Geothermal well temperature sequence prediction method

Abstract

The invention discloses a geothermal well temperature sequence prediction method, belongs to the technical field of geothermal energy development, and can solve the problems that in an existing prediction method, seasonal modeling is single, and the multi-cycle superimposed effect is difficult to process. The method comprises the following steps: S1, constructing a daily cycle term and an annual cycle term of the geothermal well temperature, and determining a seasonal term of the geothermal well temperature according to the daily cycle term and the annual cycle term; s2, constructing an autoregression item, a moving average item and an external variable item of the geothermal well temperature, and constructing a regression model of the geothermal well temperature according to the autoregression item, the moving average item, the external variable item and the seasonal item; s3, training the regression model by using the historical temperature sequence and the historical external variable sequence of the geothermal well to obtain a prediction model; and S4, inputting the current temperature sequence and the current external variable sequence of the geothermal well into the prediction model to obtain a temperature prediction value of the geothermal well at the next moment. The method is used for predicting the geothermal well temperature.

Description

Technical Field

[0001] The invention relates to a geothermal well temperature sequence prediction method, belonging to the technical field of geothermal energy development. Background Art

[0002] In the process of geothermal energy development and utilization, wellbore temperature is an important indicator for judging reservoir energy status, optimizing mining plans, controlling water flow and power generation / heating efficiency. Accurately predicting well temperature changes can not only guide production scheduling, but also assist in fan (water pump / heat pump) power regulation, downhole equipment selection and maintenance planning. Existing geothermal well temperature prediction methods are mainly divided into three categories: numerical simulation based on physical mechanisms, time series model based and pure data-driven machine learning methods. Specifically, (1) Based on physical mechanism model: by establishing the geothermal reservoir heat transfer-seepage coupling equation, combined with geological parameters (such as rock thermal conductivity and permeability) to simulate the wellbore temperature dynamics. For example, the finite element method is used to solve the heat conduction equation, or the deep geothermal field is predicted by combining magnetotelluric inversion data. (2) Based on time series model: The ARMA / ARIMA model is used to describe the autocorrelation and trend of the temperature series. Some studies introduce a single seasonal term (such as an annual cycle) or an external variable (such as flow), but the lag order of the external variable is fixed and limited. (3) Data-driven machine learning models use algorithms such as LSTM and random forest to learn the nonlinear relationship between historical temperature and influencing factors. Some studies introduce wavelet decomposition to preprocess high-frequency noise. During use, purely data-driven LSTM predicts geothermal production capacity, ignoring physical boundary constraints.

[0003] However, the above prediction methods usually have the following problems: (1) Seasonal modeling is single and difficult to handle the superposition effect of multiple cycles. Existing models usually only consider a single cycle (such as an annual cycle or a daily cycle), while the temperature of geothermal wells is affected by both diurnal production scheduling (24 hours) and annual climate fluctuations (8760 hours). A single model cannot capture the multi-scale periodic coupling effect, resulting in significant fitting deviations. (2) Insufficient utilization of external variables and rigid hysteresis mechanism. Existing ARMAX models only introduce 1-2 external variables (such as flow or temperature) and the hysteresis order is fixed. In fact, well temperature is driven by multiple factors (pumping flow, well pressure, surface temperature, power generation load), and the time delay of each factor is different (such as temperature lag 6 hours, load lag 0 hours). Ignoring the dynamic hysteresis relationship between variables weakens the physical interpretability of the model. (3) Static parameters cannot adapt to dynamic geological and equipment conditions. Traditional models use fixed parameters or fixed time windows for updating, and do not consider performance drift caused by formation permeability attenuation, equipment scaling, etc. For example, the thermal wash cycle of an oil well needs to be adjusted dynamically due to a drop in formation pressure, but a static model cannot respond in real time. (4) Anomaly detection relies on thresholds and has poor robustness. Existing methods (such as wavelet threshold denoising) require a fixed threshold to be preset and cannot adapt to dynamic changes in data distribution. Geothermal well data often produce outliers due to sensor failures or short-term geological events (such as fracture blockage). Fixed thresholds can easily lead to misjudgments or missed judgments, contaminating the training data. Summary of the Invention

[0004] The present invention provides a geothermal well temperature series prediction method, which can solve the problem that the existing prediction methods have single seasonal modeling and difficulty in dealing with multi-period superposition effects.

[0005] The present invention provides a method for predicting geothermal well temperature series, the method comprising:

[0006] S1. Constructing a daily cycle term and an annual cycle term of the geothermal well temperature, and determining a seasonal term of the geothermal well temperature based on the daily cycle term and the annual cycle term;

[0007] S2. constructing an autoregressive term, a sliding average term, and an external variable term of the geothermal well temperature, and constructing a regression model of the geothermal well temperature based on the autoregressive term, the sliding average term, the external variable term, and the seasonal term;

[0008] S3. Using the historical temperature series and the historical external variable series of the geothermal well to train the regression model to obtain a prediction model;

[0009] S4. Input the current temperature sequence of the geothermal well and the current external variable sequence into the prediction model to obtain the temperature prediction value of the geothermal well at the next moment.

[0010] Optionally, the external variable item for constructing the geothermal well temperature in S2 specifically includes:

[0011] Identify multiple external variables that affect geothermal well temperature and determine the lag order of each external variable;

[0012] The external variable term of geothermal well temperature is constructed based on multiple external variables and their lag orders.

[0013] Optionally, the objective function of the prediction model is a weighted least squares objective function; the weights in the objective function are exponentially decaying weights.

[0014] Optionally, after S3, the method further includes:

[0015] Determining a time rolling window, and determining a predicted temperature sequence of the geothermal well within the time rolling window using the prediction model;

[0016] Using the predicted temperature sequence to update the historical temperature sequence in the time rolling window to obtain an updated temperature sequence, and using the updated temperature sequence and the historical external variable sequence to train the prediction model to obtain an updated model;

[0017] Correspondingly, the step S4 specifically includes: inputting the current temperature sequence of the geothermal well and the current external variable sequence into the update model to obtain the temperature prediction value of the geothermal well at the next moment.

[0018] Optionally, the updating of the historical temperature sequence in the time rolling window by using the predicted temperature sequence to obtain an updated temperature sequence specifically includes:

[0019] Obtaining a residual sequence of the historical temperature sequence and the predicted temperature sequence within the time rolling window, and determining a confidence interval based on the residual sequence;

[0020] The temperature values ​​in the historical temperature sequence that are beyond the confidence interval are removed to obtain an updated temperature sequence.

[0021] Optionally, determining a confidence interval according to the residual sequence specifically includes:

[0022] Determining a weighted residual mean and a weighted residual variance according to the residual sequence and the exponential decay weight;

[0023] An upper threshold and a lower threshold are determined according to the weighted residual mean and the weighted residual variance, and the upper threshold and the lower threshold are combined to form a confidence interval.

[0024] Optionally, determining a confidence interval according to the residual sequence specifically includes:

[0025] Determine the residual moving mean and the residual standard deviation according to the residual sequence;

[0026] An upper threshold and a lower threshold are determined according to the residual moving mean and the residual standard deviation, and the upper threshold and the lower threshold are combined to form a confidence interval.

[0027] Optionally, the daily cycle term and the annual cycle term are both in double harmonic sine and cosine form.

[0028] Optionally, before S3, the method further includes:

[0029] A historical temperature sequence and a historical external variable sequence of a geothermal well are collected, and the historical temperature sequence and the historical external variable sequence are preprocessed.

[0030] Optionally, the preprocessing includes interpolation processing, denoising processing and smoothing processing.

[0031] The beneficial effects that the present invention can produce include:

[0032] The geothermal well temperature series prediction method provided by the present invention introduces daily and annual cycle terms into the regression model, simultaneously capturing the responses of the diurnal and annual cycles to geothermal well temperature changes. This "double seasonality" harmonic modeling approach can overcome the defect of insufficient fitting of existing single seasonal models when multiple cycles are superimposed at the same time, thereby achieving high-precision predictions.

[0033] The geothermal well temperature series prediction method proposed in this paper not only provides a mathematical model but also a detailed algorithmic process from data acquisition, preprocessing, parameter estimation, to prediction output. In implementation, the method offers optional modules (such as anomaly detection and weighted adaptation) and a default core module (ARMAX + seasonality), which can be freely tailored to project requirements to achieve the optimal balance between performance and computational efficiency. This provides flexible solutions for diverse industry needs (from small-scale shallow-level projects to deep-level large-scale projects), expanding the method's applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Flowchart of a method for predicting geothermal well temperature series provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0035] The present invention is described in detail below with reference to the embodiments, but the present invention is not limited to these embodiments.

[0036] The embodiment of the present invention provides a method for predicting geothermal well temperature series. Figure 1 As shown, the method includes:

[0037] S1. Construct a daily cycle term and an annual cycle term of the geothermal well temperature, and determine the seasonal term of the geothermal well temperature based on the daily cycle term and the annual cycle term.

[0038] In one embodiment of the present invention, both the daily cycle term and the annual cycle term are in the form of double harmonic sine and cosine waves.

[0039] Specifically, daily cycle items The expression is: ;

[0040] Annual cycle items The expression is: ;

[0041] According to the daily cycle With annual cycle term Constructing seasonal terms , specifically: ;

[0042] In the above formula, is the timestamp (hour); is the length of the daily cycle ( ); is the length of the annual cycle ( ); is the harmonic order, which can be 1 to 3 to capture the main cycle; 、 、 and These are seasonal parameters to be estimated.

[0043] Optionally, in another embodiment of the present invention, both the daily cycle term and the annual cycle term are in sinusoidal form.

[0044] Specifically, daily cycle items The expression is: ;

[0045] Annual cycle items The expression is: ;

[0046] According to the daily cycle With annual cycle term Constructing seasonal terms , specifically: ;

[0047] In the above formula, is the timestamp (hour); and These are seasonal parameters to be estimated.

[0048] The use of a sinusoidal seasonal term can simplify the model and reduce the number of parameters, but is slightly inferior to the biharmonic sine-cosine form in fitting accuracy. It is suitable for shallow geothermal systems that are less stringent on seasonal changes.

[0049] S2. Construct the autoregressive term, sliding average term and external variable term of geothermal well temperature, and construct a regression model of geothermal well temperature based on the autoregressive term, sliding average term, external variable term and seasonal term.

[0050] In the embodiment of the present invention, the autoregressive term The expression is: ;

[0051] in, is the autoregressive coefficient; for Temperature values ​​of geothermal wells.

[0052] Sliding average term The expression is: ;

[0053] in, is the sliding mean coefficient; is a white noise sequence.

[0054] The external variables for constructing geothermal well temperature include:

[0055] Firstly, multiple external variables that affect the geothermal well temperature are determined, and the lag order of each external variable is determined. Then, the external variable term of the geothermal well temperature is constructed based on the multiple external variables and their lag orders.

[0056] External variable items The expression is: ;

[0057] Among them, external variables Include:

[0058] : wellhead pumping flow (unit: m³ / h);

[0059] : wellhead production pressure (unit: MPa);

[0060] : surface air temperature (unit: ℃);

[0061] : heating / power generation load factor (dimensionless);

[0062] Other optional external variables: wellhead pressure, well inclination, injection temperature, wellhead mud density, wellbore inclination change, injection water temperature, etc., which can be expanded to indivual.

[0063] For external variables Linear regression coefficients for different lag orders; lag order It can be determined based on the physical influence of external variables. For example, the influence of air temperature on well temperature lags by 6 to 12 hours. (6 hours per level).

[0064] Compared with the existing practice of introducing only a single or a few external variables with fixed hysteresis, the present invention can flexibly select external variables and their lag orders , realizing the comprehensive interpretation of well temperature changes based on multi-source information.

[0065] In another embodiment of the present invention, when the external variable Contains only one external variable, such as only the pumping flow or surface air temperature When the external variable The expression is: .

[0066] Using a single external variable can greatly simplify data collection and model complexity, and is suitable for sites with scarce data sources.

[0067] According to the autoregressive , sliding average item , external variable items and seasonal terms Constructing a regression model for geothermal well temperature , whose expression is: .

[0068] S3. Use the historical temperature series and historical external variable series of the geothermal well to train the regression model to obtain a prediction model.

[0069] Among them, the objective function of the prediction model is a weighted least squares objective function; the weight in the objective function is an exponential decay weight.

[0070] Furthermore, before S3, the method further includes:

[0071] The historical temperature series and the historical external variable series of the geothermal well are collected and preprocessed, wherein the preprocessing may include interpolation processing, denoising processing and smoothing processing.

[0072] In the present invention, the specific process of model training may include the following steps:

[0073] (1) Data collection and preprocessing.

[0074] (1.1) Use downhole real-time temperature measuring instrument to collect continuous temperature signal at wellhead. The sampling interval can be 、 、 or higher frequency, recorded as , which is the historical temperature series.

[0075] (1.2) Use wellhead flowmeter and pressure gauge to record pumping flow simultaneously (Unit: m³ / h), production pressure (Unit: MPa), etc.; use ground weather stations or integrated weather sensors to collect surface air temperature (Unit: °C); Using the geothermal system supporting power generation / heating load collection equipment, the heating / power generation load coefficient can be obtained (Normalized dimensionless [0, 1]); after aggregation, recorded as external variables , that is, the historical external variable sequence.

[0076] (1.3) The above data is aggregated and uploaded to the ground monitoring center for formatting, missing value detection, and marking. If there are short-term data loss or abnormal mutations caused by temperature sensor drift, temporary interpolation or manual filling can be used. The pre-sorted sequence can also be pre-processed for "denoising" or "smoothing." Specifically, if the noise level is low, a moving average (window width of 3-5 points) can be used for rough filtering; if the noise level is high, wavelet threshold denoising (such as the DB4 wavelet, hard thresholding) can be used.

[0077] (2) Parameter initialization of the regression model.

[0078] (2.1) Based on the cross-correlation analysis, determine the lag order of the main external variables, specifically:

[0079] If the maximum correlation lag between pumping flow and well temperature is about , then suppose .

[0080] If the maximum correlation lag between production pressure and well temperature is about , then suppose .

[0081] If the air temperature and well temperature lag by about , then suppose .

[0082] If the load is not significantly related to the well temperature, you can first set .

[0083] (2.2) Selection of the initial order of the regression model: usually If the amount of data is large, you can try .

[0084] (2.3) Initialize the parameters of the regression model , specifically, it can be set randomly or based on experience; parameters include: , , ,Will Initially set to a small random number or an initial value determined based on simple linear regression results.

[0085] (3) Construct the response vector and objective function.

[0086] (3.1) Set the length of the time rolling window , usually select the hourly data of the last 3 to 6 months, for example, if the sampling frequency , then we can set or .

[0087] (3.2) For each moment in the time rolling window Assign exponential decay weights: ;

[0088] in, for The exponential decay weight of time, is the attenuation coefficient.

[0089] (3.3) Construct the response vector: For each ( from arrive ),

[0090] According to the historical temperature series of the geothermal wells collected, the autoregressive term vector of the model input is determined .

[0091] Determine the sliding average term vector ,initial It can be set to 0 first.

[0092] According to the historical external variable sequence collected, the external variable term vector of the model input is determined .

[0093] Determine the seasonal term vector .

[0094] The above response vector is input into the following regression model:

[0095] .

[0096] (3.4) Construct weighted least squares objective function , the expression is as follows: .

[0097] By assigning higher weights to recent data, the model parameters can respond to changes in formation conditions and equipment performance drift in real time, thus avoiding the drawbacks of parameter failure under fixed parameters or fixed windows.

[0098] (3.5) Use numerical optimization algorithms such as iterative weighted least squares (IRLS) or quasi-Newton method to optimize the parameters Solve until the objective function converges or reaches the preset number of iterations, and finally obtain the Model parameter estimation .

[0099] S4. Input the current temperature sequence of the geothermal well and the current external variable sequence into the prediction model to obtain the temperature prediction value of the geothermal well at the next moment.

[0100] At the moment After completing all parameter updates, you can directly update the Time period( Can 、 、 ) to make a rolling forecast:

[0101] ;

[0102] right Use the "previous step prediction value" to replace Re-forecast to form a rolling forecast sequence.

[0103] Preferably, after S3, the method further includes:

[0104] (1) Determine the time rolling window and use the prediction model to determine the predicted temperature sequence of the geothermal well within the time rolling window.

[0105] (2) Using the predicted temperature sequence to update the historical temperature sequence in the time rolling window to obtain an updated temperature sequence, and using the updated temperature sequence and the historical external variable sequence to train the prediction model to obtain an updated model.

[0106] Correspondingly, S4 specifically includes: inputting the current temperature sequence of the geothermal well and the current external variable sequence into the update model to obtain the temperature prediction value of the geothermal well at the next moment.

[0107] The predicted temperature sequence is used to update the historical temperature sequence in the time rolling window to obtain an updated temperature sequence, which specifically includes:

[0108] First, the residual sequence of the historical temperature sequence and the predicted temperature sequence within the time rolling window is obtained, and the confidence interval is determined based on the residual sequence; then the temperature values ​​outside the confidence interval in the historical temperature sequence are removed to obtain the updated temperature sequence.

[0109] The residual sequence of the historical temperature series and the predicted temperature series within the above-mentioned time rolling window can be calculated using the following formula:

[0110] ;

[0111] in, is the residual sequence; is the historical temperature series; To predict the temperature series.

[0112] The above confidence interval is determined based on the residual sequence, specifically including:

[0113] Determine the weighted residual mean and weighted residual variance based on the residual sequence and exponential decay weights;

[0114] The upper and lower thresholds are determined based on the weighted residual mean and weighted residual variance, and the upper and lower thresholds are combined to form a confidence interval.

[0115] Specifically, the weighted residual mean is calculated using the following formula: and weighted residual variance : , ;

[0116] at this time, .

[0117] The confidence interval is [ ].

[0118] If at some moment If the value exceeds the above confidence interval, the moment is determined to be an abnormal point, the temperature value at that moment is removed from the historical temperature sequence, and the point is not used for the next round of parameter update.

[0119] The present invention calculates the weighted residual mean in the time rolling window and weighted residual variance , with a threshold Detect outliers and remove them from the historical temperature series without including them in the next round of parameter updates. Compared to methods that only use wavelet thresholds or fixed thresholds for elimination, this method can dynamically determine anomalies based on the prediction results, preventing the model from being dragged back by outliers.

[0120] In another embodiment of the present invention, determining the confidence interval based on the residual sequence specifically includes:

[0121] Determine the residual moving mean and residual standard deviation based on the residual sequence;

[0122] The upper and lower thresholds are determined based on the residual moving mean and residual standard deviation, and the upper and lower thresholds are combined into a confidence interval.

[0123] For example, directly calculate the recent Time period (such as ) Residual moving mean of the residual sequence and the residual standard deviation ,like , the moment is considered an outlier, the temperature value at that moment is removed from the historical temperature sequence, and the point is not used for the next round of parameter updates. This method does not require exponential weighting and is suitable for scenarios with relatively low frequency of abnormal fluctuations and relatively stable data.

[0124] After removing abnormal points from the historical temperature series, an updated temperature series is obtained.

[0125] Furthermore, the attenuation coefficient can be determined based on the updated temperature sequence and the predicted temperature sequence. The calculation formula is as follows:

[0126] .

[0127] After getting the updated temperature series and attenuation coefficient After that, the parameters of the prediction model can be estimated again, and the cycle iterates until all residuals are within the confidence interval or the maximum number of iterations is reached.

[0128] Finally, the predicted temperature series and confidence intervals are output to the ground monitoring center for real-time reference by the power generation / heating system. Future load scheduling recommendations, heat distribution plans, or maintenance warnings can be generated based on the predicted temperature series. Model parameters can also be periodically saved for quarterly / annual review and analysis, and recalibrated regularly. etc. model structures.

[0129] Compared with the prior art, the present invention has the following significant beneficial effects:

[0130] (1) High-precision prediction.

[0131] The present invention uses "double seasonal harmonics + multi-source external variable fusion + adaptive weighted update" to simultaneously capture the diurnal and annual cycles, multi-source physical driving factors and real-time updates to make the model respond more quickly and accurately to geothermal well temperature changes. For example, In short-term forecasts, the root mean square error (RMSE) is reduced from 1.5°C of traditional ARMA to 0.4°C; in 7-day medium-term forecasts, the RMSE is reduced from 1.5°C to 0.6°C.

[0132] (2) Strong robustness and strong exception handling capabilities.

[0133] The present invention adopts "dynamic residual statistical anomaly detection + local interpolation correction". The dynamic judgment based on residuals is combined with bilinear interpolation correction, making the model more robust when facing outliers. It can automatically filter out sudden anomalies such as well shutdown maintenance and temperature meter drift, and avoid the influence of abnormal points on subsequent model parameters. Experiments have shown that high prediction accuracy can still be maintained when the occurrence rate of abnormal points is about 1% to 2%.

[0134] (3) Strong adaptive ability and adaptability to long-term non-stationary changes.

[0135] The present invention is based on the basic principle that exponential weighting makes new data have a greater impact and old data decay quickly, and parameters can be dynamically adjusted, which is suitable for slow non-stationary systems. By adopting "rolling window exponential weighted least squares online update", the parameter drift caused by formation heat storage decay and equipment aging can be captured in real time, so that the parameters are updated smoothly over time throughout the year. A single model can maintain stable prediction effects in different time periods without human intervention.

[0136] (5) The project has strong usability and scalability.

[0137] This method significantly improves the accuracy and robustness of geothermal well temperature prediction. Furthermore, the parameters involved in the method can be flexibly adjusted based on the actual project site. This method has excellent engineering applicability and can provide a reliable prediction reference for geothermal power generation and geothermal heating systems, helping to further improve resource utilization efficiency and reduce operation and maintenance costs.

[0138] The above descriptions are merely a few embodiments of the present application and do not constitute any form of limitation to the present application. Although the present application discloses the preferred embodiments as above, they are not intended to limit the present application. Any technical personnel familiar with the present profession, without departing from the scope of the technical solution of the present application, using the technical content disclosed above to make slight changes or modifications are equivalent to equivalent implementation cases and fall within the scope of the technical solution.

Claims

1. A method for predicting geothermal well temperature series, characterized in that: The method comprises: S1. Constructing a daily cycle term and an annual cycle term of the geothermal well temperature, and determining a seasonal term of the geothermal well temperature based on the daily cycle term and the annual cycle term; S2. constructing an autoregressive term, a sliding average term, and an external variable term of the geothermal well temperature, and constructing a regression model of the geothermal well temperature based on the autoregressive term, the sliding average term, the external variable term, and the seasonal term; S3. Using the historical temperature series and the historical external variable series of the geothermal well to train the regression model to obtain a prediction model; S4. Input the current temperature sequence of the geothermal well and the current external variable sequence into the prediction model to obtain the temperature prediction value of the geothermal well at the next moment.

2. The method according to claim 1, characterized in that The external variable term for constructing the geothermal well temperature in S2 specifically includes: Identify multiple external variables that affect geothermal well temperature and determine the lag order of each external variable; The external variable term of geothermal well temperature is constructed based on multiple external variables and their lag orders.

3. The method according to claim 1, characterized in that The objective function of the prediction model is a weighted least squares objective function; the weights in the objective function are exponential decay weights.

4. The method according to claim 3, characterized in that After S3, the method further includes: Determining a time rolling window, and determining a predicted temperature sequence of the geothermal well within the time rolling window using the prediction model; Using the predicted temperature sequence to update the historical temperature sequence in the time rolling window to obtain an updated temperature sequence, and using the updated temperature sequence and the historical external variable sequence to train the prediction model to obtain an updated model; Correspondingly, the step S4 specifically includes: inputting the current temperature sequence of the geothermal well and the current external variable sequence into the update model to obtain the temperature prediction value of the geothermal well at the next moment.

5. The method according to claim 4, characterized in that The method of updating the historical temperature sequence in the time rolling window by using the predicted temperature sequence to obtain an updated temperature sequence specifically includes: Obtaining a residual sequence of the historical temperature sequence and the predicted temperature sequence within the time rolling window, and determining a confidence interval based on the residual sequence; The temperature values ​​in the historical temperature sequence that are beyond the confidence interval are removed to obtain an updated temperature sequence.

6. The method according to claim 5, characterized in that Determining the confidence interval according to the residual sequence specifically includes: Determining a weighted residual mean and a weighted residual variance according to the residual sequence and the exponential decay weight; An upper threshold and a lower threshold are determined according to the weighted residual mean and the weighted residual variance, and the upper threshold and the lower threshold are combined to form a confidence interval.

7. The method according to claim 5, characterized in that Determining the confidence interval according to the residual sequence specifically includes: Determine the residual moving mean and the residual standard deviation according to the residual sequence; An upper threshold and a lower threshold are determined according to the residual moving mean and the residual standard deviation, and the upper threshold and the lower threshold are combined to form a confidence interval.

8. The method according to claim 1, characterized in that The daily cycle term and the annual cycle term are both in the form of double harmonic sine and cosine.

9. The method according to claim 1, characterized in that Before S3, the method further includes: A historical temperature sequence and a historical external variable sequence of a geothermal well are collected, and the historical temperature sequence and the historical external variable sequence are preprocessed.

10. The method according to claim 9, characterized in that The preprocessing includes interpolation processing, noise removal processing and smoothing processing.

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