A deep learning-based foundation pit support pile deformation prediction method

Abstract

The application provides a kind of based on deep learning's foundation pit support pile deformation prediction method, it is related to foundation pit engineering safety monitoring technical field, the application is by establishing monitoring network continuous acquisition multidimensional feature data and support pile horizontal deformation value and record time stamp;Set time window length and prediction step, generate sample along time axis, divide into training set and test set;Build AM-TKAN initial model, determine the type and initial range of to-be-optimized hyperparameters, generate several hyperparameter combinations as individuals;Train each individual corresponding model on the training set and calculate the error, update the hyperparameters according to the hippo optimization algorithm, output the candidate optimal hyperparameter combination that meets the error requirement;Use the validation set to select the model with the smallest validation error as the final prediction model;Input real-time data into the final prediction model, and output the deformation prediction result.The application realizes high-precision prediction of foundation pit support pile horizontal deformation.

Description

Technical Field

[0001] This invention relates to the field of safety monitoring and deformation prediction technology for foundation pit engineering, specifically a method for predicting the deformation of foundation pit support piles based on deep learning. Background Technology

[0002] In deep foundation pit engineering, predicting the deformation of the retaining structure is a crucial step in ensuring construction safety. With the development of data-driven technologies, deep learning-based prediction methods have gradually become a research hotspot.

[0003] In the prior art, for example, Chinese patent application CN111680343A, entitled "A Method for Predicting Deformation of Deep Foundation Pit Retaining Structures Based on Deep Learning," discloses a method for predicting the deformation of deep foundation pit retaining structures based on deep learning. This method first analyzes the factors affecting deformation, selects several of the most important influencing factors, and divides them into dynamic and static influencing factors. Historical data is then initialized and normalized. Next, a tensor generator is constructed, and according to a preset backtesting and prediction period, tensors and deformation variables of training data, validation data, and test data are generated from the historical data. Then, a deep learning network model coupling a convolutional neural network and a long short-term memory network is constructed, where the convolutional neural network branch inputs static influencing factors, and the long short-term memory network branch inputs dynamic influencing factors. Finally, a prediction model is obtained through training, which is used to output the deformation variables of the retaining structure.

[0004] The above method, by coupling convolutional neural networks and long short-term memory networks, has achieved a certain degree of prediction of the deformation of the foundation pit retaining structure. However, this method still has the following shortcomings: First, this method uses a structure that couples convolutional neural networks with long short-term memory networks. Its model architecture is relatively fixed, making it difficult to adaptively adjust the temporal dependencies within the model according to the data characteristics. It also has limited ability to model complex and nonlinear time dynamic features during the deformation of the foundation pit.

[0005] Second, although the method sets back and prediction periods before model training, it does not systematically optimize the model's hyperparameters (such as learning rate, number of network layers, number of hidden units, etc.). The selection of hyperparameters depends on human experience or simple trial and error, making it difficult to guarantee the optimal performance of the model under different engineering conditions.

[0006] Third, this method does not incorporate model interpretability analysis. The prediction results only output the numerical values ​​of deformable variables, which cannot quantify the contribution of each influencing factor to the prediction results. This makes it difficult for engineers to understand the basis of the model's decision-making, which is not conducive to the formulation of on-site early warning and targeted prevention and control measures.

[0007] Therefore, there is an urgent need to provide a method for predicting the horizontal deformation of foundation pit support piles that can enhance time-series modeling capabilities, adaptively optimize hyperparameters, and possess interpretability, in order to solve the aforementioned problems existing in the prior art.

[0008] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0009] The purpose of this invention is to provide a deep learning-based method for predicting the deformation of foundation pit support piles, so as to solve the problems mentioned in the background art.

[0010] To achieve the above objectives, the present invention provides the following technical solution: A deep learning-based method for predicting the deformation of foundation pit support piles, comprising the following steps: Step 1: Establish a monitoring network within the target foundation pit, continuously collect multidimensional feature data and horizontal deformation values ​​of the support piles in chronological order through the monitoring network, and record the corresponding timestamps; Step 2: Set the time window length and prediction step size, use multidimensional feature data within multiple consecutive time windows as input samples, use the horizontal deformation value of the support pile at the time corresponding to the prediction step size as the label, slide along the time axis to generate samples, and divide the samples into training sets. Step 3: Construct the initial AM-TKAN model and determine the types of hyperparameters to be optimized. Set the initial range for each type of hyperparameter, extract the values ​​of each type of hyperparameter within the initial range to form several hyperparameter combinations, and treat each hyperparameter combination as an individual. Step 4: Construct the AM-TKAN initial model for each individual's corresponding hyperparameter combination, train each individual on the training set and calculate the error value, evaluate the fitness of the individual based on the error value, generate a new generation of hyperparameter individuals according to the position update rule of the Hippo optimization algorithm, and perform boundary pruning on hyperparameters that exceed the limit. After reaching the preset number of iterations, output the hyperparameter combination with the required error value as the candidate optimal hyperparameter combination. Step 5: Validate the initial AM-TKAN model corresponding to the candidate optimal hyperparameter combination based on the training set, calculate the validation error, and select the model with the smallest validation error as the final AM-TKAN prediction model. Step 6: Input the real-time collected multidimensional feature data into the final AM-TKAN prediction model according to the time window, and output the prediction results of the horizontal deformation of the support pile at the time corresponding to the prediction step length; Boundary clipping is performed on hyperparameters that exceed the limits. The specific operation is as follows: For the model training learning rate and model regularization coefficient, if the hyperparameter value obtained after position update is greater than the upper limit of the initial range of the model training learning rate and model regularization coefficient, then the hyperparameter value is modified to the upper limit value. If the hyperparameter value obtained after the position update is less than the initial lower limit of the model training learning rate and the model regularization coefficient, then the hyperparameter value is modified to the lower limit value. For batch size, number of model layers, and model hidden layer dimension, after the position is updated, the discrete value closest to the updated hyperparameter value is selected from the discrete value sets corresponding to each of the batch size, number of model layers, and model hidden layer dimension as the pruned hyperparameter value; if there are two discrete values ​​with the same difference from the updated hyperparameter value, the smaller discrete value is selected as the pruned hyperparameter value.

[0011] Furthermore, data on settlement of surrounding buildings, displacement of existing culvert structures, deformation of support piles, changes in anchor cable axial force, fluctuations in groundwater level, and settlement of pipelines are also collected.

[0012] Furthermore, the monitoring network is deployed with monitoring points in the following manner: Settlement data of surrounding buildings: monitoring points are set up on existing buildings within the excavation influence range of the target foundation pit. The excavation influence range refers to the area extending outward from the edge of the target foundation pit by 1 to 2 times the excavation depth of the foundation pit. Monitoring points for each existing building are set up at the four corners of the building or at the load-bearing wall. Displacement monitoring points for existing culvert structures: These are set up above and on both sides of the existing culvert structure within the influence range of the target pit. A monitoring section is set up at a preset interval along the culvert direction. Monitoring points are set up at the top of the culvert and on both wing walls of each section. Support pile deformation monitoring points: A clinometer tube is laid at a preset interval along the perimeter of the target foundation pit. The depth of the clinometer tube is consistent with the depth of the bottom of the support pile. It is used to collect horizontal displacement data at different depths along the pile body. The horizontal displacement data at the top of the pile is used as the horizontal deformation value of the support pile, and the horizontal displacement data at other depths of the pile body is used as a one-dimensional feature in the multi-dimensional feature data. Anchor cable axial force change monitoring points: These points are set on the anchor cables according to a preset percentage of the total number of anchor cables. The locations include the long side, short side, and inside and outside corners of the foundation pit. Groundwater level fluctuation monitoring points: Water level observation holes are set up at preset intervals around the perimeter of the foundation pit, with the hole depth being lower than the preset depth below the design bottom elevation of the foundation pit; Pipeline settlement monitoring points: These are set up above existing pipelines within the influence range of the foundation pit, with one monitoring point placed at a predetermined interval along the pipeline route.

[0013] Furthermore, the types of hyperparameters to be optimized include: model training learning rate, batch size, number of model layers, hidden layer dimension, and model regularization coefficient.

[0014] Furthermore, based on the initial range of each type of hyperparameter, the values ​​of each type of hyperparameter are extracted within this initial range to form several sets of hyperparameter combinations: The initial range is formed by the lower and upper limits of the model training learning rate and the model regularization coefficient, respectively. Based on the lower limit, the pre-selected parameter set of the model training learning rate and the model regularization coefficient is gradually generated at logarithmic intervals until the preset upper limit is reached or exceeded. The initial range is formed by the preset lower and upper limits of batch size, number of model layers, and hidden layer dimension, respectively. Based on the preset lower limit, the set of pre-selected parameters for batch size, number of model layers, and hidden layer dimension is generated step by step with a linear step size until the preset upper limit is reached or exceeded. By performing a Cartesian product on the preselected parameter sets for each type of hyperparameter, several sets of hyperparameter combinations are obtained.

[0015] Furthermore, the hyperparameters corresponding to each individual are combined to construct the initial AM-TKAN model, which is then trained on the training set one by one and the error value is calculated. The specific operation is as follows: For each individual, an initial AM-TKAN model is constructed based on its corresponding hyperparameter combination; Each AM-TKAN initial model is trained using the training set, specifically as follows: The multidimensional feature data within each time window of the training set is input into the AM-TKAN initial model to obtain the predicted value of the horizontal deformation of the support pile at the prediction step time corresponding to that time window. Subtract the predicted horizontal deformation value of the support pile at each prediction step from the actual horizontal deformation value of the support pile at the same time point to obtain the prediction error value corresponding to that time window. Calculate the average of the prediction error values ​​for all time windows, and use this average as the fitness value for that individual.

[0016] Furthermore, based on the position update rules of the Hippo optimization algorithm, a new generation of hyperparameter individuals is generated, and boundary pruning is performed on hyperparameters that exceed the limits. After a preset number of iterations, the hyperparameter combination whose output error value meets the requirements is selected as the candidate optimal hyperparameter combination. The specific operation is as follows: The hyperparameter combination corresponding to each individual is encoded as a hippo individual in the hippo optimization algorithm; Based on the fitness value of each individual hippopotamus, perform the following operations: Hippos with fitness values ​​lower than the current population average fitness value are moved toward the position of the hippo with the highest fitness value. The movement step size is the product of a preset first random number and the movement distance. A new hippopotamus individual is randomly generated. If the fitness value of the new hippopotamus individual is greater than the fitness value of the current hippopotamus individual, the current hippopotamus individual is updated to the new hippopotamus individual. Otherwise, the current hippopotamus individual is moved a preset second random number of times in the direction of the new hippopotamus individual's position. The current hippopotamus individual is taken as a hippopotamus juvenile. Based on the position of the current hippopotamus juvenile, a random perturbation vector within a preset range is added to generate a new hippopotamus juvenile. If the fitness value of the new hippopotamus juvenile is greater than the fitness value of the current hippopotamus individual, then the new hippopotamus juvenile is updated; otherwise, the current hippopotamus individual remains unchanged. The updated hippo individual is decoded into the corresponding hyperparameter combination; For hyperparameter values ​​that exceed the initial range of each type of hyperparameter, clip them to the corresponding initial range boundary; Repeat the above steps until the preset number of iterations is reached; The hyperparameter combinations corresponding to the top few individuals with the smallest fitness values ​​at the end of the iteration are taken as candidate optimal hyperparameter combinations.

[0017] Furthermore, the AM-TKAN initial model corresponding to the candidate optimal hyperparameter combination is validated using a validation set, and the model with the smallest validation error is selected as the final AM-TKAN prediction model. The specific operation is as follows: The training set is divided into a training subset and a validation set according to a preset ratio; Substitute the candidate optimal hyperparameter combination into the AM-TKAN initial model to obtain the hyperparameter-optimized AM-TKAN model; The AM-TKAN model with optimized hyperparameters is trained using a training subset, specifically as follows: Input the multidimensional feature data of each time window in the training subset into the trained model to obtain the predicted value of the horizontal deformation of the support pile at the predicted step time corresponding to that time window. The predicted value of the horizontal deformation of the support pile at the predicted step length is subtracted from the actual horizontal deformation value of the support pile at the same time point to obtain the prediction error value corresponding to the time window. Adjust the internal weights of the model using the backpropagation algorithm, and repeat the above process until the prediction error value converges. The trained AM-TKAN model was validated using a validation set, specifically as follows: The multidimensional feature data in each time window of the validation set is input into the trained AM-TKAN model to obtain the predicted value of the horizontal deformation of the support pile at the prediction step time corresponding to that time window. The predicted value of the horizontal deformation of the support pile at the predicted step length is subtracted from the actual horizontal deformation value of the support pile at the same time point to obtain the prediction error value corresponding to the time window. Calculate the average of the prediction error values ​​for all time windows, and use it as the validation error of the AM-TKAN model; Repeat the above steps to calculate the validation error of the model corresponding to each candidate optimal hyperparameter combination, and select the model with the smallest validation error as the final AM-TKAN prediction model.

[0018] Compared with the prior art, the beneficial effects of the present invention are: Based on the time-series characteristics of foundation pit monitoring data, this invention establishes a monitoring network to continuously collect multi-dimensional feature data and horizontal deformation values ​​of support piles in chronological order and record timestamps. By setting the time window length and prediction step size, training samples are generated by sliding along the time axis, clarifying the temporal correspondence between input and output, and providing a well-structured training data foundation for subsequent time-series prediction models.

[0019] This invention constructs an AM-TKAN initial model and uses the Hippo optimization algorithm to globally optimize the model's hyperparameters. Several hyperparameter combinations are randomly generated within the initial range to form an initial population. Through iterative training, error evaluation, position update, and boundary pruning, the hyperparameter combinations whose error values ​​meet the requirements are output as candidate optimal hyperparameter combinations. This achieves adaptive optimization of the model's hyperparameters, overcoming the limitations of existing technologies that rely on human experience or simple trial and error to select hyperparameters. It significantly improves the model's adaptability and prediction accuracy under different engineering conditions.

[0020] This invention further validates the model corresponding to the candidate optimal hyperparameter combination through a validation set, selects the model with the smallest validation error as the final prediction model, inputs the real-time collected multidimensional feature data into the final prediction model according to the time window, and outputs the prediction result of the horizontal deformation of the support pile at the time corresponding to the prediction step length, thus realizing high-precision prediction of the horizontal deformation of the foundation pit support pile. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the steps of the present invention; Figure 2 This is a schematic diagram illustrating the construction of a sliding time window according to the present invention. Figure 3 This is a schematic diagram illustrating the construction of hyperparameter combinations and model training according to the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0023] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0024] Example: Please see Figure 1-3 The present invention provides a technical solution: A deep learning-based method for predicting the deformation of foundation pit support piles, comprising the following steps: Step 1: Establish a monitoring network within the target foundation pit. Continuously collect multidimensional feature data and horizontal deformation values ​​of the support piles in chronological order through the monitoring network, and record the corresponding timestamps.

[0025] This embodiment uses a specific foundation pit project as an example. The project covers a total area of ​​approximately 9.04 hectares, with a total building area of ​​approximately 199,800 square meters. The total perimeter of the foundation pit is approximately 1047 meters, and the excavation depth ranges from 13.95 meters to 21.75 meters. The main structure adopts a layout combining one floor above ground (partially semi-underground) and two floors underground, primarily serving as a public transportation transfer center, long-distance passenger transport hub, parking area for private vehicles, and related supporting services. Due to the large excavation depth and complex surrounding environment, real-time monitoring of the support structure and the surrounding environment is necessary to ensure construction safety.

[0026] To achieve accurate prediction of the horizontal deformation of foundation pit support piles, it is first necessary to construct an intelligent monitoring network capable of real-time and continuous acquisition of multi-dimensional feature data. The specific implementation method is as follows: Determine the monitoring points and sensor deployment plan: Settlement monitoring points for surrounding buildings: Settlement monitoring points were set up on existing buildings within the excavation influence area of ​​the foundation pit. The excavation influence area refers to the region extending outward from the edge of the foundation pit by 1 to 2 times the excavation depth. In this embodiment, the maximum excavation depth of the foundation pit is 21.75 meters, therefore the excavation influence area is a strip-shaped area approximately 22 to 44 meters beyond the edge of the foundation pit. Within this area, at least 4 monitoring points were set up on each existing building. The monitoring points were selected at the four corners of the building or at the load-bearing walls. For frame structures, the monitoring points were set up on the frame columns at the four corners of the building; for masonry structures, the monitoring points were set up on the load-bearing walls of the building. The location of the monitoring points should ensure that they can reflect the overall settlement changes of the building. In this embodiment, a total of 32 settlement monitoring points were set up on surrounding buildings. Displacement monitoring points for existing culvert structures: Displacement monitoring points are set up above and on both sides of the existing culvert structure within the influence range of the foundation pit. A monitoring section is set up every 15 meters along the culvert direction. Monitoring points are set up at the top of the culvert and at the wing walls on both sides of each section to monitor the vertical and horizontal displacement of the culvert structure. In this embodiment, a total of 18 displacement monitoring points for existing culvert structures are set up.

[0027] Deformation monitoring points for support piles: Inclined tubes are installed on the support piles in the foundation pit to monitor the horizontal displacement of the support piles along the depth direction. One inclined tube is installed every 20 to 30 meters around the perimeter of the foundation pit, with the burial depth of the inclined tube consistent with the bottom depth of the support pile. In this embodiment, a total of 42 deformation monitoring points for the support piles are installed, and displacement data is collected every 0.5 meters along the depth direction at each monitoring point. It should be noted that the deformation data of the support piles collected in this step includes horizontal displacement values ​​at different depths along the pile body. The horizontal displacement value at the pile top is used as the horizontal deformation value of the support pile in subsequent steps, while the horizontal displacement values ​​at other depths along the pile body are used as one-dimensional features in the multi-dimensional feature data for model input.

[0028] Anchor cable axial force variation monitoring points: Axial force gauges are installed on the anchor cables of the foundation pit support structure to monitor the changes in anchor cable axial force as construction progresses. Representative anchor cables are selected, typically with axial force gauges installed on 5% to 10% of the total number of anchor cables in each layer. The locations include key areas such as the long and short sides of the foundation pit and internal and external corners. In this embodiment, a total of 56 anchor cable axial force monitoring points are installed.

[0029] Groundwater level fluctuation monitoring points: Groundwater level observation wells are installed around and inside the foundation pit to monitor changes in the groundwater level. One well is installed every 30 to 50 meters around the perimeter of the foundation pit, and the well depth should be 5 meters below the designed bottom elevation of the foundation pit. In this embodiment, a total of 24 groundwater level monitoring points are installed.

[0030] Pipeline settlement monitoring points: Settlement monitoring points are directly installed above existing pipelines within the influence range of the foundation pit, including water supply pipelines, drainage pipelines, gas pipelines, and power pipelines, with one monitoring point every 15 to 20 meters along the pipeline route. In this embodiment, a total of 45 pipeline settlement monitoring points are installed.

[0031] To achieve real-time synchronous acquisition and transmission of data from the aforementioned monitoring points, this embodiment employs multi-sensor fusion technology and an Internet of Things (IoT) architecture for system integration, specifically including: Appropriate sensors were selected based on the measurement requirements of each monitoring point. Settlement data for surrounding buildings and pipelines were collected using a hydrostatic level or electronic level, with a measurement accuracy of [insert accuracy here]. 0.1mm; The displacement of the existing culvert structure is measured using a wire-type displacement sensor, with a measurement accuracy of [missing information]. 0.5mm; the deformation of the support piles was measured using a servo accelerometer-type inclinometer, with an accuracy of [missing information]. 0.02mm / 500mm; the anchor cable axial force is measured using a vibrating wire axial force gauge with an accuracy of [missing information]. 0.5%FS; Groundwater level is measured using a pressure level gauge with an accuracy of [missing information]. 0.5%FS. All sensors have digital signal output capabilities, enabling them to directly output monitored values.

[0032] A data acquisition terminal is set up near each monitoring point. This terminal connects wirelessly to the sensor and collects data at a preset frequency (in this embodiment, once every 6 hours). It automatically reads the sensor data and converts it into a standard format. The wireless communication module within the acquisition terminal uploads the monitoring data to a cloud data server in real time via an Internet of Things (IoT) protocol.

[0033] The cloud data server receives monitoring data uploaded by various data collection terminals, categorizes and stores it according to timestamps and monitoring point numbers, forming the original monitoring database.

[0034] The intelligent monitoring network has been in operation since the commencement of the foundation pit project. Each sensor continuously collects data according to the set acquisition frequency. The collected data includes: settlement data of surrounding buildings, displacement data of existing culvert structures, deformation data of support piles, axial force change data of anchor cables, groundwater level fluctuation data, and pipeline settlement data, as well as horizontal deformation values ​​of support piles extracted from the support pile deformation monitoring points.

[0035] Since subsequent steps in this embodiment require time-series prediction of the horizontal deformation of the support piles, all monitoring data must be organized and stored in chronological order. Specifically, the data management platform organizes all monitoring data collected at each time point into a single record. This record includes a timestamp, the aforementioned six types of monitoring data, and the corresponding horizontal deformation value of the support pile at that time point, forming a multidimensional feature data sequence arranged chronologically. As construction progresses, the multidimensional feature data sequence continues to grow, eventually forming a complete dataset containing multiple time points, each corresponding to six-dimensional feature data.

[0036] In this embodiment, from the start of the foundation pit excavation to the completion of the main structure construction, the cumulative time span for collecting monitoring data was approximately 18 months, resulting in approximately 2160 sets of multidimensional feature data sequences. These multidimensional feature data sequences will serve as the basic input for data preprocessing, model training, and prediction in subsequent steps.

[0037] Because the data collected by field sensors may be affected by factors such as equipment failure, signal interference, construction disturbances, and environmental changes, the original multidimensional feature data sequence inevitably contains outliers, missing values, noise interference, and non-equidistant sampling. Therefore, after obtaining the original multidimensional feature data sequence, it is preprocessed. The specific steps are as follows: Data Cleaning: This embodiment uses the Z-Score method to identify outliers. The principle of the Z-Score method is: for a set of data, calculate the degree of deviation of each data point from the population mean, and use the standard deviation as a scale for measurement. Specifically, the calculation method is as follows: for any data point in the multidimensional feature data sequence... Calculate its Z-Score value using the following formula: ,in, This represents the mean of the variable at that monitoring point across all time points. This represents the standard deviation of the monitored variable over all time points; According to statistical principles, when the distribution of data approximately follows a normal distribution, about 99.7% of the data points will fall on the mean. Within three standard deviations. Therefore, in this embodiment, data points with an absolute Z-Score greater than 3 are identified as outliers and removed from the multidimensional feature data sequence.

[0038] Abrupt Point Correction: After data cleaning, the multidimensional feature data sequence may still contain local abrupt changes caused by sudden geological conditions, instantaneous disturbances during construction, or occasional sensor drift. This embodiment uses nearest-neighbor interpolation to correct these abrupt changes. Specifically, for each data point in the multidimensional feature data sequence, the rate of change between it and the previous data point is calculated. If the rate of change exceeds a preset threshold (in this embodiment, it is set to exceed 30% between adjacent time points), then the point is identified as an abrupt change. For data identified as a abrupt change, linear interpolation is performed using the two nearest valid data points before and after the abrupt change, and the interpolated result replaces the original abrupt change value. The calculation formula is as follows: ,in, The nearest valid data point before the mutation point. The nearest valid data point after the mutation point. This is the new value after smoothing. Equal-time interval conversion: In practical engineering, due to sensor failures, communication interruptions, equipment maintenance, etc., data at some time points may be missing, resulting in equal intervals in the multi-dimensional feature data sequence. In addition, the data acquisition frequency of different detection projects may differ, which also leads to the misalignment of multi-dimensional data in time. Therefore, it is necessary to perform equal-time interval conversion on the data. In this embodiment, linear interpolation is used to uniformly convert all monitoring data into an equal-time interval sequence with an interval of 1 day. The specific operation is as follows: Using 8:00 AM every day as the baseline time point, a continuous time point sequence is generated, with the time span from the date of the first monitoring data point to the date of the last monitoring data point, resulting in a total of N equally spaced time points; For each target time point t, if original monitoring data exists for that time point, it is used directly; otherwise, linear interpolation is performed using the two most recent valid data points before and after that time point to calculate the estimated value for that time point. The formula for linear interpolation is as follows: ,in, The time point to be inserted. and They are respectively The time corresponding to the two most recent valid data points. and They are respectively Time and The observed value at time, For insertion The estimated value of the time.

[0039] Signal denoising: Foundation pit monitoring data often contains various noise components, including random noise caused by construction machinery vibration, sensor measurement noise, and background noise generated by geological activities. These noises can mask the true variation patterns in the data and affect the model's accurate capture of the deformation trend of the support piles. This embodiment uses wavelet threshold denoising to denoise the time interval sequence of equal-interval detection. The basic principle of wavelet thresholding denoising is as follows: The signal is decomposed into sub-signals of different frequency bands. Noise components are usually concentrated in the high-frequency sub-signals. By setting a threshold, components with smaller amplitudes in the high-frequency sub-signals are removed (considered as noise). Then, the remaining components are reconstructed to obtain the denoised signal. The specific operation steps are as follows: Wavelet decomposition: Wavelet basis functions are selected; in this embodiment, the db4 wavelet, i.e., the fourth-order wavelet in the Daubechies orthogonal wavelet family, is used to perform multi-level wavelet decomposition on the equidistant multidimensional feature data sequence, obtaining low-frequency approximation coefficients and high-frequency detail coefficients. In this embodiment, the number of decomposition levels is set to 5. Thresholding: For the high-frequency detail coefficients of each layer, a soft thresholding function is used. The soft thresholding function sets wavelet coefficients with amplitudes less than the threshold to zero and shrinks coefficients with amplitudes greater than the threshold towards zero. The threshold is selected using an unbiased risk estimation threshold criterion, which adaptively determines the optimal threshold based on the signal's noise level. The thresholding formula can be expressed as: ,in, These are the original wavelet coefficients. For the threshold, For symbolic functions, These are the wavelet coefficients after thresholding. Signal reconstruction: The processed high-frequency detail coefficients and the original low-frequency approximation coefficients are subjected to inverse wavelet transform to reconstruct the denoised signal; Feature Selection: This embodiment collected six types of multidimensional feature data, including: settlement data of surrounding buildings, displacement data of existing culvert structures, deformation data of support piles, axial force variation data of anchor cables, groundwater level fluctuation data, and pipeline settlement data. However, not all features have a significant impact on the horizontal deformation of support piles. Including features with weak correlation or no correlation as model input would not only increase the computational complexity of the model but also potentially introduce noise, reducing the model's prediction accuracy and generalization ability. Therefore, this embodiment uses Spearman correlation coefficient analysis to select features with high correlation to the horizontal displacement of support piles as model input.

[0040] The Spearman correlation coefficient is a nonparametric statistical method used to measure the monotonic correlation between two variables. It does not require the data to follow a normal distribution and is suitable for scenarios such as foundation pit monitoring data where nonlinear relationships may exist. Its calculation method is as follows: for two variables... and First, the observations are sorted by size to obtain their respective ranks. Then, the Pearson correlation coefficient between the ranks is calculated. The specific calculation formula is as follows: ,in, The number of observations, i.e., the total number of time points. For the first The difference in rank between two observations, i.e. First take out the first Feature values ​​at each time point (For example, the axial force value of an anchor cable on a certain day), sort this value among the feature values ​​at all time points, and obtain its rank in the feature sequence. Then retrieve the target variable values ​​at the same time point. (The horizontal displacement value of the support piles on the same day), sort this value among the target variables at all time points, and obtain its rank in the target variable sequence. Subtracting the two ranks gives the result. ; Spearman correlation coefficient is the number of observations. The value range of is [-1, 1]: when When the value is close to 1, it indicates a strong positive correlation between the two variables (an increase in one variable leads to an increase in the other); when... When the value is close to -1, it indicates a strong negative correlation (when one variable increases, the other decreases); when... When the value is close to 0, it indicates that there is no obvious monotonic correlation between the two.

[0041] The specific operations in this embodiment are as follows: Determine the target variable: The horizontal displacement data of the support pile is taken as the target variable, i.e. the prediction object. This data comes from the deformation monitoring points of the support pile. Displacement data is collected every 0.5 meters along the depth direction at each monitoring point. In this embodiment, the horizontal displacement of the pile top is selected as the target variable. Calculate the correlation coefficient: For each of the six multidimensional feature data, calculate the Spearman correlation coefficient between it and the horizontal displacement of the support pile; Feature selection: In this embodiment, the threshold for Spearman correlation coefficient is set to 0.3. The specific selection rule is as follows: if the absolute value of the Spearman correlation coefficient between a feature and the horizontal displacement of the support pile is greater than or equal to 0.3, then the feature is retained as the model input; if the absolute value of the correlation coefficient is less than 0.3, then the feature is considered to have a weak correlation with the horizontal displacement of the support pile and is removed.

[0042] After feature selection, this embodiment identified four categories of features highly correlated with the horizontal displacement of the support piles: support pile deformation data, anchor cable axial force variation data, settlement data of surrounding buildings, and groundwater level fluctuation data. Existing culvert structure displacement data and pipeline settlement data, whose Spearman correlation coefficients with the horizontal displacement of the support piles are less than 0.3 in this embodiment, are not used as model inputs.

[0043] Table 1 shows the feature selection results. According to Table 1, the deformation data of the support piles, the axial force variation data of the anchor cables, and the settlement data of surrounding buildings show a strong positive correlation with the horizontal deformation value of the support piles (correlation coefficients are 0.85, 0.72, and 0.58, respectively). The groundwater level fluctuation data shows a moderate negative correlation (correlation coefficient of -0.43). The correlation between these four types of features and the target variable all meet the preset threshold of greater than or equal to 0.3, and therefore are retained as model input. However, the absolute values ​​of the correlation coefficients for the existing culvert structure displacement data and pipeline settlement data are 0.21 and 0.18, respectively, which are lower than the preset threshold, indicating a weak correlation with the horizontal deformation value of the support piles; therefore, they are discarded. This selection result effectively reduces the dimensionality of the input features and avoids redundant features interfering with the model's prediction accuracy.

[0044] Table 1: Feature Filtering Results Normalization: After feature filtering, the remaining feature data have different units and numerical ranges. For example, the unit of horizontal displacement data of support piles is mm, and the numerical range is usually between 0 and 1. The anchor cable axial force data is in units of kN, with values ​​potentially reaching hundreds of kN; the groundwater level data is in units of meters, typically ranging from a few meters to tens of meters. If these data with different dimensions are directly input into the model, the features with larger values ​​will dominate the model training process, causing the features with smaller values ​​to be ineffective and affecting the model's learning performance. Therefore, this embodiment uses the Min-Max normalization method to uniformly map all feature data to the interval [0,1]. The calculation formula is as follows: ,in, These are the original eigenvalues. This is the minimum value of the feature across all time points. This represents the maximum value of the feature across all time points. These are the normalized eigenvalues.

[0045] Through the above processing, all feature data are converted into dimensionless values ​​in the range [0,1], eliminating the difference between dimensions and numerical ranges, and enabling the model to treat each feature dimension equally during training.

[0046] Step 2: Set the time window length and prediction step size, use multidimensional feature data within multiple consecutive time windows as input samples, use the horizontal deformation value of the support pile at the time corresponding to the prediction step size as the label, slide along the time axis to generate samples, and divide the samples into training sets.

[0047] The time window length is denoted as L, which refers to the time range covered by the historical data used for prediction, i.e., the number of consecutive time points included in the model input. The prediction step size is denoted as S, which refers to the time interval between the future time point that the model needs to predict and the current time point, i.e., the offset between the time point where the label is located and the last time point of the window.

[0048] This embodiment, through multiple preliminary experiments and comparisons, comprehensively considers prediction accuracy and model complexity, setting the time window length L=7 days and the prediction step size S=1 day. Specifically, this setting means using historical monitoring data from seven consecutive days (including multidimensional feature data and historical values ​​of the horizontal deformation of the support piles) to predict the horizontal deformation value of the support piles on the eighth day. This setting aligns with the practical engineering scenario of foundation pit deformation prediction, where deformation is a continuous and gradual process, and the deformation trend over the past week provides a good indication of short-term future deformation.

[0049] It should be noted that the specific values ​​of the time window length and prediction step size can be adjusted according to the characteristics of different projects and prediction needs. If the deformation of the foundation pit is greatly affected by construction disturbances and changes drastically, the window length can be appropriately shortened to enhance the model's sensitivity to recent changes; if the deformation trend of the foundation pit is relatively gentle and has strong long-term dependence, the window length can be appropriately extended to capture patterns over longer periods.

[0050] After determining the time window length L=7 and the prediction step size S=1, the sliding window method is used to convert the preprocessed time series data into samples. The specific operation is as follows: Suppose that the preprocessed time series data has N time points, each time point contains multidimensional feature data and horizontal deformation value of the support pile, where t represents the time point number, t=1,2,…,N.

[0051] The sliding window method's generation rule is as follows: For each time point t, starting from L+1 and ending at N-S+1, the multidimensional feature data of the L consecutive time points preceding that time point are taken as input samples, and the horizontal deformation value of the support pile at the S-th time point following that time point is taken as the label of that sample. Specifically: The input sample consists of multi-dimensional feature data from day tL to day t-1, a total of L days. The feature data of each day contains all feature dimensions retained after filtering in step 1. The label represents the horizontal deformation value of the support pile on day t+S-1.

[0052] like Figure 2The sliding time window construction sample diagram is shown in the figure (this diagram is based on 5 time points as an example, but the actual time window length in this embodiment is 7 days). By using the sliding time window, the multidimensional feature data of L consecutive time points are used as input to predict the horizontal deformation value of the support pile after the prediction step length S.

[0053] Taking L=7 and S=1 in this embodiment as an example: When t=8, the input sample is the multidimensional feature data from day 1 to day 7, and the label is the horizontal deformation value of the support pile on day 8; when t=9, the input sample is the multidimensional feature data from day 2 to day 8, and the label is the horizontal deformation value of the support pile on day 9; and so on, a new sample is generated each day the window slides forward. In this way, the original time series data is reconstructed into multiple samples with temporal correlation.

[0054] Through the sliding window operation described above, a total of M samples are generated. M equals the total number of time points N minus the time window length L, minus the prediction step size S, and finally added by 1. In this embodiment, the total number of time points N=540, the time window length L=7, and the prediction step size S=1, thus generating a total of 533 samples. The input of each sample is a two-dimensional data matrix, the first dimension of which is the time window length (7 days in this embodiment), and the second dimension is the number of feature dimensions (4 dimensions after feature filtering in step 1 in this embodiment). The output of each sample is a scalar value, namely the horizontal deformation value of the support pile at the prediction time.

[0055] After generating the samples, the training set consists of all 533 samples.

[0056] To facilitate model input in subsequent steps, this embodiment standardizes the data structure for each sample: The shape of the input sample X is (size, L, D), where size is the number of samples input in each training session, which is determined by the batch size, L is the length of the time window (7 in this embodiment), and D is the number of feature dimensions (4 in this embodiment). The shape of the label y is (size, 1), meaning that each sample corresponds to a prediction target value.

[0057] Step 3: Construct the initial AM-TKAN model and determine the types of hyperparameters to be optimized. Set the initial range for each type of hyperparameter, and extract the values ​​of each type of hyperparameter within the initial range to form several hyperparameter combinations. Each hyperparameter combination is treated as an individual.

[0058] The AM-TKAN model constructed in this embodiment is a hybrid neural network model that integrates the Temporal Kolmogorov-Arnold Network (TKAN) and the Attention Mechanism. The model is designed to model and predict time-series data of horizontal deformation of foundation pit support piles. The basic architecture of the model is as follows: Input layer: Receives the input samples generated in step 2. Each sample has a shape of (time window length L, feature dimension D). In this embodiment, L=7, D=4, therefore the input layer receives a 7×4 two-dimensional matrix, representing historical data of 4-dimensional features over 7 consecutive days; TKAN Layer: Input data first enters the TKAN layer for processing. The TKAN layer, through an external memory module and gating mechanisms including input gates, forget gates, and output gates, models long-term dependencies in time-series data, effectively capturing the evolution of horizontal deformation of foundation pit support piles over time. In this embodiment, the TKAN layer contains multiple sub-layers, and the specific structure of each sub-layer will serve as a hyperparameter to be optimized, which will be sought by the Hippo optimization algorithm in subsequent steps.

[0059] Attention Layer: An attention mechanism is introduced after the TKAN layer. The role of the attention layer is to dynamically assign weights to the features of each time step output by the TKAN layer, enabling the model to automatically identify key time steps in the input sequence that contribute significantly to the prediction results and assign higher weights to these key time steps, thereby improving the model's prediction accuracy and interpretability.

[0060] Output layer: Finally, a fully connected layer maps the output of the attention layer to the final predicted value, i.e., the horizontal deformation value of the support pile at a future moment. The output layer has 1 neuron, corresponding to a single prediction target.

[0061] It should be noted that in the above model architecture, the specific structural parameters of the TKAN layer, the learning rate during training, the batch size, and the regularization coefficient all significantly affect the model's predictive performance. These parameters are called hyperparameters and need to be set before model training. Since the optimal hyperparameter values ​​vary in different engineering scenarios, this embodiment uses the Hippo Optimization Algorithm to automatically optimize these hyperparameters to maximize the model's predictive accuracy.

[0062] Based on the model architecture and training requirements of this embodiment, the following five types of hyperparameters are identified as objects to be optimized: Model training learning rate: The learning rate is a hyperparameter in deep learning that controls the step size of model parameter updates. An excessively large learning rate may cause the model to fail to converge or even diverge during training; an excessively small learning rate will result in slow convergence, excessively long training time, and potential getting stuck in local optima. Therefore, the choice of learning rate has a decisive impact on the model's training performance and convergence speed. In this embodiment, the model training learning rate is treated as a first-type hyperparameter to be optimized. Batch size: Batch size refers to the number of samples used in each model parameter update. A batch size that is too small can lead to unstable model training and large fluctuations in gradient updates; a batch size that is too large will increase memory consumption and may cause the model to converge to a poor local optimum. Furthermore, the choice of batch size also affects the model's generalization ability. In this embodiment, batch size is treated as a second type of hyperparameter to be optimized. Model Layers: The number of model layers refers to the number of layers in the TKAN part of the AM-TKAN model. Increasing the number of layers can enhance the model's expressive power, enabling it to capture more complex nonlinear relationships. However, too many layers may lead to overfitting and increase training difficulty and computational cost; too few layers may lead to underfitting, failing to fully learn the patterns in the data. In this embodiment, the number of model layers is treated as a third type of hyperparameter to be optimized. Model hidden layer dimension: The model hidden layer dimension refers to the number of neurons in each hidden layer of the TKAN layer, or the feature dimension. The size of the hidden layer dimension determines the capacity of the model: the larger the dimension, the stronger the expressive power of the model, but the more prone it is to overfitting; the smaller the dimension, the more limited the expressive power of the model, and it may not be able to fully learn the complex patterns in the data. In this embodiment, the model hidden layer dimension is regarded as the fourth type of hyperparameter to be optimized; Model regularization coefficient: Regularization is a technique used to prevent model overfitting by limiting the complexity of model parameters by adding a penalty term to the loss function. The regularization coefficient controls the strength of the penalty term: too large a coefficient may lead to underfitting, while too small a coefficient cannot effectively suppress overfitting. In this embodiment, the model regularization coefficient is used as the fifth type of hyperparameter to be optimized.

[0063] To facilitate hyperparameter optimization in subsequent steps using the Hippo optimization algorithm, a reasonable initial search range needs to be set for each type of hyperparameter. The initial range must ensure coverage of possible optimal values ​​while avoiding an excessively large search space that leads to inefficient optimization. Based on experience and multiple pre-experiments in the field of deep learning, this embodiment sets the following initial ranges for the five types of hyperparameters: Initial range of model training learning rate: The initial range of the model training learning rate is set to 0.0001 to 0.1, using a logarithmic scale for search. The logarithmic scale means that within the range of 0.0001 to 0.1, the candidate learning rate values ​​are uniformly distributed according to powers of 10, i.e., possible values ​​include 0.0001, 0.0005, 0.001, 0.005, 0.01, 0.05, 0.1, etc. The reason for using a logarithmic scale instead of a non-linear scale is that the impact of changes in the learning rate on the model training effect is usually logarithmically sensitive; that is, changes in magnitude are more critical than small numerical changes. In this embodiment, the Hippo optimization algorithm will search for the optimal learning rate value within this range. The initial range of batch size is set to a discrete value set {16, 32, 64, 128, 256}. The choice of batch size is limited by hardware memory; an excessively large batch size may lead to insufficient GPU memory or system memory, while an excessively small batch size may affect training stability. The aforementioned discrete value set covers commonly used batch size values ​​in deep learning practice and can meet the training requirements of this embodiment. The Hippo Optimization Algorithm will search for the optimal batch size within this discrete set. Initial range of model layers: The initial range of model layers is set to a discrete set of values ​​{1, 2, 3, 4, 5}. This range covers common values ​​from shallow networks (1 layer) to medium-depth networks (5 layers). A model with too few layers (e.g., 1 layer) has limited expressive power, while too many layers (more than 5 layers) may increase the risk of overfitting and make training more difficult. The Hippo Optimization algorithm will search for the optimal number of model layers within this discrete set. The initial range of hidden layer dimensions is set to a discrete set of values ​​{32, 64, 128, 256, 512}. This range covers common hidden layer dimension values ​​from small capacity (32 dimensions) to large capacity (512 dimensions). Too small a hidden layer dimension (e.g., 32 dimensions) may lead to underfitting, while too large a hidden layer dimension (e.g., 512 dimensions or more) may increase the risk of overfitting and significantly increase computational cost. The Hippo Optimization Algorithm will search for the optimal hidden layer dimension within this discrete set. Initial range of model regularization coefficient: The initial range of the model regularization coefficient is set to 0.00001 to 0.01, and a logarithmic scale is used for the search. Regularization coefficients are typically small; excessively large regularization coefficients can over-constrain model parameters, leading to underfitting. In this embodiment, the logarithmic scale range is set to 10⁻⁵ to 10⁻², meaning possible values ​​include 0.00001, 0.00005, 0.0001, 0.0005, 0.001, 0.005, and 0.01. The Hippo optimization algorithm will search for the optimal regularization coefficient within this range.

[0064] After determining the hyperparameter types and setting the initial range, it is necessary to extract the values ​​of each type of hyperparameter within this initial range to form several hyperparameter combinations. Each hyperparameter combination is considered an individual and used for population initialization in the subsequent Hippo optimization algorithm. The specific operation is as follows: For each type of hyperparameter, a value is randomly selected within its set initial range. The values ​​extracted from the five types of hyperparameters are combined to form a five-dimensional vector, which represents a set of hyperparameter combinations, called an individual. For example, if a random selection yields a learning rate of 0.001, a batch size of 64, a model layer count of 3, a hidden layer dimension of 128, and a regularization coefficient of 0.0001, then these five values ​​together constitute an individual.

[0065] In this embodiment, according to the requirements of the Hippo optimization algorithm, the initial population size is set to 30 individuals. Therefore, the above method is repeated 30 times to generate 30 different hyperparameter combinations, i.e., 30 individuals, constituting the initial population. The hyperparameter combination represented by each individual will be substituted into the AM-TKAN model for training in subsequent steps, and the fitness value of that individual will be calculated based on the prediction error of the model on the validation set, thereby guiding the Hippo optimization algorithm to gradually search for the optimal hyperparameter combination.

[0066] It should be noted that the initial population size was determined through preliminary experiments: too few individuals may lead to insufficient search space coverage, making it difficult to find the global optimum; too many individuals will increase computational overhead. A population of 30 individuals strikes a good balance between search efficiency and computational cost.

[0067] Step 4: Construct the AM-TKAN initial model for each individual's corresponding hyperparameter combination, train each model on the training set and calculate the error value, evaluate the fitness of the individual based on the error value, generate a new generation of hyperparameter individuals according to the position update rule of the Hippo optimization algorithm, and perform boundary pruning on hyperparameters that exceed the limit. After reaching the preset number of iterations, output the hyperparameter combination whose error value meets the requirements as the candidate optimal hyperparameter combination.

[0068] For the model training learning rate, this embodiment sets its initial range to 0.0001 to 0.1. This range is set based on the following: when the learning rate is below 0.0001, the model parameter update step size is too small, resulting in extremely slow convergence and excessively long training time; when the learning rate is above 0.1, the parameter update step size is too large, easily leading to oscillations or even divergence in the loss function, preventing the model from converging. A logarithmic scale is used to generate the pre-selected parameter set, i.e., starting from 0.0001, it is generated progressively in powers of 10, resulting in the pre-selected parameter set {0.0001, 0.0005, 0.001, 0.005, 0.01, 0.05, 0.1}. The reason for using a logarithmic scale is that the impact of changes in the learning rate on the model training effect is usually logarithmically sensitive, meaning that changes in magnitude are more critical than small numerical changes.

[0069] For the model regularization coefficient, this embodiment sets its initial range to 0.00001 to 0.01. This range is set based on the following: when the regularization coefficient is below 0.00001, the penalty term is too weak and cannot effectively suppress model overfitting; when the regularization coefficient is above 0.01, the penalty term is too strong and may lead to model underfitting. A pre-selected parameter set is generated using a logarithmic scale, that is, starting from 0.00001, it is generated stepwise in powers of 10, resulting in the pre-selected parameter set {0.00001, 0.00005, 0.0001, 0.0005, 0.001, 0.005, 0.01}.

[0070] For batch size, this embodiment sets its initial range to 16 to 256. This range is based on the following: when the batch size is less than 16, gradient updates fluctuate significantly, leading to unstable training; when the batch size is greater than 256, memory consumption is excessive, and the model may converge to a poor local optimum. A pre-selected parameter set is generated with a linear step size of 16, i.e., starting with 16 and gradually increasing by 16, resulting in the pre-selected parameter set {16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256}.

[0071] Regarding the number of model layers, this embodiment sets the initial range to 1 to 5. This range is based on the following: if the number of layers is less than 1, the model cannot be built; if the number of layers is greater than 5, the model becomes too complex, prone to overfitting, and training becomes significantly more difficult. A pre-selected parameter set is generated with a linear step size of 1, that is, starting with 1 and gradually increasing by 1 to obtain the pre-selected parameter set {1,2,3,4,5}.

[0072] For the hidden layer dimension of the model, this embodiment sets its initial range to 32 to 512. This range is based on the following: when the hidden layer dimension is less than 32, the model capacity is too small to fully learn complex patterns in the data; when the hidden layer dimension is greater than 512, the number of model parameters is too large, easily leading to overfitting and a significant increase in computational cost. A pre-selected parameter set is generated with a linear step size of 32, i.e., starting with 32 and gradually increasing by 32, resulting in the pre-selected parameter set {32, 64, 96, 128, 160, 192, 224, 256, 288, 320, 352, 384, 416, 448, 480, 512}.

[0073] The pre-selected parameter sets of the above five categories of hyperparameters are combined using Cartesian products to obtain several sets of hyperparameter combinations. In this embodiment, the model training learning rate has 7 values, the batch size has 16 values, the number of model layers has 5 values, the hidden layer dimension has 16 values, and the model regularization coefficient has 7 values. Therefore, the total number of Cartesian product combinations is 7 × 16 × 5 × 16 × 7 = 62720 sets. Each set of hyperparameter combinations is treated as an individual.

[0074] like Figure 3 The diagram illustrates the construction and training of hyperparameter combinations. Each set of hyperparameters (including model training learning rate, batch size, number of model layers, hidden layer dimension, and model regularization coefficient) is used to construct an initial AM-TKAN model and train the model using the training set to evaluate the quality of the hyperparameter combination.

[0075] in accordance with Figure 3 As can be seen, each hyperparameter combination consists of five types of hyperparameters: model training learning rate, batch size, number of model layers, model hidden layer dimension, and model regularization coefficient. This combination is used to construct the initial AM-TKAN model and train it on the training set to calculate the fitness value.

[0076] It should be noted that the aforementioned 62,720 hyperparameter combinations cover all possible value combinations, ensuring the integrity of the hyperparameter search space. In actual computation, due to the large number of combinations, training and evaluating all 62,720 hyperparameter combinations one by one would be computationally too expensive. Therefore, this embodiment uses random sampling to select 30 individuals from the Cartesian product combinations as the initial population, ensuring search space coverage while controlling computational cost.

[0077] Fitness evaluation is a core step in hyperparameter optimization, aiming to quantify the merits of each hyperparameter combination. This embodiment uses the model's prediction error on the validation set as the fitness metric; a smaller error indicates a better hyperparameter combination.

[0078] For each individual in the current population, i.e., each set of hyperparameters, fitness is assessed according to the following steps: Constructing the initial AM-TKAN model: Based on the hyperparameter combination corresponding to this individual, construct the initial AM-TKAN model. Specifically: Set the model training learning rate to the learning rate value of this individual (e.g., 0.001). Set the batch size to the batch size value for this individual (e.g., 64). Set the number of TKAN layers to the model layer number value for that individual (e.g., 3). Set the dimension of each hidden layer in the TKAN layer to the hidden layer dimension value of that individual (e.g., 128). Set the regularization coefficient to the value of the regularization coefficient for this individual (e.g., 0.0001). Train the model on the training set: The training set, consisting of 533 samples constructed through the above steps, is divided into a training subset (426 samples) and a validation subset (107 samples) in an 8:2 ratio. The training subset is then input into the AM-TKAN initial model constructed above for training. The training process is as follows: In each training round, the AM-TKAN initial model reads training samples in batches, with each batch containing samples of batch size; the input data from each sample, i.e., the multidimensional feature data from 7 consecutive days, is input into the model, and the model outputs the corresponding predicted value of the horizontal deformation of the support pile after forward propagation; the predicted value is compared with the true value, i.e., the label, and the loss function value is calculated; the model parameters are updated through the backpropagation algorithm to gradually reduce the loss function value. The model is iteratively trained in the above manner until the early stopping condition is met, i.e., the validation set loss does not decrease for 10 consecutive rounds or reaches the maximum number of training rounds, which is set to 200 rounds in this embodiment; Calculating the prediction error on the validation set: After model training, 107 samples from the validation set are input into the trained model for prediction. For each sample in the validation set, the model outputs a predicted value of the horizontal deformation of the support pile based on the input historical data, i.e., multidimensional feature data from 7 consecutive days. This predicted value is subtracted from the actual horizontal deformation value of the support pile corresponding to that sample to obtain the prediction error for that sample. The formula for calculating the prediction error is: Single sample error = |Predicted value - Actual value|. The arithmetic mean of the single sample errors of all samples in the validation set is taken to obtain the mean absolute error of the model on the validation set. This mean absolute error is used as the fitness value corresponding to that individual sample. The smaller the fitness value, the higher the prediction accuracy of the model trained by this set of hyperparameters, and the better the hyperparameter combination. Record fitness values: The calculated fitness values ​​are associated with the individual and recorded as the basis for subsequent population updates. In this embodiment, the fitness of each of the 30 individuals in the current population is evaluated according to the above steps to obtain the fitness value of each individual, and the individual with the smallest fitness value is identified and recorded as the optimal individual of this generation of the population.

[0079] A new generation of hyperparameter individuals is generated based on the position update rules of the hippo optimization algorithm: After completing the fitness evaluation of all individuals in the current population, this embodiment generates a new generation of hyperparameter individuals based on the three-stage position update rules of the hippo optimization algorithm. The hippo optimization algorithm simulates three behavioral modes of hippos in nature: position update of male hippos in rivers, hippo defense against predators, and hippos escaping predators. Each behavioral mode corresponds to a position update strategy, and the three work together to achieve a balance between global search and local exploitation in the algorithm. The hyperparameter combination corresponding to each individual is encoded as a hippo individual in the hippo optimization algorithm; Phase 1: Hippos with fitness values ​​lower than the current population average are moved towards the location of the hippo with the highest fitness value (simulating the behavior of adult hippos protecting their young): This phase simulates the behavior of male hippos in a river approaching the leader. The algorithm calculates the average fitness value of all hippos in the current population. Individuals with fitness values ​​lower than this average are considered hippo calves and are moved towards the hippo with the highest fitness value (i.e., the optimal hippo) to improve the overall quality of the population.

[0080] The specific update rule is as follows: For each hippopotamus individual with a fitness value lower than the current population average fitness value, a random number is generated, which controls the size of the movement step. The new position of the hippopotamus individual is calculated as follows: New position = Current position + Random perturbation factor × (Optimal hippopotamus individual position - Current position). Through this operation, hyperparameter combinations with poor fitness can learn from the excellent information of the best individual and gradually move closer to the optimal solution; Phase Two: A new hippopotamus individual is randomly generated. If the fitness value of this new hippopotamus individual is greater than that of the current hippopotamus individual, the current hippopotamus individual is updated to the new individual; otherwise, the current hippopotamus individual is moved a predetermined distance (a second random multiple) towards the location of the new individual (simulating hippopotamus defense against predators). This phase simulates the defensive behavior of the hippopotamus herd when encountering predators. In the algorithm, a new set of hyperparameters is randomly generated as the location of the "predator," which represents an external reference point used to guide the population out of local optima.

[0081] The specific update rule is as follows: For each individual in the current population, a new set of hyperparameters is randomly generated as the predator's position. The fitness value of this predator's position is calculated, i.e., the model is built, trained, and the validation set error is calculated using this hyperparameter combination. If the fitness value of the predator's position is better than the fitness value of the current individual (i.e., the error is smaller), the current individual moves directly to the predator's position; if the fitness value of the predator's position is worse than the fitness value of the current individual (i.e., the error is larger), the current individual moves a small distance towards the predator. Through this operation, the population can explore new regions of the hyperparameter space and avoid getting trapped in local optima too early. The third stage: Treating the current hippopotamus individual as a juvenile, a random perturbation vector within a preset range is added to the current juvenile's position to generate a new juvenile. If the fitness value of the new juvenile is greater than that of the current hippopotamus individual, it is updated to the new juvenile (simulating the behavior of hippopotamus juveniles learning from their mothers). This stage simulates the behavior of a hippopotamus performing a local search in the vicinity after successfully escaping a predator. In the algorithm, this stage is used to perform a fine-grained search near the current optimal solution to further improve the quality of the solution.

[0082] The specific update rule is as follows: For each individual in the current population, a random perturbation is generated near its current hyperparameter combination, forming a new hyperparameter combination. The amplitude of the perturbation is controlled by a random number, and the perturbation range is usually small to achieve a fine-grained local search near the current solution. After generating the new combination, the fitness value of the new combination is calculated. If the fitness value of the new combination is better than that of the original individual, the individual is updated to the new combination; if the fitness value of the new combination is worse, the original individual remains unchanged.

[0083] Through the position updates in the three stages described above, this embodiment generates a new generation of hyperparameter individuals, forming a new population.

[0084] After updating the position using the Hippo optimization algorithm, some hyperparameter values ​​may exceed the set initial range. These out-of-bounds hyperparameter values ​​may not be usable in subsequent training. Therefore, it is necessary to perform boundary pruning on these out-of-bounds hyperparameters to bring them back to the valid initial range. This embodiment employs different boundary pruning strategies for different types of hyperparameters: Boundary pruning for continuous hyperparameters: Model training learning rate and model regularization coefficient are two types of continuous hyperparameters, meaning their values ​​fall within a continuous interval. The pruning rule is as follows: If the updated value is greater than the preset upper limit, then set it as the upper limit. If the updated value is less than the preset lower limit, then set it as the lower limit. If the updated value is between the upper and lower limits, it remains unchanged.

[0085] Boundary pruning for discrete hyperparameters: Batch size, number of model layers, and hidden layer dimension are three types of discrete hyperparameters, whose values ​​are within a preset set of discrete values. The pruning rule is as follows: From the preset set of discrete values, select the discrete value that is closest to the updated value as the pruned value. If there are two discrete values ​​with the same difference from the updated hyperparameter value, select the smaller discrete value as the pruned hyperparameter value. For example, in this embodiment, the set of discrete values ​​for a batch size is {16, 32, 64, 128, 256}, and the updated batch size is calculated to be 50. The closest discrete value is 64 (50 differs from 64 by 14 and from 32 by 18, so 64 is closer), and 64 is taken after pruning. The same pruning rules are applied to both the discrete value set of the model layer number and the discrete value set of the model hidden layer dimension.

[0086] Through the above boundary pruning operation, all hyperparameter individuals in the new generation population are kept within an effective initial range, ensuring that subsequent training can proceed normally.

[0087] After pruning, iterative optimization is required to output candidate optimal hyperparameter combinations. This embodiment follows the iterative optimization process as follows: Initialization: Generate an initial population of 30 individuals, evaluate the fitness of each individual, and record the current best individual; Iterative Update: Repeat the following operations until the preset number of iterations is reached: Based on the three-stage position update rules of the hippo optimization algorithm, a new generation of hyperparameter individuals is generated; Perform boundary pruning on the updated hyperparameter individuals; Fitness assessment was performed on each individual in the new population; Record the best individual in the current population, that is, the individual with the smallest fitness value.

[0088] In this embodiment, the preset number of iterations is 50. The number of iterations was determined through preliminary experiments: too few iterations may lead to non-convergence of the algorithm and failure to find the optimal hyperparameters; too many iterations will significantly increase computational overhead and limit the extent of improvement in later stages. 50 iterations achieve a good balance between search performance and computational efficiency.

[0089] After the iteration terminates, the three individuals with the smallest fitness values ​​from the last generation of the population are selected, representing the three hyperparameter combinations with the smallest prediction errors, as candidate optimal hyperparameter combinations. The purpose of selecting multiple candidate combinations is that different hyperparameter combinations may not differ much in prediction accuracy, but may have different model complexity or training efficiency. In subsequent steps, the most suitable set can be selected from the candidate combinations according to actual needs.

[0090] In this embodiment, the optimal hyperparameter combination obtained after optimization using the Hippo optimization algorithm is as follows: model training learning rate = 0.0032, batch size = 64, number of model layers = 3, hidden layer dimension = 128, and regularization coefficient = 0.0005. This set of hyperparameters will be used in subsequent steps to build the final AM-TKAN prediction model.

[0091] Table 2 shows the candidate optimal hyperparameter combinations and their fitness values. According to Table 2, candidate 1's hyperparameter combination achieved the smallest mean absolute error on the validation set, at 0.87 mm. Its corresponding hyperparameter configuration is: learning rate 0.0032, batch size 64, number of model layers 3, hidden layer dimension 128, and regularization coefficient 0.0005. The fitness values ​​of candidates 2 and 3 are 0.92 mm and 0.95 mm, respectively, slightly higher than candidate 1.

[0092] Table 2: Candidate optimal hyperparameter combinations and their fitness values Step 5: Use the validation set to validate the AM-TKAN initial model corresponding to the candidate optimal hyperparameter combination, calculate the validation error, and select the model with the smallest validation error as the final AM-TKAN prediction model.

[0093] Before training and validating the model, the training set needs to be divided into a training subset and a validation set. The training subset is used to train the model's parameters, that is, to learn the model's internal weights and biases. The validation set is used to evaluate the model's generalization ability, that is, to test the model's performance on data that was not used in the training, and to serve as the basis for selecting the optimal combination of hyperparameters.

[0094] In this embodiment, step 2 has already divided the original data into a training set (533 samples in total). It should be noted that the validation set, which was partitioned from the training set in step 4, is used for fitness evaluation of each individual during the hippo optimization algorithm iteration process, i.e., to assist in hyperparameter optimization. However, in this step, the original training set needs to be further divided into a training subset and a validation set for the final model selection. The purposes of these two partitions are different, and the data sources are also different.

[0095] The specific division process is as follows: A total of 533 samples from the training set were used as the original dataset; The training set was further divided into a training subset and a validation set in chronological order, with a ratio of 7:3, meaning the training subset comprised 70% and the validation set comprised 30%. Since the training set contained 533 samples, after the 7:3 ratio, the training subset consisted of the first 373 samples, and the validation set consisted of the last 160 samples. The time sequence is maintained during the partitioning process, meaning the training subset's time period is earlier than the validation set's time period. This is done because, in time series prediction tasks, training the model with earlier data and validating it with slightly later data better aligns with real-world engineering applications.

[0096] It is important to note that the validation set in this step is used to select the final model, and it is a different dataset from the validation set in step 2, which is used for evaluating the fitness of the Hippo Optimization Algorithm. The validation set in step 2 participated in the iterative process of the Hippo Optimization Algorithm, while the validation set in this step is independent of the iterative process and is used for objective selection of the final model to avoid the risk of overfitting.

[0097] After the partitioning is completed, each of the constructed candidate models needs to be trained and validated: Constructing the AM-TKAN model: For each candidate optimal hyperparameter combination, substitute it into the initial AM-TKAN model architecture to construct the corresponding AM-TKAN model. Specifically: Set the model training learning rate to the value of the learning rate in this set of hyperparameter combinations; Set the batch size to the value of the batch size in this group of hyperparameters; Set the number of TKAN layers to the model layer number value in this hyperparameter combination; Set the dimension of each hidden layer in the TKAN layer to the value of the hidden layer dimension in this set of hyperparameters; Set the regularization coefficient to the value of the regularization coefficient in this set of hyperparameter combinations.

[0098] The model was trained using a training subset: A training subset of 373 samples was input into the constructed AM-TKAN model for training. First, each sample in the training subset was input into the model in batches according to batch size. The input for each sample was multi-dimensional feature data (4-dimensional features) for 7 consecutive days, and the output was the predicted value of the horizontal deformation of the corresponding support pile, i.e., the predicted value for the 8th day. Then, the predicted value of the horizontal deformation of the support pile output by the model was subtracted from the corresponding actual horizontal deformation value of the support pile in the sample to obtain the prediction error for that sample. The prediction error was calculated as follows: Single sample error = Predicted value - Actual value. The mean squared error of the prediction error for all samples was calculated as the loss function value, and the calculation formula was: Loss function value = (1 / m) × , where m is the number of samples in the current batch; then, the gradient of the loss function value with respect to the internal weight parameters of the model is calculated through the backpropagation algorithm, and the internal weights and bias parameters of the model are updated according to the settings of the optimizer and learning rate, so that the loss function value gradually decreases.

[0099] Repeat the above process, inputting all samples from the training subset into the model in batches for training. After each round of training on all samples, calculate the loss function value of the current model on the validation set. If the validation set loss does not decrease for 10 consecutive rounds, trigger the early stopping mechanism to stop training and avoid model overfitting; if early stopping is not triggered, continue training until the maximum number of training rounds is reached, which is set to 200 rounds in this embodiment. Validate the trained model using a validation set: After the model training is complete, input the validation set (85 samples in total) obtained in this step into the trained model for validation. The validation process does not involve backpropagation or parameter updates; it only performs forward propagation to calculate the predicted values.

[0100] The specific operation is as follows: Input the input data of each sample in the validation set, i.e., the multidimensional feature data of 7 consecutive days, into the trained model. The model outputs the corresponding predicted value of the horizontal deformation of the support pile after forward propagation. Subtract the predicted value from the corresponding actual horizontal deformation value of the support pile in the sample to obtain the prediction error of the sample. The prediction error is calculated as follows: Single sample error = |predicted value - actual value|. The arithmetic mean of the single sample errors of all validation set samples is taken to obtain the mean absolute error of the model on the validation set. This mean absolute error is used as the validation error of the model. The formula for calculating the validation error is: Validation error = (1 / p) × Σ|predicted value - actual value|, where p is the number of samples in the validation set. In this embodiment, p = 160. Record the verification error: Associate the calculated verification error with the set of hyperparameter combinations and record it as the basis for subsequent screening.

[0101] Following the above procedure, the AM-TKAN models corresponding to the three candidate optimal hyperparameter combinations were trained and validated respectively, resulting in three validation error values. These three validation error values ​​were compared, and the model with the smallest validation error was selected as the final AM-TKAN prediction model.

[0102] The specific screening rules are as follows: If there is a unique minimum value among the three validation error values, then the model corresponding to the minimum value is determined as the final AM-TKAN prediction model; If multiple models have the same minimum validation error, i.e. tied for first place, then the mean squared errors of these models on the validation set are further compared, and the model with the smaller mean squared error is selected; if the mean squared errors are still the same, then the model with a simpler structure (fewer layers and smaller hidden layer dimensions) is selected, in order to give priority to the model with higher computational efficiency.

[0103] In this embodiment, after the above screening process, the final selected model hyperparameter combination is as follows: model training learning rate = 0.0032, batch size = 64, number of model layers = 3, hidden layer dimension = 128, and regularization coefficient = 0.0005. This model has a mean absolute error of 0.87 mm on the validation set defined in this step, making it the best performing model among the three candidate models.

[0104] The selected hyperparameter combination is substituted into the AM-TKAN model architecture to construct the final AM-TKAN prediction model.

[0105] Table 3 shows the performance evaluation results of the final AM-TKAN prediction model. According to Table 3, the final AM-TKAN prediction model has a mean absolute error of 0.87 mm, a root mean square error of 1.10 mm, a mean absolute percentage error of 2.35%, and a coefficient of determination of 0.94 on the test set. These indicators demonstrate that the model has high prediction accuracy and can accurately capture the changing trend of horizontal deformation of the foundation pit support piles, meeting the needs of engineering applications.

[0106] Table 3: Performance Evaluation Results of the Final AM-TKAN Prediction Model Step 6: Input the real-time collected multidimensional feature data into the final AM-TKAN prediction model according to the time window, and output the prediction results of the horizontal deformation of the support pile at the time corresponding to the prediction step length; Boundary clipping is performed on hyperparameters that exceed the limits. The specific operation is as follows: For the model training learning rate and model regularization coefficient, if the hyperparameter value obtained after position update is greater than the upper limit of the initial range of the model training learning rate and model regularization coefficient, then the hyperparameter value is modified to the upper limit value. If the hyperparameter value obtained after the position update is less than the initial lower limit of the model training learning rate and the model regularization coefficient, then the hyperparameter value is modified to the lower limit value. For batch size, number of model layers, and model hidden layer dimension, after the position is updated, the discrete value closest to the updated hyperparameter value is selected from the discrete value sets corresponding to each of the batch size, number of model layers, and model hidden layer dimension as the pruned hyperparameter value; if there are two discrete values ​​with the same difference from the updated hyperparameter value, the smaller discrete value is selected as the pruned hyperparameter value.

[0107] After the above steps, the final AM-TKAN prediction model is obtained. This model has completed hyperparameter optimization and internal weight parameter training, and has the ability to predict future horizontal deformation of the support piles based on historical monitoring data. In practical engineering applications, the real-time collected multidimensional feature data is input into the final AM-TKAN prediction model according to a set time window format. After calculation, the model outputs the predicted horizontal deformation of the support piles at the time corresponding to the prediction step. The specific implementation method is as follows: In actual engineering operations, the monitoring network operates continuously, collecting various monitoring data in real time according to the set acquisition frequency. However, the set time window length is 7 days, the prediction step size is 1 day, and the input samples are required to be time-series data with equal intervals of 1 day. Therefore, the following preprocessing operations are required before inputting the real-time data into the model: Equal time interval conversion: Taking 8:00 AM each day as the base time point, if original monitoring data exists at this time point, it is used directly; if no original monitoring data exists at this time point, linear interpolation is performed using the two nearest valid data points before and after this time point to calculate the estimated value for that time point. Through this operation, the original high-frequency data is converted into time-series data with a 1-day interval. Feature selection: Only four types of feature data with high correlation to the horizontal deformation of the support piles are retained, including: support pile deformation data, anchor cable axial force variation data, settlement data of surrounding buildings, and groundwater level fluctuation data. Other features are not included in the model input; Normalization: Using the minimum and maximum values ​​of each feature calculated in step 1, the real-time data is subjected to Min-Max normalization, mapping each feature value to the [0,1] interval. It is crucial that the maximum and minimum values ​​used for normalization are exactly the same as those used in the training set in step 1 to ensure data scale consistency. If values ​​in the real-time data exceed the training set range, they are handled as follows: if greater than the maximum value in the training set, they are set to 1; if less than the minimum value in the training set, they are set to 0. Constructing Input Samples: After preprocessing the real-time data, input samples need to be constructed according to the set time window format. The specific steps are as follows: The input sample is constructed from preprocessed data collected over seven consecutive days prior to the current moment. This input sample contains seven time points (t-7, t-6, ..., t-1), each containing four-dimensional feature data (support pile deformation data, anchor cable axial force variation data, surrounding building settlement data, and groundwater level fluctuation data). The input sample is a 7×4 two-dimensional matrix. If the data prior to the current moment is less than 7 days, a complete input sample cannot be constructed, and the model cannot make predictions. In practical engineering applications, predictions are typically initiated only after the monitoring network has been running for a full 7 days.

[0108] Input Model for Prediction: The constructed input samples are fed into the final AM-TKAN prediction model. This model has been trained and validated in the above steps, and its internal structure includes a TKAN layer, an attention layer, and an output layer. After receiving the input samples, the model sequentially passes through the TKAN layer to extract long-term dependencies in the time series, the attention layer to assign weights to key time steps, and the output layer to map features to predicted values, finally outputting a scalar value, which is the horizontal deformation value of the support pile at the time corresponding to the prediction step size. In this embodiment, the prediction step size S=1, so the model outputs the horizontal deformation value of the support pile on the first day in the future. Output Prediction Results: After the model calculation is complete, a scalar value is output, representing the predicted horizontal deformation of the support pile at the corresponding prediction step. It is important to note that this predicted value is a normalized value (i.e., mapped to the [0,1] interval) and cannot be directly compared with the actual displacement value (in mm) in engineering. Therefore, the prediction results need to be denormalized to restore their original dimensions. The denormalization process uses the maximum and minimum values ​​used in step 1 during normalization, and the calculation formula is as follows: Predicted value (original dimensions) = Predicted value (normalized) ,in, This represents the maximum horizontal deformation value of the support pile within the training set. The minimum value in the training set is used. After normalization, the predicted value of the horizontal deformation of the support pile in millimeters (mm) is obtained, which can be directly used in engineering applications.

[0109] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0110] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0111] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0112] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for predicting the deformation of foundation pit support piles based on deep learning, characterized in that, The specific steps include: Step 1: Establish a monitoring network within the target foundation pit, continuously collect multidimensional feature data and horizontal deformation values ​​of the support piles in chronological order through the monitoring network, and record the corresponding timestamps; Step 2: Set the time window length and prediction step size, use multidimensional feature data within multiple consecutive time windows as input samples, use the horizontal deformation value of the support pile at the time corresponding to the prediction step size as the label, slide along the time axis to generate samples, and divide the samples into training sets. Step 3: Construct the initial AM-TKAN model and determine the types of hyperparameters to be optimized. Set the initial range for each type of hyperparameter, extract the values ​​of each type of hyperparameter within the initial range to form several hyperparameter combinations, and treat each hyperparameter combination as an individual. Step 4: Construct the AM-TKAN initial model for each individual's corresponding hyperparameter combination, train each individual on the training set and calculate the error value, evaluate the fitness of the individual based on the error value, generate a new generation of hyperparameter individuals according to the position update rule of the Hippo optimization algorithm, and perform boundary pruning on hyperparameters that exceed the limit. After reaching the preset number of iterations, output the hyperparameter combination with the required error value as the candidate optimal hyperparameter combination. Step 5: Validate the initial AM-TKAN model corresponding to the candidate optimal hyperparameter combination based on the training set, calculate the validation error, and select the model with the smallest validation error as the final AM-TKAN prediction model. Step 6: Input the real-time collected multidimensional feature data into the final AM-TKAN prediction model according to the time window, and output the prediction results of the horizontal deformation of the support pile at the time corresponding to the prediction step length; Boundary clipping is performed on hyperparameters that exceed the limits. The specific operation is as follows: For the model training learning rate and model regularization coefficient, if the hyperparameter value obtained after position update is greater than the upper limit of the initial range of the model training learning rate and model regularization coefficient, then the hyperparameter value is modified to the upper limit value. If the hyperparameter value obtained after the position update is less than the initial lower limit of the model training learning rate and the model regularization coefficient, then the hyperparameter value is modified to the lower limit value. For batch size, number of model layers, and model hidden layer dimension, after the position is updated, the discrete value closest to the updated hyperparameter value is selected from the discrete value sets corresponding to each of the batch size, number of model layers, and model hidden layer dimension as the pruned hyperparameter value; if there are two discrete values ​​with equal differences from the updated hyperparameter value, the smaller discrete value is selected as the pruned hyperparameter value. The initial AM-TKAN model is a hybrid neural network model that integrates a temporal Kolmogorov-Arnold network with an attention mechanism. The model architecture includes: Input layer: Receives the input samples generated in step 2. The shape of each sample includes the length of the time window and the number of feature dimensions D. TKAN layer: The TKAN layer uses an external memory module and a gating mechanism, including an input gate, a forget gate, and an output gate; Attention layer: The attention layer is used to dynamically assign weights to the features at each time step output by the TKAN layer; Output layer: Used to map the output of the attention layer to the final predicted value through a fully connected layer. The output layer has 1 neuron.

2. The method for predicting the deformation of foundation pit support piles based on deep learning according to claim 1, characterized in that... The multidimensional feature data includes: settlement data of surrounding buildings, displacement data of existing culvert structures, deformation data of support piles, axial force variation data of anchor cables, groundwater level fluctuation data, and pipeline settlement data.

3. The method for predicting the deformation of foundation pit support piles based on deep learning according to claim 2, characterized in that: The monitoring network is deployed with monitoring points in the following manner: Settlement data of surrounding buildings: monitoring points are set up on existing buildings within the excavation influence range of the target foundation pit. The excavation influence range refers to the area extending outward from the edge of the target foundation pit by 1 to 2 times the excavation depth of the foundation pit. Monitoring points for each existing building are set up at the four corners of the building or at the load-bearing wall. Displacement monitoring points for existing culvert structures: These are set up above and on both sides of the existing culvert structure within the influence range of the target pit. A monitoring section is set up at a preset interval along the culvert direction. Monitoring points are set up at the top of the culvert and on both wing walls of each section. Support pile deformation monitoring points: A clinometer tube is laid at a preset interval along the perimeter of the target foundation pit. The depth of the clinometer tube is consistent with the depth of the bottom of the support pile. It is used to collect horizontal displacement data at different depths along the pile body. The horizontal displacement data at the top of the pile is used as the horizontal deformation value of the support pile, and the horizontal displacement data at other depths of the pile body is used as a one-dimensional feature in the multi-dimensional feature data. Anchor cable axial force change monitoring points: These points are set on the anchor cables according to a preset percentage of the total number of anchor cables. The locations include the long side, short side, and inside and outside corners of the foundation pit. Groundwater level fluctuation monitoring points: Water level observation holes are set up at preset intervals around the perimeter of the foundation pit, with the hole depth being lower than the preset depth below the design bottom elevation of the foundation pit; Pipeline settlement monitoring points: These are set up above existing pipelines within the influence range of the foundation pit, with one monitoring point placed at a predetermined interval along the pipeline route.

4. The method for predicting the deformation of foundation pit support piles based on deep learning according to claim 1, characterized in that: The types of hyperparameters to be optimized include: model training learning rate, batch size, number of model layers, hidden layer dimension, and model regularization coefficient.

5. The method for predicting the deformation of foundation pit support piles based on deep learning according to claim 4, characterized in that: Based on the initial range of each type of hyperparameter, the values ​​of each type of hyperparameter are extracted within the initial range to form several sets of hyperparameter combinations: The initial range is formed by the lower and upper limits of the model training learning rate and the model regularization coefficient, respectively. Based on the lower limit, the pre-selected parameter set of the model training learning rate and the model regularization coefficient is gradually generated at logarithmic intervals until the preset upper limit is reached or exceeded. The initial range is formed by the preset lower and upper limits of batch size, number of model layers, and hidden layer dimension, respectively. Based on the preset lower limit, the set of pre-selected parameters for batch size, number of model layers, and hidden layer dimension is generated step by step with a linear step size until the preset upper limit is reached or exceeded. By performing a Cartesian product on the preselected parameter sets for each type of hyperparameter, several sets of hyperparameter combinations are obtained.

6. The method for predicting the deformation of foundation pit support piles based on deep learning according to claim 5, characterized in that: The initial AM-TKAN model is constructed by combining the hyperparameters corresponding to each individual, and then trained and the error value is calculated on the training set one by one. The specific operation is as follows: For each individual, an initial AM-TKAN model is constructed based on its corresponding hyperparameter combination; Each AM-TKAN initial model is trained using the training set, specifically as follows: The multidimensional feature data within each time window of the training set is input into the AM-TKAN initial model to obtain the predicted value of the horizontal deformation of the support pile at the prediction step time corresponding to that time window. Subtract the predicted horizontal deformation value of the support pile at each prediction step from the actual horizontal deformation value of the support pile at the same time point to obtain the prediction error value corresponding to that time window. Calculate the average of the prediction error values ​​for all time windows, and use this average as the fitness value for that individual.

7. The method for predicting the deformation of foundation pit support piles based on deep learning according to claim 6, characterized in that: A new generation of hyperparameter individuals is generated based on the position update rules of the Hippo Optimization Algorithm. Boundary pruning is performed on hyperparameters that exceed the limits. After a preset number of iterations, the hyperparameter combination whose output error value meets the requirements is taken as the candidate optimal hyperparameter combination. The specific operation is as follows: The hyperparameter combination corresponding to each individual is encoded as a hippo individual in the hippo optimization algorithm; Based on the fitness value of each individual hippopotamus, perform the following operations: Hippos with fitness values ​​lower than the current population average fitness value are moved toward the position of the hippo with the highest fitness value. The movement step size is the product of a preset first random number and the movement distance. A new hippopotamus individual is randomly generated. If the fitness value of the new hippopotamus individual is greater than the fitness value of the current hippopotamus individual, the current hippopotamus individual is updated to the new hippopotamus individual. Otherwise, the current hippopotamus individual is moved a preset second random number of times in the direction of the new hippopotamus individual's position. The current hippopotamus individual is taken as a hippopotamus juvenile. Based on the position of the current hippopotamus juvenile, a random perturbation vector within a preset range is added to generate a new hippopotamus juvenile. If the fitness value of the new hippopotamus juvenile is greater than the fitness value of the current hippopotamus individual, then the new hippopotamus juvenile is updated; otherwise, the current hippopotamus individual remains unchanged. The updated hippo individual is decoded into the corresponding hyperparameter combination; For hyperparameter values ​​that exceed the initial range of each type of hyperparameter, clip them to the corresponding initial range boundary; Repeat the above steps until the preset number of iterations is reached; The hyperparameter combinations corresponding to the top few individuals with the smallest fitness values ​​at the end of the iteration are taken as candidate optimal hyperparameter combinations.

8. The method for predicting the deformation of foundation pit support piles based on deep learning according to claim 6, characterized in that: The AM-TKAN initial model corresponding to the candidate optimal hyperparameter combination is validated using a validation set, and the model with the smallest validation error is selected as the final AM-TKAN prediction model. The specific operation is as follows: The training set is divided into a training subset and a validation set according to a preset ratio; Substitute the candidate optimal hyperparameter combination into the AM-TKAN initial model to obtain the hyperparameter-optimized AM-TKAN model; The AM-TKAN model with optimized hyperparameters is trained using a training subset, specifically as follows: Input the multidimensional feature data of each time window in the training subset into the trained model to obtain the predicted value of the horizontal deformation of the support pile at the predicted step time corresponding to that time window. The predicted value of the horizontal deformation of the support pile at the predicted step length is subtracted from the actual horizontal deformation value of the support pile at the same time point to obtain the prediction error value corresponding to the time window. Adjust the internal weights of the model using the backpropagation algorithm, and repeat the above process until the prediction error value converges. The trained AM-TKAN model was validated using a validation set, specifically as follows: The multidimensional feature data in each time window of the validation set is input into the trained AM-TKAN model to obtain the predicted value of the horizontal deformation of the support pile at the prediction step time corresponding to that time window. The predicted value of the horizontal deformation of the support pile at the predicted step length is subtracted from the actual horizontal deformation value of the support pile at the same time point to obtain the prediction error value corresponding to the time window. Calculate the average of the prediction error values ​​for all time windows, and use it as the validation error of the AM-TKAN model; Repeat the above steps to calculate the validation error of the model corresponding to each candidate optimal hyperparameter combination, and select the model with the smallest validation error as the final AM-TKAN prediction model.

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