transfer coefficient using the number of heat transfer units method includes: calculating the exhaust steam flow rate based on the turbine variable operating condition model and the current steam parameters. and exhaust enthalpy Based on the condenser back pressure, determine the corresponding saturated water enthalpy using the IAPWS-IF97 table. Based on exhaust steam flow enthalpy of exhaust vapor and saturated water enthalpy Calculate the total heat exchange of the condenser. The calculation formula is as follows: Based on the heat transfer relationship between the air and steam sides, and combined with the oncoming wind speed, oncoming area, and ambient air properties, the number of heat transfer units (NTU) of the condenser is calculated; based on the total heat transfer, the number of heat transfer units, and the total heat transfer area of ​​the condenser, the overall heat transfer coefficient is calculated.

[0025] For example, the calculation formula is as follows: in, The outlet temperature of the condenser air is expressed in °C. The ambient air temperature at the condenser inlet is expressed in °C. This represents the saturation temperature corresponding to the condenser back pressure, in °C. The frontal area of ​​the condenser, in units of ; The frontal wind speed of the axial flow fan group is expressed in units of 1000 m / s. ; This represents ambient air density, in units of... ; This indicates the specific heat capacity of ambient air, in units of... .

[0026] As one possible implementation method, the headwind speed The calculation is performed based on the wind turbine similarity theorem. The input parameters for the wind turbine similarity theorem include the design volumetric flow rate of the wind turbine, the wind turbine cluster factor, the actual average operating speed of the wind turbine, the actual number of wind turbines in operation, and the design speed of the wind turbine. For example, the calculation formula is as follows: in, The design volumetric flow rate of the fan is expressed in units of... ; For wind turbine cluster factors; The average speed of the fan, in units of ; This represents the actual number of wind turbines in operation. The design speed of the fan, in units of .

[0027] It should be understood that the overall heat transfer coefficient in the process of calculating the overall heat transfer coefficient using the number of heat transfer units method in steps S2 and S3 includes the following: When executing step S2, the input is the operating parameters of the clean state period, and the calculated overall heat transfer coefficient is the clean overall heat transfer coefficient; when executing step S3, the input is the operating parameters of the current moment, and the calculated overall heat transfer coefficient is the current actual overall heat transfer coefficient. It does not specifically refer to the "clean" or "current actual" state, but rather to the heat transfer coefficient value obtained through the calculation process.

[0028] For example, the overall heat transfer coefficient can be calculated using the following formula: in, The overall heat transfer coefficient of the condenser, in units of... ; The total heat exchange area is expressed in units of... .

[0029] In step S3, the difference between the reciprocal of the overall clean heat transfer coefficient output by the clean heat transfer coefficient benchmark model and the reciprocal of the current actual overall heat transfer coefficient is the preliminary fouling thermal resistance, calculated as follows: S4. Based on the deposition-erosion kinetics mechanism of condenser fouling accumulation, a discrete linear recursive physical filtering model for fouling thermal resistance is established. The initial fouling thermal resistance is used as an observation, and the parameters of the physical filtering model are identified in real time using an online parameter identification method. The identified parameters are then used to perform physical constraint filtering on the initial fouling thermal resistance, and the final online estimate of the fouling thermal resistance is output.

[0030] For example, the discrete linear recursive physical filter model is constructed based on the mass balance mechanism of dirt deposition and erosion, and models the change in dirt thermal resistance per unit time as a recursive form that is linearly related to the current dirt thermal resistance value.

[0031] For example, refer to Figure 3 , Figure 3 The curves in the figures represent typical variations in the fouling thermal resistance accumulation process on the heat exchanger surface, proposed by different scholars. Curve 1 shows the variation curve using a linear fouling model, curve 2 shows the variation curve using a deceleration rate model, curve 3 shows the variation curve using a power-law model, curve 4 shows the variation curve using an asymptotic model, and curve 5 shows the actual variation curve of fouling accumulation on the surface of a direct-drive air-cooled condenser. Based on... Figure 3 Curve 5 shows that fouling growth generally goes through initial deposition, continuous growth and stabilization stages. Its thermal resistance changes with time according to a clear physical law. In order to overcome the fluctuations in engineering estimates, this application uses the Kern-Seaton theory to construct a mass balance model of fouling deposition and erosion.

[0032] More specifically, based on the Kern-Seaton theory, a mass balance model of fouling deposition and erosion is established, and the dynamic balance equation of fouling mass per unit heat exchange area is derived: in, The mass of fouling deposited per unit heat exchange area, in units of ; The percentage of dirt deposited is expressed in units of... ; The percentage of dirt erosion is expressed in units of... .

[0033] Furthermore, considering the quality of the dirt thermal resistance to dirt Physical relationship model: in, Fouling thermal resistance density, in units of ; The thermal resistance of the fouling is the thermal conductivity, and the unit is . Combining the above equations, we obtain the fouling growth model as follows: in, is the sedimentation coefficient, in units of ; This is the erosion coefficient, in units of... .

[0034] The fouling growth mechanism equation is discretized according to the sampling period, letting ,get: in, The sampling time is preferably 1 minute.

[0035] make The aforementioned fouling growth mechanism can then be discretized into a linear recursive form: This leads to a linear recursive model with clear physical meaning, used to describe the time evolution of fouling thermal resistance.

[0036] As a possible implementation, to adapt to seasonal changes in dust concentration, environmental conditions, and wind speed, the online parameter identification method is the sliding window online robust least squares method. The sliding window online robust least squares algorithm is employed to... For output, For input parameters Real-time identification is performed to enable the identification of model parameters. The online estimation eliminates or reduces the weight of gross errors caused by sudden changes in operating conditions, thereby improving the stability of parameter identification. Subsequently, the updated parameters are used to iteratively filter the initial value of fouling thermal resistance to obtain a smooth, continuous, and physically consistent estimate of fouling thermal resistance.

[0037] Reference Figure 4 The mechanistic filtering results obtained by the method provided in this application embodiment show a smooth upward trend (solid line), which truly reveals the accumulation process of condenser fouling; while the unfiltered engineering estimate (dashed line) fluctuates significantly.

[0038] For example, step S5 is included after step S4: based on the fouling thermal resistance output in step S4. Online estimates and clean overall heat transfer coefficient output from the clean heat transfer coefficient benchmark model Calculate the cleaning factor of the condenser When the cleaning factor remains below a preset threshold, the condenser is deemed to be in poor cleanliness and requires cleaning. For example, if the preset threshold is 0.75, and the cleaning factor remains below 0.75, it indicates that the surface of the air-cooled condenser fins is heavily soiled and should be subjected to high-pressure flushing or mechanical cleaning to ensure the long-term stability of the unit's back pressure and cold-end performance.

[0039] The cleaning factor is obtained by summing the reciprocal of the overall clean heat transfer coefficient and the online estimate of the fouling thermal resistance, and taking the reciprocal of the overall clean heat transfer coefficient as the numerator. The ratio of the two is calculated as follows: .

[0040] After each condenser cleaning is completed, the online estimate of the fouling thermal resistance is reset to the initial value of the clean state, and step S2 is re-executed using the operating data within the predetermined time window after cleaning to update and calibrate the clean heat transfer coefficient benchmark model.

[0041] For example, the initial cleanliness level is in the range of 0 to 0.003. This includes the inherent pipe thermal resistance and pipe wall thermal resistance of the condenser.

[0042] In the description of this specification, specific features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments or examples.

[0043] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method of estimating the fouling resistance of a direct air-cooled condenser incorporating the fouling mechanism, characterized by, include: S1. Real-time acquisition of operating parameters of the direct air-cooled unit, including at least ambient air temperature, fan speed, number of operating fans, unit power, steam parameters, and condenser back pressure; and preprocessing of the operating parameters to form a continuous time series; S2. Based on the operating parameters of the condenser during the clean period in the continuous time series, the overall heat transfer coefficient of multiple clean periods is calculated using the number of heat transfer units method; Using the operating parameters of the clean state period and their corresponding overall clean heat transfer coefficient as training samples, a machine learning model is trained to establish a benchmark model for the clean heat transfer coefficient. S3. Based on the operating parameters at the current moment in the continuous time series, calculate the current actual overall heat transfer coefficient using the heat transfer unit number method; Input the current operating parameters into the clean heat transfer coefficient benchmark model to obtain the corresponding clean overall heat transfer coefficient; Calculate the preliminary fouling thermal resistance based on the overall clean heat transfer coefficient and the current actual overall heat transfer coefficient; S4. Based on the deposition-erosion kinetics mechanism of condenser fouling accumulation, a discrete linear recursive physical filtering model for fouling thermal resistance is established; the preliminary fouling thermal resistance is used as an observation, and the parameters of the physical filtering model are identified in real time using an online parameter identification method; the identified parameters are used to perform physical constraint filtering on the preliminary fouling thermal resistance, and the final online estimate of the fouling thermal resistance is output.

2. A direct air-cooled condenser fouling resistance estimation method incorporating fouling mechanism according to claim 1, characterized in that, In steps S2 and S3, the process of calculating the overall heat transfer coefficient using the heat transfer unit number method includes: calculating the exhaust steam flow rate and exhaust steam enthalpy based on the turbine variable operating condition model and current steam parameters; determining the corresponding saturated water enthalpy based on the condenser back pressure; calculating the total heat exchange of the condenser based on the exhaust steam flow rate, the exhaust steam enthalpy, and the saturated water enthalpy; calculating the number of heat transfer units in the condenser based on the heat exchange relationship between the air side and the steam side, combined with the face wind speed, windward area, and ambient air properties; and calculating the overall heat transfer coefficient based on the total heat exchange, the number of heat transfer units, and the total heat exchange area of ​​the condenser.

3. A direct air-cooled condenser fouling resistance estimation method incorporating a fouling mechanism as claimed in claim 2, characterized in that, The oncoming wind speed is calculated based on the wind turbine similarity theorem. The input parameters of the wind turbine similarity theorem include the design volume flow rate of the wind turbine, the wind turbine cluster factor, the actual average operating speed of the wind turbine, the actual number of wind turbines in operation, and the design speed of the wind turbine.

4. A direct air-cooled condenser fouling resistance estimation method incorporating fouling mechanism as claimed in claim 1, wherein, In step S2, the clean heat transfer coefficient benchmark model is a machine learning model based on an improved gradient boosting decision tree; the input features of the training samples include at least unit load, ambient air temperature, fan speed, oncoming wind speed, and condenser back pressure; and the output of the clean heat transfer coefficient benchmark model is the overall clean heat transfer coefficient under the corresponding operating condition.

5. A direct air-cooled condenser fouling resistance estimation method incorporating fouling mechanism as claimed in claim 1, wherein, In step S3, the difference between the reciprocal of the clean overall heat transfer coefficient output by the clean heat transfer coefficient benchmark model and the reciprocal of the current actual overall heat transfer coefficient is the preliminary fouling thermal resistance.

6. A direct air-cooled condenser fouling resistance estimation method incorporating fouling mechanism as claimed in claim 1, wherein, In step S4, the discrete linear recursive physical filtering model is a mass balance model of dirt deposition and erosion based on Kern-Seaton theory, and the change in dirt thermal resistance per unit time is modeled as a recursive form that is linearly related to the current dirt thermal resistance value.

7. A direct air-cooled condenser fouling resistance estimation method incorporating a fouling mechanism as claimed in claim 6, characterized in that, The online parameter identification method is a sliding window online robust least squares method, which is used to estimate the deposition coefficient and erosion coefficient in the discrete linear recursive physical filter model in real time.

8. A direct air-cooled condenser fouling resistance estimation method incorporating fouling mechanism as claimed in claim 1, wherein, Step S5 is included after step S4: Based on the online estimated value of fouling thermal resistance output in step S4 and the overall clean heat transfer coefficient output by the clean heat transfer coefficient benchmark model, the cleaning factor of the condenser is calculated; when the cleaning factor is continuously lower than a preset threshold, the condenser is determined to be in poor clean condition and needs to be cleaned.

9. A direct air-cooled condenser fouling resistance estimation method incorporating a fouling mechanism as claimed in claim 8, characterized in that, The cleaning factor is obtained by taking the sum of the reciprocal of the overall cleaning heat transfer coefficient and the online estimated value of the fouling thermal resistance as the denominator, and taking the reciprocal of the overall cleaning heat transfer coefficient as the numerator.

10. A direct air-cooled condenser fouling resistance estimation method incorporating fouling mechanism as claimed in claim 1, wherein, After each condenser cleaning is completed, the online estimated value of the fouling thermal resistance is reset to the initial value of the clean state, and step S2 is re-executed using the operating data within a predetermined time window after cleaning to update and calibrate the clean heat transfer coefficient benchmark model.

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