A method for arranging foundation pit monitoring points based on improved greedy algorithm

Abstract

The application belongs to the technical field of foundation pit monitoring, and particularly relates to a foundation pit monitoring point arrangement method based on an improved greedy algorithm, which comprises the following steps: firstly, obtaining foundation pit basic data and determining a target monitoring area and a key part area, then generating candidate monitoring points in a ring area outside the foundation pit, then respectively calculating a risk score, a coverage score and a coupling score, then determining the weights of the three scores by using an analytic hierarchy process and calculating the weighted sum of the three scores, and finally selecting the monitoring point with the highest weighted sum in each round by greedy iteration to add the monitoring point to a point arrangement scheme, updating the scores of the remaining monitoring points and continuing the iteration until a termination condition is met to output a final point arrangement scheme. The foundation pit monitoring point arrangement method aims to improve the evaluation criterion of the greedy algorithm from a single coverage area to a three-dimensional weighted comprehensive evaluation of risk, coverage and coupling, so as to solve the problem that the traditional point arrangement method is highly subjective, the risk area lacks point arrangement and the monitoring points are redundant and miscellaneous.

Description

Technical Field

[0001] This invention belongs to the field of foundation pit monitoring technology, specifically relating to a method for arranging foundation pit monitoring points based on an improved greedy algorithm. Background Technology

[0002] Foundation pit monitoring is crucial for ensuring safety and environmental stability in deep foundation pit engineering. The rational layout of monitoring points directly determines the effectiveness, reliability, and cost control of monitoring data. Currently, manual point placement remains the industry mainstream, relying primarily on personnel experience. Under complex geological and environmental conditions, manual point placement suffers from problems such as high workload, strong subjectivity, layout coupling, and omissions. Therefore, determining monitoring points scientifically, efficiently, and safely has clear application value and engineering significance.

[0003] To address these issues, researchers have begun to introduce algorithm optimization methods into the field of monitoring point placement.

[0004] One study proposed using a greedy algorithm to optimize monitoring points. The mechanism uses the monitoring area per unit monitoring point as the evaluation index and adopts the principle of local optimum to generate a layout scheme.

[0005] Other studies have attempted to prioritize monitoring resources in high-risk areas based on risk assessment theory to increase the rationality of monitoring point deployment. However, in actual engineering projects, the data to be measured in foundation pits exhibit coupling relationships. If risk assessment is used solely as the principle for point deployment, it can easily lead to redundant monitoring points in highly coupled areas and insufficient points in low-coupling areas, resulting in wasted monitoring resources and low overall efficiency in acquiring monitoring data. Furthermore, the risk levels vary significantly across different areas of a foundation pit. Using only the monitoring area as the evaluation criterion can easily lead to insufficient deployment in critical areas. As foundation pit engineering is a project where safety is paramount, its monitoring point deployment plan must simultaneously balance factors such as safety, economy, and time efficiency. If only one indicator is used as the basis for point deployment, or if the deployment plan is continuously optimized using multiple indicators, it will inevitably lead to an unreasonable deployment plan and excessively long deployment time, failing to perfectly adapt to the actual engineering situation.

[0006] Furthermore, in recent years, methods integrating finite element numerical simulation and multi-objective optimization algorithms have emerged for monitoring point placement. Some studies, focusing on monitoring point placement for foundation pit support structures, have proposed a method integrating numerical simulation and NSGA-II, establishing a multi-objective optimization mathematical model that simultaneously optimizes monitoring standardization, measurement point sensitivity, and economy. Other studies have proposed optimization methods for complex foundation pit support structure monitoring point layout, integrating modal analysis and particle swarm optimization, using the MAC matrix of candidate measurement points at sensor locations to evaluate the information redundancy of measurement point schemes. However, these multi-objective optimization methods typically require extensive iterative calculations, resulting in long placement times. The optimization results are Pareto solutions rather than a single deterministic placement scheme, posing challenges for engineers in selecting the appropriate scheme. More importantly, multi-objective optimization methods struggle to effectively integrate the "safety first" priority judgment from engineering experience into the algorithm logic, leading to deviations between the optimization results and actual engineering requirements.

[0007] Therefore, how to provide a reasonable deployment scheme that simultaneously takes into account monitoring risks, monitoring scope, and economic effects is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0008] In view of this, the present invention provides a method for the layout of monitoring points for foundation pits based on an improved greedy algorithm. The method aims to generate a feasible set of candidate monitoring points by expanding the foundation pit outline and discretizing the grid, and to establish a risk field for the foundation pit by combining three-dimensional numerical simulation. The risk, coverage and coupling of the candidate monitoring points are quantified into risk score, coverage score and coupling score, respectively, and then weighted greedy iterative point selection is performed. This method solves the problems of strong subjectivity in existing manual point layout, traditional greedy algorithms only considering the coverage area, and data redundancy and resource waste caused by excessive density of monitoring points. The method achieves the effect of increasing the proportion of monitoring points in key areas, reducing duplicate coverage and data coupling, improving the information value of individual monitoring points and the overall economic efficiency and automation efficiency of point layout, while meeting the target coverage rate and key area coverage requirements.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for arranging monitoring points in a foundation pit based on an improved greedy algorithm includes the following steps: S1. Obtain basic data of the foundation pit, and determine the target monitoring area and key parts based on the basic data of the foundation pit; The foundation pit basic data includes foundation pit outline information, foundation pit engineering parameters, monitoring equipment parameters, and algorithm control parameters; S2. Establish a set of candidate measurement points; Specifically, based on the outline of the foundation pit, the effective monitoring radius of the monitoring equipment is extended outward from the foundation pit to form a ring-shaped candidate arrangement area around the outline of the foundation pit; regular grid points are generated within the ring-shaped candidate arrangement area according to the preset candidate grid spacing; the regular grid points are screened according to the external deployment conditions, and the regular grid points that meet the external deployment conditions are used to construct a candidate measurement point set; S3. Establish a three-dimensional model of the foundation pit based on some foundation pit basic data, and establish a foundation pit risk field based on the foundation pit three-dimensional model. Calculate the risk score of each candidate measuring point in the candidate measuring point set based on the foundation pit risk field. The risk field of the foundation pit is established using three-dimensional numerical simulation results; S4. Calculate the coverage score and coupling score of each candidate measurement point in the candidate measurement point set; The coverage score is determined based on the monitoring coverage area corresponding to the candidate monitoring point, the target monitoring area, and the coverage area of ​​the selected monitoring points; the coupling score is determined based on the distance parameter between the candidate monitoring point and the set of selected monitoring points, the soil-related distance, and the coverage score. S5. Use the analytic hierarchy process (AHP) to determine the weights corresponding to the coverage score, risk score, and coupling score, and calculate the weighted sum of the three scores of the candidate test points based on the coverage score, risk score, coupling score, and corresponding weights. S6. Use a greedy iterative method to select measurement points; In each round, the candidate measurement point with the highest current weighted sum is selected and added to the final measurement point layout scheme. After being added, the coverage score, coupling score, and weighted sum of the three scores of the remaining candidate measurement points are updated until the preset termination condition is met, and the final measurement point layout scheme is output.

[0010] Preferably, in step S1: The excavation pit outline information includes the coordinates of the outer boundary of the excavation pit, the coordinates of the corner points of the excavation pit, the edge line information of the excavation pit, the plan shape of the excavation pit, the outline image of the excavation pit, and CAD drawing data; The parameters of the foundation pit project include at least one of the following: foundation pit excavation depth, foundation pit support type, foundation pit safety level, soil layer parameters, groundwater conditions, location of surrounding buildings, location of surrounding roads, location of underground pipelines, surrounding load conditions, and construction stage information. Monitoring equipment parameters include monitoring equipment type, effective monitoring radius, monitoring range shape, maximum number of equipment, and minimum spacing between monitoring points; The algorithm control parameters include target coverage, upper limit of the number of measuring points, candidate grid spacing, minimum allowable spacing of final measuring points, soil correlation distance, coverage requirements for key parts, and analytic hierarchy process (AHP) judgment matrix.

[0011] Preferably, in step S1: Monitoring tasks include at least one of the following: displacement monitoring tasks, settlement monitoring tasks, deformation monitoring tasks of surrounding buildings, deformation monitoring tasks of underground pipelines, video monitoring tasks, and comprehensive monitoring tasks; The target monitoring area includes the area of ​​the foundation pit support structure, the area near the foundation pit outline, and the surrounding influence area of ​​the foundation pit formed by extending the foundation pit outline outward by a preset distance; the preset distance is determined based on at least one of the foundation pit excavation depth, engineering safety level, monitoring specification requirements, and effective monitoring range of the monitoring equipment. Key areas include at least one of the following: the external corner of the foundation pit, the internal corner of the foundation pit, areas with large deformation of the support structure, areas adjacent to roads, areas adjacent to buildings, areas adjacent to underground pipelines, and areas with weak soil.

[0012] Preferably, in step S2, establishing the candidate measurement point set specifically includes: Based on the outline of the excavation pit, extend the effective monitoring radius of the monitoring equipment outward from the pit. r This forms a ring-shaped candidate arrangement area around the outline of the foundation pit; Within the annular candidate arrangement area, according to the preset candidate grid spacing g Generate regular grid points, each regular grid point being an initial candidate test point. The initial candidate test point set is represented as follows:

[0013] In the formula: , indicating the first i The planar coordinates of the candidate measurement points; n represents the initial number of candidate measurement points; The initial candidate measurement points are filtered based on the external deployment conditions. Initial candidate measurement points that do not meet the external deployment conditions are deleted, resulting in a set of candidate measurement points:

[0014] In the formula: N represents the number of initial candidate measurement points remaining after deleting initial candidate measurement points that do not meet the external deployment conditions; The external deployment conditions include at least one of the following: safety distance conditions, equipment installation conditions, construction accessibility conditions, and line-of-sight conditions.

[0015] Preferably, in step S3, establishing the foundation pit risk field using three-dimensional numerical simulation results includes: a. Establish a three-dimensional model of the foundation pit; b. Input soil parameters and support structure parameters into the three-dimensional model of the foundation pit; c. Set boundary conditions and initial geostress; d. Numerical simulation of the foundation pit excavation process; e. Derive the internal force and displacement values ​​of each spatial discrete element in the three-dimensional model of the foundation pit; f. Establish the foundation pit risk field based on the internal force and displacement values; map the spatial discrete elements in the three-dimensional numerical model to the target monitoring area to obtain the internal force and displacement values ​​of the candidate measuring points, and then obtain the foundation pit risk field. The three-dimensional numerical simulation is implemented using FLAC3D. The internal force values ​​include at least one of soil stress, internal force of the support structure, axial force of the support, bending moment of the retaining structure, and equivalent plastic strain. The displacement value includes at least one of the following: horizontal displacement, vertical displacement, ground settlement, support structure displacement, settlement of surrounding buildings, and deformation of underground pipelines.

[0016] Preferably, in step S3, the risk score is calculated according to the following formula:

[0017] In the formula: For the first i Risk scores for each candidate measurement point; For the first i The internal force values ​​of the spatial discrete element corresponding to each candidate measuring point; This represents the maximum internal force value of each spatial discrete element in the three-dimensional model of the foundation pit; For the first i The displacement values ​​of the spatial discrete element corresponding to each candidate measurement point; This represents the maximum displacement value of each spatial discrete element in the three-dimensional model of the foundation pit.

[0018] Preferably, in step S4, the coverage score is calculated according to the following formula:

[0019] In the formula: The coverage score of the i-th candidate measurement point; Let i be the monitoring coverage area corresponding to the i-th candidate monitoring point; The target monitoring area; The union of the areas covered by the selected measurement points; S( represents the theoretical coverage area of ​​the monitoring equipment) The parentheses indicate that the area within the region is to be calculated. When the monitoring equipment has a circular coverage area, the theoretical coverage area of ​​the monitoring equipment is:

[0020] In the formula: r The effective monitoring radius of the monitoring equipment; When the monitoring equipment has one of the following: a fan-shaped coverage area, a rectangular coverage area, or an irregular coverage area, the theoretical coverage area of ​​the monitoring equipment is determined based on the actual field of view of the monitoring equipment. When the monitoring device is a point-type monitoring device, the monitoring coverage area is the monitoring area covered by the device itself.

[0021] Preferably, in step S4, the coupling score is used to measure the degree of data duplication between the candidate measurement point and the selected measurement point; If the currently selected set of measurement points is:

[0022] In the formula: m is the number of currently selected measurement points; Then the first i The distance parameter between each candidate measurement point and the set of selected measurement points is:

[0023] In the formula: For the first i One candidate measurement point; These are the measurement points in the selected set of measurement points; express and The Euclidean distance between two measuring points; The coupling fraction is calculated according to the following formula:

[0024] In the formula: For the first i Coupling score of each candidate measurement point; For the first i Coverage score of each candidate measurement point; For the first i Distance parameters between each candidate measurement point and the set of selected measurement points; Relevant distances to the soil; When the set of selected measurement points is empty, the coupling score of the candidate measurement points is set to 1; The soil-related distance is determined based on at least one of the following: geotechnical engineering investigation data, field test results, statistical results of soil parameters at the project site, empirical values ​​from literature, and fitting results from Vanmarcke random field theory.

[0025] Preferably, in step S5, determining the weights using the analytic hierarchy process includes: Establish a hierarchical structure with the weighted sum of candidate measurement points as the target layer and coverage, risk, and coupling as the criteria layers; A nine-scale method is used to perform pairwise comparisons of coverage, risk, and coupling to construct a judgment matrix; The weights corresponding to the coverage score, risk score, and coupling score are calculated using the square root method. A consistency check is performed on the judgment matrix. If the consistency ratio is less than a preset threshold, the weight is accepted. The weighted sum of the three scores for each candidate test point is calculated using the following formula:

[0026] In the formula: For the first i The weighted sum of the three scores for each candidate test point; For the first i Coverage score of each candidate measurement point; For the first i Risk scores for each candidate measurement point; For the first i The coupling score of each candidate measurement point , , These are the weights corresponding to the coverage score, risk score, and coupling score, respectively, and: .

[0027] Preferably, in step S6, the greedy iterative method for selecting measurement points includes: Initialize the selected measurement point set to an empty set; The first round of point selection is performed, and the coverage score, risk score, coupling score, and weighted sum of the three scores of each candidate point in the candidate point set are calculated. The candidate point with the highest current weighted sum is selected and added to the selected point set. Then, the candidate point with the highest current weighted sum is deleted from the candidate point set. Update the coverage area of ​​the selected measurement points based on the newly added candidate measurement points; Recalculate the coverage score, coupling score, and weighted sum of the three scores for the remaining candidate measurement points; Repeat the above process until the preset termination condition is met; The final site layout plan was obtained; The preset termination conditions include at least one of the following: the coverage rate of the final deployment plan reaches the target coverage rate, the coverage rate of key parts reaches the preset key part coverage rate, the number of selected measurement points reaches the upper limit of the number of measurement points, and the candidate measurement point set is empty. Coverage is calculated using the following formula:

[0028] In the formula: For coverage; The area covered by the selected measurement points; The target monitoring area; The coverage rate of key areas is calculated using the following formula:

[0029] In the formula: Coverage rate of key areas; This refers to critical areas.

[0030] The beneficial effects of this invention are as follows: This invention improves the traditional greedy algorithm's selection method, which relies solely on coverage area, into a multi-dimensional comprehensive evaluation method that simultaneously considers risk, coverage, and coupling. By weighting and selecting candidate monitoring points using risk scores, coverage scores, and coupling scores, the layout of monitoring points no longer simply pursues the maximum coverage area, but also takes into account priority monitoring of key areas, contributions from new coverage, and data redundancy control between monitoring points.

[0031] In addition, the risk field of the foundation pit is established by FLAC3D three-dimensional numerical simulation, and the internal force and displacement values ​​are mapped to the discrete elements of the risk field. This gives the risk assessment a clear engineering physical basis and can guide limited monitoring resources to areas with greater stress on the support structure, significant soil deformation, or sensitive surrounding environment, thereby improving the safety and relevance of foundation pit monitoring.

[0032] Based on this, by expanding the excavation pit outline to form a ring-shaped candidate layout area, and combining grid discretization and external layout condition screening, the continuous construction site can be transformed into a finite, calculable, and field-implementable set of candidate monitoring points, avoiding the output of a scheme that is "algorithm-selectable but not field-implementable." The new coverage area of ​​the target monitoring area by candidate monitoring points is calculated using coverage scores, and the coverage area of ​​selected monitoring points is updated after each iteration, effectively reducing duplicate coverage. By constructing coupling scores based on Vanmarcke random field theory and soil correlation distance, data duplication and resource waste caused by monitoring points that are too close together can be suppressed. Furthermore, this invention uses the analytic hierarchy process (AHP) to determine the weights of each score, transforming expert engineering experience into quantitative weights, making the point layout scheme both objectively calculated and engineering-adaptable.

[0033] Overall, this invention can increase the proportion of monitoring points in high-risk areas, reduce the duplication rate of monitoring points, enhance the information value of individual monitoring points and the overall economic efficiency of monitoring point layout, and improve the automation and calculation efficiency of foundation pit monitoring point layout, while meeting the requirements for coverage and coverage of key parts. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is a flowchart illustrating the overall steps of the foundation pit monitoring point layout method based on the improved greedy algorithm in this invention. Figure 2 This is a cloud diagram of the internal forces in the XX direction of the three-dimensional model of the foundation pit in a specific example of the present invention; Figure 3 This is a cloud diagram of the internal forces in the YY direction of the three-dimensional model of the foundation pit in a specific example of the present invention; Figure 4 This is a ZZ direction internal force cloud diagram of the three-dimensional model of the foundation pit in a specific example of the present invention; Figure 5 This is a ZZ-direction displacement cloud diagram of the three-dimensional model of the foundation pit in a specific example of the present invention; Figure 6 The diagram shows the placement of points in the improved greedy algorithm in a specific example of this invention. Figure 7 This is a diagram showing the manual point layout using the line-of-sight method in a specific example of the present invention. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] The core idea of ​​this application is as follows: First, a batch of candidate measurement points are generated on the outside of the foundation pit according to the outline of the foundation pit. Then, the candidate measurement points are scored from three perspectives: "coverage contribution", "risk importance" and "data duplication". The weight of each score is determined by the analytic hierarchy process. Finally, a greedy iterative method is adopted to select the candidate measurement point with the highest comprehensive score in each round, and the final measurement point layout scheme is gradually formed.

[0038] like Figure 1 As shown in the figure, the specific steps of the foundation pit monitoring point layout method based on the improved greedy algorithm proposed in this embodiment are as follows: S1. Obtain basic data of the foundation pit, and determine the target monitoring area and key parts based on the basic data of the foundation pit.

[0039] In step S1, the basic data of the foundation pit includes foundation pit outline information, foundation pit engineering parameters, monitoring equipment parameters, and algorithm control parameters. Among them, the foundation pit outline information is used to represent the shape and position of the foundation pit on the plane, including: the coordinates of the outer boundary of the foundation pit; the coordinates of the corner points of the foundation pit; the edge line information of the foundation pit; the planar shape of the foundation pit; the outline image of the foundation pit; and CAD drawing data. Based on this information, a closed boundary is formed on the plane. For example, for a rectangular foundation pit, it can be represented by the coordinates of the four corner points; for an irregular foundation pit, multiple boundary points can be connected in sequence to form a closed polygon.

[0040] Excavation pit engineering parameters describe the excavation pit itself and its surrounding environmental conditions, including: excavation depth; support method; safety level; soil parameters; groundwater conditions; location of surrounding buildings; location of surrounding roads; location of underground pipelines; surrounding load conditions; and construction stage information. Soil parameters include soil thickness, natural moisture content, cohesion, angle of internal friction, unit weight, permeability coefficient, elastic modulus, and Poisson's ratio.

[0041] The monitoring equipment parameters describe the capabilities and deployment limitations of the monitoring equipment used, including: monitoring equipment type; effective monitoring radius; effective monitoring distance; shape of the monitoring area; maximum number of devices; and minimum spacing between measuring points. Monitoring equipment can be total stations, prisms, settlement monitoring points, displacement sensors, surveillance cameras, laser scanners, or radar monitoring equipment, etc. In this embodiment, displacement monitoring is used as an example, a total station can be used; however, when used for on-site visual monitoring, a surveillance camera can also be used.

[0042] Algorithm control parameters are used to control the algorithm's operation and termination conditions, including: target coverage; upper limit of the number of measurement points; candidate grid spacing; minimum allowable spacing of final measurement points; soil correlation distance; coverage requirements for key areas; and the analytic hierarchy process (AHP) judgment matrix. Among these, the candidate grid spacing is used to generate candidate measurement points, while the minimum allowable spacing of final measurement points is used to limit the proximity of the finally selected measurement points; these two parameters have different meanings. For example, in one embodiment, a candidate grid spacing of 2.0m can be used to generate denser candidate points; while the minimum allowable spacing of final measurement points can be set to 20m to avoid overly dense final point distribution.

[0043] More specifically, the algorithm control parameters are used to control the generation of candidate monitoring points, weight calculation, and iteration termination in subsequent steps, and are not used to determine the target monitoring area and key component areas. The target monitoring area is determined based on the pit outline information, pit engineering parameters, and monitoring tasks.

[0044] The monitoring tasks include: displacement monitoring; settlement monitoring; deformation monitoring of surrounding buildings; deformation monitoring of underground pipelines; video monitoring; and comprehensive monitoring.

[0045] The target monitoring area is the area that needs to be monitored and covered in this monitoring task. It should not be simply understood as the "inside the foundation pit." In foundation pit engineering, the objects that truly need to be monitored typically include: the area of ​​the foundation pit support structure, the area near the foundation pit outline, and the surrounding influence area of ​​the foundation pit formed by extending a predetermined distance outward from the foundation pit outline. For example, when the foundation pit excavation depth is... H At that time, the outline of the foundation pit can be expanded outward by 2. H The affected area around the foundation pit is obtained and used as part of the target monitoring area.

[0046] Key areas are locations or regions within the target monitoring area that require focused coverage, including: the external corners of the foundation pit; the internal corners of the foundation pit; areas with significant deformation of the support structure; areas adjacent to roads; areas adjacent to buildings; areas adjacent to underground pipelines; and areas with weak soil.

[0047] To facilitate understanding of the technical solution of this application, the following explanations are provided for some concepts involved in step S1 and related steps: In this application, the terms used for foundation pit outline information, foundation pit engineering parameters, monitoring equipment type, and some terms in key areas are all technical terms known to those skilled in the art during construction. Their meanings are based on the conventional understanding in the art, and this application will not point them out or elaborate on them one by one.

[0048] Meanwhile, to support the operation of the improved greedy algorithm proposed in this application, this application has provided specific definitions or quantitative restrictions on some concepts, including: The “algorithm control parameters” are not existing parameters in foundation pit engineering, but rather a set of custom parameters introduced in this application to control the generation of candidate measuring points, weight calculation and iteration termination, including candidate grid spacing, minimum allowable spacing of final measuring points, target coverage, soil correlation distance and analytic hierarchy process (AHP) judgment matrix, etc.

[0049] In this application, the "effective monitoring radius" and "monitoring range shape" in the "monitoring equipment parameters" are not only used to characterize the equipment capabilities, but also further used to determine the outer range of the candidate arrangement area in step S2 and to calculate the coverage score in step S4.

[0050] "Monitoring tasks" include types such as displacement monitoring, settlement monitoring, deformation monitoring of surrounding buildings, deformation monitoring of underground pipelines, and video monitoring. The specific task names and basic meanings are well-known in the art and will not be elaborated upon here. It should be noted that in this application, monitoring tasks do not exist in isolation, but are one of the criteria for determining the target monitoring area in step S1. That is, the key coverage area of ​​the target monitoring area is determined according to the different focuses of the monitoring tasks. For example, when the monitoring task is deformation monitoring of surrounding buildings, the target monitoring area focuses on the area adjacent to the buildings; when the monitoring task is displacement monitoring, the target monitoring area focuses on the area near the foundation pit support structure and its outline. This application does not impose a unique limitation on the correspondence between each type of monitoring task and the target monitoring area; those skilled in the art can flexibly configure it according to actual engineering needs.

[0051] The specific calculation methods or value determination methods of the concepts defined or quantified in this application will be described in subsequent steps S2 to S6.

[0052] S2. Establish a set of candidate monitoring points; taking the outline of the foundation pit as a reference, extend the effective monitoring radius of the monitoring equipment outward from the foundation pit to form a ring-shaped candidate arrangement area around the outline of the foundation pit; generate regular grid points within the ring-shaped candidate arrangement area according to the preset candidate grid spacing; screen the regular grid points according to the external layout conditions, and construct a set of candidate monitoring points based on the regular grid points that meet the external layout conditions.

[0053] Specifically, in step S2, the candidate measurement point set is established using the method of "expanding the pit outline + mesh discretization + layout condition screening", and the specific process is as follows: ① Forming a ring-shaped candidate layout area: Based on the outline of the foundation pit, extend the effective monitoring radius of the monitoring equipment outward from the foundation pit. r This forms a ring-shaped candidate arrangement area around the outline of the foundation pit.

[0054] The ring-shaped candidate layout area represents the range of locations where monitoring equipment, monitoring markers, or monitoring points may be deployed at the engineering site.

[0055] ② Grid discretization: Generate regular grid points within the annular candidate arrangement area according to the preset candidate grid spacing.

[0056] Candidate grid spacing is denoted as g For example, referring to the "Technical Standard for Monitoring of Building Foundation Pit Engineering" (GB50497 2019), which stipulates that the minimum spacing between monitoring points should be limited to [2,4], we can take: g =2.0.

[0057] At this point, a regular grid point is generated every 2.0m in the annular candidate arrangement area, and each regular grid point is an initial candidate measurement point.

[0058] The initial candidate measurement point set can be represented as:

[0059] in: , indicating the first i The planar coordinates of the candidate measuring points, the coordinate system on which the planar coordinates are based can be divided with any corner of the foundation pit as the origin; n represents the number of initial candidate measuring points.

[0060] ③ External deployment condition screening: The generated initial candidate measurement points are screened, and initial candidate measurement points that do not meet the external deployment conditions are deleted.

[0061] External deployment conditions include: safety distance conditions; equipment installation conditions; construction accessibility conditions; and line-of-sight conditions.

[0062] For example, candidate measuring points that do not meet the safety distance requirements, such as those located within the slope area of ​​the foundation pit, adjacent to areas where collisions with supporting structures may occur, or within the influence range of falling objects from heights, should be deleted. Candidate measuring points that do not meet the equipment installation requirements, such as those that cannot provide a flat installation surface, lack a fixed anchor foundation, or are located directly below a vibration interference source, should be deleted. Candidate measuring points in areas that are not safely accessible to personnel, such as those located on steep slopes, at locations where there is no safe passage at the top of the support in the foundation pit, or at locations that require crossing construction barriers or obstacles to reach, should be deleted. Candidate measuring points that are obstructed by existing buildings, construction barriers, stacked materials, or construction machinery, and cannot meet the observation line requirements of total station or visual monitoring equipment, should be deleted.

[0063] The aforementioned external layout conditions can be pre-filtered by overlaying the overall site plan of the foundation pit construction, surrounding environment map, and on-site survey records before the greedy algorithm runs. The filtered set of candidate measurement points then serves as the input for subsequent steps of the greedy algorithm. By pre-selecting the external layout conditions, repeated manual judgments during the greedy iteration process can be avoided, ensuring the automation and efficiency of the greedy algorithm.

[0064] The set of candidate measurement points after filtering is denoted as:

[0065] In the formula: N is the number of initial candidate measurement points remaining after deleting initial candidate measurement points that do not meet the external deployment conditions.

[0066] This set of candidate test points forms the search space for the subsequent greedy algorithm.

[0067] At this point, the construction of the candidate monitoring point set is complete. Through the aforementioned strategy of "expanding the pit outline + mesh discretization + filtering the layout conditions," the originally infinitely continuous discrete space of the site is transformed into a finite and controllable set of candidate monitoring points, giving the subsequent greedy algorithm a clear search space and solution boundary. The expansion range of the annular candidate layout area is related to the effective monitoring radius of the monitoring equipment, ensuring a reasonable spatial correspondence between the candidate monitoring points and the target monitoring area, and avoiding the failure of actual monitoring coverage due to the candidate monitoring points being too far from the target area. The adjustable mesh spacing allows the candidate monitoring point density to balance search accuracy and computational efficiency. The pre-filtering of external layout conditions eliminates the need for repeated manual judgments in the subsequent iterations of the greedy algorithm, ensuring the automation of the layout method and avoiding the problem of "algorithm selectable, but unusable on site" in the final output layout scheme.

[0068] It should be noted that candidate monitoring points do not necessarily completely overlap with the target monitoring area. Candidate monitoring points answer the question "Where can the points be placed?", while the target monitoring area answers "Where does it need to be monitored?". Candidate monitoring points are connected to the target monitoring area through their monitoring coverage area, which will be explained later.

[0069] Having established a set of candidate measurement points, the next step is to quantitatively evaluate the merits of each candidate measurement point.

[0070] To this end, this application constructs evaluation indicators from three dimensions: risk importance, coverage contribution, and data coupling degree. First, step S3 establishes the foundation pit risk field and calculates a risk score for each candidate measurement point. Second, step S4 calculates the coverage score and coupling score. Finally, step S5 weights and synthesizes the three indicators as the evaluation criteria for the greedy iteration. Details are as follows: S3. Based on some foundation pit basic data, establish a three-dimensional model of the foundation pit, and based on the three-dimensional model of the foundation pit, establish the foundation pit risk field, that is, the set of risk scores for each candidate measuring point.

[0071] Specifically, the risk score of each candidate measuring point in the candidate measuring point set is calculated based on the internal force and displacement values ​​of each spatial discrete element in the three-dimensional model of the foundation pit; wherein, the internal force and displacement values ​​of each spatial discrete element in the three-dimensional model of the foundation pit are obtained from the results of three-dimensional numerical simulation.

[0072] More specifically, in step S3, the internal force and displacement values ​​of each spatial discrete element in the three-dimensional model of the foundation pit are preferably determined using FLAC3D three-dimensional numerical simulation software. The specific process is as follows: a. Establish a three-dimensional model of the foundation pit; Based on the foundation pit design drawings, foundation pit outline, excavation depth and surrounding environment, a three-dimensional model of the foundation pit is established. The model includes: soil area; foundation pit excavation area; support structure; internal support or anchor; load of surrounding buildings or roads; groundwater conditions.

[0073] b. Input soil parameters and support structure parameters into the three-dimensional model of the foundation pit; According to the geotechnical engineering investigation report, the soil parameters are input, including: soil layer thickness; natural moisture content; cohesion; internal friction angle; natural unit weight; permeability coefficient; elastic modulus; and Poisson's ratio.

[0074] The parameters of the support structure include: the type of support structure; the dimensions of the support piles or diaphragm wall; the support stiffness; the support location; and the material parameters of the support structure.

[0075] c. Set boundary conditions and initial geostress; Set displacement constraints at the model boundaries, such as setting normal displacement constraints on the sides of the model and vertical displacement constraints on the bottom of the model; at the same time, apply gravity and perform initial ground stress balance calculations.

[0076] d. Numerical simulation of the foundation pit excavation process; The excavation process was simulated based on the actual construction process, including: layered excavation; phased installation of supports; simulation of groundwater changes; application of surrounding loads; and calculation of the response of the support structure and surrounding soil.

[0077] FLAC3D can solve the response of the soil and support structure around the foundation pit step by step based on the explicit finite difference method.

[0078] e. Derive the internal force and displacement values ​​of each spatial discrete element in the three-dimensional model of the foundation pit; After the numerical simulation is completed, the internal force and displacement values ​​of each spatial discrete element are exported from the three-dimensional model of the foundation pit.

[0079] Internal force values ​​include: soil stress; internal forces of the support structure; axial force of the support; bending moment of the retaining structure; and equivalent plastic strain.

[0080] Displacement values ​​include: horizontal displacement; vertical displacement; ground settlement; displacement of supporting structures; settlement of surrounding buildings; and deformation of underground pipelines.

[0081] It should be noted that this implementation method prioritizes using FLAC3D to output model mechanical cloud maps and displacement cloud maps to establish the risk field. In fact, FLAC3D is a commonly used 3D numerical simulation software in the existing construction field. When using it, spatial meshing needs to be performed according to its own software operation process. For ease of understanding, the unit of this spatial mesh is the spatial discrete unit mentioned in this step. In the step of establishing the 3D model of the foundation pit, the 3D model of the foundation pit is established in layers according to the actual geological conditions. Different colors are defined for the soil at the bottom of the foundation pit and the soil above it. Then, when exporting, the outline of the foundation pit can be identified by recognizing the boundary between different colors, and the outline size of the model foundation pit can be obtained. In this step, the outline size of the model foundation pit is measured by the 3D model of the foundation pit itself, which is reflected as the perimeter pixel length of the model foundation pit. At the same time, the model mechanical cloud map and displacement cloud map are exported from this perspective. The scale of the cloud map can be obtained by the ratio of the outline size of the model foundation pit in the top view of the 3D model of the foundation pit to the actual outline size of the foundation pit. Thus, the stress value and displacement value corresponding to all candidate measurement points in the actual candidate mesh can be obtained in the subsequent calculation. The actual foundation pit outline size is determined by the foundation pit outline information of the annular candidate arrangement area in step S2, and is reflected as the actual foundation pit perimeter pixel length.

[0082] f. Establish the foundation pit risk field based on the internal force and displacement values; Specifically, the spatial discrete units in the three-dimensional model of the foundation pit are mapped to the target monitoring area to obtain the internal force and displacement values ​​of the candidate measuring points, thereby obtaining the foundation pit risk field, i.e., the set of risk scores of the candidate measuring points.

[0083] It should be noted that after obtaining the internal force and displacement values ​​of each spatial discrete element, it is necessary to establish a correspondence between the candidate measurement points and the internal force and displacement values ​​of each spatial discrete element.

[0084] Among them, for the first i Candidate measurement points The internal force and displacement values ​​are determined based on the model's mechanical cloud map and displacement cloud map. After obtaining the cloud map scale, the data of the model's mechanical cloud map and displacement cloud map are converted to the same size as the actual foundation pit outline. Then, the candidate measuring points obtained in step S2 can be used to extract the corresponding internal force and displacement values ​​from the converted model's mechanical cloud map and displacement cloud map.

[0085] In this embodiment, through the aforementioned process of "three-dimensional numerical simulation + discrete result extraction + candidate measuring point mapping," the internal force and displacement values ​​of the soil and support structure during the excavation of the foundation pit are incorporated into the measuring point evaluation system, enabling the point layout scheme to quantitatively reflect the differences in safety risk levels in different areas of the foundation pit. It should be noted that obtaining the internal force and displacement values ​​corresponding to candidate measuring points using FLAC3D's output model mechanical cloud map and displacement cloud map is a common analytical method for engineering mechanics and displacement in the prior art; this application will not elaborate on its detailed construction process and calculation method.

[0086] Based on this, a risk score is calculated for each candidate test point in the candidate test point set, as follows: The risk score is used to characterize the degree of danger of the spatial discrete unit corresponding to the candidate measurement point.

[0087] In one implementation, the risk score is calculated according to the following formula:

[0088] In the formula: For the first i Risk scores for each candidate measurement point; For the first i The internal force values ​​of the spatial discrete element corresponding to each candidate measuring point; This represents the maximum internal force value of each spatial discrete element in the three-dimensional model of the foundation pit; For the first i The displacement values ​​of the spatial discrete element corresponding to each candidate measurement point; This represents the maximum displacement value of each spatial discrete element in the three-dimensional model of the foundation pit.

[0089] The formula means that risk is controlled by the worst-case scenario indicator. If any indicator in the mechanical response or deformation response of a certain region is large, the region is considered to have a high risk. At the same time, normalization is performed by dividing by the maximum value to keep the risk score between 0 and 1, avoiding weighting and calculation imbalances caused by differences in the units and orders of magnitude of different physical quantities.

[0090] Therefore, the risk scores corresponding to each candidate test point are collected to construct a risk field. The data of the risk field is the set of risk scores of the candidate test points. Once the risk field data is established, it can be repeatedly indexed and called by all candidate test points. In the subsequent greedy iteration process, there is no need to repeat numerical simulation calculations, which ensures the computational efficiency of the algorithm.

[0091] The risk score calculated in this step reflects the safety risk level of the area corresponding to each candidate monitoring point and is one dimension of the monitoring point evaluation system. However, in the problem of pit monitoring point deployment, the quality of a monitoring point depends not only on the risk level of its corresponding area, but also on the monitoring coverage contribution it can provide and the degree of data redundancy between the monitoring point and the selected monitoring points. A single-dimensional risk score is insufficient to comprehensively evaluate the overall value of candidate monitoring points. Therefore, this application will further calculate the coverage score and coupling score of each candidate monitoring point.

[0092] S4. Calculate the coverage score and coupling score of each candidate measurement point in the candidate measurement point set; The coverage score is determined based on the monitoring coverage area corresponding to the candidate monitoring point, the target monitoring area, and the coverage area of ​​the selected monitoring points; the coupling score is determined based on the distance parameters between the candidate monitoring point and the set of selected monitoring points, the soil-related distance, and the coverage score.

[0093] In step S4, the coverage score is calculated for each candidate measurement point in the candidate measurement point set, as follows: Coverage score is used to measure the additional coverage contribution that a candidate monitoring point can bring to the target monitoring area.

[0094] In one implementation, the coverage score is calculated according to the following formula:

[0095] In the formula: For the first i Coverage score of each candidate measurement point; For the first i The monitoring coverage area corresponding to each candidate monitoring point; The target monitoring area; The union of the areas covered by the currently selected measurement points; This refers to the theoretical coverage area of ​​the monitoring equipment. S ( The parentheses indicate that the area within the parentheses is to be calculated.

[0096] This formula can be understood in three levels: First, This indicates the portion of the target monitoring area that the candidate monitoring points can cover. second, This indicates the newly added effective area that can be covered by the candidate measuring points but has not yet been covered by the selected measuring points; Third, divide the newly added effective coverage area by the theoretical coverage area. This yields the dimensionless coverage score.

[0097] When the algorithm has not yet selected any measurement points, the area covered by the selected measurement points is empty, that is: The algorithm here refers to the greedy algorithm used in subsequent steps. "The algorithm has not yet selected any measurement points" means that the greedy algorithm is running for the first time to select points, so there is no area covered by selected measurement points yet.

[0098] The coverage score at this point is:

[0099] When the monitoring equipment has a circular coverage area, the theoretical coverage area of ​​the monitoring equipment is:

[0100] In the formula: r The effective monitoring radius of the monitoring equipment; If the monitoring equipment has a fan-shaped, rectangular, or irregular coverage area, the theoretical coverage area is determined based on the actual field of view of the equipment.

[0101] If the monitoring equipment is a point-type monitoring device, the theoretical coverage area can be determined based on the monitoring area covered by the device itself.

[0102] Furthermore, the coupling score is used to measure the degree of data overlap between candidate monitoring points and selected monitoring points. The displacement, settlement, stress, and other responses of the soil around the foundation pit exhibit spatial correlation. According to Vanmarcke random field theory, soil parameters are spatially correlated; the closer the distance, the more similar the soil properties and responses at the two locations, and the more likely the monitoring data are to overlap.

[0103] Therefore, this implementation calculates the coupling score based on the distance between the candidate measurement point and the nearest measurement point in the set of selected measurement points.

[0104] If the currently selected set of measurement points is:

[0105] In the formula: m is the number of currently selected measurement points.

[0106] Then the first i The distance parameter between each candidate measurement point and the set of selected measurement points is:

[0107] in: For the first i One candidate measurement point; These are the measurement points in the selected set of measurement points; express and The Euclidean distance between two measuring points.

[0108] The coupling score is calculated using the following formula:

[0109] In the formula: For the first i Coupling score of each candidate measurement point; For the first i Coverage score of each candidate measurement point; For the first i Distance parameters between each candidate measurement point and the set of selected measurement points; This represents the distance related to the soil mass.

[0110] when When the value approaches 0, it indicates that the candidate measurement point is very close to a certain selected measurement point. At this time: This indicates that the candidate measurement point's data highly overlaps with the already selected measurement points, which will lower the overall score. However, since step S2 already determined the minimum distance between candidate measurement points to be 2 based on the minimum distance limit [2,4], therefore... The minimum is 2.

[0111] When the set of selected measurement points is empty, i.e., there are no selected measurement points in the first round of point selection, the coupling score of all candidate measurement points is set as follows: This indicates that the initial point selection is not affected by coupling factors.

[0112] Soil-related distance It can be determined based on geotechnical engineering investigation data, field test results, statistical results of soil parameters at the project site, empirical values ​​from literature, or fitting results from Vanmarcke random field theory.

[0113] Thus, combined with the risk score completed in step S3, each candidate monitoring point has obtained a three-dimensional quantitative evaluation index: the risk score represents the safety risk level of the area corresponding to the candidate monitoring point, the coverage score represents the contribution of the candidate monitoring point to the new monitoring coverage of the overall deployment plan, and the coupling score represents the degree of data redundancy between the candidate monitoring point and the selected monitoring points.

[0114] The three scores characterize the value of candidate monitoring points from three different perspectives: "necessity of safety monitoring," "efficiency of monitoring resource utilization," and "economic efficiency of monitoring point layout," forming a complete monitoring point evaluation index system. However, although the three scores have the same dimensions, their physical meanings are different. In actual decision-making, it is necessary to determine their relative importance based on the project safety level and monitoring objectives.

[0115] Therefore, this application employs the Analytic Hierarchy Process (AHP) to determine the weights corresponding to the three scores, and then combines the three scores into a total score for each candidate measurement point through a weighted summation. The AHP can transform the engineering experience of domain experts into quantitative weight values, ensuring that the weight allocation is both theoretically sound and reflects actual engineering needs.

[0116] S5. Use the analytic hierarchy process (AHP) to determine the weights corresponding to the coverage score, risk score, and coupling score, and calculate the weighted sum of the three scores of the candidate test points based on the coverage score, risk score, coupling score, and corresponding weights.

[0117] Specifically, in step S5, in order to integrate the coverage score, risk score, and coupling score, it is necessary to determine the weights of each of them in the weighted total score. This implementation method uses the analytic hierarchy process (AHP) to determine the weights, and the specific steps are as follows: S51. Establish a hierarchical structure; the hierarchical structure includes a target layer and a criterion layer. The target layer is a weighted sum of candidate measurement points; the criterion layer includes: coverage; risk; coupling.

[0118] S52. Construct a judgment matrix; use the nine-scale method to compare coverage, risk and coupling pairwise.

[0119] The meaning of the nine-scale method is shown in the table below: Table 1 Nine-scale method

[0120] In one specific embodiment, the indicators are ordered as follows: [ R , D , C ] That is, coupling score, risk score, and coverage score, construct a judgment matrix. An example judgment matrix is ​​as follows:

[0121] This judgment matrix indicates that risk is more important than coupling and coverage, and coupling is more important than coverage.

[0122] S53. Calculate the weights using the root method; For the judgment matrix B, the weights are calculated using the square root method, and the calculation formula is as follows:

[0123] In the formula: The row number represents the target criterion whose weights are currently being calculated. In this example, Corresponding to coupling, Corresponding risk, Corresponding coverage; Indicates the total number of rows for the target criteria; The column index of the judgment matrix is ​​used to traverse the first... All elements in a row represent the criteria. Relative to criteria Importance ratio ; Then, it serves as a virtual row number in the denominator summation process, its function being to iterate from 1 to... The geometric mean of each row is summed up to form the denominator of the sum when normalizing.

[0124] Based on the example judgment matrix in step S52, the example weights can be obtained: , ,

[0125] In the formula: For coupling weights; Risk weights; For coverage weights.

[0126] S54. Consistency check; To ensure the validity of the judgment matrix, a consistency check can also be performed.

[0127] Calculate the consistency index:

[0128] In the formula: To determine the largest eigenvalue of the matrix; z is the number of indicators.

[0129] Calculate the consistency ratio:

[0130] In the formula: RI The random consistency index can be found in Table 6-2 of the third edition of "Mathematical Modeling Methods and Their Applications".

[0131] when: CR When the value is less than 0.1, the judgment matrix is ​​considered to have passed the consistency test, and the weight result is acceptable.

[0132] S55. Calculate the weighted sum of the three scores for each candidate test point in the candidate test point set.

[0133] The weighted sum of the three scores for each candidate test point is calculated using the following formula:

[0134] In the formula: For the first i The weighted sum of the three scores for each candidate test point; For the first i Coverage score of each candidate measurement point; For the first i Risk scores for each candidate measurement point; For the first i The coupling score of each candidate measurement point , , These are the weights corresponding to the coverage score, risk score, and coupling score, respectively, and: .

[0135] The weighted sum represents the overall deployment value of the candidate measurement points. The higher the weighted sum, the more worthy the candidate measurement point is of priority selection.

[0136] As the core of this application, unlike traditional greedy algorithms that only use coverage area as the selection criterion, this implementation method incorporates coverage contribution, risk importance and data duplication into the greedy strategy, so that each round of point selection takes into account monitoring coverage, engineering safety and deployment economy.

[0137] S6. Use a greedy iterative method to select measurement points.

[0138] Specifically, in each round, the candidate test point with the highest current weighted sum is selected to be added to the final test point layout scheme. After being added, the coverage score, coupling score, and weighted sum of the three scores of the remaining candidate test points are updated until the preset termination condition is met, and the final test point layout scheme is output.

[0139] In step S6, the specific steps for selecting measurement points using a greedy iterative method are as follows: S61. Initialize the selected measurement point set to an empty set, i.e. If the selected measurement point coverage area is empty, then: .

[0140] S62, Conduct the first round of site selection.

[0141] In the first round of point selection, since no selected measurement points exist yet, the coupling score of all candidate measurement points is set as follows: Then, the coverage score, risk score, coupling score, and weighted sum of the three scores for each candidate measurement point are calculated.

[0142] Select the candidate test point with the highest current weighted sum and add it to the set of selected test points. Then delete the candidate test point with the highest current weighted sum from the set of candidate test points P.

[0143] S63. Update the coverage area of ​​the selected measurement points based on the newly added candidate measurement points. ; S64. Recalculate the coverage score, coupling score, and weighted sum of the three scores for the remaining candidate measurement points.

[0144] The coverage score needs to be recalculated because some areas have been covered by newly added measurement points. The new coverage score is still calculated using the following formula:

[0145] The coupling score also needs to be recalculated because the set of selected measurement points has changed. The new distance parameters are still calculated using the following formula:

[0146] The new coupling score is still calculated using the following formula:

[0147] Risk scores typically do not need to be recalculated for each round because the risk field remains constant within the same construction phase; however, if the construction phase changes, the numerical simulation in step S3 can be repeated or the risk field updated, and then the risk scores can be recalculated.

[0148] S65. Repeat the above process until the preset termination condition is met.

[0149] It should be noted that this implementation method does not select all candidate measurement points sequentially after sorting them by the initial weighted sum at once. Instead, after each measurement point is selected, the coverage score, coupling score, and weighted sum of the three scores of the remaining candidate measurement points are recalculated and reordered for selection. This can effectively avoid duplicate coverage of measurement points and overly dense distribution of points in local areas.

[0150] Specifically, iteration stops when at least one of the following termination conditions is met: ① Stop iterating when the coverage reaches the target coverage.

[0151] Coverage is calculated using the following formula:

[0152] In the formula: For coverage; The area covered by the selected measurement points; The target monitoring area.

[0153] when When the coverage rate is considered to have reached the preset target coverage rate, The preset target coverage rate.

[0154] ② Stop iterating when the coverage rate of key parts reaches the preset coverage rate of key parts.

[0155] The coverage rate of key areas is calculated using the following formula:

[0156] In the formula: Coverage rate of key areas; This refers to critical areas.

[0157] When the coverage of key parts reaches the preset requirement, such as 100%, the iteration stops.

[0158] ③ Stop iterating when the number of selected measurement points reaches the upper limit.

[0159] ④ Stop iterating when the set of candidate measurement points is empty.

[0160] S66. Obtain the final point layout scheme, which includes the coordinates of the measuring points and a schematic diagram of the plane layout of the measuring points. In fact, the measuring points in the final layout scheme are selected from the candidate measuring point set obtained in step S2. Therefore, the coordinates of the measuring points in the final layout scheme are the plane coordinates corresponding to the selected candidate measuring points. The schematic diagram of the plane layout of the measuring points is the construction engineering document obtained based on the coordinates of each measuring point, such as CAD drawings, which will not be described in detail here.

[0161] Therefore, this method improves the single "coverage area" evaluation criterion in the traditional greedy algorithm into a three-dimensional weighted comprehensive evaluation criterion of "risk-coverage-coupling". Under the condition of ensuring monitoring coverage, it realizes the reasonable tilt of monitoring resources towards high-risk areas such as key parts and areas. At the same time, by introducing coupling score, it effectively controls the data redundancy caused by excessively dense monitoring points, and improves the economy and information acquisition efficiency of the overall deployment scheme.

[0162] To further illustrate the implementation effect of the foundation pit monitoring point layout method based on the improved greedy algorithm described in this invention, the following explanation uses a regular rectangular foundation pit as an example. It should be noted that the following examples are only used to explain the technical solution of this invention and do not constitute a limitation on the scope of protection of this invention.

[0163] In a specific example, to verify the point placement performance of the improved greedy algorithm described in this invention and to comprehensively evaluate the reliability of the algorithm results, the method of this invention is compared with the line-of-sight method, i.e., the manual point placement method. The comparison indicators include coverage rate, repetition rate, proportion of measurement points in high-risk areas, and coverage rate of key parts.

[0164] Currently, rectangular, circular, and irregular shapes are all common forms of foundation pit outlines. To facilitate verification of the algorithm's effectiveness, this example uses a rectangular foundation pit as the test object. The dimensions of this rectangular foundation pit are set to 160. m ×110 m ×8 m .

[0165] The foundation pit is 160m long, 110m wide, and 8m deep, with a total area of ​​217,600 square meters. m 2 .

[0166] The foundation pit uses internally supported piles as the retaining structure, and the soil parameters around the construction site are shown in Table 2.

[0167] Table 2 Soil layer parameters

[0168] According to the "Technical Standard for Monitoring of Building Foundation Pit Engineering" (GB 50497—2019), for Class I foundation pit engineering, monitoring items such as vertical displacement of retaining walls, horizontal displacement of retaining walls, internal force of anchor bolts, and inspection are typically required. The improved greedy algorithm described in this invention can be used for both the placement of displacement monitoring points and the placement of visual monitoring equipment such as auxiliary cameras for inspection.

[0169] In this example, only the layout of displacement monitoring points is used for illustration. A total station is used as the displacement monitoring equipment, and the effective monitoring radius is taken as: r =30 m The final minimum spacing between measuring points is set to 20. m The minimum distance between the total station's working reference point and the foundation pit is taken as: 50. m .

[0170] It should be noted that the minimum distance between the working benchmark and the foundation pit is used to ensure the stability and safety of the total station's observation benchmark; the effective monitoring radius is used to determine the expansion range of the candidate layout area and the monitoring coverage area; and the minimum layout spacing of the final measuring points is used to avoid the adjacent measuring points being too dense in the final layout scheme. The three are used for different constraints.

[0171] In this example, based on the foundation pit outline information, the effective monitoring radius of the monitoring equipment is extended by 30m outward from the outer boundary of the rectangular foundation pit, forming a ring-shaped candidate arrangement area around the foundation pit outline. Subsequently, regular grid points are generated within this ring-shaped candidate arrangement area according to the preset candidate grid spacing, and the regular grid points are screened in combination with safety distance conditions, equipment installation conditions, construction accessibility conditions and line-of-sight conditions to obtain a set of candidate measuring points.

[0172] After constructing the candidate measurement point set, a 3D model of the foundation pit was established using FLAC3D 3D numerical simulation software. Based on the foundation pit dimensions, retaining structure form, and soil layer parameters shown in Table 2, soil parameters and support structure parameters were input. Model boundary conditions and initial ground stress were set to simulate the foundation pit excavation process, and the internal force and displacement values ​​of each spatial discrete element in the 3D foundation pit model were exported. These internal force and displacement values ​​can be obtained from numerical results data or visualized using corresponding contour plots. For example, in this example, the following can be obtained: Figures 2 to 4 The mechanical contour diagrams of the model in the XX direction, YY direction, and ZZ direction are shown below, as well as... Figure 5 The displacement contour map in the ZZ direction is shown.

[0173] In this example, the soil correlation distance is taken as: Lc =19 m， This value can be determined based on the statistical results of soil parameters at the project site, geotechnical engineering investigation data, field test results, or Vanmarcke random field theory fitting results.

[0174] The risk score, coverage score, and coupling score of each candidate measurement point are calculated separately, and the weights corresponding to the three scores are determined by the analytic hierarchy process (AHP). Then, the weighted sum of the candidate measurement points is calculated. A greedy iterative approach is adopted, in each round selecting the candidate measurement point with the highest current weighted sum to be added to the final measurement point layout scheme. After addition, the coverage score, coupling score, and weighted sum of the three scores of the remaining candidate measurement points are updated until the preset termination condition is met.

[0175] To control for variables, this example employs both an improved greedy algorithm and the line-of-sight method for measuring point placement. The improved greedy algorithm and the line-of-sight method described in this invention use identical engineering conditions, and both methods ultimately place 30 measuring points. The measuring point placement results of the two methods can be plotted as measuring point planar layout diagrams, as shown below. Figure 6 The improved greedy algorithm point layout diagram shown is as follows: Figure 7 The line-of-sight method manual point layout diagram shown can be used to visually compare the distribution of measuring points. In the diagram, the working benchmark point represents the additional measuring point. In actual foundation pit construction projects, the measuring point close to the foundation pit may be subject to settlement, and the monitoring position may have displacement. This will result in the monitoring displacement result being the displacement of the monitoring area plus the displacement of the measuring point. Therefore, in actual foundation pit construction projects, additional measuring points, namely working benchmark points, are usually set up. The location of the working benchmark point is generally 50m away from the foundation pit, and the purpose is to determine the displacement of the measuring point.

[0176] According to such Figure 6 , Figure 7 The two point layout diagrams shown below yield the results of the two methods, as shown in Table 3.

[0177] Table 3. Calculation Results of Rectangular Foundation Pit

[0178] In this example, the proportion of monitoring points in high-risk areas refers to the percentage of monitoring points located within high-risk areas out of the total number of monitoring points. High-risk areas can be determined based on the geometric characteristics of the foundation pit and the risk distribution, generally referring to critical areas. In this example, high-risk areas include: a circular area centered on the corner of the foundation pit and with the monitoring radius as the radius, and the area within one-third of the middle span of each side span of the foundation pit. These areas are typically locations where the foundation pit is most sensitive to stress and deformation, and are therefore areas requiring focused monitoring.

[0179] As shown in Table 3, under the conditions that the number of measurement points is 30 and the coverage rate of key parts reaches 100%, compared with the line-of-sight method, the coverage rate of the improved greedy algorithm described in this invention is increased from 61.46% to 65.1%, an improvement of 3.64%; the repetition rate is reduced from 67.02% to 57.37%, a reduction of 9.65%; and the proportion of measurement points in high-risk areas is increased from 53.33% to 56.67%, an improvement of 3.34%.

[0180] As can be clearly seen from the measurement point layout diagram, in local areas such as the external corners of the foundation pit, the manual point layout using the line-of-sight method is more prone to result in concentrated and redundant measurement points. The improved greedy algorithm described in this invention, however, suppresses candidate points that are close together and have high data repetition through coupling scores, resulting in a more balanced distribution of measurement points. Furthermore, guided by risk scores, this invention can place more measurement points in high-risk areas while ensuring coverage of critical locations, thereby improving the targeting and effectiveness of monitoring point placement.

[0181] Therefore, this example demonstrates that the improved greedy algorithm described in this invention can improve the coverage level of the target area, reduce the degree of overlapping coverage, and increase the proportion of measurement points in high-risk areas under the same number of measurement points and the same engineering conditions, thereby enhancing the information value of a single measurement point and the economy of the overall measurement point layout scheme.

[0182] As can be seen from the above rectangular foundation pit example, the foundation pit monitoring point layout method based on the improved greedy algorithm provided by this invention can achieve effective coverage of the target monitoring area and key parts area under the same number of monitoring points, and can reduce the repetition rate and increase the proportion of monitoring points in high-risk areas.

[0183] Specifically, this invention establishes a candidate measuring point set through "expansion of the foundation pit outline + grid discretization + screening of external layout conditions," ensuring that the candidate measuring points are both computationally feasible and meet on-site layout conditions; it establishes a foundation pit risk field through FLAC3D three-dimensional numerical simulation, giving the risk score an engineering mechanics basis; it calculates the coverage score by adding coverage area, making the algorithm tend to select measuring points that can provide new effective coverage; it constructs a coupling score based on Vanmarcke random field theory and soil correlation distance, enabling the algorithm to suppress data duplication caused by nearby measuring points; and it determines the weights through the analytic hierarchy process, ensuring that the point placement results take into account both algorithm objectivity and engineering experience.

[0184] Therefore, this invention is applicable to both regular rectangular foundation pits and complex engineering scenarios such as irregular polygonal deep foundation pits. It can improve the efficiency of monitoring resource utilization and the engineering rationality of the site layout scheme while meeting the coverage requirements for key parts.

[0185] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for arranging monitoring points for foundation pits based on an improved greedy algorithm, characterized in that, Includes the following steps: S1. Obtain basic data of the foundation pit, and determine the target monitoring area and key parts based on the basic data of the foundation pit; The foundation pit basic data includes foundation pit outline information, foundation pit engineering parameters, monitoring equipment parameters, and algorithm control parameters; S2. Establish a set of candidate measurement points; Specifically, based on the outline of the foundation pit, the effective monitoring radius of the monitoring equipment is extended outward from the foundation pit to form a ring-shaped candidate arrangement area around the outline of the foundation pit; regular grid points are generated within the ring-shaped candidate arrangement area according to the preset candidate grid spacing; the regular grid points are screened according to the external deployment conditions, and the regular grid points that meet the external deployment conditions are used to construct a candidate measurement point set; S3. Establish a three-dimensional model of the foundation pit based on some foundation pit basic data, and establish a foundation pit risk field based on the foundation pit three-dimensional model. Calculate the risk score of each candidate measuring point in the candidate measuring point set based on the foundation pit risk field. The risk field of the foundation pit is established using three-dimensional numerical simulation results; The risk score is calculated according to the following formula: ， In the formula: For the first i Risk scores for each candidate measurement point; For the first i The internal force values ​​of the spatial discrete element corresponding to each candidate measuring point; This represents the maximum internal force value of each spatial discrete element in the three-dimensional model of the foundation pit; For the first i The displacement values ​​of the spatial discrete element corresponding to each candidate measurement point; This represents the maximum displacement value of each spatial discrete element in the three-dimensional model of the foundation pit; S4. Calculate the coverage score and coupling score of each candidate measurement point in the candidate measurement point set; The coverage score is determined based on the monitoring coverage area corresponding to the candidate monitoring point, the target monitoring area, and the coverage area of ​​the selected monitoring points; the coupling score is determined based on the distance parameter between the candidate monitoring point and the set of selected monitoring points, the soil-related distance, and the coverage score. The coverage score is calculated according to the following formula: ， In the formula: The coverage score of the i-th candidate measurement point; Let i be the monitoring coverage area corresponding to the i-th candidate monitoring point; The target monitoring area; The union of the areas covered by the selected measurement points; S( represents the theoretical coverage area of ​​the monitoring equipment) () indicates calculating the area of ​​the region within the parentheses; The coupling score is used to measure the degree of data duplication between candidate measurement points and selected measurement points; If the currently selected set of measurement points is: ， In the formula: m is the number of currently selected measurement points; Then the first i The distance parameter between each candidate measurement point and the set of selected measurement points is: ， In the formula: For the first i One candidate measurement point; These are the measurement points in the selected set of measurement points; express and The Euclidean distance between two measuring points; The coupling fraction is calculated according to the following formula: ， In the formula: For the first i Coupling score of candidate measurement points; For the first i Coverage score of each candidate measurement point; For the first i Distance parameters between each candidate measurement point and the set of selected measurement points; Relevant distances to the soil; S5. Use the analytic hierarchy process (AHP) to determine the weights corresponding to the coverage score, risk score, and coupling score, and calculate the weighted sum of the three scores of the candidate test points based on the coverage score, risk score, coupling score, and corresponding weights. S6. Use a greedy iterative method to select measurement points; In each round, the candidate measurement point with the highest current weighted sum is selected and added to the final measurement point layout scheme. After being added, the coverage score, coupling score, and weighted sum of the three scores of the remaining candidate measurement points are updated until the preset termination condition is met, and the final measurement point layout scheme is output.

2. The method for arranging monitoring points for foundation pits based on an improved greedy algorithm according to claim 1, characterized in that: In step S1: The excavation pit outline information includes the coordinates of the outer boundary of the excavation pit, the coordinates of the corner points of the excavation pit, the edge line information of the excavation pit, the plan shape of the excavation pit, the outline image of the excavation pit, and CAD drawing data; The parameters of the foundation pit project include at least one of the following: foundation pit excavation depth, foundation pit support type, foundation pit safety level, soil layer parameters, groundwater conditions, location of surrounding buildings, location of surrounding roads, location of underground pipelines, surrounding load conditions, and construction stage information. Monitoring equipment parameters include monitoring equipment type, effective monitoring radius, monitoring range shape, maximum number of equipment, and minimum spacing between monitoring points; The algorithm control parameters include target coverage, upper limit of the number of measuring points, candidate grid spacing, minimum allowable spacing of final measuring points, soil correlation distance, coverage requirements for key parts, and analytic hierarchy process (AHP) judgment matrix.

3. The method for arranging foundation pit monitoring points based on an improved greedy algorithm according to claim 2, characterized in that: In step S1: Monitoring tasks include at least one of the following: displacement monitoring tasks, settlement monitoring tasks, deformation monitoring tasks of surrounding buildings, deformation monitoring tasks of underground pipelines, video monitoring tasks, and comprehensive monitoring tasks; The target monitoring area includes the area of ​​the foundation pit support structure, the area near the foundation pit outline, and the area of ​​influence around the foundation pit formed by extending the foundation pit outline outward by a preset distance. The preset distance is determined based on at least one of the following: the excavation depth of the foundation pit, the engineering safety level, the monitoring specifications, and the effective monitoring range of the monitoring equipment. Key areas include at least one of the following: the external corner of the foundation pit, the internal corner of the foundation pit, areas with large deformation of the support structure, areas adjacent to roads, areas adjacent to buildings, areas adjacent to underground pipelines, and areas with weak soil.

4. The method for arranging foundation pit monitoring points based on an improved greedy algorithm according to claim 3, characterized in that: In step S2, establishing the candidate measurement point set specifically includes: Based on the outline of the excavation pit, extend the effective monitoring radius of the monitoring equipment outward from the pit. r This forms a ring-shaped candidate arrangement area around the outline of the foundation pit; Within the annular candidate arrangement area, according to the preset candidate grid spacing g Generate regular grid points, each regular grid point being an initial candidate test point. The initial candidate test point set is represented as follows: ， In the formula: , indicating the first i The planar coordinates of the candidate measurement points; n represents the initial number of candidate measurement points; The initial candidate measurement points are filtered based on the external deployment conditions, and those that do not meet the conditions are deleted, resulting in a set of candidate measurement points: ， In the formula: N represents the number of initial candidate measurement points remaining after deleting initial candidate measurement points that do not meet the external deployment conditions; The external deployment conditions include at least one of the following: safety distance conditions, equipment installation conditions, construction accessibility conditions, and line-of-sight conditions.

5. The method for arranging foundation pit monitoring points based on an improved greedy algorithm according to claim 4, characterized in that: In step S3, establishing the foundation pit risk field using three-dimensional numerical simulation results includes: a. Establish a three-dimensional model of the foundation pit; b. Input soil parameters and support structure parameters into the three-dimensional model of the foundation pit; c. Set boundary conditions and initial geostress; d. Numerical simulation of the foundation pit excavation process; e. Derive the internal force and displacement values ​​of each spatial discrete element in the three-dimensional model of the foundation pit; f. Establish the foundation pit risk field based on the internal force and displacement values; map the spatial discrete elements in the three-dimensional numerical model to the target monitoring area to obtain the internal force and displacement values ​​of the candidate measuring points, and then obtain the foundation pit risk field. The three-dimensional numerical simulation is implemented using FLAC3D. The internal force values ​​include at least one of soil stress, internal force of the support structure, axial force of the support, bending moment of the retaining structure, and equivalent plastic strain. The displacement value includes at least one of the following: horizontal displacement, vertical displacement, ground settlement, support structure displacement, settlement of surrounding buildings, and deformation of underground pipelines.

6. The method for arranging foundation pit monitoring points based on an improved greedy algorithm according to claim 5, characterized in that: In step S4, when the monitoring device has a circular coverage area, the theoretical coverage area of ​​the monitoring device is: ， In the formula: r The effective monitoring radius of the monitoring equipment; When the monitoring equipment has one of the following: a fan-shaped coverage area, a rectangular coverage area, or an irregular coverage area, the theoretical coverage area of ​​the monitoring equipment is determined based on the actual field of view of the monitoring equipment. When the monitoring device is a point-type monitoring device, the monitoring coverage area is the monitoring area covered by the device itself.

7. The method for arranging monitoring points for foundation pits based on an improved greedy algorithm according to claim 6, characterized in that: In step S4, when the set of selected measurement points is empty, the coupling score of the candidate measurement points is set to 1; The soil-related distance is determined based on at least one of the following: geotechnical engineering investigation data, field test results, statistical results of soil parameters at the project site, empirical values ​​from literature, and fitting results from Vanmarcke random field theory.

8. The method for arranging monitoring points for foundation pits based on an improved greedy algorithm according to claim 7, characterized in that: In step S5, the weights are determined using the analytic hierarchy process (AHP), including: Establish a hierarchical structure with the weighted sum of candidate measurement points as the target layer and coverage, risk, and coupling as the criteria layers; A nine-scale method is used to perform pairwise comparisons of coverage, risk, and coupling to construct a judgment matrix; The weights corresponding to the coverage score, risk score, and coupling score are calculated using the square root method. A consistency check is performed on the judgment matrix. If the consistency ratio is less than a preset threshold, the weight is accepted. The weighted sum of the three scores for each candidate test point is calculated using the following formula: ， In the formula: For the first i The weighted sum of the three scores for each candidate test point; For the first i Coverage score of each candidate measurement point; For the first i Risk scores for each candidate measurement point; For the first i The coupling score of each candidate measurement point , , These are the weights corresponding to the coverage score, risk score, and coupling score, respectively, and: .

9. A method for arranging foundation pit monitoring points based on an improved greedy algorithm according to claim 8, characterized in that: In step S6, the selection of measurement points using a greedy iterative method includes: Initialize the selected measurement point set to an empty set; The first round of point selection is performed, and the coverage score, risk score, coupling score, and weighted sum of the three scores of each candidate point in the candidate point set are calculated. The candidate point with the highest current weighted sum is selected and added to the selected point set. Then, the candidate point with the highest current weighted sum is deleted from the candidate point set. Update the coverage area of ​​the selected measurement points based on the newly added candidate measurement points; Recalculate the coverage score, coupling score, and weighted sum of the three scores for the remaining candidate measurement points; Repeat the above process until the preset termination condition is met; The final site layout plan was obtained; The preset termination conditions include at least one of the following: the coverage rate of the final deployment plan reaches the target coverage rate, the coverage rate of key parts reaches the preset key part coverage rate, the number of selected measurement points reaches the upper limit of the number of measurement points, and the candidate measurement point set is empty. Coverage is calculated using the following formula: ， In the formula: For coverage; The area covered by the selected measurement points; The target monitoring area; The coverage rate of key areas is calculated using the following formula: ， In the formula: Coverage rate for key areas; This refers to critical areas.

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