A Multi-Objective Optimization-Based Reverse Design Method for Wharf Foundation Piles

Abstract

This invention provides a reverse design method for wharf foundation piles based on multi-objective optimization, belonging to the field of civil engineering structural design technology. In the composite load space composed of vertical, horizontal loads, and bending moments, this invention uses a shape parameter vector containing dimensions and coupling coefficients to define and parameterize the target failure envelope. By performing numerical limit state analysis and fitting on design samples, the actual shape parameters are obtained. This is used to train a machine learning model that can quickly predict the shape of the corresponding envelope from the design parameters. Using the difference between the predicted shape and the target shape as the optimization objective, and combined with construction costs, the model is used to evaluate candidate designs. A multi-objective optimization algorithm is used iteratively to obtain a set of design parameters that optimally balance performance and cost. The selected design is verified through high-precision simulation. After confirming that its actual performance matches the target, the parameters and performance information are integrated into a standard digital file to directly drive automated construction.

Description

Technical Field

[0001] This invention relates to the field of civil engineering structural design technology, specifically to a reverse design method for wharf foundation piles based on multi-objective optimization. Background Technology

[0002] As a key load-bearing component in port engineering, wharf foundation piles must be designed to ensure safety and reliability under complex marine environmental loads, such as vertical and horizontal loads and bending moments generated by ship impact forces and mooring forces. Traditional foundation pile design follows a forward design model, where engineers first determine design parameters such as pile diameter and length based on experience, and then verify whether the bearing capacity meets the specifications through numerical simulation. This iterative calculation process is inefficient and heavily reliant on personal experience, making it difficult to systematically find the globally optimal solution under multiple constraints such as safety, economy, and construction convenience. In recent years, the concept of reverse design has been introduced into this field, aiming to directly specify the desired structural performance targets and use optimization algorithms to find the optimal design parameters. However, realizing this concept faces a core challenge: how to accurately and efficiently quantify and match the design performance targets with the limit state behavior of complex foundation pile systems under real three-dimensional composite loads.

[0003] In existing technologies, some studies have attempted to combine optimization algorithms with structural analysis to assist in pile design. A common approach is to simplify the bearing capacity of the pile into several independent limit values, such as the vertical ultimate bearing capacity and the horizontal ultimate bearing capacity, as optimization targets or constraints, and then optimize the design parameters. Another slightly improved method is to use finite element analysis to calculate the response under a small number of specific load conditions and use this to build a surrogate model to accelerate the optimization process. However, these methods have fundamental shortcomings. First, they fail to scientifically characterize the comprehensive bearing boundary of the pile under the real combined action of vertical, horizontal and bending moments. The actual failure of the pile is not controlled by a single load, but is defined by a complex curved surface boundary in a three-dimensional load space. Existing technologies simplify it to a few isolated points or a simple linear combination, which seriously deviates from the real mechanical behavior, resulting in optimized designs that may have safety hazards or be too conservative under complex load combinations.

[0004] Secondly, in the optimization process, the performance evaluation of each candidate design scheme relies heavily on time-consuming finite element analysis. Even when a surrogate model is introduced, it often only predicts the response to individual load conditions, rather than conducting a rapid and complete morphological evaluation of the entire three-dimensional failure boundary. This makes the optimization search inefficient and makes it difficult to explore a broad design space within an acceptable computational cost. Finally, in the existing process, the design, analysis, optimization and the final buildable digital results are usually disconnected, lacking a digital thread that connects performance goals, optimization results and automated construction instructions.

[0005] 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

[0006] The purpose of this invention is to provide a reverse design method for wharf foundation piles based on multi-objective optimization, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A reverse design method for wharf foundation piles based on multi-objective optimization, comprising the following steps:

[0009] Step 1: In the composite load space consisting of vertical load, horizontal load and bending moment, define a target failure envelope surface to describe the ultimate state of the pile-soil system of the wharf foundation piles, and use the target shape parameter vector to perform a parameterized mathematical description of the geometry of the target failure envelope surface.

[0010] Step 2: Perform numerical limit state analysis on multiple sets of preset pile design parameter samples to obtain the discrete limit point set of each sample in the composite load space. Perform surface fitting on the discrete limit point set to calculate the actual shape parameter vector corresponding to each sample. Train the machine learning model based on the sample and the corresponding actual shape parameter vector to make it a fast prediction model that outputs the predicted shape parameter vector based on the input pile design parameters.

[0011] Step 3: Using the difference between the predicted shape parameter vector and the target shape parameter vector as the optimization objective and the pile design parameters as the optimization variables, the multi-objective optimization algorithm is used to iteratively solve the problem. In each iteration, the candidate pile design parameters in the fast prediction model are called to predict and evaluate the shape, so as to obtain the optimized pile design parameters that make the predicted failure envelope shape closest to the target failure envelope shape.

[0012] Step 4: Input the optimized pile design parameters into the simulation model for forward analysis, obtain the true shape parameter vector, compare the true shape parameter vector with the target shape parameter vector to verify their consistency. After verification, convert the optimized pile design parameters into a standard digital design file to guide the automated construction of wharf piles.

[0013] Furthermore, a three-dimensional Cartesian coordinate system is established, with its three orthogonal axes representing vertical load, horizontal load, and bending moment, respectively, to form a composite load space. In this composite load space, based on the composite bearing capacity requirements of the wharf structure for the foundation piles, a closed, smooth surface is defined as the target failure envelope surface. This target failure envelope surface characterizes the limit state boundary of the pile-soil system as designed.

[0014] The target failure envelope is parameterized using a target shape parameter vector, which includes a set of size scaling factors and a set of coupling interaction factors. The size scaling factors are used to adjust the limit dimensions of the target failure envelope in the directions of the vertical load axis, the horizontal load axis, and the bending moment axis. The coupling interaction factors are used to adjust the deviation shape of the envelope surface from the linear superposition surface of each load limit value when two or more loads act together.

[0015] Furthermore, an implicit equation containing eight components is adopted as a general parametric model to describe the geometry of the failure envelope surface, and its expression is: Its specific display format is as follows:

[0016]

[0017] Wherein, the shape parameter vector is , These represent vertical load, horizontal load, and bending moment, respectively. They are coordinate variables in the composite load space, representing an arbitrary combination of loads acting on the foundation pile. The coordinates of the center point of the failure envelope in the composite load space represent the basic bearing capacity level under static load conditions. These are the scaling factors along the vertical load N-axis, the horizontal load H-axis, and the bending moment M-axis, respectively. , These are all coupling interaction coefficients, used to adjust the nonlinear convex or concave morphology of the failure envelope surface in the vertical-horizontal load plane and the horizontal-bending moment load plane, respectively.

[0018] Furthermore, numerical limit state analysis is performed on the pile design parameter samples, specifically using the finite element method considering material nonlinearity and geometric nonlinearity. For each sample, a corresponding three-dimensional finite element model of the pile-soil system is established. During the analysis, various load combinations with different proportions of vertical load, horizontal load, and bending moment are sequentially applied to the finite element model. For each load combination, the load proportion is kept constant, and incremental loading nonlinear calculations are performed until the model reaches the limit state, causing the iterative calculation to fail, or the displacement of the control node of the maximum bending moment section of the pile exceeds the preset failure displacement limit. The load combination recorded at this time is a discrete limit point. All discrete limit points are collected to form the discrete limit point set of the sample. The iterative calculation failure refers to the finite element equilibrium equation failing to converge within the preset maximum number of iterations.

[0019] Surface fitting calculations are performed on the discrete limit point set of each sample to obtain the actual shape parameter vector corresponding to each sample. This process is achieved by solving a nonlinear least squares optimization problem, specifically including:

[0020] For any sample, its discrete limit point set , This is the index of the discrete limit points in the discrete limit point set. Given the number of discrete limit points in the discrete limit point set, an iterative optimization algorithm is used to find a set of shape parameter vectors such that... The defined surface minimizes the overall fitting error to all discrete limit points, i.e., minimizes the loss function: Solving the problem through an iterative optimization algorithm makes smallest Then this That is, the actual shape parameter vector corresponding to the sample;

[0021] The machine learning model is trained to become a fast prediction model, and the loss function used is an adaptive weighted mean square error function, the expression of which is:

[0022]

[0023] in, For the indices of the components in the shape parameter vector, correspond , correspond And so on, To output the predicted shape parameter vector for the fast prediction model The j-th component, Let the j-th component of the actual shape parameter vector obtained from the sample fitting be used as the training label. The static basic weight coefficients are pre-defined and reflect the importance of the j-th component. This is the standard deviation of the prediction error for all samples in this training batch on the j-th component. It is a division-by-zero constant.

[0024] Furthermore, with the optimization objective being the difference between the predicted shape parameter vector and the target shape parameter vector, a quantified difference measurement function is defined. To achieve the difference measurement function Defined as weighted Euclidean distance:

[0025]

[0026] in, and These are the j-th components of the predicted shape parameter vector and the target shape parameter vector, respectively. The difference weighting coefficient assigned to the j-th component;

[0027] Construct a multi-objective optimization problem, specifically a difference metric function for shape parameter vectors. Minimize, and the construction cost function Minimize the construction cost function The calculation is based on the pile diameter, pile length, material usage, and preset unit cost coefficient in the pile design parameters.

[0028] Furthermore, a multi-objective optimization algorithm is used for iterative solution, specifically a genetic algorithm based on reference points and non-dominated sorting. This algorithm maintains a population consisting of multiple candidate foundation pile design parameters. In each iteration of the algorithm, when evaluating the candidate foundation pile design parameters within the population, a fast prediction model is invoked to obtain the corresponding predicted shape parameter vector, and then the difference metric function is calculated. Construction cost function ;

[0029] Based on calculations and The value is used to perform a non-dominated ranking of all individuals in the population, and the ranking is based on the non-dominated ranking level and the optimization objective. The distribution density in the defined space is used to comprehensively evaluate and select individuals. For the selected individuals, crossover and mutation operations are performed to generate a new generation of candidate pile design parameters. The above steps are repeated until the preset maximum number of iterations is reached. All non-dominated pile design parameters in the final generation population are output as optimized pile design parameters.

[0030] The optimized pile design parameters are input into the simulation model. Numerical limit state analysis is performed to obtain the discrete limit point set. The true shape parameter vector is obtained through surface fitting. The specific operation to verify the consistency is as follows: the relative error between the true shape parameter vector and the target shape parameter vector is calculated. The relative error of each component is compared with the preset allowable error threshold for that component. When the relative error of all compared components is less than the corresponding threshold, the verification is considered successful.

[0031] Furthermore, the specific steps for converting the design into a standard digital design file are as follows: the verified optimized foundation pile design parameters and their corresponding real shape parameter vectors are written together into a building information model file that conforms to the industrial foundation category standard; this file is used to transfer the design data to the automated construction system to guide the construction of the wharf foundation piles.

[0032] Compared with the prior art, the beneficial effects of the present invention are:

[0033] This invention, through its proposed parameterized description method for the three-dimensional failure envelope surface based on shape parameter vectors, fundamentally overcomes the shortcomings of existing technologies that simplify composite load-bearing performance to a few isolated limit values. By introducing a parameterized vector containing size scaling factors and load coupling interaction factors, it can accurately and flexibly define any complex three-dimensional load-bearing boundary desired by the design in a compact mathematical form. This not only scientifically characterizes the nonlinear coupling effect under the real combined action of vertical and horizontal loads and bending moments, making the performance target itself more consistent with the actual mechanical mechanism, but also establishes a unified and quantitative geometric standard for subsequent optimization and comparison.

[0034] This invention transforms the high-precision finite element simulation evaluation, which originally required several hours, into a surrogate model prediction in milliseconds by training a fast prediction model that can instantly map design parameters to envelope shape parameters. This enables rapid evaluation and screening of a massive number of candidate design schemes in multi-objective optimization iterations, thereby achieving a full exploration of the design space within an acceptable time. At the same time, with the matching degree of the envelope shape as one of the core objectives of the optimization process, it ensures that the final optimized foundation pile design parameters can approach the preset ideal performance boundary in the real three-dimensional load space, realizing a paradigm shift from parameter trial and error to performance-driven approach.

[0035] This invention uses high-precision simulation to rigorously verify the optimization results based on real shape parameters, ensuring the credibility of the proxy model's optimization results. The verified design parameters and their corresponding targets and verification performance data are encapsulated into a standard building information model file, generating a digital twin design result that simultaneously carries geometric, material, and performance information. This digital asset can be directly connected to an automated construction system, thereby achieving full-process digital integration from performance target definition and optimized design to the generation of automated construction instructions, significantly improving the reliability and implementation efficiency of the design results. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0037] Figure 2 This is a 3D scatter plot of the horizontal load, vertical load, and bending moment values ​​of this invention.

[0038] Figure 3 This is a broken line graph showing the horizontal-bending moment coupling interaction coefficient and the vertical-horizontal coupling interaction coefficient of the present invention.

[0039] Figure 4 This is a violin diagram of the box body with vertical-horizontal-bending moment dimension scaling factor for the present invention. Detailed Implementation

[0040] 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.

[0041] 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.

[0042] Example:

[0043] Please see Figures 1-4 The present invention provides a technical solution:

[0044] A reverse design method for wharf foundation piles based on multi-objective optimization, comprising the following steps:

[0045] Step 1: In the composite load space consisting of vertical load, horizontal load and bending moment, define a target failure envelope surface to describe the ultimate state of the pile-soil system of the wharf foundation piles, and use the target shape parameter vector to perform a parameterized mathematical description of the geometry of the target failure envelope surface.

[0046] A three-dimensional Cartesian coordinate system is established, with its three orthogonal axes representing vertical load, horizontal load, and bending moment, respectively, to form a composite load space. In this composite load space, according to the composite bearing capacity requirements of the wharf structure on the foundation piles, a closed, smooth surface is defined as the target failure envelope surface. This target failure envelope surface characterizes the limit state boundary of the pile-soil system as designed.

[0047] In a specific implementation, it is first necessary to construct a mathematical space to describe the complex stress state of the wharf foundation piles, called the composite load space. The reason for establishing such a three-dimensional space is that the wharf foundation piles do not only bear forces in a single direction in actual work, but are simultaneously subjected to the combined action of vertical pressure, horizontal shear force, and bending moment. In order to comprehensively characterize this composite stress state, the vertical load, horizontal load, and bending moment are set as three mutually perpendicular coordinate axes, thus forming a three-dimensional Cartesian coordinate system. In this space, any possible combination of loads, such as a certain vertical force, a certain horizontal force, and a certain bending moment, corresponds to a unique coordinate point.

[0048] In this composite load space, a target failure envelope is defined. The engineering purpose of this step is to set an ideal, pre-defined safety boundary for the ultimate bearing capacity of the pile-soil system. The shape of this boundary is not arbitrary, but determined according to the specific design requirements of the wharf project, such as considering comprehensive performance requirements such as seismic fortification intensity, ship impact force standards, and surcharge requirements. The target failure envelope is an imaginary, closed, and smooth surface. Its core physical meaning is that any load point located inside the surface represents the working condition under which the pile can safely bear the load; the point that falls exactly on the surface represents the limit state that the load has reached, bringing the system to the brink of failure; and the point outside the surface represents exceeding the safety limit, which will lead to structural failure. Therefore, defining this target failure envelope essentially transforms the engineering safety performance requirements into a clear and visualized geometric target.

[0049] The target failure envelope is parameterized using a target shape parameter vector, which includes a set of size scaling factors and a set of coupling interaction factors. The size scaling factors are used to adjust the limit dimensions of the target failure envelope in the directions of the vertical load axis, the horizontal load axis, and the bending moment axis. The coupling interaction factors are used to adjust the deviation shape of the envelope surface from the linear superposition surface of each load limit value when two or more loads act together.

[0050] To accurately describe and manipulate this geometric target in a computer, this invention employs a parameterized mathematical method. This method uses a target shape parameter vector containing eight independent values ​​to completely determine the surface's morphology. This vector includes two core parameters: the first is three size scaling factors, which independently control the extension range of the target failure envelope in the three single directions: vertical load axis, horizontal load axis, and bending moment axis. Adjusting these factors is equivalent to setting the design ultimate bearing capacity of the pile under three ideal conditions: pure compression, pure shear, or pure bending. The second is two coupling interaction factors, which are crucial for describing and adjusting the difference between the actual shape of the envelope when two or more loads act together and the shape obtained by simply superimposing the ultimate values ​​of each load acting alone. This difference reflects the nonlinear interaction between loads in actual engineering, which can lead to an increase or decrease in bearing capacity. The coupling interaction factors are used to quantitatively characterize this complex effect.

[0051] Specifically, an implicit equation containing eight components is used as a general parametric model to describe the geometry of the failure envelope surface, and its expression is: Its specific display format is as follows:

[0052]

[0053] Wherein, the shape parameter vector is , These represent vertical load, horizontal load, and bending moment, respectively. They are coordinate variables in the composite load space, representing an arbitrary combination of loads acting on the foundation pile. The coordinates of the center point of the failure envelope in the composite load space represent the basic bearing capacity level under static load conditions. These are the scaling factors along the vertical load N-axis, the horizontal load H-axis, and the bending moment M-axis, respectively. , These are all coupling interaction coefficients, used to adjust the nonlinear convex or concave morphology of the failure envelope surface in the vertical-horizontal load plane and the horizontal-bending moment load plane, respectively. By adjusting the sign and magnitude of these two parameters, the nonlinear morphology of the failure envelope surface in the corresponding load coupling plane can be adjusted to exhibit convex or concave morphology, thereby characterizing the enhancement or weakening effect of load synergy on bearing capacity in actual engineering.

[0054] Specifically, this invention uses an implicit equation containing the above eight parameters as a general mathematical model to describe the geometry of the failure envelope surface. The expression of this equation is as follows: the square of the vertical load value minus the vertical coordinate of the center point is divided by the square of the vertical dimension scaling factor, the square of the horizontal load value minus the horizontal coordinate of the center point is added and divided by the square of the horizontal dimension scaling factor, the square of the bending moment value minus the bending moment coordinate of the center point is added and divided by the square of the bending moment dimension scaling factor, then the coupling interaction coefficient of the vertical and horizontal loads is multiplied by the corresponding product of the centralized load and divided by the product of the two-scale scaling factors, the coupling interaction coefficient of the horizontal load and the bending moment is multiplied by the corresponding product of the centralized load and divided by the product of the two-scale scaling factors, and the sum of all these terms equals one.

[0055] It should be noted that, It represents the vertical load acting on the foundation pile and is a coordinate variable in space; Represents horizontal load; Representing bending moments, these elements together form the coordinates of a specific load case in space; symbols The coordinates of the center of the target failure envelope along the vertical load axis are represented. Physically, they are generally understood as the baseline ultimate bearing capacity that the foundation pile should possess under pure vertical static load conditions without horizontal forces or bending moments, as designed. Similarly, and These represent the center coordinates on the horizontal load axis and the bending moment axis, respectively. In most symmetrical design scenarios, they are often set to zero to indicate an ideal initial state with no horizontal force or bending moment.

[0056] This is the scaling factor along the vertical load axis. It is a key design parameter whose value directly determines the width of the target failure envelope in the vertical direction, when all other parameters remain constant. The larger the value, the greater the vertical load needs to satisfy the condition that the sum equals one in the equation. Relative to the center point The greater the range of variation, the higher the expected pure vertical compressive bearing capacity of the pile in the design; conversely, A decrease in the value indicates a reduction in the allowable pure vertical bearing capacity of the design. It is a scaling factor along the horizontal load axis, and its mechanism of action is similar to... It is exactly the same, but it controls the width of the envelope in the horizontal direction. A larger value indicates a stronger desired pure shear resistance. It is a scaling factor along the bending moment axis, controlling the width of the envelope surface in the bending moment direction. A larger value indicates a stronger desired bending resistance.

[0057] It is the coupling interaction coefficient between vertical and horizontal loads. It does not directly control the dimension in a single direction, but rather regulates the coupling effect produced when vertical and horizontal forces act together. When the value is zero, it indicates that the vertical bearing capacity and the horizontal bearing capacity are considered to be independent of each other in the design, and that they do not affect each other. When the value of is greater than zero, in the load quadrant where both vertical and horizontal loads are simultaneously positive or simultaneously negative, the cross term in the equation is positive. This leads to a reduction in the sum of the pure vertical and pure horizontal terms in order to satisfy the equation summing to one. Geometrically, this manifests as the envelope surface bulging outwards along the diagonal direction of the NH plane, indicating that the design expectation is that when vertical pressure and horizontal shear force coexist, the pile-soil system will exhibit a higher overall bearing capacity due to their interaction than when they are individually superimposed, i.e., a synergistic enhancement effect is produced. Conversely, when... When the value is less than zero, the cross term is negative, forcing the sum of the pure load terms to increase. This causes the envelope to concave inward along the diagonal direction, indicating that the design expects the two loads to weaken each other when they act simultaneously, resulting in a combined bearing capacity lower than the linear superposition value. It is the coupling interaction coefficient between horizontal load and bending moment, and its physical meaning and mechanism of action are similar to those of horizontal load and bending moment. It is completely similar, but it regulates the nonlinear interaction between horizontal shear force and bending moment, and affects the convex or concave shape of the envelope surface in the HM plane.

[0058] Table 1 shows some sample numbers and specific data of implicit equations.

[0059] Table 1 Statistical Data

[0060]

[0061] Analysis of the data revealed a clear correlation among the key parameters describing the shape of the failure envelope. These relationships reflect the mathematical logic defined in the formula of this invention, which uses coupling interaction coefficients to finely adjust load interactions. Specifically, the data shows that the sign of the vertical-horizontal load coupling interaction coefficient is closely related to the synergistic change trend of the vertical and horizontal load values. When the coupling interaction coefficient is positive, for example, in sample number 4, the coefficient is 0.500, corresponding to positive values ​​for both the vertical and horizontal loads, indicating a synergistic state of forces acting in the same direction. Conversely, when the coefficient is negative, for example, in sample number 2, the coefficient is -0.800, corresponding to negative vertical load values ​​and positive horizontal load values, indicating an antagonistic state of forces acting in opposite directions. This clearly demonstrates that the coupling interaction coefficient, as a design control parameter, can effectively characterize and adjust whether the combined action of vertical and horizontal loads produces an enhancing or weakening effect, thereby determining whether the failure envelope bulges outward or concave inward in the corresponding quadrant.

[0062] Similarly, the horizontal-bending moment coupling interaction coefficient also exhibits a similar regulatory pattern. When the coefficient is positive, the corresponding horizontal load value and bending moment value tend to have the same sign. For example, in the data with sample number 10, the coefficient is 0.450, and both the horizontal load and bending moment are positive. When the coefficient is negative, the corresponding load value tends to have opposite signs. For example, in the data with sample number 3, the coefficient is -0.400, the horizontal load is negative, and the bending moment is positive. This pattern indicates that the coefficient is specifically used to characterize the complex nonlinear interaction between horizontal shear force and bending moment.

[0063] Furthermore, data analysis reveals that the scaling factor has a fundamental constraining effect on the range of ultimate load values. For example, in samples with a large vertical scaling factor, such as sample number 9 with a factor of 1.950, the corresponding absolute value of the vertical load tends to be larger; while in samples with a smaller factor, such as sample number 5 with a factor of 0.850, the absolute value of the vertical load is correspondingly smaller. This confirms that the scaling factor, as a fundamental parameter in the model, independently sets the basic bearing capacity scale of the structure in each single load direction. In summary, these data relationships fully present the core mathematical logic and engineering physical significance of the parameterized model proposed in this invention, where the dimensional parameter defines the bearing range and the coupling parameter finely controls the interaction mode.

[0064] In summary, by assigning specific design values ​​to these eight parameters, a target failure envelope with clear physical meaning and engineering orientation is uniquely determined. This envelope equation is the mathematical foundation and core objective of all subsequent analysis, model training, and optimization design processes.

[0065] Step 2: Perform numerical limit state analysis on multiple sets of preset pile design parameter samples to obtain the discrete limit point set of each sample in the composite load space. Perform surface fitting on the discrete limit point set to calculate the actual shape parameter vector corresponding to each sample. Train the machine learning model based on the sample and the corresponding actual shape parameter vector to make it a fast prediction model that outputs the predicted shape parameter vector based on the input pile design parameters.

[0066] In a specific implementation, the goal of this step is to establish a mathematical model that can quickly predict the shape of the failure envelope surface based on the input foundation pile design parameters, i.e., a rapid prediction model. To achieve this goal, three key operations need to be completed sequentially: First, obtain a large number of limit state data corresponding to different foundation pile design parameter samples through high-precision numerical simulation; second, extract the quantitative shape description of the failure envelope surface of each sample from these simulation data, i.e., the actual shape parameter vector; third, use these paired data to train a machine learning model so that it can master the mapping law from design parameters to shape parameters.

[0067] First, a sample set of pile design parameters needs to be generated for analysis. Pile design parameters refer to all variables that affect the bearing capacity of the pile and can be adjusted during the design phase. These parameters specifically include pile geometry parameters, pile material parameters, reinforcement parameters, and the mechanical parameters of the surrounding soil. Pile geometry parameters mainly refer to the pile diameter and length; pile material parameters mainly refer to the concrete strength grade; reinforcement parameters mainly refer to the longitudinal reinforcement ratio, stirrup spacing, and diameter; and the mechanical parameters of the surrounding soil mainly refer to the soil cohesion, internal friction angle, elastic modulus, and layer thickness. To comprehensively cover a reasonable design space, the Latin hypercube sampling method is used to randomly generate a large number of different parameter combinations within the engineering feasible range of each parameter. Each parameter combination is called a pile design parameter sample, and the number of samples is set to several thousand to ensure that the model subsequently established has broad representativeness.

[0068] Numerical limit state analysis was performed on the sample of pile design parameters, specifically using the finite element method considering material and geometric nonlinearity. For each sample, a corresponding three-dimensional finite element model of the pile-soil system was established. During the analysis, various load combinations with different proportions of vertical loads, horizontal loads, and bending moments were sequentially applied to the finite element model. For each load combination, the load proportion was kept constant, and incremental loading nonlinear calculations were performed until the model reached the limit state, causing the iterative calculation to fail, or the displacement of the control node of the maximum bending moment section of the pile exceeded the preset failure displacement limit. The load combination recorded at this point is a discrete limit point. All discrete limit points are collected to form the discrete limit point set of the sample. The iterative calculation failure refers to the finite element equilibrium equation failing to converge within the preset maximum number of iterations.

[0069] Numerical limit state analysis is performed on each pile design parameter sample. Numerical limit state analysis refers to the process of accurately solving the ultimate bearing capacity state of the pile-soil system corresponding to the pile design under various combinations of external loads through numerical calculation methods. This invention specifically uses the three-dimensional finite element method, which can consider the nonlinear behavior of materials and the effect of large geometric deformation, to perform this analysis. For any pile design parameter sample, a corresponding refined three-dimensional finite element calculation model of the pile-soil system needs to be established. This model is constructed according to the specific parameters of the sample: the pile body is discretized using three-dimensional solid elements and given a nonlinear elastoplastic material constitutive relationship that matches the concrete strength grade in the sample; the reinforcing cage is simulated by truss elements embedded in the solid elements and given an ideal elastoplastic material model; the soil around the pile and at the pile tip is simulated using three-dimensional solid elements and given a nonlinear soil constitutive model that considers plastic yielding; contact elements are set at the contact surface between the pile and the soil to simulate slippage and separation. This model is a verified high-fidelity model that can realistically simulate the response of the pile-soil system under complex loads.

[0070] Material nonlinearity refers to the fact that the stress-strain relationship of concrete, steel bars and soil no longer follows the linear elastic law during the process of being stressed, but will enter the plastic, cracking or crushing state; geometric nonlinearity refers to the large displacement and large rotation effects generated by the structure under load, which will affect the establishment of equilibrium equations. For each pile design parameter sample, it is necessary to establish its corresponding unique three-dimensional finite element model of the pile-soil system.

[0071] After establishing the finite element model, limit state analysis is performed to obtain discrete limit points. Discrete limit points refer to the specific load coordinate points in the composite load space that indicate the ultimate bearing capacity of the foundation pile. The specific operation method for obtaining discrete limit points is as follows: On the established finite element model, various combinations of vertical loads, horizontal loads, and bending moments with different predetermined proportions are applied in a programmed manner. Each fixed load proportion represents a specific load action mode. For each load mode, nonlinear finite element calculation is performed using incremental loading, that is, keeping the proportion between vertical loads, horizontal loads, and bending moments constant, and gradually increasing their amplitudes synchronously. Under each step of load increment, the finite element equilibrium equations are solved, and the stress, strain, and displacement of the entire field are iteratively updated.

[0072] Each load combination is defined by a fixed set of proportional coefficients. For example, the ratio of vertical load, horizontal load, and bending moment in a combination is 1.0:0.2:0.05, which means that the horizontal force is approximately 20% of the vertical force, and the bending moment is approximately 5% of the vertical force. These proportional coefficients cover various stress conditions, from pure compression, compression-bending, compression-shear to compression-bending-shear, to ensure that the final discrete limit point set can fully depict the three-dimensional morphology of the failure envelope. When performing incremental loading nonlinear calculations, the loading process does not use a fixed percentage step size, but implements a dynamic step size strategy automatically controlled by the solver. The specific operation is as follows: Based on the analysis of the initial stiffness and estimated bearing capacity of the structure, an initial load increment is set, for example, five to ten percent of the estimated total ultimate load is used as the load increment value for the first loading step; in each loading calculation, the finite element method... The solver attempts to iterate and solve the problem at the current load level to reach equilibrium. If the calculation converges successfully within a preset number of iterations, the solver will automatically predict and increase the step size of the next loading step based on the difficulty of convergence, for example, increasing the step size to 120% to improve computational efficiency. Conversely, if iterative solving is difficult at a certain step size and fails to converge, the solver will automatically backtrack and reduce the step size to half or less of the original value, for example, to 50%, and retry the calculation. This process of dynamically adjusting the loading amplitude of the next step based on the convergence of the previous step is called automatic step size control. In this way, the calculation process can use large step sizes to advance quickly in the relatively flat phase of the load-displacement curve, and use small step sizes to capture the nonlinear drastic changes in the near-limit state until the stopping conditions of iteration failure or displacement exceeding the limit are finally met.

[0073] This calculation process continues until one of the following two limit state judgment conditions is met: First, the finite element equilibrium equation solver cannot reach the convergence tolerance requirement within the preset maximum number of iterations, indicating that the structural system has become unstable or has failed; Second, monitoring reveals that the displacement value of the preset control node at the section with the maximum bending moment of the pile exceeds the failure displacement limit defined in advance according to engineering specifications or design experience, indicating that the structural deformation has exceeded the permissible range. Once either condition is met, the calculation of the current load step is terminated. At this time, the final values ​​of the applied vertical load, horizontal load, and bending moment are recorded. These three values ​​constitute a three-dimensional coordinate point, i.e., a discrete limit point. Repeating the above process for each preset load ratio mode will yield a series of discrete limit points. The set of all these discrete limit points is called the discrete limit point set corresponding to the pile design parameter sample. This set of points approximately outlines the shape of the true failure envelope of the pile design in the composite load space.

[0074] The failure of iterative calculation here specifically refers to the inability of the finite element equilibrium equation to converge within the preset maximum number of iterations. In nonlinear finite element analysis, each loading step requires multiple iterations to find the displacement and stress field that satisfy the equilibrium conditions. When the structure approaches or reaches its bearing limit, the stiffness matrix becomes singular or ill-conditioned, causing the iterative process to fail to converge within the set tolerance range. The preset maximum number of iterations in this invention is set to 25 to 50 times, with the specific value set according to the solver recommendation and problem size. When convergence is still not achieved after reaching this number of iterations, it is determined that the structure has lost its ability to continue bearing loads, and the previous converged load step is the limit state.

[0075] The section with the maximum bending moment of the pile refers to the horizontal section location where the bending moment of the pile is the maximum under bending action, as predicted in advance based on elastic analysis or experience. It is generally located at a certain depth below the mud surface. The control node is a representative node selected on this section for monitoring displacement. The failure displacement limit is an allowable displacement value pre-set according to engineering specifications, design experience, and structural usage requirements. Its specific value originates from one of the following two approaches: First, directly adopting the explicit provisions in the current design specifications. For example, under horizontal load, the horizontal displacement limit at the pile top should be 10% of the pile diameter. Therefore, for a pile with a diameter of 1.2 meters, the failure displacement limit of its control node can be set as follows: 0.12 meters; secondly, when the specification does not directly stipulate for a specific situation, it is necessary to deduce based on the functional requirements of the component. For example, for reinforced concrete piles designed with crack width control, the failure displacement limit is determined by back-calculating the corresponding pile curvature and displacement using structural mechanics formulas based on the maximum allowable crack width. In a specific embodiment of the present invention, if a steel pipe pile with a diameter of 1.5 meters is used, and referring to the relevant specification's control requirements for the horizontal displacement of the pile top, the failure displacement limit is preset to eight percent of the pile diameter, which is 0.12 meters. For concrete piles, in order to control concrete cracking, a more stringent limit is generally adopted, such as five percent of the pile diameter.

[0076] Furthermore, surface fitting calculations are performed on the discrete limit point set of each sample to obtain the actual shape parameter vector corresponding to each sample. This process is achieved by solving a nonlinear least squares optimization problem, specifically including:

[0077] For any sample, its discrete limit point set , This is the index of the discrete limit points in the discrete limit point set. Given the number of discrete limit points in the discrete limit point set, an iterative optimization algorithm is used to find a set of shape parameter vectors such that... The defined surface minimizes the overall fitting error to all discrete limit points, i.e., minimizes the loss function: Solving the problem through an iterative optimization algorithm makes smallest Then this That is, the actual shape parameter vector corresponding to the sample;

[0078] Quantitative shape description indices, i.e., actual shape parameter vectors, are extracted from the discrete limit point set of each sample. This step is accomplished through surface fitting calculation. The purpose of surface fitting calculation is to find an optimal shape parameter vector such that the implicit equation surface determined by the shape parameter vector minimizes the overall distance error between the sample and all discrete limit points. This invention uses a nonlinear least squares optimization method to achieve this fitting. Specifically, for any sample containing n discrete limit points, its discrete limit point set is denoted as a series of coordinate points: the coordinates of the first point, the coordinates of the second point, and so on up to the coordinates of the nth point; here, i is the index of the discrete limit point in the set, and n is the total number of points in the set. An implicit equation F equal to zero, which is completely consistent with the form in step one, is used as the surface model, where the shape parameter vector is the unknown quantity to be solved. The fitting loss function L is defined as the sum of the squares of the function values ​​obtained after substituting all discrete limit points into the equation, i.e., L is equal to the sum of i from 1 to n, where each term is the value of F at the point coordinates. The square of the value; the magnitude of this loss function value intuitively represents the overall deviation of the surface defined by the current shape parameter vector from all actual data points. When the surface just passes through all points, the F value at each point is zero, and the loss function value is zero; the farther the surface deviates from the data points, the larger the absolute value of the F value at each point, and the larger the loss function value. Therefore, the problem of finding the best fitting parameters is transformed into an optimization problem of finding the minimum value of the loss function L. This is a standard nonlinear least squares problem. In practice, numerical optimization algorithms such as the Levenburg-Marquardt algorithm are used for iterative solution. The final optimal solution is the shape parameter vector that makes the theoretical surface most closely approximate the actual discrete limit point set of the sample. This is called the actual shape parameter vector corresponding to the sample. Through this process, an actual shape parameter vector is calculated for each pile design parameter sample, thus constructing a complete training dataset, where each data pair uses the pile design parameters as input and the actual shape parameter vector as the expected output.

[0079] Finally, a machine learning model is trained using the above dataset to learn the complex nonlinear mapping relationship between the foundation pile design parameters and the actual shape parameter vector. The trained model is the fast prediction model. For any new set of foundation pile design parameters, the model can predict the approximate shape parameters of its failure envelope in a very short time, thereby greatly improving design efficiency. In order to better balance the learning accuracy of the model for different shape parameter components during training, this invention designs an adaptive weighted loss function.

[0080] The machine learning model is trained to become a fast prediction model, and the loss function used is an adaptive weighted mean square error function, the expression of which is:

[0081]

[0082] in, For the indices of the components in the shape parameter vector, correspond , correspond And so on, To output the predicted shape parameter vector for the fast prediction model The j-th component, Let the j-th component of the actual shape parameter vector obtained from the sample fitting be used as the training label. The static basic weight coefficients are pre-defined and reflect the importance of the j-th component. This is the standard deviation of the prediction error for all samples in this training batch on the j-th component. It is a division-by-zero constant;

[0083] The mathematical expression for the adaptive weighted loss function is: This is equivalent to summing j from 1 to 8, with each term consisting of a product of three parts; the first part is the basic weight coefficient. Divide by the dynamic variance term and constant The summation is as follows: the first part is the sum of the predicted and actual values; the second part is the square of the difference between the predicted and actual values; the summation index j represents the index of the eight components in the shape parameter vector, and j equal to 1 corresponds to the first component of the shape parameter vector, i.e., the vertical coordinate of the center point. j equals 2, corresponding to the horizontal coordinate of the center point. j equals 3, corresponding to the bending moment coordinates at the center point. j equals 4, corresponding to the vertical scale scaling factor. j equals 5, corresponding to the horizontal scaling factor. j equals 6, corresponding to the bending moment scaling factor. j equals 7, corresponding to the vertical and horizontal load coupling interaction coefficient. j equals 8, corresponding to the interaction coefficient between horizontal load and bending moment. ; This represents the j-th component of the predicted shape parameter vector output by the fast prediction model for the current input sample; this is the model's predicted value. This represents the j-th component of the actual shape parameter vector corresponding to the current sample, calculated through the aforementioned surface fitting. It serves as the target value or label during training. Therefore, the difference within the parentheses represents the model's prediction error on the j-th component. It is a static foundation weight coefficient pre-set based on engineering experience. It reflects the importance of the j-th shape parameter component in the overall evaluation; the higher the importance, the higher the weight assigned. The larger the value, the more normalized it should be set between 0.1 and 10.0, with 1.0 serving as the baseline importance; for core size scaling factors (such as those controlling vertical load-bearing capacity) If the design requires higher precision in bearing capacity in a certain direction, a larger static foundation weighting coefficient is assigned, such as 2.0 to 5.0; for center point coordinate parameters If it is considered relatively minor, assign a smaller static base weight coefficient, such as 0.5 to 1.0; for critical coupling interaction coefficients... , Assign a weight no less than the size scaling factor, for example, 1.0 to 3.0; The essence is to artificially inject engineering experience into the learning process before training begins; for example, if the design code specifies the ultimate bearing capacity in the bending moment direction... If there are stricter tolerance requirements, then... (correspond Setting it to a higher value (such as 3.0) makes the model focus more on reducing the prediction error of this parameter in the early stages of training;

[0084] This is the standard deviation of the model's prediction error for the j-th component across all samples in the current batch of training samples. It is a dynamically changing statistic that reflects the instability of the model's prediction for the j-th component during the current training phase. If the prediction error fluctuates significantly... A larger value indicates that the model has difficulty learning this component; It is a very small positive real number, on the order of ten to the power of negative 8. Its main function is to prevent when... A mathematical error occurs when the denominator is exactly zero; It's not a preset hyperparameter, but a statistic dynamically calculated based on the model's current performance in each training batch. In a training batch containing Q samples, the model outputs a predicted shape parameter vector for each sample. For the j-th component, the prediction error (predicted value minus the true value) for the Q samples in that batch on that component is first calculated, and then the sample standard deviation of these Q error values ​​is calculated. , The range of values ​​is Its magnitude directly reflects the model's predictive consistency on this parameter in the current batch; A value close to 0 means that the model predicts the j-th component of all samples in this batch very accurately and the error values ​​are highly consistent, indicating that the model has a good grasp of the mapping relationship between the parameter and the input features. The larger the value, the greater the fluctuation in the model's predictions for that component. It may predict accurately for some samples but have large errors for others, indicating that the model has not yet stably learned the pattern of that parameter, or that the relationship between that parameter and the input features is inherently very complex and difficult to learn. In adaptive weighted loss functions, This constitutes dynamic weights, when When the value is large (prediction is unstable), the weight automatically decreases, temporarily reducing the contribution of this difficult parameter to the total loss in the current training step. This prevents its unstable gradient from interfering with the model's learning of other parameters. As training progresses and the model's capabilities improve, Overall, it will gradually decrease;

[0085] It is a very small positive constant introduced purely for numerical stability, and is taken to be much smaller than the typical value. The floating-point value, within the deep learning framework involved in this invention, Set at 1e -8 up to 1e -12 Between; at the start of training, the model is randomly initialized, resulting in large and unstable prediction errors. The values ​​are all relatively large, the dynamic weights are relatively small, and all parameters have a certain learning opportunity. As training progresses, for parameters that are easy to learn (their values ​​are relatively large), the learning opportunities increase. (rapidly decreases), its dynamic weight It will increase rapidly, combined with its The loss function guides the model to continue optimizing the accuracy of these parameters; for parameters that are difficult to learn, its... The slower descent and relatively low dynamic weights avoid excessive gradient interference, allowing the model to learn complex relationships at a smoother pace. This mechanism ultimately contributes to the model's balanced and accurate predictive ability across all shape parameter components.

[0086] The entire score term constitutes a dynamically adjusted weight, and the core function of this loss function is that it is based not only on static importance. Allocating attention, also through the denominator The squared term introduces a dynamic assessment of prediction difficulty; for parameter components that currently exhibit large prediction fluctuations and are difficult to learn, due to their... A larger value will lead to a decrease in the weight of this component, thus appropriately reducing the penalty for the error of this component in the current optimization step. This allows the model to learn all parameters more evenly and avoids the training process being dominated by a few hard-to-fit components. As the model training progresses, its predictive ability changes continuously. It is also recalculated and updated in each training batch, thereby achieving adaptive adjustment of the training focus; the entire training process continuously adjusts the millions of connection weights within the fast prediction model through optimization methods such as backpropagation, making this adaptive weighted loss function... The average value across the entire training dataset continuously decreases, eventually resulting in an accurate, robust, and fast prediction model.

[0087] Step 3: Using the difference between the predicted shape parameter vector and the target shape parameter vector as the optimization objective and the pile design parameters as the optimization variables, the multi-objective optimization algorithm is used to iteratively solve the problem. In each iteration, the candidate pile design parameters in the fast prediction model are called to predict and evaluate the shape, so as to obtain the optimized pile design parameters that make the predicted failure envelope shape closest to the target failure envelope shape.

[0088] In a specific implementation, the goal of this step is to embed the aforementioned fast prediction model into an automated optimization framework to solve in reverse the pile design scheme that can make the shape of the failure envelope conform to the predetermined target and control the project cost. This process is mathematically constructed as a multi-objective optimization problem and is solved automatically through an intelligent optimization algorithm.

[0089] The degree of closeness between the desired and predicted shapes is transformed into a calculable, single numerical metric as the primary optimization objective. This metric is achieved by defining a mathematical formula called the difference metric function D. The core idea of ​​the difference metric function D is to calculate the comprehensive distance between the predicted and target shape parameter vectors at each component. Specifically, the function uses a weighted Euclidean distance, expressed as follows: summing over j from 1 to 8, first calculating the difference between the j-th component of the predicted shape parameter vector and the j-th component of the target shape parameter vector, then squared this difference, and multiplied by a difference weight coefficient pre-assigned to that component. Finally, perform this weighted sum of squares operation on all eight components, and take the square root of the sum to obtain the final difference measure. ;

[0090] The optimization objective is to determine the difference between the predicted shape parameter vector and the target shape parameter vector by defining a quantified difference measurement function. To achieve the difference measurement function Defined as weighted Euclidean distance:

[0091]

[0092] in, and These are the j-th components of the predicted shape parameter vector and the target shape parameter vector, respectively. The difference weighting coefficient assigned to the j-th component;

[0093] This represents the j-th component of the predicted shape parameter vector output by the fast prediction model for a specific set of foundation pile design parameters. This represents the j-th component of the target shape parameter vector, which is predefined in step one and reflects the ideal performance target; therefore, the difference within the parentheses directly reflects the deviation between the model-predicted shape and the design target on a specific geometric feature; (symbol) This is the differential weighting coefficient assigned to the j-th shape parameter component. It is a positive number pre-set based on engineering experience. The reason for setting the weighting coefficient is that the geometric features described by the eight shape parameters are not equally important to the overall safety; for example, the size scaling factor representing the overall load-bearing capacity. The parameter represents a slight offset from the center position. More critically, the negative coupling interaction coefficient, which reflects unfavorable load coupling, may require even stricter control than the positive coefficient, which reflects favorable coupling, through adjustment. The magnitude of the value can significantly amplify or reduce the contribution of the corresponding component deviation to the overall difference measure function D, thereby guiding the optimization process to prioritize the matching of those key shape features; the value of the difference measure function D is a non-negative real number. The smaller the value, the closer the predicted failure envelope corresponding to the current pile design parameters is to the target failure envelope in a weighted comprehensive sense; when the value is zero, it means that the predicted shape is completely consistent with the target shape.

[0094] Difference weighting coefficient It is a positive real number weight assigned to the j-th component in the shape parameter vector. Its core function is to quantify the importance of this specific shape feature in the overall shape matching optimization objective. There is no absolute upper limit to the value of , but for numerical stability and ease of interpretation, its normalized value range is set between 0 and 2, with the value 1 considered as the baseline weight. When the value is greater than 1, it indicates that the contribution of the j-th component's deviation to the total difference measure function D is amplified, and the optimization algorithm will be forced to more strictly control the error of that component; when A value less than 1 but greater than 0 indicates that a relatively larger deviation is allowed for that component; if Setting it to 0 means that the difference between this component and the target is completely ignored during optimization;

[0095] about The specific numerical judgment and setting need to be determined in layers based on the engineering physical meaning and design priority of each shape parameter: the first layer is the key load-bearing dimension parameter, namely the scale factor. These parameters directly determine the limiting range of the failure envelope in the pure axial force direction, corresponding to the most basic vertical, horizontal, and flexural bearing capacities of the pile. These parameters are considered the most important; therefore, they are given relatively high weights. For example, they can be adjusted according to the safety factor requirements in the design specifications. Corresponding weights The weight is set in the range of 1.2 to 1.8. If a certain bearing capacity (such as the horizontal bearing capacity required for seismic resistance) is particularly critical, its corresponding weight is set to 1.5 or higher.

[0096] The second layer consists of load coupling interaction parameters, i.e. and These parameters control the nonlinear morphology of the envelope surface under coupled loads, and are related to the structural safety reserve under complex stresses. The direction (positive or negative) and magnitude of their weights must be determined in conjunction with the specific design intent. If the design aims to avoid unfavorable coupling weakening effects (i.e., avoid inward concavity of the envelope surface), then... or Set a high positive weight (e.g., 1.0 to 1.5) to severely penalize the negative deviation of the predicted coupling interaction coefficients from the target value. If there are no special requirements for the coupling pattern, assign a medium or low weight (e.g., 0.5 to 1.0).

[0097] The third layer consists of the coordinate parameters of the center point of the envelope surface, i.e. They represent a baseline equilibrium state in most symmetrical designs. and The target value is often set to zero; the weights of these parameters are set lower than those of the size parameters, for example, by... weight Set it to 0.8 to 1.2, and weight , Setting it to 0.5 to 1.0 indicates that the optimized design scheme is allowed some flexibility at the baseline static load equilibrium point; in practice, the initial set of weight coefficients is set to a set of default values ​​(e.g., all...). All are set to 1), and adjustments are made according to the specific focus of this design; for example, in cost-sensitive projects, the weights of all shape parameters are appropriately reduced (e.g., all are set to 0.8), so that the construction cost function C plays a more dominant role in the optimization; in critical projects with extremely high requirements for load-bearing shape, the weights of critical dimension parameters are significantly increased (e.g., all ... The weighting has been increased to 2.0).

[0098] Simply pursuing shape matching can lead to an overly conservative design and uneconomical material usage. Therefore, construction costs must also be considered as a secondary optimization objective to be minimized. To this end, a construction cost function C is constructed. This function directly calculates an estimated total cost based on the evaluated pile design parameters. Its calculation logic is based on the bill of quantities and market price information. Specifically, the input of the construction cost function C is the pile design parameters, from which it extracts key information such as pile diameter, pile length, concrete strength grade, and steel reinforcement specifications and quantities. Then, it calculates the volume of concrete based on the pile diameter and length, and the total weight of steel reinforcement based on the reinforcement parameters. These are then multiplied by the unit price per cubic meter of concrete and the unit price per ton of steel reinforcement, based on current market conditions or company quotas, to obtain the material costs. On this basis, it further considers construction measures costs and machinery operating costs related to pile length and diameter, and adds these sub-items together to obtain the value of the estimated construction cost function C for this design scheme. The specific calculation formula of the construction cost function C is determined according to the actual pricing specifications, and its core lies in establishing a clear mapping relationship from pile design parameters to monetary costs.

[0099] Construct a multi-objective optimization problem, specifically a difference metric function for shape parameter vectors. Minimize, and the construction cost function Minimize the construction cost function The calculation is based on the pile diameter, pile length, material usage, and preset unit cost coefficient in the pile design parameters.

[0100] The construction cost function C is a deterministic mathematical function that estimates costs based on the pile design parameters. Its purpose is to map the physical parameters of the design scheme to an estimated total cost. First, the pile diameter and pile length are extracted from the pile design parameters. Based on these two parameters, the material usage of the pile body is directly calculated. The first material usage is the total volume of concrete, which is calculated using the formula for the volume of a cylindrical pile body. That is, the concrete usage equals pi multiplied by the square of half the pile diameter, and then multiplied by the pile length. The second material usage is the total weight of steel reinforcement. Based on the longitudinal reinforcement ratio, stirrup specifications, and spacing specified in the pile design parameters, the weight of steel reinforcement per meter of pile length is calculated, multiplied by the pile length, and summed to obtain the total weight of steel reinforcement.

[0101] The calculated material quantities are multiplied by their corresponding preset unit cost coefficients to obtain the material costs for each item. These preset unit cost coefficients are fixed parameters pre-input based on market prices or company quotas and mainly include the unit price coefficient per cubic meter of concrete and the unit price coefficient per ton of steel reinforcement. For example, the cost of concrete equals the concrete quantity multiplied by the unit price coefficient per cubic meter of concrete; the cost of steel reinforcement equals the total weight of steel reinforcement multiplied by the unit price coefficient per ton of steel reinforcement. This provides a reliable economic evaluation index for multi-objective optimization. Finally, all the material costs are summed to obtain the total construction cost function C of the design scheme. The entire process is a deterministic arithmetic operation. Its input is a vector of design parameters containing pile diameter, pile length, and reinforcement information, and its output is a scalar cost value representing the economic objective, thus providing a direct and quantitative cost assessment for the optimization algorithm.

[0102] The two objectives that need to be minimized simultaneously are the shape difference metric function D and the construction cost function C. This is a typical multi-objective optimization problem. Its solution is not a single solution, but a set of compromise solutions that make different trade-offs between D and C, called the Pareto optimal solution set. In order to automatically find this solution set, this invention uses a genetic algorithm based on reference points and non-dominated sorting for iterative solution.

[0103] A multi-objective optimization algorithm is used for iterative solution, specifically a genetic algorithm based on reference points and non-dominated sorting. This algorithm maintains a population consisting of multiple candidate pile design parameters. In each iteration of the algorithm, when evaluating the candidate pile design parameters within the population, a fast prediction model is invoked to obtain the corresponding predicted shape parameter vector, and then the difference metric function is calculated. Construction cost function ;

[0104] The implementation of this optimization algorithm starts with a randomly generated initial population. The population is a core concept in genetic algorithms, referring to a set of multiple solutions to be evaluated in the same generation. In this invention, the population consists of dozens to hundreds of randomly generated candidate piling design parameters. Each vector represents a possible design scheme and is called an individual.

[0105] The core of the algorithm is an iterative process, with each iteration called a generation. In each generation, a population evaluation is first performed. This evaluation involves automatically calling the fast prediction model trained in step two for each candidate pile design parameter in the current population, i.e., each individual. The design parameters of the current individual are input into the fast prediction model, which outputs its corresponding predicted shape parameter vector. Then, using this predicted vector and the target shape parameter vector, the first optimization objective, i.e., the value of the shape difference metric function D, is calculated according to the aforementioned formula. Simultaneously, based on the design parameters such as pile diameter and pile length contained in the individual, the second optimization objective, i.e., the value of the estimated construction cost function C, is calculated through the calculation logic of the construction cost function C. Thus, each individual is mapped to a specific coordinate point in the two-dimensional optimization objective space composed of D and C.

[0106] Based on calculations and The value is used to perform a non-dominated ranking of all individuals in the population, and the ranking is based on the non-dominated ranking level and the optimization objective. The distribution density in the defined space is used to comprehensively evaluate and select individuals. For the selected individuals, crossover and mutation operations are performed to generate a new generation of candidate pile design parameters. The above steps are repeated until the preset maximum number of iterations is reached. All non-dominated pile design parameters in the final generation population are output as optimized pile design parameters.

[0107] The algorithm performs a non-dominated ranking of all individuals in the current population, which is a key step in multi-objective optimization. The non-dominated ranking is based on the Pareto dominance relation: for a minimization problem, if an individual A has two objective values... and The target value of each individual B is not less than or equal to the target value of the other individual B. and And there exists at least one objective whose function value is less than B, i.e. or If individual A dominates individual B, then the algorithm finds all individuals that are not dominated by any other individual, marks them as the first non-dominated frontier, and assigns them the highest ranking rank (e.g., rank 1). Then, these individuals are temporarily removed from the population, and non-dominated individuals are searched again among the remaining individuals to form the second non-dominated frontier, which is assigned the second highest ranking rank (e.g., rank 2), and so on. The smaller the ranking rank number, the better the overall quality of the individual.

[0108] To further differentiate between superior and inferior individuals among those with the same non-dominated ranking and to maintain population diversity, the algorithm calculates the distribution density of each individual in the optimization target space. The distribution density reflects the crowding of other individuals around a particular individual. The farther an individual is from its neighbors in the target space, the smaller its distribution density value, indicating that the solution in its region is relatively sparse and worth preserving to explore a wider search space. The algorithm prioritizes individuals with high non-dominated ranking and low distribution density as superior parents.

[0109] Then the algorithm enters the evolutionary stage. From the excellent parent individuals selected through comprehensive evaluation, it generates new offspring individuals by simulating biological genetic operations. There are two main operations: crossover and mutation. The crossover operation refers to randomly selecting two parent individuals and exchanging some of their foundation pile design parameter components, thereby generating a new individual that integrates the characteristics of both parents. The mutation operation refers to randomly perturbing a certain design parameter component of an individual, thereby introducing new genetic characteristics, which helps to escape local optima. Through crossover and mutation, a completely new set of candidate foundation pile design parameters is generated, forming a new generation of population.

[0110] The evaluation, sorting, selection, and evolution processes described above will be repeated continuously. In each generation, the overall quality of the population evolves towards a direction with smaller shape differences and lower costs. When the cycle reaches the preset maximum number of iterations, the algorithm terminates. At this point, all individuals belonging to the first non-dominated frontier in the final generation population, i.e. those individuals whose D and C cannot be improved simultaneously in all existing schemes, are output as a set. This set is called the optimized piling design parameter set. Each optimized piling design parameter in this set represents a feasible design scheme that achieves the best balance between performance and cost under the preset objective.

[0111] Step 4: Input the optimized pile design parameters into the simulation model for forward analysis, obtain the true shape parameter vector, compare the true shape parameter vector with the target shape parameter vector to verify their consistency. After verification, convert the optimized pile design parameters into a standard digital design file to guide the automated construction of wharf piles.

[0112] In a specific implementation, the goal of this step is to perform a final verification of the optimized foundation pile design parameters obtained in step three, and convert them into a data format that can directly drive automated production equipment, thereby completing the closed loop from digital design to industrialized construction.

[0113] The optimized pile design parameter set output in step three is the result of optimization based on the fast prediction model, which is a surrogate model. Although the fast prediction model has been fully trained, its prediction still has certain uncertainties. Therefore, the selected design scheme is handed over to a high-fidelity simulation model for final verification to ensure that its performance is real and reliable. This verification process is called verification. The simulation model used for verification is the three-dimensional finite element model that considers material and geometric nonlinearity and is used to generate training samples in step two. Its calculation accuracy is much higher than that of the fast prediction model used as a surrogate model.

[0114] The optimized pile design parameters are input into the simulation model. Numerical limit state analysis is performed to obtain the discrete limit point set. The true shape parameter vector is obtained through surface fitting. The specific operation to verify the consistency is as follows: calculate the relative error between the true shape parameter vector and the target shape parameter vector for each corresponding component. Compare the relative error of each component with the preset allowable error threshold for that component. When the relative error of all compared components is less than the corresponding threshold, the verification is considered successful.

[0115] The first step in the verification process is to obtain the true shape parameter vector. Specifically, one or more of the most representative design schemes are selected from the optimized pile design parameter set, and their complete pile design parameters are input into the aforementioned high-fidelity three-dimensional finite element simulation model. Then, the numerical limit state analysis process in step two is completely reproduced: a detailed pile-soil finite element model is established for this specific design scheme, and multiple load combinations with different proportions are applied for incremental loading calculations until the model reaches the limit state, thereby obtaining the discrete limit point set corresponding to the scheme; then, for this discrete limit point set, the same surface fitting algorithm and nonlinear least squares optimization method as in step two are used to calculate an optimal shape parameter vector. This vector is entirely derived from the high-precision simulation results and represents the true performance that the design scheme can achieve, hence it is called the true shape parameter vector of the scheme.

[0116] After obtaining the true shape parameter vector, the core consistency comparison verification can be performed. The purpose of the verification is to determine whether the actual performance of the design scheme is close enough to the preset design target. The specific operation process is as follows: First, calculate the relative error between the true shape parameter vector and the target shape parameter vector at each corresponding component. The relative error is calculated by subtracting the target value from the true value, dividing by the absolute value of the target value, and then multiplying by 100% to obtain a percentage value. For example, for the vertical scale scaling factor... Its relative error is equal to the true error. Value minus target Difference of values ​​divided by the target The absolute value is calculated; next, the relative error value of each component is calculated and compared one by one with the pre-set allowable error threshold for that component; the allowable error threshold is a set of percentage values ​​determined in advance by the designer based on engineering specifications, safety margins, and technological level. Each shape parameter component has its own independent threshold, for example, the critical load-bearing parameter. The threshold is set at 5%, while the threshold for secondary or coupling parameters is relaxed to 10% or 15%. The conditions for passing the verification are strict: the optimized pile design parameters are considered to have passed the verification only if the relative errors of all eight components in the true shape parameter vector are less than their respective allowable error thresholds; if the error of any component exceeds the threshold, the design scheme is considered to have failed the verification and needs to be reviewed or removed from the optimization results.

[0117] The specific steps for converting to a standard digital design file are as follows: the verified optimized foundation pile design parameters and their corresponding real shape parameter vectors are written together into a building information model file that conforms to the industrial foundation category standard; this file is used to transfer the design data to the automated construction system to guide the construction of the wharf foundation piles;

[0118] For the optimized foundation pile design parameters that have passed verification, they need to be converted into a data format commonly used in the industry for transmission and execution. This process is called digital delivery, and its output is a standard digital design file. In this invention, the file specifically adopts the building information model file format that conforms to the Industrial Basic Standard. The Industrial Basic Standard is a globally recognized and open standard for exchanging building engineering data. It defines how information about buildings and infrastructure is organized throughout their entire life cycle. The building information model file is a structured digital file created under this standard that contains a three-dimensional geometric model, engineering attributes, and management information.

[0119] The specific steps to generate this file are as follows: Create a new Building Information Model (BIM) file and, based on the validated optimized pile design parameters, accurately generate the three-dimensional geometric entity of the wharf pile. The geometric properties of this entity, such as diameter and length, are driven by the design parameters. At the same time, material properties such as concrete strength grade and steel reinforcement specifications are assigned as labels to this three-dimensional entity. In addition, a crucial step is to store the performance data of this pile, namely the target shape parameter vector and the validated actual shape parameter vector, as extended attributes in the database entries of this pile component. This makes the file not only contain the physical description of the component but also embed its performance indicators, forming a digital asset that carries complete information.

[0120] Ultimately, this building information model file, which contains geometric, material, and performance data, can be transmitted to downstream automated construction systems via standard application programming interfaces (APIs) or data export functions. The automated construction system parses the file, extracts the precise dimensions, spatial positioning, material type, and reinforcement information of the foundation piles, and converts this data into control instructions for CNC machining equipment, automated rebar tying robots, or intelligent concrete pouring systems. This precisely guides the entire process of automated construction, from component prefabrication to on-site installation, achieving lossless transfer and efficient execution of design information to physical construction.

[0121] 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.

[0122] 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.

[0123] 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.

[0124] 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 reverse design method for wharf foundation piles based on multi-objective optimization, characterized in that, The specific steps include: Step 1: In the composite load space consisting of vertical load, horizontal load and bending moment, define a target failure envelope surface to describe the ultimate state of the pile-soil system of the wharf foundation piles, and use the target shape parameter vector to perform a parameterized mathematical description of the geometry of the target failure envelope surface. Step 2: Perform numerical limit state analysis on multiple sets of preset pile design parameter samples to obtain the discrete limit point set of each sample in the composite load space. Perform surface fitting on the discrete limit point set to calculate the actual shape parameter vector corresponding to each sample. Train the machine learning model based on the sample and the corresponding actual shape parameter vector to make it a fast prediction model that outputs the predicted shape parameter vector based on the input pile design parameters. Step 3: Using the difference between the predicted shape parameter vector and the target shape parameter vector as the optimization objective and the pile design parameters as the optimization variables, the multi-objective optimization algorithm is used to iteratively solve the problem. In each iteration, the candidate pile design parameters in the fast prediction model are called to predict and evaluate the shape, so as to obtain the optimized pile design parameters that make the predicted failure envelope shape closest to the target failure envelope shape. Step 4: Input the optimized pile design parameters into the simulation model for forward analysis, obtain the true shape parameter vector, compare the true shape parameter vector with the target shape parameter vector to verify their consistency. After verification, convert the optimized pile design parameters into a standard digital design file to guide the automated construction of wharf piles.

2. The reverse design method for wharf foundation piles based on multi-objective optimization according to claim 1, characterized in that: A three-dimensional Cartesian coordinate system is established, with its three orthogonal axes representing vertical load, horizontal load, and bending moment, respectively, to form a composite load space. In this composite load space, according to the composite bearing capacity requirements of the wharf structure on the foundation piles, a closed, smooth surface is defined as the target failure envelope surface. This target failure envelope surface characterizes the limit state boundary of the pile-soil system as designed. The target failure envelope is parameterized using a target shape parameter vector, which includes a set of size scaling factors and a set of coupling interaction factors. The size scaling factors are used to adjust the limit dimensions of the target failure envelope in the directions of the vertical load axis, the horizontal load axis, and the bending moment axis. The coupling interaction factors are used to adjust the deviation shape of the envelope surface from the linear superposition surface of each load limit value when two or more loads act together.

3. The reverse design method for wharf foundation piles based on multi-objective optimization according to claim 2, characterized in that: An implicit equation containing eight components is used as a general parametric model to describe the geometry of the failure envelope surface, and its expression is: Its specific display format is as follows: Wherein, the shape parameter vector is , These represent vertical load, horizontal load, and bending moment, respectively. They are coordinate variables in the composite load space, representing an arbitrary combination of loads acting on the foundation pile. The coordinates of the center point of the failure envelope in the composite load space represent the basic bearing capacity level under static load conditions. These are the scaling factors along the vertical load N-axis, the horizontal load H-axis, and the bending moment M-axis, respectively. , These are all coupling interaction coefficients, used to adjust the nonlinear convex or concave morphology of the failure envelope surface in the vertical-horizontal load plane and the horizontal-bending moment load plane, respectively.

4. The reverse design method for wharf foundation piles based on multi-objective optimization according to claim 3, characterized in that: Numerical limit state analysis was performed on the sample of pile design parameters, specifically using the finite element method considering material and geometric nonlinearity. For each sample, a corresponding three-dimensional finite element model of the pile-soil system was established. During the analysis, various load combinations with different proportions of vertical loads, horizontal loads, and bending moments were sequentially applied to the finite element model. For each load combination, the load proportion was kept constant, and incremental loading nonlinear calculations were performed until the model reached the limit state, causing the iterative calculation to fail, or the displacement of the control node of the maximum bending moment section of the pile exceeded the preset failure displacement limit. The load combination recorded at this point is a discrete limit point. All discrete limit points are collected to form the discrete limit point set of the sample. The iterative calculation failure refers to the finite element equilibrium equation failing to converge within the preset maximum number of iterations. Surface fitting calculations are performed on the discrete limit point set of each sample to obtain the actual shape parameter vector corresponding to each sample. This process is achieved by solving a nonlinear least squares optimization problem, specifically including: For any sample, its discrete limit point set , This is the index of the discrete limit points in the discrete limit point set. Given the number of discrete limit points in the discrete limit point set, an iterative optimization algorithm is used to find a set of shape parameter vectors such that... The defined surface minimizes the overall fitting error to all discrete limit points, i.e., minimizes the loss function: Solving the problem through an iterative optimization algorithm makes smallest Then this That is, the actual shape parameter vector corresponding to the sample; The machine learning model is trained to become a fast prediction model, and the loss function used is an adaptive weighted mean square error function, the expression of which is: in, For the indices of the components in the shape parameter vector, correspond , correspond And so on, To output the predicted shape parameter vector for the fast prediction model The j-th component, Let the j-th component of the actual shape parameter vector obtained from the sample fitting be used as the training label. The static basic weight coefficients are pre-defined and reflect the importance of the j-th component. This is the standard deviation of the prediction error for all samples in this training batch on the j-th component. It is a division-by-zero constant.

5. The reverse design method for wharf foundation piles based on multi-objective optimization according to claim 4, characterized in that: The optimization objective is to determine the difference between the predicted shape parameter vector and the target shape parameter vector by defining a quantified difference measurement function. To achieve the difference measurement function Defined as weighted Euclidean distance: in, and These are the j-th components of the predicted shape parameter vector and the target shape parameter vector, respectively. The difference weighting coefficient assigned to the j-th component; Construct a multi-objective optimization problem, specifically a difference metric function for shape parameter vectors. Minimize, and the construction cost function Minimize the construction cost function The calculation is based on the pile diameter, pile length, material usage, and preset unit cost coefficient in the pile design parameters.

6. The reverse design method for wharf foundation piles based on multi-objective optimization according to claim 1, characterized in that: A multi-objective optimization algorithm is used for iterative solution, specifically a genetic algorithm based on reference points and non-dominated sorting. This algorithm maintains a population consisting of multiple candidate pile design parameters. In each iteration of the algorithm, when evaluating the candidate pile design parameters within the population, a fast prediction model is invoked to obtain the corresponding predicted shape parameter vector, and then the difference metric function is calculated. Construction cost function ; Based on calculations and The value is used to perform a non-dominated ranking of all individuals in the population, and the ranking is based on the non-dominated ranking level and the optimization objective. The distribution density in the defined space is used to comprehensively evaluate and select individuals. For the selected individuals, crossover and mutation operations are performed to generate a new generation of candidate pile design parameters. The above steps are repeated until the preset maximum number of iterations is reached. All non-dominated pile design parameters in the final generation population are output as optimized pile design parameters. The optimized pile design parameters are input into the simulation model. Numerical limit state analysis is performed to obtain the discrete limit point set. The true shape parameter vector is obtained through surface fitting. The specific operation to verify the consistency is as follows: the relative error between the true shape parameter vector and the target shape parameter vector is calculated. The relative error of each component is compared with the preset allowable error threshold for that component. When the relative error of all compared components is less than the corresponding threshold, the verification is considered successful.

7. The reverse design method for wharf foundation piles based on multi-objective optimization according to claim 6, characterized in that: The specific steps for converting to a standard digital design file are as follows: the verified optimized foundation pile design parameters and their corresponding real shape parameter vectors are written together into a building information model file that conforms to the industrial foundation category standard; This document is used to transfer design data to an automated construction system to guide the construction of the wharf foundation piles.

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