Expressway gpr re-measurement point recommendation method based on posterior uncertainty

Abstract

The application provides a highway GPR re-measurement point recommendation method based on posterior uncertainty, and belongs to the technical field of road intelligent detection management based on computer data processing; first, highway GPR initial measurement data are acquired, and observation characteristics of a detection unit are extracted; candidate hidden states, a physical response proxy model and prior information are used to calculate state posterior probability and deep posterior distribution of each detection unit; state entropy, state competition degree and deep interval uncertainty are quantified according to the above, and candidate re-measurement points are generated; for each candidate point, possible re-measurement observation is simulated, expected uncertainty reduction after re-measurement and regional information gain are calculated; expected return, road structure sensitivity and re-measurement cost are comprehensively considered, and recommended re-measurement points are output under the constraints of re-measurement number, budget and spatial interval. The application makes the re-measurement points have clear recommendation basis, and can update the posterior result by using actual re-measurement data, so as to form a closed loop of initial measurement, recommendation, re-measurement and update.

Description

Technical Field

[0001] This invention belongs to the field of intelligent road detection and management technology based on computer data processing, and particularly relates to a method for recommending highway GPR re-measurement points based on posterior uncertainty. Background Technology

[0002] In highway maintenance and inspection, GPR (Geometric Response) is typically used to continuously acquire the electromagnetic response within the pavement structural layers and subgrade, thereby assisting in the identification of hidden conditions such as voids, interlayer segregation, abnormal water content, abnormal structural layer thickness, and subgrade loosening. Current technologies usually first perform time-zero correction, background removal, filtering, and gain processing on the initial measurement data. Then, based on the abnormal amplitude, waveform morphology, layer continuity, empirical thresholds, or identification model output, suspected abnormal sections are identified. For suspected sections, technicians, based on experience, arrange for repeated scanning, local densification of survey lines, changing antenna frequencies, or core drilling verification.

[0003] However, GPR response is simultaneously affected by road material dielectric parameters, structural layer thickness, antenna frequency, coupling state, vehicle speed, noise, and processing parameters. The same anomalous response may correspond to different implicit states, and a large anomalous amplitude does not necessarily mean that retesting will eliminate judgment discrepancies. Existing methods for determining retesting locations based on anomaly intensity, fixed thresholds, or manual experience are insufficient to quantitatively assess the degree to which new observations at each location improve the current judgment. They also struggle to simultaneously address on-site constraints such as information redundancy between adjacent points, road structure sensitivity, retesting costs, budget, and spatial spacing. Therefore, given limited retesting resources, determining from initial test results locations that are more likely to reduce judgment uncertainty through retesting while balancing engineering importance and implementation costs is a technical problem that current highway GPR retesting arrangements need to solve. Summary of the Invention

[0004] To address the above problems, this invention proposes a method for recommending highway GPR re-measurement points based on posterior uncertainty, comprising the following steps: S101, acquire the initial measurement data of the highway GPR and its collected metadata, divide the detection units according to road mileage and lane, and obtain the initial measurement observation data of each detection unit; S102, preprocess and extract features from the initial observation data to obtain the observation feature vector of each detection unit; S103, establish a candidate state set including normal state and at least one hidden abnormal state of the road, and calculate the state posterior probability and depth posterior distribution of each detection unit based on the observed feature vector, physical response proxy model and state prior probability. S104, Calculate the current posterior uncertainty of each detection unit based on the state posterior probability and depth posterior distribution; S105, Generate a set of candidate retest points based on the current posterior uncertainty; S106, For each candidate point in the candidate retest point set, generate possible retest observations and update the corresponding posterior results, and calculate the expected uncertainty reduction and regional information gain of the candidate point; S107, Taking into account the expected decrease in uncertainty, regional information gain, road structure sensitivity and retesting cost, calculate the retesting value of each candidate point; S108, under at least one constraint among the number of retests, retest budget, and minimum spatial spacing of candidate points, select and output recommended retest points from the set of candidate retest points based on the retest value.

[0005] Preferably, the preprocessing in S102 includes at least one of time-zero correction, DC removal, background removal, bandpass filtering, gain compensation, and inter-channel normalization; the observation feature vector includes at least one of amplitude features, phase features, spectral features, stratigraphic continuity features, attenuation features, and anomalous geometric features.

[0006] Preferably, the candidate state set in S103 also includes unmodeled abnormal states; the hidden abnormal states of the road include voiding, interlayer segregation, water content anomaly, structural layer thickness anomaly, and loose roadbed.

[0007] Preferably, in step S103, the state posterior probability and depth posterior distribution of each detection unit are calculated, and the specific process is as follows: Parameter samples are generated within the parameter domain of each candidate state; predicted features of each parameter sample are obtained through a physical response surrogate model; sample likelihood is calculated based on the difference between predicted features and observed features; the sample likelihoods within the same candidate state are weighted and summed, and combined with state prior probability normalization to obtain state posterior probability; deep posterior distribution is obtained based on the posterior weights of parameter samples corresponding to abnormal states. The physical response proxy model is a fast approximation of electromagnetic forward modeling, used to convert certain road structures and anomaly parameters into GPR characteristics expected to occur under the same equipment and processing procedures.

[0008] Preferably, the current posterior uncertainty in S104 includes: normalized posterior entropy used to represent the overall confusion level of multiple candidate states. State competition degree, which is difficult to distinguish between the two candidate states with the highest posterior probability. And depth interval uncertainty used to represent the width of the confidence interval for anomaly depth. ; The normalized posterior entropy The posterior probabilities of each candidate state are measured by entropy and normalized according to the maximum entropy corresponding to the number of candidate states. The closer the posterior probabilities of each candidate state are, the larger the normalized posterior entropy is, indicating that the overall confusion of multiple candidate states is higher. The state competition The posterior probabilities of each candidate state are sorted from largest to smallest and determined based on the difference between the largest and second largest posterior probabilities; the smaller the difference, the greater the state competition, indicating that the two most likely candidate states are more difficult to distinguish. The uncertainty in the depth range The width of the confidence interval is determined based on the preset confidence interval of the depth posterior distribution and normalized in combination with a reference depth scale; the wider the confidence interval, the greater the uncertainty of the depth interval, indicating that the possible range of abnormal depth values ​​is more dispersed.

[0009] Preferably, the specific process of S105 includes: Initial candidate points are generated from abnormal response locations, high posterior entropy locations, high state competition locations, high depth interval uncertainty locations, spatial interpolation locations between adjacent survey lines, structural layer boundary locations, and road structure sensitive locations, respectively. Initial candidate points with a distance less than a preset deduplication distance are merged to obtain the candidate re-survey point set. The high posterior entropy position, high state competition position, and high depth interval uncertainty position are all positions that exceed the corresponding threshold.

[0010] Preferably, the specific process of S106 includes: A posterior prediction distribution is formed based on the current posterior result of the candidate point and the observation noise model; multiple possible re-measurement observations are generated from the posterior prediction distribution; the state posterior probability and depth posterior distribution are recalculated for each possible re-measurement observation; the expected uncertainty reduction is obtained by probability weighting based on the difference in uncertainty before and after recalculation; and the regional information gain is obtained based on the expected change in the posterior distribution in the neighborhood of the candidate point.

[0011] Preferably, the specific process of S107 includes: normalizing the expected posterior entropy decrease, expected state competition decrease, expected depth interval uncertainty decrease, regional information gain, road structure sensitivity, and retest cost to a unified dimension; weighting the first five items and deducting the retest cost penalty to obtain the retest value.

[0012] Preferably, in step S108, the output recommended retest points include at least road mileage, lane, lateral position, and retest priority, and simultaneously output the retest value, main reasons for recommendation, and suggested retest parameters; when selecting points, the total cost of the selected points is limited to not exceeding the retest budget, and the distance between any two selected points is limited to not less than the preset minimum spatial spacing.

[0013] Preferably, the process also includes the following: The actual retest data obtained from the recommended retest points are registered with the corresponding initial test data. The actual retest data is processed according to the preprocessing and feature extraction process adopted in S102. The processing results are added to the observation dataset, and S103 to S108 are re-executed based on the updated observation dataset. After the actual retest results are verified, at least one of the following is updated: state prior probability, physical response surrogate model parameters, observation noise parameters, and retest value weight.

[0014] Preferably, after outputting the recommended retest points, suggestions for local densification of survey lines are further generated based on the spatial clustering of the recommended retest points, the continuity across survey lines, and the posterior state results; when there is still high posterior uncertainty or high road structure sensitivity after retesting, suggestions for core drilling verification are further generated.

[0015] Compared with the prior art, the present invention has the following innovative features and beneficial effects: Compared with selecting points solely based on abnormal amplitudes or human experience, this invention has at least the following advantages: First, it explicitly represents the source of uncertainty in the current judgment using posterior entropy, state competitiveness, and depth interval width; second, it directly estimates the expected reduction in uncertainty that each candidate point can bring through posterior prediction simulation retesting; third, it simultaneously considers regional information gain, road structure sensitivity, cost, and spatial spacing to avoid ineffective clustering of recommended points; fourth, each output point carries a value score and reason code, facilitating verification by non-algorithm professionals; and fifth, real retesting data can be used to update the model and the next round of recommendations, forming a closed loop of sustainable improvement. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method for recommending retesting points in this invention.

[0017] Figure 2 This is a schematic diagram of candidate retest points, recommended retest points, and road layers.

[0018] Figure 3 A schematic diagram of generating a recommended retest point table based on retest value and on-site constraints.

[0019] Figure 4 The flowchart shows the verification process for thresholds, weights, and retest budgets. Detailed Implementation

[0020] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in this specification. The following embodiments are used to illustrate how the above process is implemented into an executable calculation. Unless otherwise stated, each threshold, weight, distance, budget, and sample number can be determined by historical calibration data and fixed on an independent validation set before being used on the road segment to be inspected.

[0021] Example 1: Main Process for Recommending Retesting Points Data, output, and symbol conventions: As shown in Table 1, the road segment to be inspected is divided into lanes and mileage. J The detection unit. j Each detection unit is denoted as u j Its center position is denoted as xj The initial measurement data includes raw A-scan or B-scan data, mileage, lane, lateral position, antenna frequency, sampling interval, vehicle speed, device number, and acquisition time. The output of each step is directly used as the input for subsequent steps to avoid inconsistencies in the meaning of the same symbol at different stages.

[0022] Table 1. Meaning of Main Parameters

[0023] The overall process of this invention is as follows Figure 1 As shown: S101: Acquire data and divide detection units The input consists of preliminary GPR measurement data and metadata for the road segment to be inspected. The metadata includes at least one or more of the following: road mileage, lane number, lateral position, survey line direction, antenna center frequency, sampling interval, time window, lane spacing, vehicle speed, positioning accuracy, device number, acquisition time, and device calibration parameters. First, the mileage coordinates of different survey lines are unified to the road centerline coordinate system. Then, detection units are divided according to a preset unit length and lane boundaries. The unit length can be determined based on the antenna frequency, the minimum target size, and the vehicle positioning accuracy, for example, 0.5 m to 2 m. The output is a set of detection units and the preliminary observation data contained in each unit.

[0024] S102: Preprocessing and extracting observation features For the data within each detection unit, perform at least one of the following processing steps sequentially: zero correction, DC removal, background removal, bandpass filtering, gain compensation, and inter-channel normalization. Processing parameters should be determined by equipment calibration data or a fixed training set, and should not be repeatedly adjusted on the section under inspection.

[0025] Extract at least one feature from the processed data, including amplitude, phase, spectral center, band energy ratio, reflector continuity, propagation attenuation, hyperbolic geometry, stratigraphic undulation, and differences between adjacent survey lines, and construct an observation feature vector. y j To make features with different dimensions comparable, standardization is performed using the training set mean and standard deviation; if the standard deviation is zero, the feature is deleted or its standardized value is set to zero. The output is for each detection unit. y j .

[0026] S103: Calculate the state posterior probability and depth posterior distribution The candidate state set S includes at least normal states and hidden road anomaly states to be identified, and preferably includes unmodeled anomaly states to accommodate observations that cannot be explained by existing anomaly models, avoiding the forced assignment of unknown responses to a known anomaly. Each state s corresponds to a parameter domain Θs. For example, the parameters of the vacant state may include top surface depth, thickness, lateral scale, and equivalent dielectric constant.

[0027] The physical response surrogate model is a fast approximation of electromagnetic forward modeling. Its function is to transform "a certain road structure and abnormal parameters" into "the GPR characteristics expected to appear under the same equipment and processing procedures", thereby enabling rapid comparison of predicted and measured characteristics on a large number of parameter samples.

[0028] The surrogate model can be pre-established as follows: First, determine the parameter domain for each candidate state, such as the range of values ​​for structural layer thickness, equivalent dielectric constant, anomalous top surface depth, anomalous thickness, and lateral scale; Second, generate parameter combinations using Latin hypercube sampling, uniform sampling, or stratified sampling, and generate the corresponding GPR response using a finite-difference time-domain electromagnetic forward model or a calibrated equivalent electromagnetic model; Third, perform the same time-zero correction, filtering, gain, and feature extraction process as in S102 on the forward response to form a "parameter combination - predicted feature" sample pair; Fourth, train the surrogate model using at least one of Gaussian process regression, random forest, neural network, or multinomial response surface, and fix the model parameters on independent validation samples.

[0029] Before deploying the surrogate model, prediction errors should be checked on forward modeling samples that were not used in training and on calibration samples with retesting or core drilling results. If the error of a key feature exceeds a preset threshold, the forward modeling samples within the corresponding parameter range should be expanded, or the electromagnetic forward model should be directly called for that range, without using the surrogate output whose error does not meet the requirements. Field calibration data can be used to correct system bias and observation error covariance Σo, but data from the road segment to be recommended should not be used to repeatedly adjust the model to avoid using the results to be evaluated for self-validation.

[0030] Generate within the parameter domain of state s Parameter samples And set sample weights for them. Through the above electromagnetic forward model or physical response proxy model To obtain predicted features : ; in, Representing state Next Predicted features corresponding to each parameter sample Representing state The corresponding electromagnetic forward model or physical response surrogate model, Representing state Next One parameter sample, Indicates the first Equipment parameters, road layer, and data collection conditions for each detection unit; For the detection unit index, For candidate state index, Let be the sample index for the in-state parameters. Let the observation error covariance matrix be... Given a positive definite matrix, the relative likelihood of the parameter samples is: ; in, Indicates the first Each detection unit is in status Next The relative likelihood of each parameter sample. Indicates the first Measured observation characteristics of each detection unit Indicates the corresponding predicted features, The superscript represents the inverse of the observation error covariance matrix. Indicates matrix transpose. This represents an exponential function. The sample likelihoods within the same state are weighted and summed to form state evidence. The sample weights are non-negative, and the sum of the weights within the same state is 1. ; in, Indicates the first Each detection unit checks the status. Evidence of the state, Representing state The total number of parameter samples under, Representing state Next The weights of each parameter sample, Let represent the relative likelihood of the corresponding parameter sample. For state The prior probability, If the prior probabilities of all candidate states are non-negative and the sum of their probabilities is 1, then the posterior probability of a state is: ; in, Indicates the observed features Under the conditions Each detection unit belongs to the state. The posterior probability, This represents the prior probability of a state. Indicates evidence of state. This represents the total number of candidate states. This represents the candidate state index in normalized summation. When the denominator is less than a preset lower limit... When an anomalous state has insufficient model evidence, it is marked as such and prioritized for handling by unmodeled anomalous states, without directly outputting a definitive anomalous conclusion. For anomalous states with depth parameters, the posterior weights of the parameter samples under that state are normalized, and a depth posterior distribution is constructed from the sample depths, outputting its 5%, 50%, and 95th percentiles. , and .

[0031] S104: Quantifying Current Posterior Uncertainty Normalized posterior entropy It reflects the overall confusion level of all candidate states. By convention, 0·ln0=0, and K is greater than 1. The closer the result is to 1, the closer the posterior probabilities of the multiple states are, and the less certain the current judgment is.

[0032] ; in, Indicates the first Normalized posterior entropy of each detection unit Indicates the first Each detection unit belongs to the state. The posterior probability, This represents the total number of candidate states. Indicates the candidate state index. Represents the natural logarithm; by convention ,and .

[0033] Arrange the posterior probabilities of the states from largest to smallest, and denote the maximum and second largest values ​​as follows: and State contention Used to indicate whether the two most likely states are difficult to distinguish: ; in, Indicates the first State contention of each detection unit and Let represent the posterior probabilities of the largest and second largest states, sorted from largest to smallest, respectively. The closer it is to 1, the more difficult it is to distinguish between the top two positions.

[0034] The closer the value is to 1, the more difficult it is to distinguish between the top two positions. Depth range uncertainty. Represented by the 90% posterior interval width, where A positive number determined based on the road structure thickness or acceptable depth error: ; in, Indicates the first Depth range uncertainty of each detection unit and Let represent the 95th and 5th percentiles of the depth posterior distribution, respectively. This indicates a positive reference scale determined based on the thickness of the road structure or acceptable depth error. This means that the calculation result will be truncated to the range of 0 to 1.

[0035] For detection units that do not have depth parameters or cannot form a valid depth posterior, U(d,j) is marked as unavailable; in subsequent value calculations, the corresponding depth descent term is set to 0, and the "insufficient depth evidence" reason code is output.

[0036] S105: Generate candidate retest points Candidate points are not generated solely from locations of strong anomalies. Initial candidate points are generated from the following locations: where the anomaly magnitude or geometric indices exceed a threshold. , or Locations exceeding the corresponding threshold; locations with large interpolation errors between adjacent survey lines; structurally sensitive locations such as structural layer boundaries, bridge abutment joints, weak drainage areas, and heavy-load lanes. Each threshold is fixed on the validation set.

[0037] The initial candidate points from each source are merged. If the planar distance between two candidate points is less than the deduplication distance dmerge, the point with higher uncertainty or higher structural sensitivity is retained, and the source of the merged point is recorded in the reason code of the retained point. The output contains N positions. x i The set of candidate retest points X.

[0038] S106: Decrease in uncertainty after prediction retesting The input for the active learning step is candidate points. x i The current posterior result. In layman's terms, this step sequentially assumes "at the candidate point..." x i After retesting, possible observation results 1, 2, ... are generated. The improvement in the current judgment caused by each of these results is calculated, and then the average is calculated based on the probability of each result. The posterior prediction distribution p(...) of the candidate points is constructed based on the posterior probability of the current state, the in-state parameter samples, and the observation noise model. |D, x i), where D represents the currently existing data, This indicates a retest that has not yet taken place.

[0039] Extracted or discretized from the posterior prediction distribution One possible re-measurement observation and its probability weights ,in Indicates the candidate point index. Indicates the retest scenario index. Indicates the number of possible retest scenarios. Non-negative weights sum to 1 for the same candidate point. For each... The posterior result is recalculated according to S103, and the result is obtained according to S104. Under the retest scenario , and Therefore, the expected decrease in posterior entropy, the expected decrease in state competitiveness, and the expected decrease in uncertainty in the depth interval are respectively: ; ; ; in, , and Representing candidate points respectively The expected posterior entropy decreases, the expected state competition decreases, and the expected depth interval uncertainty decreases. , and Indicates the corresponding uncertainty before the retest, marked with a superscript. The parameter represents the first The corresponding uncertainty under each retest scenario This represents the probability weight of the scenario. Indicates the total number of scenarios. Used to truncate negative expected declines to 0.

[0040] The above three items only evaluate the expected improvement of the candidate point itself. To evaluate the impact of retesting on surrounding detection units, the candidate point's neighborhood is considered. Distribution of combined or aggregated states within For the object, calculate the regional information gain. : ; in, Indicate candidate points Regional information gain, Indicate candidate points The neighborhood, This represents the combined or aggregated state distribution of detection units within the neighborhood before the retest. Indicates joining the The neighborhood distribution after possible retest observation Indicates the Kullback-Leibler divergence. Indicates the first The probability weights of each retest scenario. This indicates an improvement in the uncertainty of the candidate point itself. This indicates new information that the retest brought to the surrounding area; the two have different meanings.

[0041] S107: Calculate the value of the retest Road structure sensitivity Ri This represents the potential impact of the implicit state corresponding to the candidate point on road performance. Non-negative weights are assigned to Class G indicators such as load-bearing capacity, inter-layer continuity, water damage, and traffic safety. The state s at the candidate point is given by the calibration samples or expert rules. i For indicators g Impact score Each score ranges from 0 to 1.

[0042] ; in, Indicate candidate points In state The overall impact score is as follows: This represents the road structure sensitivity obtained by combining the posterior probabilities of each state. This indicates the total number of influencing indicators. Indicates the index of the influencing indicators. Indicates the first Non-negative weights of class-related indicators Representing state At candidate point For the The impact score of category indicators Indicate candidate points Belongs to state The posterior probability.

[0043] The cost of retesting consists of at least one of the following: arrival distance, traffic organization, lane closure time, equipment operation time, and data processing time. To avoid the influence of different units of measurement on the outcome by a single indicator, fixed upper and lower bounds are applied to any indicator z. and Normalization; upper and lower bounds are determined by training or calibration data, and > .

[0044] ; in, Indicate candidate points Indicators The normalized value, This represents the original index value before normalization. and These represent the lower and upper bounds of the metric, determined by the training or calibration data, respectively. This indicates that the result will be truncated to the range of 0 to 1. If the calibration data makes... If the index is not distinguishable in this batch of data, its normalized value is set to 0 and it is not included in the ranking. The retest value of a candidate point is defined as: ; in, Indicate candidate points The value of retesting , , , , and These represent the normalized expected posterior entropy decrease, expected state competitiveness decrease, expected depth interval uncertainty decrease, regional information gain, road structure sensitivity, and retesting cost, respectively. , , , and The weights are non-negative and their sum is greater than 0. This is a non-negative cost penalty coefficient. The weights and... The model is determined on a fixed training set and locked after being verified on an independent validation set. The larger the value, the more worthwhile the location is to be retested.

[0045] S108: Output recommended retest points under on-site constraints Press only Cutting from high to low may lead to clustering of adjacent points. Therefore, a binary variable is introduced. and in actual cost Retest budget B, maximum number of points and minimum spatial spacing Point selection under constraints: ; ; in, Indicate candidate points Whether it is selected or not, the value is 1 if selected and 0 if not selected; This represents the total number of candidate points. Indicate candidate points The value of retesting Indicate candidate points The actual cost of retesting Indicates the budget for retesting. This indicates the maximum number of points that can be selected. and Indicates the location of the candidate point. Indicates the spatial distance between two points. This represents the minimum spatial spacing. The objective function aims to maximize the total remeasurement value of the selected points, with constraints limiting the total cost, the number of points, and the spacing between adjacent points.

[0046] The 0-1 optimization described above can be solved using integer programming, greedy selection, or a constrained sorting algorithm. The output recommended retest point list should include at least mileage, lane, lateral location, and retest value. The document outlines the retest priority, main reasons for recommendations, suggested antenna frequency, and suggested acquisition direction. The main reasons for recommendations are generated from the two highest-contributing benefit indicators and structural sensitivity, such as "high state contention + high regional information gain," enabling field personnel to directly understand the basis for the recommendations.

[0047] Example 2: A complete numerical example from initial measurement data to retest update This embodiment illustrates the connection between each step in the following order: initial measurement, post-hoc judgment, candidate points, simulated re-measurement, value ranking, actual re-measurement, and result update. The following values ​​are for demonstrating the calculation process and do not represent actual measurement conclusions for specific road sections. The distribution relationship of candidate points in the road plane and structural layers is as follows: Figure 2 As shown, the process of generating a recommended retesting point list based on the retesting value and on-site constraints is as follows: Figure 3 As shown.

[0048] 1. Preliminary test data and candidate retest points A sample section from mileage K102+000 to K102+120 was selected for initial measurements using a 400 MHz ground-coupled antenna with a channel spacing of 0.05 m, a time window of 60 ns, and a detection unit of 1 m. S102 employed a fixed process of time-zero correction, background removal, bandpass filtering, gain compensation, and channel normalization to extract four types of features: reflection amplitude ratio, spectral center shift, layer continuity, and propagation attenuation. Candidate states were set as normal, interlayer gap, water-bearing anomaly, and unmodeled anomaly.

[0049] S103 uses a surrogate model to calculate the posterior probability of each state, and S104 further calculates... H, C and U dS105 merges locations with high a posteriori uncertainty, anomalous response locations, and structurally sensitive locations and removes duplicates, resulting in four candidate points: A, B, C, and D. Taking point A as an example, its standardized feature vector is (1.20, -0.85, -1.10, 0.95), indicating that this point simultaneously exhibits enhanced reflection, spectral downshift, decreased stratigraphic continuity, and enhanced attenuation. The a posteriori probabilities of interlayer voids and water-bearing anomalies at point A are 0.43 and 0.34, respectively. Since these probabilities are close, they cannot be distinguished solely based on the stability of the initial measurement data.

[0050] Table 2. Preliminary post-test results and candidate sources for candidate retest points.

[0051] As shown in Table 2, the larger the value of H, the more difficult it is to distinguish multiple states as a whole; the larger the value of C, the closer the two most likely states are. U d The larger the value, the wider the anomaly depth range. Therefore, the main problems with A and D are the obvious competition between the first two states, while the main problem with C is the overall dispersion of multiple states.

[0052] 2. Simulate and retest, and calculate the expected return at point A. Taking point A as an example, three representative retest scenarios were obtained by merging the posterior prediction distributions: the retest results support interlayer voiding, the retest results support water-bearing anomalies, and the retest results still cannot distinguish between the two. The probability weights of the three scenarios are 0.45, 0.35, and 0.20, respectively, with a sum of 1. The posterior uncertainty is recalculated for each scenario according to S103 and S104.

[0053] Table 3 Possible retest results for point A

[0054] The expected posterior entropy after retesting point A is 0.45×0.550+0.35×0.620+0.20×0.840=0.633. Therefore, the original expected posterior entropy decreases to 0.857. 0.633 = 0.224; similarly, the original expected state competition level decreases to 0.910. (0.45×0.350+0.35×0.420+0.20×0.820)=0.442, the uncertainty of the original expected depth interval decreases to 0.667-(0.45×0.400+0.35×0.500+0.20×0.650)=0.182. After normalization according to the pre-fixed upper and lower bounds on the validation set, the ΔH, ΔC, and ΔUd of point A are 0.80, 0.75, and 0.60, respectively; the information gain I of the normalized region corresponding to the change in its neighborhood distribution is 0.70.

[0055] 3. Consider all factors and select a site under on-site constraints. Let the revenue weights be α=0.25, β=0.20, χ=0.15, γ=0.15, and η=0.25, and the cost penalty coefficient be λ=0.10. Process B, C, and D using the same procedure as point A, resulting in Table 4. All revenue, sensitivity, and cost indicators in Table 4 have been normalized using fixed upper and lower bounds on the validation set.

[0056] Table 4. Normalized benefits, costs, and retest value of candidate retest points

[0057] Taking candidate point A as an example, its retest value is 0.25×0.80+0.20×0.75+0.15×0.60+0.15×0.70+0.25×0.85-0.10×0.35=0.7225, rounded to three decimal places, which is 0.723. The values ​​are ranked as A, B, D, and C. Although candidate point D has a higher expected uncertainty reduction, its retest cost is higher, therefore its overall value is lower than B. If the maximum number of points is 2, and A and B satisfy the minimum spatial distance and budget constraints, then output A and B; otherwise, output the value if the distance between them is less than d. min If so, retain A, which has higher value, and then select from D and C to satisfy the constraints.

[0058] This example illustrates that the recommended results are not simply selected from the locations with the strongest anomalies or the most uncertainties, but rather from locations that are "expected to reduce uncertainty after retesting, are important to the road, and have acceptable on-site costs."

[0059] 4. Actual retesting and result updates Assume that points A and B are remeasured on-site according to the recommended results. New data is first registered with the initial measurement data by mileage, lane, and lateral position, then undergoes the same preprocessing and feature extraction process as in S102, and is then merged with the original observation data. After re-executing S103 and S104, the posterior probability of point A's state is updated from (0.18, 0.43, 0.34, 0.05) to (0.07, 0.78, 0.10, 0.05), and the 90% depth range narrows from 0.12–0.22 m to 0.15–0.19 m; the posterior probability of point B's state is updated from (0.10, 0.58, 0.26, 0.06) to (0.06, 0.72, 0.15, 0.07), and the 90% depth range narrows from 0.18–0.29 m to 0.20–0.24 m. The results indicate that this round of re-measurement has led to a more concentrated interlayer voiding state and a reduction in the range of abnormal depths.

[0060] The updated posterior results are used in S105 to S108 to delete points that have been fully confirmed and to generate candidate points for the next round from adjacent locations that still have high posterior uncertainty. Only after the remeasurement or core drilling results have been confirmed are they added to the calibration data to update the state prior probability, observation error covariance, or surrogate model parameters; a single unconfirmed remeasurement result does not directly change the surrogate model. This completes the closed loop of initial measurement, recommendation, actual remeasurement, posterior update, and further recommendation.

[0061] Example 3: Extended Suggestions and Closed-Loop Updates The output of the retested points is the complete result of the main process of this invention. Local densification of survey lines and core drilling verification are optional extensions and are not necessary conditions for completing the point recommendations.

[0062] When multiple recommended resurvey points are continuously distributed along the same mileage interval or across adjacent survey lines, and the posterior results of the adjacent points are consistent, a suggestion for local densification of survey lines can be generated along the abnormal long axis or perpendicular to the existing survey line. The suggestion includes the start and end mileage, lateral range, survey line spacing, and suggested antenna frequency.

[0063] After completing the actual re-measurement, the new data is registered with the initial measurement data by mileage, lane, and lateral position. Preprocessing and feature extraction are then performed using the same process as in S102. S103 to S108 are then re-executed based on the updated observation dataset. If the actual re-measurement still satisfies both high posterior uncertainty and high road structure sensitivity, core drilling verification recommendations can be output. These recommendations should at least specify the location, target depth range, and triggering reason.

[0064] Adding confirmed retest or core drilling results to the calibration data can update the prior state probability πs, error covariance Σo, surrogate model parameters, candidate point thresholds, or value weights. To avoid validation bias caused by using future information, model updates only use the actual results obtained and validated in the current round.

[0065] Example 4: Parameter Calibration and Effect Verification Historical road segments with retest or core drilling verification results are divided into training, validation, and test sets at the road segment level. Adjacent detection units of the same road segment must not be distributed across different datasets to avoid spatial leakage. The training set is used to build the surrogate model and candidate state parameter domains; the validation set is used to fix the threshold, weights, budget, and minimum spatial spacing; the test set is only used for final comparison. The calibration and effect verification process for the threshold, weights, and retest budget is as follows: Figure 4 As shown.

[0066] Under the same set of candidate retest points and the same retest budget, point selection was carried out using random selection, selection prioritizing abnormal amplitudes, selection prioritizing current uncertainties, and the method of this invention, respectively. For the point selection results obtained from actual execution or from the playback of reserved retest data, the following indicators were calculated: ; ;

[0067] in, This represents the selected set of remeasured points. This indicates the number of points within the set. Indicates the index of the selected retest point; and They represent the points respectively. The posterior entropy decreases and the state competition decreases. A value of 1 is used if a retest or core drilling confirms the presence of an anomaly requiring attention; otherwise, a value of 0 is used. Indicates the information gain of the region. This indicates the actual cost of retesting; and These represent the decrease in total posterior entropy and the decrease in total state competitiveness at the selected points, respectively. Indicates the effective anomaly hit rate. The regional information gain represents the unit actual cost. All methods use the same data partitioning, candidate points, and budget, repeated multiple times, and the mean and confidence interval are reported. The corresponding threshold and weights are only applied when the method of this invention consistently outperforms the control method on predetermined key metrics.

[0068] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0069] While the specific embodiments of the present invention have been described above, they are not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for recommending highway GPR resurvey points based on posterior uncertainty, characterized in that, Includes the following steps: S101, acquire the initial measurement data of the highway GPR and its collected metadata, divide the detection units according to road mileage and lane, and obtain the initial measurement observation data of each detection unit; S102, preprocess and extract features from the initial observation data to obtain the observation feature vector of each detection unit; S103, establish a candidate state set including normal state and at least one hidden abnormal state of the road; calculate the posterior probability and depth posterior distribution of each detection unit based on the observed feature vector, physical response surrogate model and state prior probability; the specific process is as follows: Parameter samples are generated within the parameter domain of each candidate state; predicted features of each parameter sample are obtained through a physical response surrogate model; sample likelihood is calculated based on the difference between predicted features and observed features; the sample likelihoods within the same candidate state are weighted and summed, and combined with state prior probability normalization to obtain state posterior probability; deep posterior distribution is obtained based on the posterior weights of parameter samples corresponding to abnormal states. The physical response proxy model is a fast approximation of electromagnetic forward modeling, used to convert certain road structures and anomaly parameters into GPR features expected to appear under the same equipment and processing procedures. S104, based on the state posterior probability and depth posterior distribution, calculate the current posterior uncertainty of each detection unit, including: normalized posterior entropy representing the overall confusion level of multiple candidate states. State competition degree, which is difficult to distinguish between the two candidate states with the highest posterior probability. And depth interval uncertainty used to represent the width of the confidence interval for anomaly depth. ; The normalized posterior entropy The posterior probabilities of each candidate state are measured by entropy and normalized according to the maximum entropy corresponding to the number of candidate states. The closer the posterior probabilities of each candidate state are, the larger the normalized posterior entropy is, indicating that the overall confusion of multiple candidate states is higher. The state competition The posterior probabilities of each candidate state are sorted from largest to smallest and determined based on the difference between the largest and second largest posterior probabilities; the smaller the difference, the greater the state competition, indicating that the two most likely candidate states are more difficult to distinguish. The uncertainty in the depth range The width of the confidence interval is determined based on the posterior depth distribution and normalized by combining it with a reference depth scale. The wider the confidence interval, the greater the uncertainty of the depth interval, indicating that the possible range of abnormal depth values ​​is more dispersed; S105, Generate a set of candidate retest points based on the current posterior uncertainty; S106, For each candidate point in the candidate retest point set, generate possible retest observations and update the corresponding posterior results, and calculate the expected uncertainty reduction and regional information gain of the candidate point; S107, Taking into account the expected decrease in uncertainty, regional information gain, road structure sensitivity and retesting cost, calculate the retesting value of each candidate point; S108, under at least one constraint among the number of retests, retest budget, and minimum spatial spacing of candidate points, select and output recommended retest points from the set of candidate retest points based on the retest value.

2. The method for recommending highway GPR re-measurement points based on posterior uncertainty as described in claim 1, characterized in that: The preprocessing in S102 includes at least one of time-zero correction, DC removal, background removal, bandpass filtering, gain compensation, and inter-channel normalization; the observation feature vector includes at least one of amplitude features, phase features, spectral features, layer continuity features, attenuation features, and anomalous geometric features.

3. The method for recommending highway GPR re-measurement points based on posterior uncertainty as described in claim 1, characterized in that: The candidate state set in S103 also includes unmodeled abnormal states; the hidden abnormal states of the road include voiding, interlayer segregation, water content anomaly, structural layer thickness anomaly, and loose roadbed.

4. The method for recommending highway GPR re-measurement points based on posterior uncertainty as described in claim 1, characterized in that: The specific process of S105 includes: Initial candidate points are generated from abnormal response locations, high posterior entropy locations, high state competition locations, high depth interval uncertainty locations, spatial interpolation locations between adjacent survey lines, structural layer boundary locations, and road structure sensitive locations, respectively. Initial candidate points with a distance less than a preset deduplication distance are merged to obtain the candidate re-survey point set. The high posterior entropy position, high state competition position, and high depth interval uncertainty position are all positions that exceed the corresponding threshold.

5. The method for recommending highway GPR re-measurement points based on posterior uncertainty as described in claim 1, characterized in that: The specific process of S106 includes: A posterior prediction distribution is formed based on the current posterior result of the candidate point and the observation noise model; multiple possible re-measurement observations are generated from the posterior prediction distribution; the state posterior probability and depth posterior distribution are recalculated for each possible re-measurement observation; the expected uncertainty reduction is obtained by probability weighting based on the difference in uncertainty before and after recalculation; and the regional information gain is obtained based on the expected change in the posterior distribution in the neighborhood of the candidate point.

6. The method for recommending highway GPR re-measurement points based on posterior uncertainty as described in claim 1, characterized in that: The specific process of S107 includes: normalizing the expected posterior entropy decrease, expected state competition decrease, expected depth interval uncertainty decrease, regional information gain, road structure sensitivity, and retest cost to a unified dimension; weighting the first five items and deducting the retest cost penalty to obtain the retest value.

7. The method for recommending highway GPR re-measurement points based on posterior uncertainty as described in claim 1, characterized in that: In step S108, the output recommended retest points include at least road mileage, lane, lateral position, and retest priority, and simultaneously output the retest value, main reasons for recommendation, and suggested retest parameters; when selecting points, the total cost of the selected points is limited to not exceeding the retest budget, and the distance between any two selected points is limited to not less than the preset minimum spatial spacing.

8. The method for recommending highway GPR re-measurement points based on posterior uncertainty as described in claim 1, characterized in that: It also includes the following processes: The actual retest data obtained from the recommended retest points are registered with the corresponding initial test data. The actual retest data is processed according to the preprocessing and feature extraction process adopted in S102. The processing results are added to the observation dataset, and S103 to S108 are re-executed based on the updated observation dataset. After the actual retest results are verified, at least one of the following is updated: state prior probability, physical response surrogate model parameters, observation noise parameters, and retest value weight.

Images