A method and system for combined inversion and volume calibration of a buried foundation

Abstract

The application discloses a kind of abandoned slag body hidden base joint inversion and volume calibration method and system, method includes: obtaining multi-phase topography, independent check point and geophysical data;Convert the original surface that historical phase has shown and then covered into base constraint with error boundary;To geophysical response, keep mutually exclusive interface candidate, do not establish depth equality constraint to the section of undetected effective interface, and joint calibration zero time correction amount, propagation velocity and positioning deviation;The above-mentioned candidate, error boundary and physical condition are composed of feasible solution set, respectively, to obtain lower bound and upper bound of volume;With candidate supplementary line, the maximum volume absolute difference between two groups of feasible solutions that still cannot be distinguished after post-prediction response is used to evaluate the value of supplementary measurement, return the new data to geophysical interpretation and joint solving step until the relative half-width of volume interval and the interval of absolute optimality are not greater than the preset threshold;Thus, under the condition of incomplete historical topography and multiple solutions of geophysical interface, the volume range that can be reviewed is given.

Description

Technical Field

[0001] This invention relates to the fields of engineering surveying, near-surface geophysical exploration, and space data processing, specifically to a method and system for joint inversion and volume determination of concealed basement of waste disposal bodies. Background Technology

[0002] With the expansion of linear engineering construction, the determination of spoil disposal volume has become a common basis for construction measurement, soil and water conservation acceptance, and environmental supervision. The spoil volume is obtained by integrating the elevation difference between the target temporal surface and the pre-disposal base; photogrammetry, lidar, and ground surveying can acquire the target temporal surface; multi-temporal digital elevation model registration, independent checkpoint accuracy verification, and digital elevation model differentiation can be used to identify topographic changes; ground penetrating radar estimates the depth of the subsurface interface by using the two-way travel time of reflected waves and the propagation velocity of the medium.

[0003] In reality, there are three interconnected problems with spoil disposal sites: First, historical imagery and topographic data coverage is incomplete; different registration results may be similar in accuracy, but the base elevations given in steep slopes will differ. Second, radar profiles may show multiple reflection interfaces; zero-time correction, propagation velocity, antenna distance from the ground, and positioning errors all affect depth conversion, and there may be no usable reflections in areas of strong attenuation. Third, supplementary surveys using equally spaced grids can only improve spatial coverage; they cannot determine whether a particular survey line can reduce the final volume range.

[0004] Based on this, the existing practice usually selects a single historical topography and a single geophysical interface first, and then calculates a volume value. This cannot reflect the volume uncertainty caused by historical topography errors and multiple geophysical solutions, and it also lacks the means to organize historical topography constraints, geophysical interpretation, volume upper and lower bound solutions, and field supplementary measurements into a continuous processing flow. Summary of the Invention

[0005] This invention aims to address the problems of incomplete historical topography, multiple solutions for geophysical interfaces, and the disconnect between supplementary survey layout and the final volume verification target. It proposes a method and system for joint inversion and volume verification of concealed basement in spoil heaps. The technology chain sequentially outputs the surface allowable set, historical basement interval, geophysical calibration candidates, joint feasible solution, global volume boundary, and supplementary survey update results, with the output of the previous step serving as the input for the next step.

[0006] In a first aspect, the present invention provides a method for joint inversion and volume determination of concealed substrates of waste disposal bodies, which is executed using a topographic surveying device, an interface detection device, a positioning device, a processor, and a field navigation terminal, and includes the following steps: S1. Acquire and retain candidate surface elevations, elevation error boundaries, and registration parameter combinations that meet accuracy requirements based on topographic observation data from multiple time phases and independent checkpoints; S2. Based on the topographic observation data of the multiple time phases, determine the same location where the historical time phase is determined to be the original surface and the target time phase is determined to be the location covered by waste. Add the historical surface elevation error range of this location to the elevation change range across time phases to form the base elevation constraint. S3. Establish mutually exclusive interface candidates for multiple reflection interfaces at the same location in the geophysical response. Do not establish depth equality constraints for sections where no effective interface is detected. Set the parameters affecting time-depth conversion as bounded calibration variables and exclude incompatible candidates with the base elevation constraint. S4. The candidate surface elevation, registration parameter combination, base elevation constraint, interface candidate, bounded calibration variable and non-negative thickness condition are combined into a feasible solution set. The minimization problem and maximization problem of the waste volume are solved respectively to obtain the lower bound of the volume, the upper bound of the volume and the corresponding feasible solution. S5. On the set of feasible solutions, determine the maximum absolute volume difference between two sets of feasible solutions whose predicted responses are still indistinguishable after the candidate supplementary test line is implemented, and determine the target supplementary test line based on the maximum absolute volume difference and the implementation cost. S6. After collecting the geophysical response of the target supplementary survey line, repeat S3 to S5. If the relative half-width and absolute optimality interval of the volume range are not greater than the preset threshold, output the volume verification result.

[0007] Preferably, control points for terrain reconstruction or registration are also deployed in S1. The control points participate in terrain reconstruction or registration, and the independent checkpoints are only used for accuracy verification. Areas where there may be waste are divided into calculation units. The candidate surface elevation is formed by at least two of the following: different reconstruction methods, parameter perturbation results, repeated flights, or different terrain sensors. The elevation error boundary is determined based on the residuals of independent checkpoints with similar slope, point density, texture, and occlusion conditions to the calculation unit, and extrapolation error is added when the coverage conditions of the independent checkpoints are exceeded.

[0008] Preferably, the registration parameter combination in S1 satisfies the following conditions: the registration residual on the outer stable surface area is not greater than the sum of its minimum value and tolerance, and the accuracy requirements of the control point and the independent check point are met, and the tolerance is determined by repeated registration tests; multiple registration parameter combinations that satisfy the conditions are retained simultaneously.

[0009] Preferably, in S2, object-oriented image analysis or point cloud classification is used to classify the land surface into original surface, waste material, vegetation or cover, water body, and undetermined category; the location must also be connected to the surrounding stable land surface area and meet the terrain continuity condition, which includes at least two of the following: directional slope, discrete second-order difference, ridge direction, and segmented constraints at known steep slopes; the cross-temporal elevation change range is determined based on at least one of the following: repeated measurements of stable area, settlement observation, material compression parameters, and construction records; if the classification, connectivity, or terrain continuity determination is not met, or if the cross-temporal elevation change range cannot be determined, the activation status of the base elevation constraint is set to zero.

[0010] Preferably, in S3, the original geophysical response with positioning information is acquired along the intersecting survey lines, and at least one of the redundant observations and the base elevation constraints is used to eliminate incompatible interface candidates and calibration parameter combinations.

[0011] Preferably, the bounded calibration variables include at least two of the following: zero-time correction, medium propagation velocity, air propagation path length between the antenna and the ground, positioning elevation deviation, and time synchronization deviation between positioning record and geophysical response; the lower limit of the candidate depth is determined by the product of half of the lower limit of propagation velocity and the non-negative part of the lower limit of two-way travel time after zero-time correction and air path subtraction, and the upper limit of the candidate depth is determined by the product of half of the upper limit of propagation velocity and the non-negative part of the corresponding upper limit of two-way travel time; the candidate depth, the candidate surface elevation of the target time phase, and the positioning elevation error are jointly converted into a candidate base elevation interval; The propagation velocity of the medium is determined by at least one of the following: common center point measurement, hyperbola fitting, known depth target, or base point confirmed by excavation or drilling; when the feasible solution set is empty, an infeasibility analysis is used to find a set of contradictory constraints or variable value ranges, and after deleting any one of them, the set becomes feasible again, and the locations that need to be remeasured, recalibrated, or re-examined for historical surface classification are output.

[0012] Preferably, the feasible solution set further includes the state of the waste disposal range and the terrain continuity condition, and the corresponding feasible solution includes the current minimum volume feasible solution and the current maximum volume feasible solution; the feasible solution set is represented by mixed integer linear programming, mixed integer second-order cone programming or mixed integer nonlinear programming; linear or convex models are solved using branch and bound or external approximation methods, and models containing non-convex terms are solved using spatial branch and bound methods that can return global upper and lower bounds; the lower bound of the volume is the effective lower bound of the global optimum of the minimization problem, and the upper bound of the volume is the effective upper bound of the global optimum of the maximization problem; the edge computing unit where the waste disposal range is not determined is represented by a binary variable, and the product of the binary variable and the thickness is processed by an indicator constraint or a linearization method based on the known upper and lower bounds of the elevation of the computing unit.

[0013] Preferably, the global upper bound of the maximum absolute volume difference in S5 is obtained in the following manner: the variables and constraints of the feasible solution set are copied into two sets, the volume difference between the two sets of solutions is split into two maximization subproblems in opposite directions, and the indistinguishable condition of the predicted response is expanded into a bilateral constraint that the standardized prediction difference at each sampling position does not exceed a set value; a bounded inverse of the propagation speed is introduced, and a linear envelope is established by multiplying it by the thickness; piecewise linear external approximation is performed on the remaining nonlinear terms, and the external approximation feasible region includes the original feasible region; the two subproblems are branched and bounded respectively, and the maximum value of the upper bound of the unprocessed node is taken as the global upper bound of the subproblem, and the larger of the upper bounds of the two subproblems is taken as the global upper bound of the maximum absolute volume difference; The candidate supplementary measurement line is generated in the passable area. The maximum absolute volume difference is determined within the resolution and prediction error range of the interface detection device. The determination of the target supplementary measurement line is also based on the volume difference between the current maximum volume feasible solution and the current minimum volume feasible solution. In S6, the target supplementary measurement line is sent to the field navigation terminal. The threshold includes the volume interval relative half-width threshold and the absolute optimality interval threshold between the minimization problem and the maximization problem.

[0014] Preferably, the implementation cost is determined by at least two of the following: effective length, slope, obstacle detour, equipment turning, vegetation clearing, calibration time, and safety risk level; the candidate supplementary survey line satisfies at least one of the following: intersecting with the existing survey line, passing through the area where the base elevation constraint is located, having a confirmed base point, or containing repeated survey segments; if the measured trajectory deviates from the design line, the prediction response function is re-established according to the measured trajectory.

[0015] Secondly, the present invention provides a system for joint inversion and volume determination of concealed substrates in waste disposal sites, comprising: The terrain data processing unit is used to generate candidate surface elevations, elevation error boundaries, and registration parameter combinations. Historical terrain constraint generation unit is used to identify the original surface in historical time phases and form the base elevation constraint for the target time phase; The geophysical data processing unit is used to save the original geophysical response, generate mutually exclusive interface candidates, and calibrate bounded calibration variables. The optimization solution unit is used to establish a feasible solution set and calculate the lower volume bound, upper volume bound, current minimum volume feasible solution, and current maximum volume feasible solution; The supplementary survey planning unit is used to evaluate candidate supplementary survey lines and send the target supplementary survey line to the field navigation terminal; and The data storage and output unit is used to save processing parameters, calibration records, and volume verification results.

[0016] As can be seen from the above technical solution, the present invention provides a method and system for joint inversion and volume verification of concealed substrates in waste disposal sites. Compared with the prior art, the present invention has the following beneficial effects: 1. This invention incorporates candidate ground elevations formed by different reconstruction methods, parameter disturbances, repeated flights, or different sensors, along with residuals from independent checkpoints used only for acceptance, into the calculation; it also retains multiple registration parameter combinations that meet accuracy requirements, thus avoiding the obscuring of local elevation differences in steep slopes and obstructed areas by a single ground surface or a single registration result.

[0017] 2. This invention converts historical elevations into base constraints for the target time phase only when the original surface classification of historical time phases, connectivity with the surrounding stable surface, terrain continuity, and the range of elevation changes across time phases are all reliable. The corresponding constraints are deactivated at steep slopes, cut slopes, and locations with insufficient data, thereby reducing systematic biases caused by abrupt changes across real terrain or by directly applying historical elevations.

[0018] 3. This invention retains mutually exclusive candidates for multiple geophysical reflection interfaces at the same location, does not force the establishment of depth equations for sections where no effective interfaces are detected, and uses zero-time correction, propagation velocity, air propagation path, positioning elevation deviation, and time synchronization deviation as bounded variables for joint calibration, thereby ensuring that the base interpretation is compatible with the original response, redundant observations, and historical constraints.

[0019] 4. This invention calculates the global bounds of the volume minimization and maximization problems on the same set of feasible solutions, and selects the supplementary survey line based on the maximum absolute volume difference between feasible solutions that are still indistinguishable after the candidate survey line is implemented and the implementation cost; the new data is returned to the joint solution according to the actual trajectory until the relative half-width and absolute optimality interval of the volume interval are not greater than their respective preset thresholds, so that the result range, supplementary survey basis and stopping conditions can be verified. Attached Figure Description

[0020] Figure 1 This is a schematic flowchart of a method for joint inversion and volume determination of a hidden substrate in a waste material according to the present invention.

[0021] Figure 2 This is a schematic diagram of the research area and initial data layout of the present invention.

[0022] Figure 3 This is a schematic diagram illustrating the formation process of the historical in-situ surface elevation constraint according to the present invention.

[0023] Figure 4 This is a schematic diagram illustrating the relationship between ground-penetrating radar interface candidates and calibration according to the present invention.

[0024] Figure 5 This is a schematic diagram illustrating the feasible solution set and the relationship between the upper and lower bounds of the volume in this invention.

[0025] Figure 6 This is a schematic diagram illustrating the determination of the supplementary measurement line and the results of volume range shrinkage in this invention.

[0026] Figure 7 This is a schematic diagram of the structure of a system for joint inversion and volume verification of a hidden substrate in a waste material according to the present invention. Detailed Implementation

[0027] The specific embodiments of the present invention are described below with reference to the accompanying drawings; the embodiments are used to illustrate the present invention, and not to limit the present invention.

[0028] This embodiment takes a spoil heap within a linear engineering construction area in a mountainous region as the object, with a planar range of approximately 145m × 115m, a calculated area of ​​12825m², a slope of approximately 6° to 31°, and a maximum elevation difference of approximately 37.6m. The spoil heap consists of a soil-rock mixture, with localized construction access roads, vegetation, and water accumulation, and the original surface contact points are visible on the periphery. After S1 to S6 are completed, a triangular network reference base containing fracture lines is constructed using the elevation of the exploratory pit or trench base and the existing topographic cross-section. This reference base is only used for post-verification and does not participate in constraint, interface selection, or determination of supplementary survey lines.

[0029] The study area was divided into 513 square computational units with sides of 5m. The horizontal projected area, target temporal surface elevation, base elevation, and spoil disposal area of ​​each calculation unit are respectively denoted as: , , and The relative positions of the surrounding stable surface area, construction access road, restricted area, initial longitudinal survey line, and initial transverse survey line are shown in [reference needed]. Figure 2 .

[0030] like Figure 1 As shown, a method for joint inversion and volume determination of concealed substrates in waste disposal includes the following steps.

[0031] S1. Surface reconstruction and multi-temporal registration: The target temporal phase was determined using UAV imagery and real-time dynamic carrier phase differential positioning to obtain the current terrain. Eight ground control points were established for aerial triangulation, and 30 independent checkpoints were also established. These independent checkpoints were arranged in layers according to flat bare land, steep slopes, low-texture areas, and vegetation edges, and did not participate in aerial triangulation, point cloud filtering, or registration. Three candidate surface elevations were generated using three sets of dense matching parameters, and the candidate elevations and their error ranges were stored in each computational unit.

[0032] For the first Phase Number Calculation unit, in the following formula To rebuild the results index, For its index set, For registration parameters, For unit position, For the coordinate transformation implemented according to the registration parameters, For the first One candidate elevation function, Error half-width determined for independent checkpoints; Output To allow for the union of surface elevation intervals, the multi-source reconstruction and inspection errors of S1 are uniformly transferred to S4:

[0033] In this embodiment, the root mean square of the elevation residual of the target time-phase checkpoint is 0.071m; after grouping by slope, point density, and obstruction, the unit error half-width is 0.08–0.22m. The stable ground surface is taken from bare land outside the site where there is no construction disturbance in each time phase and the repeated elevation difference does not exceed 0.10m; historical data consists of orthophotos from two time phases and incomplete elevation models. Based on the stable ground surface and permanent structures, the parameter combination is retained according to the following formula:

[0034] The above formula takes candidate registration parameters as input. And observations of the surrounding stable surface, control points, and independent checkpoints; Due to precision and value range constraints, To register residuals, To minimize residuals, To compensate for repeated registration tolerance; output The set of registration parameters to be retained is input into S4 along with the allowable set of surface parameters. In this embodiment, four sets of parameters are retained, all of which pass the check, but the local elevation difference in the maximum slope area is 0.18 to 0.34 m.

[0035] S2, Historical In-situ Surface Elevation Constraints: Object-oriented image analysis was used to segment the two historical time phases and the target time phase. Objects were categorized into in-situ, waste materials, vegetation or cover, water bodies, and undetermined categories using color, texture, local elevation difference, slope, and object adjacency. Objects identified as in-situ in the historical time phase were further connected to surrounding stable surface areas via an adjacency map. Slope and curvature continuity constraints were interrupted at natural steep slopes and artificial cuts to avoid interpolation across abrupt changes in the actual terrain.

[0036] After classification, connectivity, and topographic continuity checks, a total of 13 calculation units were found to be exposed in the historical time phase and covered by waste in the target time phase. The historical elevation cannot be directly equated to the target time phase base. In this embodiment, based on repeated measurements of the surrounding stable surface and settlement data during the construction period, the range of surface elevation change from the historical time phase to the target time phase is taken as -0.35 to 0.10m.

[0037] Settlement records during construction were first standardized to reflect the elevation changes of the target time phase relative to historical time phases. Using the median absolute deviation as a scale, each record deviating more than three times the median was reviewed, and only confirmed records or those with reading errors were discarded, resulting in a range of -0.29 to 0.04 m. The 0.06 m error half-width formed by the difference in repeated measurements at the same points and the registration residuals was then extended to both ends, resulting in a range of -0.35 to 0.10 m.

[0038] Let the enabled state be 1, indicating that the historical constraint holds in the current candidate combination. Then the base elevation satisfies the following equation:

[0039] The above formula inputs the historical in-situ surface elevation interval. Elevation variation range across time phases and enabled status ; For the target phase number The base elevation of the unit. Output when 1 is selected The allowable interval is defined, and when the value is 0, this historical constraint is not applied. This formula is used to convert the historical exposed surface into a target temporal basis constraint with error boundaries.

[0040] In this embodiment, eight neighboring pairs of a 5m calculation unit are statistically analyzed on the outer stable surface. The 95th percentile of the absolute difference in slope and the absolute difference in profile curvature are used as the terrain continuity thresholds, resulting in thresholds of 8° and 0.12m, respectively. - ¹.

[0041] The connectivity criterion is as follows: In the 8-neighborhood map composed of 5m computing units, there must be at least one path from the candidate unit to the surrounding stable surface that is entirely composed of historical phase original surface category units. The number of non-original surface category units allowed in the path is 0, and it must not cross the identified natural steep slope or artificial slope break line. The slope difference and profile curvature difference between each adjacent unit on the path must not exceed the above thresholds. When the classification, connectivity and terrain continuity conditions are met simultaneously, the activation state is set to 1.

[0042] It should be noted that if the classification, connectivity, or terrain continuity criteria are not met, or if the range of elevation changes across time phases cannot be reliably determined, the activation state is set to 0, and the historical elevation is not included in the base constraints; the formation process is described in [link to documentation]. Figure 3 .

[0043] S3. Ground Penetrating Radar Acquisition, Interpretation, and Calibration: like Figure 2As shown, the initial longitudinal and transverse survey lines used 100MHz shielded antennas, with lengths of 126m and 92m respectively, and a track spacing of 0.10m. The positioning device recorded the position, elevation, and timestamp, while the radar controller recorded the trigger time. The raw records underwent zero-time correction, DC drift removal, bandpass filtering, background removal, gain and offset processing in sequence, and the parameters were saved in association with the raw data. Repeated survey sections were set up near the intersection points, and the propagation velocity was calibrated by measuring the common center point at three locations.

[0044] For each radar record, a reflection interface that meets the requirements of continuity and signal-to-noise ratio is extracted. When two or three similar reflections appear, they are retained as mutually exclusive candidates, and selection is not based on the principle of maximum amplitude. Sections with strong attenuation or insufficient penetration are marked as having no effective interface detected, and no base depth equality constraints are generated for these sections. After initial interpretation, approximately 11% of the test sections had more than two candidates, and approximately 7% of the test sections had no effective interface detected.

[0045] Let the two-way travel time, zero-time correction, total air propagation path length between the antenna and the ground, and medium propagation speed of the candidate reflection be respectively located at... , , and The two-way travel time within the medium after zero-time correction is based on... The candidate depth range is determined by the following formula:

[0046] The input to the above formula is the two-way travel time interval. Zero-time correction range Total airborne transmission path interval and the range of medium propagation speed , The speed of electromagnetic wave propagation in air; output This represents the candidate interface depth range. The lower limit is taken as the smaller combination of the corrected effective travel time and velocity, and the upper limit is taken as the larger combination, used to convert time observation and calibration errors into candidate base elevation ranges.

[0047] In this embodiment, the propagation velocity is 0.105–0.118 m / ns obtained through common center point measurement and hyperbolic fitting, with a zero-time correction of -0.45–0.40 ns. Antenna undulation and positioning residuals are included in the error range. The candidate base elevation is obtained by subtracting the candidate depth from the ground surface elevation; the selected base intervals at the intersection point must intersect, and the round-trip travel time difference after repeated measurement and correction must not exceed the equipment repeatability limit.

[0048] The zero-time correction, propagation velocity, air propagation path length between the antenna and the ground, positioning elevation deviation, and time synchronization deviation are composed of continuous calibration variables. The interface selection state is composed of discrete variables. The calibration objective function consists of the standardized deviations and intersections of each variable relative to the calibration center, and the residuals of repeated measurements; the retained set of combinations consists of calibration variables and selection variables that satisfy the following two conditions:

[0049] The input to the above formula is a continuous calibration variable. Variable selection interface And calibration, intersection point and repeated segment observation; For the range of values, candidate mutual exclusion and redundant observation constraints, To calibrate the residuals, Its minimum value, To allow for repeated calibration tolerance; output This is a combination of geophysical interface and calibration parameters, used to simultaneously transmit multi-interface selection and time-depth calibration to S4.

[0050] Understandably, if the set is empty, the solver's infeasibility analysis function can be used to find a set of contradictory constraints or variable value ranges; deleting any one of them can restore the set to feasible. Then, the corresponding intersections, calibration segments, or historical classifications are reviewed to avoid obtaining results by arbitrarily widening the entire error range. Figure 4 The relationship between multiple candidate reflections and calibration is shown.

[0051] S4. Joint Inversion and Volume Bounds: The surface elevation, registration parameters, spoil disposal area status, historical constraint activation status, base elevation, geophysical interface selection, and calibration variables are uniformly denoted as... The above formulas, along with the non-negative thickness, candidate mutual exclusion, and terrain continuity conditions, are uniformly written in inequality form, yielding the following feasible solution set:

[0052] The inputs to the above formula are the surface allowable set and registration parameters of S1, the base zone and activation status of S2, the interface and calibration parameter combination of S3, as well as the spoil boundary, non-negative thickness and topographic continuity conditions. Indicates the first Item constraint, To constrain the total number; the equation can be written as two inequalities, with the range of discrete variables preserved separately. Output The joint feasible solution set is the common input for the volume upper and lower bounds and the evaluation of the supplementary measurement line; each element must simultaneously satisfy all observations, error ranges and physical conditions.

[0053] No. The thickness of the waste residue in each calculation unit is The volume of waste residue is calculated using the following formula:

[0054] The input to the above equation is a joint feasible interpretation. ; The total number of units, For the first Horizontal projected area of ​​the unit The waste disposal range is 0-1. , For surface and basement elevations, Non-negative thickness; output For the corresponding volume, S4 is the objective function. The range of elements within and outside the range. The values ​​are set to 1 and 0 respectively, and the undetermined edge cells are retained as binary variables; their product with the thickness is subjected to indicator constraints or linearization based on known elevation boundaries.

[0055]

[0056] The above input is and Output the theoretical minimum volume and theoretical maximum volume This refers to the maximum volumetric value allowed by all constraints, used to determine the volume range permitted by the observation conditions. This embodiment uses mixed-integer programming to represent the candidate mutually exclusive and edge cell states, and employs branch-and-bound solving. The relationship between the feasible solution objective value and the global bound of unprocessed nodes is as follows:

[0057] The inputs to the above equation are the feasible solution objective value and the node relaxation bounds; To minimize the effective lower bound of the problem, To maximize the effective upper bound of the problem; For the theoretical minimum volume, This is the theoretical maximum volume; The smallest feasible volume value found so far. Output the maximum feasible volume value found. This provides a defined range covering all feasible volumes and serves as input for the stopping criterion.

[0058]

[0059] The above formula uses the current minimum feasible volume value Current maximum feasible volume value Minimize the global lower bound of the problem And maximizing the global upper bound Given the input, output the upper bound of the absolute optimality interval. and volume range relative half width The former takes the larger of the remaining intervals of the two optimization problems, in m³, representing the calculation error; the latter is the ratio of the interval half-width to the midpoint, representing the allowable volume difference in observation. When the value is greater than 0, calculate according to the above formula; when both the upper and lower bounds are 0, let... Set the value to 0. When both values ​​are not greater than their respective thresholds, S6 outputs the volume verification result.

[0060] S5. Supplementary measurement line determined: Eighteen candidate survey lines were generated within the passable area after deducting water accumulation, steep slopes, construction equipment operation areas, and safety buffer zones. Each candidate line intersects with an existing survey line and, as far as possible, passes through calculation units with significant differences in base elevation between the two sets of currently feasible solutions. The implementation cost of the candidate lines was obtained by weighting the route length, slope, detour, turning, obstacle clearing, and calibration time after normalization to a unified dimension.

[0061] For candidate lines , No. The sampling location falls on the first When calculating one computational unit, the predicted two-way travel time under near-vertical propagation conditions is:

[0062] The input to the above equation is a joint feasible interpretation. The given surface elevation Base elevation Calibration parameters The given zero-time correction amount Total airborne transmission path Medium velocity and candidate lines Sampling location and the unit ; The speed of electromagnetic waves in air, output To predict two-way travel time, this formula converts the thickness difference into an observable time difference. To calibrate the parameter range. For non-near-vertical propagation, ray tracing or electromagnetic forward modeling is used, and discretization, positioning, and synchronization errors are included in the prediction error.

[0063] If the predicted response intervals of two feasible solutions intersect on the candidate line, then the measurement may still fail to distinguish them; suppose The diagonal element is a diagonal matrix whose diagonal elements are equal to the reciprocal of the half-width of the allowable error at each sampling position. The maximum absolute volume difference that may still be retained after the candidate line is implemented is defined by the following formula:

[0064] The above input has two feasible interpretations. Two sets of calibration parameters Volume function Predictive response and weight matrix ; To calibrate the parameter range, The diagonal element is the reciprocal of the allowable error half-width, and the constraint on the right-hand side of 2 indicates that the two prediction intervals still intersect. Output The maximum absolute volume difference that remains indistinguishable after the survey line is implemented, expressed in m³, is used to convert the distinguishability of the response into an excludeable volume difference; the current volume difference is denoted as... It is equal to the difference between the current maximum and minimum feasible volume values, and the implementation cost is... .

[0065] The global upper bound is obtained by the following steps: First, the feasible solution variables and constraints are replicated into two sets. The absolute difference in volume is decomposed into two maximization subproblems, and the infinite norm constraint is expanded into a bilateral constraint that the standardized prediction difference at each sampling location does not exceed 2.

[0066] Second, a bounded propagation velocity reciprocal is introduced, and its product with the thickness is used to establish a McCormick linear envelope. The remaining nonlinear terms are approximated by piecewise linear external approximation. The external approximation domain includes the original feasible domain, and the interface and slag disposal range states are still binary variables.

[0067] Third, branch and bound the two subproblems separately: external approximation of nodes gives the upper bound, and node solutions are substituted back into the original constraints to update the maximum feasible value; for branches with unfixed binary variables or the widest interval of continuous variables, nodes that are infeasible or have poor upper bounds are deleted.

[0068] Fourth, the maximum value of the upper bound of the unprocessed nodes is taken as the global upper bound of the subproblem; the process stops when the difference between this value and the maximum feasible value does not exceed the absolute tolerance. The larger of the upper bounds of the positive and negative subproblems is taken as the global upper bound of the maximum absolute volume difference. Since the external approximation region includes the original feasible region, this value is not less than the true optimal value.

[0069] Substituting the current feasible volume difference, the global upper bound of the maximum absolute volume difference after the candidate line is implemented, and the implementation cost into the following formula, the target supplementary measurement line is determined:

[0070] The input to the above formula is the candidate line set. Current volume difference Global upper bound of the maximum absolute volume difference after implementation Normalization cost and prevent zero small positive numbers ; To ensure the reduction amount, output The survey line is designed to maximize the reduction per unit cost. After on-site data collection, the predicted response is reconstructed based on the actual trajectory and returned to S3 to S5. The predicted reduction is not treated as the measured result.

[0071] For example, after completing two initial survey lines, the current feasible volume difference is 51858.6 m³. A candidate line contains 20 valid sampling locations, with a normalized implementation cost of 1.12 and an absolute tolerance of 500 m³. The maximum feasible value and node upper bound of the forward subproblem are 35108.6 m³ and 35420.8 m³, respectively, while those of the reverse subproblem are 34762.9 m³ and 34965.2 m³, respectively. Since the interval between these two values ​​is less than 500 m³, the global upper bound is taken as 35420.8 m³. The guaranteed reduction is 16437.8 m³, and when the small positive number is 0.01, the evaluation value is 14546.7 m³ per normalized cost. All 18 candidate lines are evaluated in the same way, and the largest one is implemented. The results are shown in [the table below]. Figure 6 .

[0072] S6. On-site updates and results: Using only the visible contact location, non-negative thickness, and terrain continuity conditions, the volume range is [59642.8, 249694.2] m³; after adding 13 historical in-situ surface constraints, it is [122471.9, 208357.1] m³; after completing the two initial radar survey lines (longitudinal and transverse), it is [132025.5, 183884.1] m³, with a relative half-width of 0.1642.

[0073] Subsequently, seven supplementary measurement lines were issued sequentially. After each acquisition, interface candidates and calibration parameters were re-extracted based on the actual trajectory, and feasible solution sets were reconstructed, without treating the evaluation value as the measurement result. After completing 3, 5, and 7 supplementary measurement lines, the intervals were [140086.7, 172548.4] m³, [142262.7, 169615.0] m³, and [143078.3, 167932.3] m³, respectively, with relative half-widths of 0.1038, 0.0877, and 0.0799. Finally, the absolute optimality interval was 826.5 m³, which was less than the 1000 m³ threshold, and the relative half-width was less than 0.08, at which point the supplementary measurement was stopped.

[0074] The final verified range is [143078.3, 167932.3] m³, with a midpoint of 155505.3 m³. The reference base volume is 155082.8 m³, located within the range, differing from the midpoint by 422.5 m³. The reference values ​​are only compared after the survey line selection and constraint update are completed, without changing the order of supplementary measurements or the upper and lower bounds of the volume.

[0075] When a new survey line conflicts with existing constraints, first check for positioning loss of lock, coupling failure, zero-time drift, and changes in propagation velocity; only expand the corresponding error term if repeated measurements or calibration prove that the error range is insufficient. Sections where no effective interface is detected are retained as blank observations, and the equipment range is not used to replace the base depth; in high water-bearing or clay areas, resistivity method, shallow seismic method, or pit / trench elevation constraints can be added to the same base variable.

[0076] like Figure 7 As shown, this embodiment also proposes a joint inversion and volume verification system for concealed substrates of waste disposal bodies, including: The terrain data processing unit executes S1, outputting the allowable set of surface elevations and the set of registration parameters; the historical terrain constraint generation unit executes S2, outputting the base elevation interval and its activation status; the geophysical data processing unit executes S3, outputting the interface and calibration parameter combination; the optimization solution unit executes S4, outputting the global volume boundary, the current feasible solution, and the stopping criterion; the supplementary survey planning unit executes S5 and S6, evaluating and sending the target survey line and receiving the actual trajectory; the data storage and output unit saves the processing parameters, constraint sources, solution records, and verification results.

[0077] Each unit of the system corresponds one-to-one with S1 to S6, and the definitions and processing rules in the method embodiment also apply.

[0078] The above system can be implemented by software, hardware, firmware or a combination thereof; when software is used, the instructions in the computer-readable storage medium are executed by the processor to implement S1 to S6.

[0079] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to the embodiments of this application is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk).

[0080] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0081] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0082] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for joint inversion and volume determination of concealed substrates in waste disposal sites, characterized in that, The process employs topographic surveying equipment, interface detection equipment, positioning equipment, a processor, and a field navigation terminal, and includes the following steps: S1. Acquire and retain candidate surface elevations, elevation error boundaries, and registration parameter combinations that meet accuracy requirements based on topographic observation data from multiple time phases and independent checkpoints; S2. Based on the topographic observation data of the multiple time phases, determine the same location where the historical time phase is determined to be the original surface and the target time phase is determined to be the location covered by waste. Add the historical surface elevation error range of this location to the elevation change range across time phases to form the base elevation constraint. S3. Establish mutually exclusive interface candidates for multiple reflection interfaces at the same location in the geophysical response. Do not establish depth equality constraints for sections where no effective interface is detected. Set the parameters affecting time-depth conversion as bounded calibration variables and exclude incompatible candidates with the base elevation constraint. S4. The candidate surface elevation, registration parameter combination, base elevation constraint, interface candidate, bounded calibration variable and non-negative thickness condition are combined into a feasible solution set. The minimization problem and maximization problem of the waste volume are solved respectively to obtain the lower bound of the volume, the upper bound of the volume and the corresponding feasible solution. S5. On the set of feasible solutions, determine the maximum absolute volume difference between two sets of feasible solutions whose predicted responses are still indistinguishable after the candidate supplementary test line is implemented, and determine the target supplementary test line based on the maximum absolute volume difference and the implementation cost. S6. After collecting the geophysical response of the target supplementary survey line, repeat S3 to S5. If the relative half-width and absolute optimality interval of the volume range are not greater than the preset threshold, output the volume verification result.

2. The method for joint inversion and volume determination of concealed substrates in waste disposal bodies according to claim 1, characterized in that: S1 also includes control points for terrain reconstruction or registration. These control points participate in terrain reconstruction or registration, while the independent checkpoints are used only for accuracy verification. Areas where waste may be present are divided into calculation units. The candidate surface elevation is formed by at least two of the following: different reconstruction methods, parameter perturbation results, repeated flights, or different terrain sensors. The elevation error boundary is determined based on the residuals of independent checkpoints that have similar slope, point density, texture, and occlusion conditions to the calculation unit, and extrapolation error is added when the coverage conditions of the independent checkpoints are exceeded.

3. The method for joint inversion and volume determination of concealed substrates in waste disposal bodies according to claim 2, characterized in that: The registration parameter combination described in S1 satisfies the following conditions: the registration residual on the outer stable surface area is not greater than the sum of its minimum value and tolerance, and the accuracy requirements of the control point and the independent check point are met, and the tolerance is determined by repeated registration tests; multiple registration parameter combinations that satisfy the above conditions are retained simultaneously.

4. The method for joint inversion and volume determination of concealed substrates in waste disposal bodies according to claim 3, characterized in that: In S2, object-oriented image analysis or point cloud classification is used to classify the land surface into original surface, waste material, vegetation or cover, water body, and undetermined category; the location must also be connected to the surrounding stable land surface area and meet the terrain continuity condition, which includes at least two of the following: directional slope, discrete second-order difference, ridge direction, and segmented constraints at known steep slopes; the cross-temporal elevation change range is determined based on at least one of the following: repeated measurements of stable areas, settlement observations, material compression parameters, and construction records; if the classification, connectivity, or terrain continuity determination is not met, or if the cross-temporal elevation change range cannot be determined, the activation status of the base elevation constraint is set to zero.

5. The method for joint inversion and volume determination of concealed substrates in waste disposal bodies according to claim 1, characterized in that: In S3, the original geophysical response with positioning information is acquired along the intersecting survey lines, and at least one of the redundant observations and the base elevation constraints is used to eliminate incompatible interface candidates and calibration parameter combinations.

6. The method for joint inversion and volume determination of concealed substrates in waste disposal bodies according to claim 1, characterized in that: The bounded calibration variables include at least two of the following: zero-time correction, medium propagation velocity, air propagation path length between the antenna and the ground, positioning elevation deviation, and time synchronization deviation between positioning record and geophysical response. The lower limit of the candidate depth is determined by the product of half of the lower limit of the propagation speed and the non-negative part of the lower limit of the two-way travel time after zero-time correction and air path subtraction; the upper limit of the candidate depth is determined by the product of half of the upper limit of the propagation speed and the non-negative part of the corresponding upper limit of the two-way travel time; the candidate depth, the candidate surface elevation of the target time phase, and the positioning elevation error are jointly converted into the candidate base elevation interval. The propagation velocity of the medium is determined by at least one of the following: common center point measurement, hyperbola fitting, known depth target, or base point confirmed by excavation or drilling; when the feasible solution set is empty, an infeasibility analysis is used to find a set of contradictory constraints or variable value ranges, and after deleting any one of them, the set becomes feasible again, and the locations that need to be remeasured, recalibrated, or re-examined for historical surface classification are output.

7. The method for joint inversion and volume determination of concealed substrates in waste disposal bodies according to claim 4, characterized in that: The feasible solution set also includes the state of the waste disposal range and the terrain continuity condition. The corresponding feasible solution includes the current minimum volume feasible solution and the current maximum volume feasible solution. The feasible solution set is represented by mixed integer linear programming, mixed integer second-order cone programming or mixed integer nonlinear programming. Linear or convex models are solved using branch and bound or external approximation methods, while models containing non-convex terms are solved using spatial branch and bound methods that can return global upper and lower bounds. The lower bound of the volume is a valid lower bound of the global optimum of the minimization problem, and the upper bound of the volume is a valid upper bound of the global optimum of the maximization problem. Edge calculation units with undetermined slag disposal ranges are represented by binary variables, and the product of the binary variables and the thickness is processed using indicator constraints or linearization methods based on the known upper and lower bounds of the elevation of the calculation unit.

8. The method for joint inversion and volume determination of concealed substrates in waste disposal bodies according to claim 7, characterized in that: The global upper bound of the maximum absolute volume difference mentioned in S5 is obtained as follows: the variables and constraints of the feasible solution set are copied into two sets, the volume difference between the two sets of solutions is split into two maximization subproblems in opposite directions, and the indistinguishable condition of the predicted response is expanded into a bilateral constraint that the standardized prediction difference at each sampling position does not exceed a set value; a bounded inverse of the propagation speed is introduced, and a linear envelope is established by multiplying it by the thickness; piecewise linear external approximation is performed on the remaining nonlinear terms, and the external approximation feasible region includes the original feasible region; the two subproblems are branched and bounded respectively, and the maximum value of the upper bound of the unprocessed node is taken as the global upper bound of the subproblem, and the larger of the upper bounds of the two subproblems is taken as the global upper bound of the maximum absolute volume difference; The candidate supplementary measurement line is generated in the passable area. The maximum absolute volume difference is determined within the resolution and prediction error range of the interface detection device. The determination of the target supplementary measurement line is also based on the volume difference between the current maximum volume feasible solution and the current minimum volume feasible solution. In S6, the target supplementary measurement line is sent to the field navigation terminal. The threshold includes the volume interval relative half-width threshold and the absolute optimality interval threshold between the minimization problem and the maximization problem.

9. The method for joint inversion and volume determination of concealed substrates in waste disposal bodies according to claim 8, characterized in that: The implementation cost is determined by at least two of the following: effective length, slope, obstacle detour, equipment turning, vegetation clearing, calibration time, and safety risk level; the candidate supplementary survey line satisfies at least one of the following: intersecting with the existing survey line, passing through the area where the base elevation constraint is located, having a confirmed base point, or containing repeated survey segments; if the measured trajectory deviates from the design line, the prediction response function is re-established according to the measured trajectory.

10. A system for joint inversion and volume determination of concealed substrates in waste disposal sites, employing the method for joint inversion and volume determination of concealed substrates in waste disposal sites according to any one of claims 1-9, characterized in that, include: The terrain data processing unit is used to generate candidate surface elevations, elevation error boundaries, and registration parameter combinations. Historical terrain constraint generation unit is used to identify the original surface in historical time phases and form the base elevation constraint for the target time phase; The geophysical data processing unit is used to save the original geophysical response, generate mutually exclusive interface candidates, and calibrate bounded calibration variables. The optimization solution unit is used to establish a feasible solution set and calculate the lower volume bound, upper volume bound, current minimum volume feasible solution, and current maximum volume feasible solution; The supplementary survey planning unit is used to evaluate candidate supplementary survey lines and send the target supplementary survey line to the on-site navigation terminal. as well as The data storage and output unit is used to save processing parameters, calibration records, and volume verification results.

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