Box culvert mechanics performance simulation and construction structure deformation early warning system

Abstract

This invention relates to the field of mechanical performance analysis technology for underground structure construction, specifically disclosing a system for simulating the mechanical performance of box culverts and providing early warning of deformation in construction structures. The system collects earth pressure, inclination angle, and displacement values ​​along the jacking direction, forming an observation data set containing missing entries. It constructs a two-dimensional spatial-temporal matrix to be completed using the low-rank spatiotemporal properties of earth pressure, and solves for the complete pressure distribution field by minimizing the nuclear norm. Based on the pressure field and the measured inclination angle, a pressure-deformation coordination relationship is established, and the soil resistance coefficients on the left and right sides and the friction coefficient at the bottom of the box culvert are inverted using the alternating direction multiplier method. The inverted coefficients are divided into completed and incomplete segments along the jacking direction, and only the coefficients of the completed segments are used to update the deformation prediction boundary conditions. The cumulative deviation between the predicted deformation and the measured inclination angle is compared, and a deformation runaway warning is output when the deviation exceeds the graded warning line. This deviation is used as a weighting factor for subsequent data acquisition. This invention achieves pressure field reconstruction and differentiated boundary updating under incomplete data.

Description

Technical Field

[0001] This invention relates to the field of mechanical performance analysis technology for underground structure construction, specifically to a system for simulating the mechanical performance of box culverts and providing early warning of structural deformation. Background Technology

[0002] During the jacking construction of box culverts, the actual stress and deformation of the structure often deviate from the initial design expectations due to the spatial variability of soil mechanical parameters, construction disturbance, and the limited deployment of monitoring sensors. Current technologies typically employ finite element simulation to pre-calculate the deformation and stress distribution at different construction stages, combined with on-site embedded sensors such as earth pressure cells and inclinometers for real-time monitoring. An early warning is issued when the measured deformation exceeds a preset threshold.

[0003] During the jacking construction of box culverts, existing technologies lack a way to simultaneously overcome the multiple solutions of inversion parameters caused by the sparse lack of monitoring data due to sensor damage or signal interruption, and to avoid the poor adaptability to geological variations and false early warnings caused by directly and globally extending the soil parameters obtained from the limited data of the completed section to the unconstructed section. This is to achieve complete reconstruction of the pressure field under incomplete data and updating of the differentiated boundary conditions of the completed and uncompleted sections. Summary of the Invention

[0004] The purpose of this invention is to provide a system for simulating the mechanical properties of box culverts and providing early warning of structural deformation during construction, so as to solve the problems mentioned above.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] The box culvert mechanical performance simulation and construction structure deformation early warning system includes a data acquisition module, which is used to collect earth pressure values, inclination angle values ​​at the four corners of the box culvert, and displacement values ​​of the jack stroke, arranged every five meters along the jacking direction, forming an observation data set including missing entries.

[0007] The pressure field reconstruction module is used to utilize the low-rank property of the spatiotemporal distribution of earth pressure to express the observation data set as a two-dimensional spatial-temporal matrix to be completed, and to solve the complete pressure distribution field with the goal of minimizing the nuclear norm;

[0008] The coefficient inversion module establishes the pressure-deformation compatibility relationship based on the complete pressure distribution field and the measured tilt angle value, and iteratively inverts the soil resistance coefficients on the left and right sides and the friction coefficient at the bottom of the box through the alternating direction multiplier method.

[0009] The segmented update module divides the inverted coefficients into completed and uncompleted segments along the jacking direction. Only the coefficients of the completed segments are used to update the deformation prediction boundary conditions under the current working conditions, while the uncompleted segments retain the geological prior constraints.

[0010] The early warning feedback module compares the predicted deformation with the measured dip angle during the current jacking progress. When the cumulative sum of the deviation sequence exceeds the graded early warning line, it outputs different levels of deformation runaway warnings and uses the deviation as a weighting factor for subsequent jacking section data acquisition.

[0011] As a further aspect of the present invention: the solution of the complete pressure distribution field specifically includes:

[0012] The known earth pressure values ​​in the observation data set are filled into the corresponding entries of the spatial-temporal two-dimensional matrix according to the jacking sequence number and cross-section location, and the missing parts are temporarily set to zero;

[0013] Singular value decomposition is performed on the space-time two-dimensional matrix. Singular values ​​in the resulting singular value sequence that are less than the arithmetic mean of all singular values ​​are set to zero, while the rest remain unchanged. The space-time two-dimensional matrix is ​​then reconstructed by inverse transformation.

[0014] Repeat the decomposition and contraction process until the norm of the difference between two adjacent reconstructed matrices is less than the convergence limit, and output the final reconstructed matrix as the complete pressure distribution field.

[0015] As a further aspect of the present invention: the reconstruction of the space-time two-dimensional matrix through inverse transformation specifically includes:

[0016] Calculate the arithmetic mean of all singular values ​​in the current singular value sequence as the first threshold, extract singular values ​​that are greater than or equal to the first threshold, and calculate the arithmetic mean of these singular values ​​as the second threshold;

[0017] Set all singular values ​​in the original singular value sequence that are less than the second threshold to zero, and leave the remaining singular values ​​unchanged;

[0018] The updated space-time two-dimensional matrix is ​​obtained by inverse transformation of the retained singular values ​​and their corresponding left and right singular vectors.

[0019] As a further aspect of the present invention: the inversion of the soil resistance coefficients on the left and right sides and the friction coefficient at the bottom of the box specifically includes:

[0020] The complete pressure distribution field is decomposed into two pressure sequences on the left and right sides, and the pressure gradient of adjacent apex steps is calculated.

[0021] Using the measured tilt angle as an equality constraint, an augmented Lagrangian function is constructed between the pressure gradient and the coefficients to be inverted.

[0022] Alternately update the Lagrange multipliers and the coefficients to be inverted;

[0023] Stop when the sum of the absolute values ​​of the coefficient differences obtained from two adjacent iterations is less than a preset limit, and output the soil resistance coefficients on the left and right sides and the friction coefficient at the bottom of the box.

[0024] As a further aspect of the present invention: the construction of the augmented Lagrangian function between the pressure gradient and the coefficients to be inverted specifically includes:

[0025] The difference between the pressure gradient on the left side wall and the pressure gradient on the right side wall is calculated according to the jacking sequence to obtain the unbalanced pressure gradient sequence.

[0026] The soil resistance coefficients on the left and right sides and the friction coefficient at the bottom of the box in the coefficients to be inverted are assigned initial guess values, and the theoretical dip angle value under the initial guess value is subtracted from the measured dip angle value to obtain the dip angle residual.

[0027] The unbalanced pressure gradient sequence is weighted and summed with the tilt angle residual, and then added to the L2 norm penalty term of the coefficients to be inverted to form the augmented Lagrangian function expression.

[0028] The expanded form of the augmented Lagrange function is output as the target for subsequent alternating updates.

[0029] As a further aspect of the present invention: the alternating update of the Lagrange multipliers and the coefficients to be inverted specifically includes:

[0030] With the current inversion coefficients fixed, calculate the partial derivatives of the augmented Lagrange function with respect to the Lagrange multipliers, and then move the multipliers by one step along the direction of increasing partial derivatives to obtain the updated multipliers.

[0031] After the update is fixed, the multipliers remain unchanged. The partial derivatives of the augmented Lagrangian function with respect to the coefficients to be inverted are calculated. The coefficients to be inverted are then moved by one step in the direction of decreasing partial derivatives. The step size is then scaled using the measured dip angle value of the current top step.

[0032] Repeat the two update steps until the sum of the absolute values ​​of the differences between the coefficients to be inverted obtained from two adjacent updates is less than the preset convergence limit, and output the updated Lagrange multipliers and the coefficients to be inverted.

[0033] As a further aspect of the present invention: the division of the inverted coefficients into completed and uncompleted segments along the jacking direction specifically includes:

[0034] The current jacking progress sequence number is determined based on the jacking stroke displacement value. The inverted coefficients are then divided into completed coefficient sequences and incomplete coefficient sequences according to the current jacking progress sequence number.

[0035] Calculate the arithmetic mean of the coefficients of the last three sections in the completed coefficient sequence, and use it as the representative coefficient of the completed segment;

[0036] The representative coefficients of the completed segments are assigned to the positions corresponding to the completed segments in the deformation prediction boundary conditions under the current working conditions. The sequence of incomplete coefficients remains unchanged and the prior coefficients obtained from the initial geological exploration are used.

[0037] The completed boundary conditions and the prior coefficients of the incomplete segments are concatenated and output as the updated complete boundary conditions.

[0038] As a further aspect of the present invention: the output of deformation runaway warnings at different levels specifically includes:

[0039] The difference between the predicted deformation and the measured dip angle of the current jacking advance is recorded as the single-step deviation. The weighted sum of the single-step deviation and the previous three jacking advance single-step deviations is calculated to obtain the cumulative deviation sequence.

[0040] The cumulative deviation sequence is compared with the preset first warning line and second warning line respectively. When the cumulative deviation exceeds the first warning line, a first-level warning is output, and when it exceeds the second warning line, a second-level warning is output.

[0041] The weighting factor is obtained by dividing the absolute value of the current single-step deviation corresponding to the output warning by the sum of the absolute values ​​of all single-step deviations of the previous step.

[0042] The weighting factor is multiplied by the next earth pressure value collected to form the weighted data, which is then used as the input for the subsequent data acquisition module.

[0043] The beneficial effects of this invention are:

[0044] (1) This invention constructs a two-dimensional spatial-temporal matrix to be completed by utilizing the low-rank property of the spatial-temporal distribution of earth pressure, and iteratively solves the complete pressure distribution field with the goal of minimizing the nuclear norm. In the case of some earth pressure cells being damaged by soil-rock collisions or signal interruption resulting in missing observation data, the pressure field continuously distributed along the jacking direction and cross-section position can be effectively recovered.

[0045] (2) This invention divides the inverted coefficients into completed and uncompleted segments along the jacking direction. Only the coefficients of the completed segments are used to update the deformation prediction boundary conditions under the current working conditions, while the uncompleted segments retain the geological prior constraints. This avoids the prediction distortion caused by directly extending the local inversion parameters to the unconstructed segments. At the same time, by using the deformation deviation of the current jacking step as a weighting factor for subsequent data acquisition, the deviation is adaptively controlled in the acquisition process. This reduces the false deformation loss warnings caused by geological variations and lowers the probability that the construction party will take unnecessary remedial measures such as lubrication and drag reduction. Attached Figure Description

[0046] The invention will now be further described with reference to the accompanying drawings.

[0047] Figure 1 This is a system block diagram of the present invention. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] Please see Figure 1 As shown, this invention is a system for simulating the mechanical properties of box culverts and providing early warning of structural deformation during construction, comprising:

[0050] The data acquisition module is used to collect earth pressure values, inclination angle values ​​at the four corners of the box culvert, and displacement values ​​of the jack stroke along the jacking direction at every five-meter cross-section, forming an observation data set including missing entries.

[0051] The pressure field reconstruction module is used to utilize the low-rank property of the spatiotemporal distribution of earth pressure to express the observation data set as a two-dimensional spatial-temporal matrix to be completed, and to solve the complete pressure distribution field with the goal of minimizing the nuclear norm;

[0052] The coefficient inversion module establishes the pressure-deformation compatibility relationship based on the complete pressure distribution field and the measured tilt angle value, and iteratively inverts the soil resistance coefficients on the left and right sides and the friction coefficient at the bottom of the box through the alternating direction multiplier method.

[0053] The segmented update module divides the inverted coefficients into completed and uncompleted segments along the jacking direction. Only the coefficients of the completed segments are used to update the deformation prediction boundary conditions under the current working conditions, while the uncompleted segments retain the geological prior constraints.

[0054] The early warning feedback module compares the predicted deformation with the measured dip angle during the current jacking progress. When the cumulative sum of the deviation sequence exceeds the graded early warning line, it outputs different levels of deformation runaway warnings and uses the deviation as a weighting factor for subsequent jacking section data acquisition.

[0055] The data acquisition module collects earth pressure values, inclination angle values ​​at the four corners of the box culvert, and displacement values ​​of the jack stroke, arranged every five meters along the jacking direction, forming an observation data set including missing entries. Specifically, this includes:

[0056] During the jacking construction of the box culvert, vibrating wire earth pressure cells are pre-embedded every 5 meters along the jacking direction. One earth pressure cell is installed on each of the left and right walls and the bottom plate of each section to collect earth pressure values ​​at that location. Biaxial inclinometers are fixed at the four corners of the box culvert to measure the lateral tilt and longitudinal pitch angles during jacking. Wire-type displacement sensors are installed at the piston rod ends of the jacking jacks to record the displacement values ​​of the jacks, which directly correspond to the jacking distance of the box culvert. All sensors are connected to a data acquisition instrument on site via shielded cables. The instrument reads data at a frequency of once every 0.5 meters of jacking and organizes the earth pressure, tilt, and displacement values ​​into a two-dimensional tabular data set according to the jacking sequence number and measuring point number. Because soil-rock collisions during the jacking process may cause damage to some earth pressure cells or signal interruption, some entries in this observation dataset are missing. Missing entries are retained as null values ​​without any interpolation or filling, thus forming an observation dataset containing missing entries.

[0057] In the pressure field reconstruction module, the low-rank property of the spatiotemporal distribution of earth pressure is used to express the observed data set as a two-dimensional spatial-temporal matrix to be completed. The complete pressure distribution field is solved with the goal of minimizing the nuclear norm. Specifically, this includes:

[0058] Utilizing the low-rank property of the spatiotemporal distribution of earth pressure, the observation dataset is expressed as a two-dimensional spatial-temporal matrix to be completed. Specifically, using the top-step sequence number as the index for the time dimension and the fixed measuring point location on each cross-section as the index for the spatial dimension, a two-dimensional matrix is ​​constructed with the number of rows equal to the total number of measuring points on the cross-section and the number of columns equal to the total number of top-steps. In this matrix, each row number corresponds to a fixed earth pressure cell installation location, each column number corresponds to a top-step sequence number, and the matrix entry is the earth pressure value collected at that measuring point during that top-step.

[0059] The known earth pressure values ​​from the observation dataset are filled into the corresponding entries of the two-dimensional matrix according to the jacking sequence number and cross-section location. For entries in the observation dataset that are missing due to sensor damage or signal interruption, the corresponding position in the matrix is ​​temporarily set to zero. After filling, an initial two-dimensional matrix to be completed is obtained, which contains the known earth pressure values ​​and the missing positions considered as zero values.

[0060] Perform singular value decomposition on the current 2D matrix to be completed, resulting in a left singular vector sequence, a singular value sequence, and a right singular vector sequence. Calculate the arithmetic mean of all singular values ​​in the current singular value sequence, denoted as the first threshold. Extract all singular values ​​greater than or equal to the first threshold from the singular value sequence, and calculate the arithmetic mean of these extracted singular values, denoted as the second threshold. Set all singular values ​​in the original singular value sequence less than the second threshold to zero, leaving the remaining singular values ​​unchanged. Perform an inverse transformation using the retained non-zero singular values ​​and their corresponding left and right singular vectors to reconstruct the updated 2D matrix.

[0061] The singular value decomposition, threshold calculation, zeroing, and inverse transformation processes are repeated, with the two-dimensional matrix output from the previous reconstruction used as input for each iteration. The difference norm between the two-dimensional matrices output from two adjacent iterations is calculated, defined as the sum of the absolute values ​​of the differences between corresponding elements in the two matrices. Iteration stops when the difference norm is less than a preset convergence limit, which is set to one ten-thousandth of the sum of the absolute values ​​of all elements in the initial two-dimensional matrix.

[0062] After the convergence condition is met, the two-dimensional matrix output from the last iteration is used as the final complete pressure distribution field. The missing entries in this complete pressure distribution field have been filled in with reasonable values, and all entries are non-zero and continuously distributed, reflecting the complete variation of earth pressure along the jacking direction and the spatial cross-section.

[0063] In each iteration, the inverse transformation is performed as follows: The retained non-zero singular values ​​are sequentially multiplied by the corresponding left and right singular vectors, where the left singular vectors are arranged column-wise and the right singular vectors are arranged row-wise. The resulting matrices from multiplying each singular value by its corresponding left and right singular vectors are summed to obtain the updated two-dimensional matrix. This updated two-dimensional matrix retains the main energy components of the original matrix while removing high-frequency noise introduced by setting empty spaces to zero.

[0064] In the coefficient inversion module, a pressure-deformation compatibility relationship is established based on the complete pressure distribution field and the measured dip angle value. The soil resistance coefficients on the left and right sides and the friction coefficient at the bottom of the box are iteratively inverted using the alternating direction multiplier method. Specifically, this includes:

[0065] The complete pressure distribution field is decomposed into two pressure sequences based on the left and right walls. Specifically, the pressure values ​​corresponding to all earth pressure cells located on the left wall of the box culvert are extracted from the complete pressure distribution field and arranged in ascending order of the top step number to form the left pressure sequence; similarly, the pressure values ​​on the right wall are extracted to form the right pressure sequence. The length of each sequence is equal to the total number of top steps. The pressure difference between adjacent top steps in each sequence is calculated and then divided by the distance between adjacent top steps (i.e., 0.5 meters) to obtain the left and right pressure gradient sequences. The length of each gradient sequence is 1 less than that of the pressure sequence.

[0066] Using the measured dip angle as an equality constraint, an augmented Lagrangian function is constructed between the pressure gradient and the coefficients to be inverted. First, the corresponding positions of the left and right pressure gradient sequences are subtracted to obtain the unbalanced pressure gradient sequence, which has the same length as the pressure gradient sequence. Second, initial guess values ​​are assigned to the left and right soil resistance coefficients and the box bottom friction coefficient in the coefficients to be inverted. The initial guess values ​​for the left and right soil resistance coefficients are both taken as one-tenth of the characteristic value of the foundation bearing capacity, and the initial guess value for the box bottom friction coefficient is taken as 0.3. Then, the measured dip angle value corresponding to the current top step sequence is subtracted from the theoretical dip angle value calculated by the initial guess coefficients using a simplified beam bending model, resulting in a dip angle residual sequence. The length of this sequence is equal to the total number of top steps.

[0067] The unbalanced pressure gradient sequence and the tilt angle residual sequence are weighted and summed, with the unbalanced pressure gradient sequence having a weight of 0.6 and the tilt angle residual sequence having a weight of 0.4, resulting in a weighted sum sequence. The L2 norm of this weighted sum sequence (i.e., the square root of the sum of squares of all elements) is added to the L2 norm penalty term of the coefficients to be inverted, forming the expression for the augmented Lagrangian function. The coefficient of the penalty term is set to 0.01. The specific mathematical form of this augmented Lagrangian function is as follows:

[0068] ;

[0069] in, This represents the total length of the unbalanced pressure gradient sequence or tilt angle residual sequence. Indicates the first One unbalanced pressure gradient value Indicates the first Each tilt angle residual value This indicates the soil resistance coefficient on the left side. Indicates the soil resistance coefficient on the right side. This indicates the coefficient of friction at the bottom of the box.

[0070] The expanded form of the augmented Lagrange function described above is output as the target for subsequent alternating updates. The expanded form is a polynomial obtained by expanding the sum of squares, which includes quadratic terms, cross terms, and constant terms determined by measured data for the coefficients to be inverted. This expanded form is used to calculate the partial derivatives of the function with respect to the coefficients to be inverted and the Lagrange multipliers in subsequent update steps. The initial values ​​of the Lagrange multipliers are set as a zero vector, with the same dimension as the unbalanced pressure gradient sequence.

[0071] The Lagrange multipliers and the coefficients to be inverted are updated alternately. First, keeping the current coefficients to be inverted unchanged, the partial derivatives of the augmented Lagrange function with respect to each component of the Lagrange multipliers are calculated. The partial derivatives are calculated by treating the augmented Lagrange function as a quadratic function of the multipliers and taking its derivative to obtain a linear expression. Each multiplier is then moved one step (0.1) in the direction of increasing partial derivatives to obtain the updated multipliers. Second, keeping the updated multipliers unchanged, the partial derivatives of the augmented Lagrange function are calculated for each coefficient in the coefficients to be inverted. The partial derivatives are calculated by treating the augmented Lagrange function as a quadratic function of the coefficients to be inverted and taking its derivative to obtain a linear expression. Each coefficient to be inverted is moved one step in the direction of decreasing partial derivative, with a step size of 0.05. The step size is then scaled using the measured dip angle value corresponding to the current step, with the scaling factor being the ratio of the measured dip angle value (in radians) to 0.01 radians. If the measured dip angle value is less than 0.001 radians, the scaling factor is set to 1.

[0072] Repeat the two update steps above: first update the Lagrange multipliers, then update the coefficients to be inverted, recalculating the augmented Lagrange function value after each update. After each iteration, calculate the sum of the absolute values ​​of the differences between the coefficients to be inverted obtained from two adjacent iterations. This sum is calculated as follows: subtract the left soil resistance coefficient obtained in the previous iteration from the left soil resistance coefficient obtained in the current iteration, and take the absolute value; similarly, calculate the absolute value of the difference between the right soil resistance coefficient and the box bottom friction coefficient; add these three absolute values ​​together to obtain the sum of the absolute values ​​of the differences.

[0073] Iteration stops when the sum of the absolute values ​​of the differences is less than a preset convergence limit of 0.001. After stopping iteration, the left and right soil resistance coefficients and the box bottom friction coefficient obtained from the last iteration are output. If convergence is not achieved after more than 100 iterations, the iteration is forcibly stopped and the current coefficients are output, with the message "Inversion not converged". The output coefficients are directly used to update the deformation prediction boundary conditions in subsequent steps.

[0074] In the above-mentioned alternating update process, each update of the coefficients to be inverted uses only the pressure data within one cross-sectional range before and after the current apex advance, i.e., the first... In the next update, the pressure gradient sequence is only taken from the first... , , The values ​​at the three positions, if If the boundary is a value, the values ​​of the two adjacent positions are taken. This constraint reduces the computational load and avoids interference from distant, irrelevant data on the inversion of local coefficients. All update steps are executed sequentially on a digital computer in the order of the top-stepping steps, and the inversion calculation for each top-stepping step takes no more than 2 seconds.

[0075] In the segmented update module, the inverted coefficients are divided into completed and uncompleted segments along the jacking direction. Only the coefficients of the completed segments are used to update the deformation prediction boundary conditions under the current working condition, while the uncompleted segments retain the geological prior constraints, specifically including:

[0076] The current jacking step number is determined based on the jack's stroke displacement value. This displacement value is directly measured by a wire-type displacement sensor installed at the end of the piston rod. This displacement value is divided by the standard jacking step distance of 0.5 meters and rounded down to obtain the current jacking step number. For example, when the displacement reading is 15.2 meters, dividing by 0.5 gives 30.4, and rounding down gives the jacking step number 30.

[0077] The inverted coefficients are divided into completed and incomplete coefficient sequences according to the current top-step sequence number. The inverted coefficients include the soil resistance coefficient on the left, the soil resistance coefficient on the right, and the box bottom friction coefficient. Each coefficient corresponds to an ordered list of the maximum top-step sequence number reached from the first top-step sequence to the current inversion. All coefficients before (and including) the current top-step sequence number are taken as the completed coefficient sequence, and all coefficients after the current top-step sequence number are taken as the incomplete coefficient sequence. If the current top-step sequence number is 30, then the coefficients corresponding to top-step sequences 1 to 30 are assigned to the completed sequence, and the coefficients from the 31st to the subsequent sequences are assigned to the incomplete sequence.

[0078] Calculate the arithmetic mean of the coefficients of the last three sections in the completed coefficient sequence, and use this as the representative coefficient of the completed segment. Specifically, if the length of the completed coefficient sequence is L, take the soil resistance coefficients on the left side of the (L-2), (L-1), and Lth sections, add these three values ​​together, and divide by 3 to obtain the representative coefficient of the left completed segment; similarly, obtain the representative coefficients of the right completed segment and the representative coefficient of the bottom friction completed segment. If the length of the completed coefficient sequence is less than 3, take the arithmetic mean of all completed coefficients as the representative coefficient.

[0079] The representative coefficient of the completed segment is assigned to the corresponding position of the completed segment in the deformation prediction boundary conditions under the current working condition. The deformation prediction boundary conditions are an array that divides the box culvert into several micro-segments along the jacking direction. The length of each micro-segment is 0.5 meters, and the micro-segment number corresponds one-to-one with the jacking step number. For all micro-segments whose number is less than or equal to the current jacking step number, the left soil resistance coefficient in its boundary conditions is updated to the representative coefficient of the left completed segment, the right soil resistance coefficient is updated to the representative coefficient of the right completed segment, and the box bottom friction coefficient is updated to the representative coefficient of the box bottom friction completed segment.

[0080] The incomplete coefficient sequence remains unchanged, and the prior coefficients obtained from the initial geological survey are used. The initial geological survey prior coefficients refer to the design values ​​of the resistance coefficients of each soil layer obtained through borehole sampling and laboratory tests before construction, as well as the box bottom friction coefficients obtained based on experience. These prior coefficients are pre-stored in an array according to different geological layers in the jacking direction. For all micro-segments with serial numbers greater than the current jacking step number, the coefficients obtained from inversion are not used; instead, the coefficients in their boundary conditions are kept as the initial geological survey values.

[0081] The completed segment boundary conditions, after assignment, are concatenated with the prior coefficients of the incomplete segments and output as the updated complete boundary conditions. The concatenation operation is performed in ascending order of micro-segment indices: first, the completed segment boundary conditions corresponding to indices 1 to the current top step number are output; then, the prior coefficients of the incomplete segments corresponding to indices 1 plus the current top step number to the maximum top step number are output. The output result is a complete array containing all micro-segment boundary conditions, which is directly used for deformation prediction calculations under the current working condition in subsequent steps.

[0082] In the early warning feedback module, the difference between the predicted deformation and the measured dip angle during the current jacking progress is compared. When the cumulative sum of the deviation sequence exceeds the graded early warning line, different levels of deformation runaway warnings are output, and the deviation is used as a weighting factor for subsequent jacking section data acquisition. Specifically, this includes:

[0083] The difference between the predicted deformation and the measured inclination angle at the current jacking step is denoted as the single-step deviation. Here, the predicted deformation refers to the predicted lateral inclination angle of the box culvert at this jacking step, obtained through finite element forward calculation using the updated complete boundary conditions. The measured inclination angle refers to the lateral inclination angle actually measured by the biaxial inclinometers installed at the four corners of the box culvert during this jacking step. Subtracting the measured value from the predicted value yields the single-step deviation for the current jacking step.

[0084] The cumulative deviation sequence is obtained by calculating the weighted sum of the single-step deviation and the single-step deviations of the previous three top steps. Specifically, the single-step deviation of the current top step is multiplied by a weight of 1, the single-step deviation of the previous top step is multiplied by a weight of 0.8, the single-step deviations of the previous two top steps are multiplied by a weight of 0.6, and the single-step deviations of the previous three top steps are multiplied by a weight of 0.4. These four products are then added together, and the result is used as the cumulative deviation value of the current top step. This calculation is performed sequentially according to the top step order to obtain the cumulative deviation sequence, which has the same length as the total number of top steps.

[0085] The cumulative deviation sequence is compared with a preset first warning line and a second warning line. The first warning line has a value of 0.01 radians, and the second warning line has a value of 0.02 radians. When the cumulative deviation value is greater than or equal to the first warning line but less than the second warning line, a level one warning is output; when the cumulative deviation value is greater than or equal to the second warning line, a level two warning is output. If the cumulative deviation value is less than the first warning line, no warning is output. The warning is issued by sending a text prompt to the field control room and triggering a buzzer to emit sounds at different frequencies.

[0086] When a Level 1 or Level 2 warning is output, the absolute value of the current single-step deviation corresponding to the output warning is extracted. Simultaneously, the sum of the absolute values ​​of all single-step deviations from the first step up to the current step up is calculated. The current single-step deviation absolute value is divided by this sum; the quotient is the weighting factor. If the sum of the absolute values ​​of all single-step deviations before the current step up is zero (i.e., no deviation has ever occurred), the weighting factor is directly set to 1.

[0087] The weighting factor is multiplied by the earth pressure value acquired in the next jacking step to form the weighted acquisition data. Specifically, during the next jacking step, the original earth pressure value is read from the vibrating wire earth pressure cell, and then multiplied by the weighting factor of that jacking step. The product is used as the actual earth pressure value for subsequent pressure field reconstruction in that jacking step. The weighting factor ranges from 0 to 1; when the current deviation is large, the weighting factor is close to 1, and when the current deviation is extremely small, the weighting factor is close to 0.

[0088] The weighted acquisition data is used as input for subsequent data acquisition, replacing the original acquisition values ​​in the corresponding entries of the observation dataset. The weighting factor is dynamically updated with each step forward and only affects the next step forward immediately following it. After weighting is completed, the weighting factor is no longer retained, and the next step forward recalculates a new weighting factor based on its own single-step deviation. This achieves adaptive control of the deviation on subsequent data acquisition.

[0089] The working principle of this invention is as follows: Earth pressure values, inclination angle values ​​at the four corners of the box culvert, and displacement values ​​of the jacks are collected along the jacking direction at five-meter cross-sections to form an observation data set containing missing entries. Utilizing the low-rank property of the spatiotemporal distribution of earth pressure, the observation data set is expressed as a two-dimensional spatial-temporal matrix to be completed, and the complete pressure distribution field is solved iteratively by singular value decomposition and nuclear norm minimization. Based on the complete pressure distribution field and the measured inclination angle values, a pressure-deformation coordination relationship is established, and the alternating direction multiplier method is used to iteratively invert the soil resistance coefficients on the left and right sides and the friction coefficient at the bottom of the box culvert. The inverted coefficients are divided into completed and uncompleted segments along the jacking direction. Only the coefficients of the completed segments are used to update the deformation prediction boundary conditions under the current working conditions, while the uncompleted segments maintain the geological prior constraints. By comparing the difference between the predicted deformation and the measured inclination angle during the current jacking, when the cumulative sum of the deviation sequence exceeds the graded warning line, different levels of deformation runaway warnings are output, and this deviation is used as a weighting factor for subsequent jacking segment data acquisition, realizing adaptive closed-loop control of deformation warning during box culvert jacking construction.

[0090] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A system for simulating the mechanical properties of box culverts and providing early warning of structural deformation during construction, characterized in that, include: The data acquisition module is used to collect earth pressure values, inclination angle values ​​at the four corners of the box culvert, and displacement values ​​of the jack stroke along the jacking direction at every five-meter cross-section, forming an observation data set including missing entries. The pressure field reconstruction module is used to utilize the low-rank property of the spatiotemporal distribution of earth pressure to express the observation data set as a two-dimensional spatial-temporal matrix to be completed, and to solve the complete pressure distribution field with the goal of minimizing the nuclear norm; The coefficient inversion module establishes the pressure-deformation compatibility relationship based on the complete pressure distribution field and the measured tilt angle value, and iteratively inverts the soil resistance coefficients on the left and right sides and the friction coefficient at the bottom of the box through the alternating direction multiplier method. The segmented update module divides the inverted coefficients into completed and uncompleted segments along the jacking direction. Only the coefficients of the completed segments are used to update the deformation prediction boundary conditions under the current working conditions, while the uncompleted segments retain the geological prior constraints. The early warning feedback module compares the predicted deformation with the measured dip angle during the current jacking progress. When the cumulative sum of the deviation sequence exceeds the graded early warning line, it outputs different levels of deformation runaway warnings and uses the deviation as a weighting factor for subsequent jacking section data acquisition.

2. The box culvert mechanical performance simulation and construction structure deformation early warning system according to claim 1, characterized in that, The solution to the complete pressure distribution field specifically includes: The known earth pressure values ​​in the observation data set are filled into the corresponding entries of the spatial-temporal two-dimensional matrix according to the jacking sequence number and cross-section location, and the missing parts are temporarily set to zero; Singular value decomposition is performed on the space-time two-dimensional matrix. Singular values ​​in the resulting singular value sequence that are less than the arithmetic mean of all singular values ​​are set to zero, while the rest remain unchanged. The space-time two-dimensional matrix is ​​then reconstructed by inverse transformation. Repeat the decomposition and contraction process until the norm of the difference between two adjacent reconstructed matrices is less than the convergence limit, and output the final reconstructed matrix as the complete pressure distribution field.

3. The box culvert mechanical performance simulation and construction structure deformation early warning system according to claim 2, characterized in that, The reconstructed space-time two-dimensional matrix through inverse transformation specifically includes: Calculate the arithmetic mean of all singular values ​​in the current singular value sequence as the first threshold, extract singular values ​​that are greater than or equal to the first threshold, and calculate the arithmetic mean of these singular values ​​as the second threshold; Set all singular values ​​in the original singular value sequence that are less than the second threshold to zero, and leave the remaining singular values ​​unchanged; The updated space-time two-dimensional matrix is ​​obtained by inverse transformation of the retained singular values ​​and their corresponding left and right singular vectors.

4. The box culvert mechanical performance simulation and construction structure deformation early warning system according to claim 1, characterized in that, The inverse calculation of the soil resistance coefficients on the left and right sides and the friction coefficient at the bottom of the box includes, in detail: The complete pressure distribution field is decomposed into two pressure sequences on the left and right sides, and the pressure gradient of adjacent apex steps is calculated. Using the measured tilt angle as an equality constraint, an augmented Lagrangian function is constructed between the pressure gradient and the coefficients to be inverted. Alternately update the Lagrange multipliers and the coefficients to be inverted; Stop when the sum of the absolute values ​​of the coefficient differences obtained from two adjacent iterations is less than a preset limit, and output the soil resistance coefficients on the left and right sides and the friction coefficient at the bottom of the box.

5. The box culvert mechanical performance simulation and construction structure deformation early warning system according to claim 4, characterized in that, The construction of the augmented Lagrangian function between the pressure gradient and the coefficients to be inverted specifically includes: The difference between the pressure gradient on the left side wall and the pressure gradient on the right side wall is calculated according to the jacking sequence to obtain the unbalanced pressure gradient sequence. The soil resistance coefficients on the left and right sides and the friction coefficient at the bottom of the box in the coefficients to be inverted are assigned initial guess values, and the theoretical dip angle value under the initial guess value is subtracted from the measured dip angle value to obtain the dip angle residual. The unbalanced pressure gradient sequence is weighted and summed with the tilt angle residual, and then added to the L2 norm penalty term of the coefficients to be inverted to form the augmented Lagrangian function expression. The expanded form of the augmented Lagrange function is output as the target for subsequent alternating updates.

6. The box culvert mechanical performance simulation and construction structure deformation early warning system according to claim 4, characterized in that, The alternating update of the Lagrange multipliers and the coefficients to be inverted specifically includes: With the current inversion coefficients fixed, calculate the partial derivatives of the augmented Lagrange function with respect to the Lagrange multipliers, and then move the multipliers by one step along the direction of increasing partial derivatives to obtain the updated multipliers. After the update is fixed, the multipliers remain unchanged. The partial derivatives of the augmented Lagrangian function with respect to the coefficients to be inverted are calculated. The coefficients to be inverted are then moved by one step in the direction of decreasing partial derivatives. The step size is then scaled using the measured dip angle value of the current top step. Repeat the two update steps until the sum of the absolute values ​​of the differences between the coefficients to be inverted obtained from two adjacent updates is less than the preset convergence limit, and output the updated Lagrange multipliers and the coefficients to be inverted.

7. The box culvert mechanical performance simulation and construction structure deformation early warning system according to claim 1, characterized in that, The process of dividing the inverted coefficients into completed and uncompleted segments along the jacking direction specifically includes: The current jacking progress sequence number is determined based on the jacking stroke displacement value. The inverted coefficients are then divided into completed coefficient sequences and incomplete coefficient sequences according to the current jacking progress sequence number. Calculate the arithmetic mean of the coefficients of the last three sections in the completed coefficient sequence, and use it as the representative coefficient of the completed segment; The representative coefficients of the completed segments are assigned to the positions corresponding to the completed segments in the deformation prediction boundary conditions under the current working conditions. The sequence of incomplete coefficients remains unchanged and the prior coefficients obtained from the initial geological exploration are used. The completed boundary conditions and the prior coefficients of the incomplete segments are concatenated and output as the updated complete boundary conditions.

8. The box culvert mechanical performance simulation and construction structure deformation early warning system according to claim 1, characterized in that, The output of different levels of deformation runaway warnings specifically includes: The difference between the predicted deformation and the measured dip angle of the current jacking advance is recorded as the single-step deviation. The weighted sum of the single-step deviation and the previous three jacking advance single-step deviations is calculated to obtain the cumulative deviation sequence. The cumulative deviation sequence is compared with the preset first warning line and second warning line respectively. When the cumulative deviation exceeds the first warning line, a first-level warning is output, and when it exceeds the second warning line, a second-level warning is output. The weighting factor is obtained by dividing the absolute value of the current single-step deviation corresponding to the output warning by the sum of the absolute values ​​of all single-step deviations of the previous step. The weighting factor is multiplied by the next earth pressure value collected to form the weighted data, which is then used as the input for the subsequent data acquisition module.

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