Vehicle detection data analysis method and system based on mathematical modeling

Abstract

The application relates to the technical field of vehicle detection analysis, and discloses a vehicle detection data analysis method and system based on mathematical modeling, which comprises the following steps: comparing the numerical consistency of each mode data of a same space-time point in an aligned multi-source data tensor set, and inversely deducing the failure mode of each sensor according to a preset sensor failure feature mapping rule based on the inconsistent amplitude and direction symbol; performing consistency comparison on a logical credibility vector, a difference attribution result and a cross-domain deviation point identification set; and generating a final vehicle detection analysis result based on a high comprehensive confidence label, a low confidence label, a corrected failure feature mapping rule and a corrected deviation allowance threshold. The application uses the inconsistent amplitude and direction symbol of sensor observation to construct an analytical redundancy residual vector, and inversely deduces the failure mode according to the preset sensor failure feature mapping rule, so that the technical problem that the existing fusion method cannot distinguish the sensor failure type is solved.

Description

Technical Field

[0001] This invention relates to the field of vehicle inspection and analysis technology, and in particular to a method and system for vehicle inspection data analysis based on mathematical modeling. Background Technology

[0002] With the rapid development of autonomous driving and intelligent transportation systems, vehicle detection data analysis technology has become a core component of environmental perception. In complex dynamic road environments, integrating data from multiple sensors, such as cameras, lidar, and millimeter-wave radar, to construct a unified environmental model is the mainstream technological paradigm for overcoming the limitations of single-sensor perception and achieving high-precision environmental perception. Using mathematical models to perform spatial positioning, motion analysis, and trajectory prediction on vehicle detection data forms the foundation for intelligent driving decision-making.

[0003] Existing vehicle detection data analysis methods can be mainly categorized as follows: The first category is weighted fusion methods based on probability distributions. For example, these methods process data from active non-contact ranging sensors and visual sensors using probability distributions, assess the confidence level of the visual data, and output the fused detection result through a weighted average. These methods rely on the sensor independence assumption, using statistical methods to combine observations from different modalities into a single estimate. The second category is multi-sensor fusion methods based on evidence theory. For example, these methods combine deep learning detection models with improved DS evidence theory, calculating compatibility coefficients between pieces of evidence to redistribute evidence conflicts, thus handling potential evidence conflicts after single-frame fusion. The third category is digital twin verification methods based on physical models. These methods verify the model output by building physical testing environments and virtual modeling environments, using interactive verification between the virtual and physical environments, and online testing of the actual vehicle under test.

[0004] However, despite the increasing complexity of existing integration strategies, they generally suffer from the following core flaws: (1) Existing methods logically follow the "information redundancy assumption," which assumes that the more redundant sensors there are, the more reliable the fusion result will be. When sensors conflict, the core processing logic is to eliminate the conflict through weighted averaging, probability product, or evidence allocation. Although such "information averaging" strategies can output a single value, they discard the key information contained in the "directional signs of differences" between multiple sensors. For example, cameras usually produce a systematic offset along a specific direction under strong light, while millimeter-wave radar exhibits monotonic expansion of radial ranging in rainy or snowy weather. The observation deviations caused by different physical failure modes have geometrically distinguishable vector characteristics. However, existing methods sum or smooth these differences indiscriminately based on their directional signs and magnitudes, making it impossible to answer the key question of "which sensor failed for what physical reason." Instead, subsequent analysis can only be carried out using fused data that may be distorted due to noise contamination.

[0005] (2) Mathematical models based on physical constraints (such as Kalman filtering and kinematic prediction models) are essentially numerical approximations in discrete time and space, while the physical motion of a vehicle occurs in a continuous spatiotemporal environment. When the output of the mathematical model deviates from the sensor observation, existing methods reduce the error by updating the noise covariance matrix of the filter or periodically retraining the model. Such approaches can only statistically compensate for the deviation, but cannot determine from the root cause whether the deviation stems from the error in the digital model's representation of physical laws or from the sensor's own measurement error. More importantly, existing technologies only utilize model prediction deviations for model calibration and have never used them as a source of judgment for consistency verification of historical data independently of the sensor itself. (3) The data processing architecture of existing vehicle detection systems usually follows the path of "receiving first, then fusing, and then diagnosing". Sensor diagnosis (such as residual sequence analysis), model verification (such as twin model consistency comparison), and fusion decision-making operate relatively independently. When low confidence levels or data conflicts occur, the system can only switch between binary values ​​using preset rules (such as "accept if confidence level is greater than 0.7"), or output the diagnostic result as an alarm signal instead of feeding it back to the core logic of the fusion decision. More importantly, there is no mechanism for mutual verification and interlocking correction among the three sources of judgment: sensor fault diagnosis, confidence assessment of mathematical model representation, and fusion decision. A judgment deviation in any module may cause the system to fall into a state of decreased confidence without self-checking capabilities. In existing technologies, this problem has not been effectively solved. Summary of the Invention

[0006] In view of the above, the main objective of this invention is to propose a vehicle detection data analysis method and system based on mathematical modeling to solve the aforementioned technical problems.

[0007] This invention proposes a vehicle detection data analysis method based on mathematical modeling, the method comprising the following steps: S1. Acquire raw data from multiple sources and perform spatiotemporal alignment to obtain an aligned multi-source data tensor set; S2. Perform numerical consistency comparison on the modal data at the same spatiotemporal point in the aligned multi-source data tensor set. Based on the preset sensor failure feature mapping rules, infer the failure mode of each sensor from the inconsistent amplitude and direction signs, and generate a logical confidence vector. S3. Based on the logical credibility vector and the preset sensor behavior rule library, perform logical reasoning and attribution on the differences in sensor observations, and output the difference attribution results; S4. For each sensor, a local prediction model is constructed using the sensor's observation sequence within a historical time window through mathematical fitting to calculate the theoretical prediction value at the current moment; the deviation between the theoretical prediction value and the actual observation value of the sensor at the current moment is compared with a preset deviation threshold, and spatiotemporal data points with deviations exceeding the preset deviation threshold are marked as cross-domain deviation points to obtain a cross-domain deviation point identifier set. S5. Perform a consistency comparison on the logical confidence vector, the difference attribution result, and the cross-domain deviation point identifier set. If the consistency comparison points to the same value, output a high comprehensive confidence label. If the consistency comparison points to different values, output a low confidence label. Then, based on the type of inconsistency, correct the preset sensor failure feature mapping rule in step S2 and the preset deviation threshold in step S4 to generate the corrected failure feature mapping rule and the corrected deviation allowable threshold. S6. Based on high-confidence labels, low-confidence labels, corrected failure feature mapping rules, and corrected deviation allowable thresholds, the final vehicle detection and analysis results are generated.

[0008] This invention also proposes a vehicle detection data analysis system based on mathematical modeling, the system comprising: The data acquisition and alignment module is used for: Acquire raw data from multiple sensors and perform spatiotemporal alignment to obtain an aligned multi-source data tensor set; The sensor status diagnostic module is used for: Numerical consistency comparison is performed on the modal data at the same spatiotemporal point in the aligned multi-source data tensor set. Based on the preset sensor failure feature mapping rules, the failure mode of each sensor is inferred from the inconsistent amplitude and direction signs, and a logical confidence vector is generated. Based on the logical credibility vector and the preset sensor behavior rule library, logical reasoning is performed to attribute the differences in sensor observations, and the difference attribution results are output. The cross-domain deviation detection module is used for: For each sensor, a local prediction model is constructed using the sensor's observation sequence within a historical time window through mathematical fitting to calculate the theoretical prediction value at the current moment. The deviation between the theoretical prediction value and the actual observation value of the sensor at the current moment is compared with a preset deviation threshold, and spatiotemporal data points with deviations exceeding the preset deviation threshold are marked as cross-domain deviation points, thus obtaining a cross-domain deviation point identifier set. The consistency comparison and adaptive correction module is used for: The logical confidence vector, the difference attribution result, and the cross-domain deviation point identifier set are compared for consistency. If the consistency comparison points to the same value, a high comprehensive confidence label is output. If the consistency comparison points to different values, a low confidence label is output. The sensor failure feature mapping rule preset in step S2 and the preset deviation threshold in step S4 are modified according to the type of inconsistency to generate the modified failure feature mapping rule and the modified deviation allowable threshold. The fusion output module is used for: Based on high-confidence labels, low-confidence labels, corrected failure feature mapping rules, and corrected deviation allowable thresholds, the final vehicle detection and analysis results are generated.

[0009] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention constructs an analytical redundant residual vector by utilizing inconsistent amplitude and direction signs observed by sensors, and inversely infers the failure mode based on a preset sensor failure feature mapping rule. For the first time in the field of vehicle detection, it realizes a paradigm shift from "numerical trade-off" to "causal attribution", solving the technical problem that existing fusion methods cannot distinguish sensor failure types.

[0010] 2. This invention utilizes the historical observation sequences of each sensor and employs mathematical fitting methods (such as linear regression, polynomial fitting, or autoregressive models) to construct a local prediction model. Data points where the deviation between the predicted and actual observation values ​​exceeds a preset threshold are marked as cross-domain deviation points, and their temporal consistency is verified. This constructs a "temporal redundancy" judgment information source independent of multi-sensor spatial consistency verification. This method does not rely on any vehicle kinematics model or environmental model, avoiding interference from model representation errors on sensor state judgment, and solving the technical problem in existing technologies that cannot quantitatively assess the consistency of sensor temporal dimension measurements online.

[0011] 3. This invention constructs a three-source interlocking verification and closed-loop self-optimization mechanism by performing sensor-by-sensor and comparison-by-comparison of three independent judgment sources: logical confidence vector, difference attribution result, and cross-domain deviation point identifier set, and by modifying the failure feature mapping rules or deviation allowable thresholds differently according to the specific type of inconsistency. This solves the technical problem in existing systems where multiple judgment sources cannot mutually verify and collaboratively correct each other.

[0012] 4. This invention achieves a confidence-driven dual-path fusion strategy by re-executing sensor failure mode inversion and cross-domain deviation point detection using modified rules and thresholds when the overall confidence label is low, and then performing weighted fusion based on the updated results. This significantly improves the reliability of vehicle detection and analysis results in low-confidence scenarios.

[0013] 5. This invention solves the technical problem that existing fusion weights rely solely on statistical confidence and ignore sensor physical differences by combining real-time confidence with prior physical knowledge such as sensor inherent accuracy and noise level through a dual weight calculation method that normalizes the maximum value of the logical confidence vector, multiplies it with the sensor physical characteristic correction factor, and then sums and normalizes it.

[0014] 6. This invention uses the fault severity rating in the difference attribution results to label or remove parts with low confidence in the fusion detection results, and organizes the structured detection results according to time and spatial location for output, realizing a closed-loop information chain from perception to diagnosis to output, thereby improving the interpretability and practicality of the system.

[0015] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by means of embodiments of the invention. Attached Figure Description

[0016] Figure 1 This is a flowchart of the vehicle detection data analysis method based on mathematical modeling proposed in this invention; Figure 2 This is a diagram showing the overall architecture of the vehicle detection data analysis system based on mathematical modeling proposed in this invention. Detailed Implementation

[0017] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0018] These and other aspects of the embodiments of the present invention will become clear from the following description and accompanying drawings. In these descriptions and drawings, some specific embodiments of the present invention are specifically disclosed to illustrate some ways of implementing the principles of the embodiments of the present invention; however, it should be understood that the scope of the embodiments of the present invention is not limited thereto.

[0019] Please see Figure 1 This embodiment provides a vehicle detection data analysis method based on mathematical modeling, the method including the following steps: Step S1: Acquire raw data from multiple sources and perform spatiotemporal alignment to obtain an aligned multi-source data tensor set.

[0020] In step S1, the raw data from the multi-source sensors is acquired and spatiotemporally aligned to obtain an aligned multi-source data tensor set, specifically including the following steps: Raw data frames are collected from cameras, millimeter-wave radar, and lidar respectively to obtain a multi-source raw data stream containing image, point cloud, and distance and velocity information; Each frame of data in the multi-source raw data stream containing image, point cloud and distance and velocity information is timestamped, and linear interpolation alignment is performed with reference to a preset reference time axis to obtain time-synchronized multi-source frame data; The coordinates of the lidar point cloud and the coordinates of the millimeter-wave radar detection points in the time-synchronized multi-source frame data are transformed to the camera image coordinate system through the extrinsic parameter matrix to obtain spatially aligned modal data. After spatial alignment, the modal data are tensorized and recombined according to the same spatiotemporal grid to generate a multi-source data tensor containing multiple dimensions of position, velocity, and reflection intensity. The multi-source data tensor containing multiple dimensions of position, velocity, and reflection intensity is then used as the aligned multi-source data tensor set.

[0021] In this embodiment of the invention, during actual data acquisition, the sampling frequencies and time bases of the camera, millimeter-wave radar, and lidar are different. Therefore, the original data frames need to be timestamped first, and then linear interpolation is used to align the data from different sensors to the same time axis. Spatial alignment relies on an extrinsic parameter matrix to transform the lidar point cloud and radar detection points to the camera image coordinate system. After spatiotemporal alignment, the multimodal data is tensor-based and recombined according to a fixed-size spatiotemporal grid. Each grid cell corresponds to a spatial location and time, containing multidimensional features such as image texture, point cloud coordinates, distance, and velocity. This process itself is a discretized mathematical model of the sensor observation process: time interpolation and spatial coordinate transformation are explicit mathematical mappings, and the tensor structure provides a unified data form for the subsequent construction of redundant equations.

[0022] Step S2: Perform numerical consistency comparison on the modal data at the same spatiotemporal point in the aligned multi-source data tensor set. Based on the preset sensor failure feature mapping rules, infer the failure mode of each sensor from the inconsistent amplitude and direction signs, and generate a logical confidence vector.

[0023] In step S2, numerical consistency comparison is performed on the modal data at the same spatiotemporal point in the aligned multi-source data tensor set. Based on the preset sensor failure feature mapping rules, the failure mode of each sensor is inferred from the inconsistent amplitude and direction signs, and a logical confidence vector is generated. Specifically, the steps are as follows: The pre-aligned multi-source data tensor sets extract the observations of each sensor at the same spatiotemporal point, and based on the differences in the physical measurement principles of the sensors, the observations are grouped to construct redundant sensor equations, resulting in multiple sets of redundant observation equations. Substitute each set of equations in the multiple sets of redundant observation equations into the corresponding sensor observation values ​​to solve the problem, calculate the absolute value of the residual between different equations in the same set, and arrange all the absolute values ​​of the residual in the order of sensor combination to obtain the analytical redundant residual vector. Traverse all non-zero elements in the parsed redundant residual vector, and match the direction sign and magnitude of each residual vector with the standard failure mode features in the rule library according to the preset sensor failure feature mapping rule library, and generate the failure mode identifier of each sensor at the current time and space point in turn. Based on the failure mode identifier of each sensor at the current spatiotemporal point, a corresponding initial logical confidence value is marked for each sensor to obtain the initial logical confidence value vector of each sensor; wherein, if there is a failure among the sensors, the initial confidence value corresponding to the failed sensor is set to be lower than the preset fault-free benchmark value; if the sensor does not fail, the initial confidence value corresponding to the non-failed sensor is set to be higher than the preset fault-free benchmark value. Each element in the initial logical confidence value vector of each sensor is normalized and weighted according to the differences in the physical characteristics of the sensors, so that the logical confidence values ​​output by different sensors under the same failure degree are comparable, thus obtaining the logical confidence vector.

[0024] To more clearly illustrate the specific implementation of "constructing a redundant sensor equation set," a typical example is given here. Assume that in a aligned multi-source data tensor set, a camera, millimeter-wave radar, and lidar jointly observe a target vehicle ahead at the same spatiotemporal point. First, redundant observation relationships are established based on the physical measurement principles of the sensors. Taking geometric projection constraints as an example, the polar coordinates (radial distance r, azimuth angle α) of the target measured by the lidar and millimeter-wave radar in the vehicle's coordinate system should be mapped to the pixel coordinates (u, v) of the camera image after coordinate transformation and the camera projection model. Let P be the intrinsic parameter projection matrix of the camera, and T be the rigid body transformation matrix from the radar or lidar coordinate system to the camera coordinate system, then the relationship [u, v, 1] should hold. T =P·T·[r·cosα, r·sinα, 0, 1] T It is valid within the preset pixel error tolerance range.

[0025] Meanwhile, for millimeter-wave radar, its ranging value r radar The distance d calculated by the camera through image ranging camera The two should also satisfy geometric consistency, and the absolute value of their difference should not exceed the preset range residual tolerance threshold. Secondly, consider motion consistency constraints: the target radial velocity v directly measured by millimeter-wave radar. radar The radial velocity v is estimated by combining the displacement of target pixels in consecutive frames with the motion of the vehicle from the camera.camera Between the two, the absolute value of the difference should not exceed the preset speed residual tolerance threshold.

[0026] For lidar, the target's velocity relative to the vehicle in its point cloud can also be obtained through continuous frame point cloud registration, and can be further combined with the velocity observations from radar or cameras to form similar redundant constraints. The aforementioned distance residual tolerance thresholds and velocity residual tolerance thresholds can be preset based on factors such as the nominal accuracy and measurement noise level of each sensor, for example, taking 2-3 times the standard deviation of the sensor's nominal accuracy, similar to the deviation allowable threshold. Combining the multiple constraints derived from the above different physical principles forms an overdetermined system of equations containing multiple unknowns (such as the target's position and velocity) but with a greater number of independent constraints than unknowns; this is a set of redundant observation equations. In practical applications, sensors participating in the combination can be dynamically selected based on sensor availability. For example, when all three sensors are effective, a redundant group containing three or more independent constraints—geometric projection constraints, radial distance consistency constraints, and radial velocity consistency constraints—can be constructed; when a sensor is missing or fails, the remaining sensors are used to construct a dimensionality-reduced redundant group.

[0027] By substituting actual observations into each set of redundant constraints, calculating the residuals between constraints, and arranging the absolute values ​​of all residuals according to the sensor combination order, the analytical redundant residual vector can be obtained. It should be noted that the above example only uses common sensor combinations and typical constraints as examples. Those skilled in the art can flexibly design different forms of redundant equations based on actual sensor configurations and vehicle detection scenarios. For example, utilizing the consistency between the point cloud depth of the lidar and the parallax depth of the camera, or utilizing the correlation between the radar's reflective area and the camera's target size, etc., all fall within the scope of "constructing a set of redundant sensor equations" described in this invention.

[0028] The pre-defined sensor failure feature mapping rule base includes the construction of the sensor failure feature mapping rule base; specifically, the construction of the sensor failure feature mapping rule base includes the following steps: For camera sensors, deviation data are collected under three failure modes: strong light glare, lens damage, and motion blur. The directional sign features of the deviations under these three failure modes are extracted to form a subset of camera failure feature maps. The directional sign features of the deviations under the three failure modes include: strong light glare produces a systematic positive offset along the image row direction; lens damage produces a radial divergence vector from the image center to the edge; and motion blur produces a trailing offset vector along the tangent direction of the target motion trajectory. For millimeter-wave radar sensors, ranging deviation data under two failure modes—rain and snow attenuation and metal multipath reflection—are collected. The directional sign features of the deviations under these two failure modes are extracted to form a subset of millimeter-wave radar failure feature maps. Specifically, the extracted directional sign features of the deviations under these two failure modes include: rain and snow attenuation causing a monotonically positive expansion of the ranging value radially, and metal multipath reflection causing a periodic alternating positive and negative shift of the ranging value along the azimuth direction. For lidar sensors, point cloud deviation data are collected under two failure modes: long-range sparsity and glass mirror reflection. The directional sign features of the deviation under these two failure modes are extracted to form a lidar failure feature mapping subset. The extracted directional sign features of the deviation under the two failure modes include: long-range sparsity causes the centroid of the point cloud to drift radially outward with an amplitude proportional to the square of the distance, and glass mirror reflection causes the point cloud to produce a completely opposite virtual mirror offset along the normal direction. The camera failure feature mapping subset, the millimeter-wave radar failure feature mapping subset, and the lidar failure feature mapping subset are merged into a multimodal failure feature mapping rule library. Each mapping rule in the multimodal failure feature mapping rule library is associated with a corresponding sensor failure degree quantification function to obtain the associated failure feature mapping rule library. The associated failure feature mapping rule library is then used as the preset sensor failure feature mapping rule.

[0029] In this embodiment of the invention, when multiple sensors observe the same target at the same spatiotemporal point, the observed values ​​of different modes necessarily satisfy the equations determined by the principles of physical measurement, such as the geometric constraints between the camera projection equation and the radar ranging equation. Combining these equations forms a redundant observation equation set. Substituting the actual observed values, the residuals between different equations within the same set are calculated, and arranged in sensor order to obtain an analytical redundant residual vector. The direction sign of this vector has a one-to-one physical intuition with different failure modes: strong glare from a camera usually causes the residual to shift positively along the image line direction, while rain and snow attenuation in millimeter-wave radar causes the radial ranging residual to expand unidirectionally in a positive direction.

[0030] The pre-defined sensor failure feature mapping rule base is constructed based on these physical laws. The base contains standard direction sign features and failure severity quantification functions corresponding to each failure mode. During matching, the rule base is searched based on the direction sign and amplitude magnitude of the residuals to determine the failure mode of each sensor and calculate the initial logical confidence value. Different sensors exhibit significant differences in their physical characteristics (such as dimensions and noise levels), therefore, normalization and weighting corrections are required according to their respective physical characteristics to ensure the comparability of the final output logical confidence vector across different sensors. This series of operations essentially utilizes analytical redundancy relationships to mathematically model the sensor system, transforming prior physical knowledge into computable failure inference rules.

[0031] Step S3: Based on the logical credibility vector and the preset sensor behavior rule library, perform logical reasoning attribution on the differences in sensor observations and output the difference attribution results.

[0032] In step S3, based on the logical confidence vector and the preset sensor behavior rule base, logical reasoning is performed to attribute the differences in sensor observations, and the difference attribution results are output. Specifically, this includes the following steps: Based on the logical confidence vector, the observation values ​​of all sensors at the same spatiotemporal point in the current frame are extracted from the aligned multi-source data tensor set to obtain the original observation data set of each sensor. Each observation data point in the raw observation data set of each sensor is compared with the corresponding theoretical prediction value point by point to calculate the observation difference vector of each sensor at each observation point, thus obtaining a set of sensor observation difference vectors; wherein, the observation difference vector includes: difference amplitude, difference direction sign and time location information of the difference occurrence; Based on the logical confidence vector, each observation difference vector in the sensor observation difference vector set is weighted by confidence. The observation differences corresponding to low confidence sensors are marked as unverified states, and the observation differences corresponding to high confidence sensors are directly used as valid differences, so as to obtain the set of observation differences after confidence screening. Each observation difference vector in the set of observation differences filtered by confidence is input into the preset sensor behavior rule base for pattern matching. The similarity between the difference amplitude, difference direction sign and the time and location information of the difference occurrence of the observation difference vector and the condition part of each rule entry in the rule base is calculated, and the rule entry with the highest similarity and exceeding the preset matching threshold is selected to obtain the matching rule identifier and associated fault type corresponding to the observation difference vector. Based on the matching rule identifier and associated fault type corresponding to the observed difference vector, the attribution conclusion corresponding to the observed difference is determined; wherein, the attribution conclusion includes: fault source sensor identifier, fault type classification, and fault severity rating; The attribution conclusions corresponding to all observed difference vectors are summarized according to the sensor dimension and the time dimension to generate a structured set of difference attribution results, and the structured set of difference attribution results is used as the difference attribution result.

[0033] The preset sensor behavior rule base includes the construction of the sensor behavior rule base; wherein the construction of the sensor behavior rule base specifically includes the following steps: For typical sensor observation difference types in vehicle detection, conditional attribute dimensions are defined in rule entries to obtain a conditional attribute definition set; wherein, the conditional attribute dimensions include: the numerical range of the difference amplitude, the positive or negative polarity of the difference direction sign, the duration of the difference, and the distribution pattern of the difference in the spatiotemporal domain. For each type of sensor observation difference, a corresponding conclusion section is set to obtain a conclusion definition set; wherein, the conclusion section includes: the sensor fault type code corresponding to the difference, the fault risk level number, and the recommended preprocessing operation identifier; Each condition attribute in the condition attribute definition set and the corresponding conclusion in the conclusion definition set are associated as a set of rule entries according to the IF-THEN logic. A matching priority weight is preset for each set of rule entries to form a set of rule entries with matching weight. All the rule entries with matching weight are merged to form a merged sensor behavior rule library. The merged sensor behavior rule library is used as the preset sensor behavior rule library.

[0034] In this embodiment of the invention, after obtaining the logical confidence vector, it is first used to filter the original observation data: observations from low-confidence sensors are temporarily marked as "to be verified" and are not directly used for attribution reasoning, thus avoiding interference from low-quality data. For each observation point, its observation difference vector is calculated—containing difference amplitude, direction sign, and time location information. These difference vectors are input into a preset sensor behavior rule base for matching. This rule base adopts an IF-THEN structure, where the condition part defines the difference amplitude range, direction sign polarity, duration length, and spatiotemporal distribution pattern, and the conclusion part corresponds to the fault type code, risk level, and preprocessing operation identifier. During matching, similarity is calculated, and the rule entry with the highest similarity exceeding the threshold is selected. The matched rule will provide the fault source sensor, fault type classification, and severity rating. Finally, the attribution conclusions of all observation points are summarized according to the sensor dimension and time dimension to form a structured difference attribution result. The mathematical modeling here is reflected in: discretizing the continuous observation difference space into rule conditions and using logical reasoning instead of statistical classification, making the attribution process deterministic and interpretable.

[0035] Step S4: For each sensor, a local prediction model is constructed using the sensor's observation sequence within the historical time window through mathematical fitting to calculate the theoretical prediction value at the current moment; the deviation between the theoretical prediction value and the actual observation value of the sensor at the current moment is compared with a preset deviation threshold, and spatiotemporal data points with deviations exceeding the preset deviation threshold are marked as cross-domain deviation points to obtain a cross-domain deviation point identifier set.

[0036] In step S4, for each sensor, a local prediction model is constructed using the sensor's observation sequence within a historical time window through mathematical fitting to calculate the theoretical prediction value at the current moment. The deviation between the theoretical prediction value and the actual sensor observation value at the current moment is compared with a preset deviation threshold, and spatiotemporal data points with deviations exceeding the preset deviation threshold are marked as cross-domain deviation points, resulting in a cross-domain deviation point identifier set. Specifically, this includes the following steps: For each sensor, the sequence of observations of that sensor at multiple consecutive historical moments is extracted from the aligned multi-source data tensor set to form a historical observation window; A mathematical fitting method is used to locally model the observation sequence within the historical observation window to obtain the theoretical prediction value at the current moment; wherein, the mathematical fitting method includes: linear regression or quadratic polynomial fitting or locally weighted regression or autoregressive model; Calculate the absolute value of the deviation between the theoretical prediction value and the actual observation value at the current moment, and compare the absolute value of the deviation with a preset allowable deviation threshold. If the absolute value of the deviation exceeds the preset allowable deviation threshold, mark the data point as a cross-domain deviation point, and record the sensor type, spatiotemporal coordinates and deviation direction sign corresponding to the data point. Then, merge all the data points marked as cross-domain deviation points according to sensor type and spatiotemporal coordinates to form a preliminary cross-domain deviation point identification set. For each identified deviation point in the preliminary set of cross-domain deviation points, a time sequence consistency check is performed. If the same sensor continuously produces cross-domain deviation points at the same spatial location in multiple consecutive time frames, the deviation point is confirmed as a valid cross-domain deviation point. Otherwise, the deviation point is marked as instantaneous noise and filtered out to form a set of cross-domain deviation point identifiers.

[0037] In this embodiment of the invention, to obtain an alternative source of information for determining spatial consistency independent of multi-sensor verification, the invention performs a time-dimensional measurement consistency analysis for each sensor. Specifically, for each sensor in the aligned multi-source data tensor set, using the current time t as a reference, observations from several consecutive historical times (e.g., t-3, t-2, t-1) are extracted to form a historical observation window. The observations within this window reflect the measurement change patterns of the same spatial point or target over a short period. Then, using the sequence of observations within this historical window, a local prediction model is constructed using mathematical fitting methods to calculate the theoretical predicted value for the current time t.

[0038] As an example, the mathematical fitting method can employ linear regression, assuming that the observed values ​​change linearly with time, fitting the parameters of a linear function using the least squares method, and then extrapolating to the current time. Alternatively, it can use quadratic polynomial fitting to adapt to uniformly accelerated motion scenarios, or use locally weighted regression to smooth nonlinear changes, or even directly use an autoregressive model to recursively predict based on the correlation of the sequences. It is important to emphasize that the calculation of the above theoretical predictions relies entirely on the sensor's own historical data, without incorporating data from any vehicle kinematics model, environmental model, or other sensors. Therefore, this method is unaffected by model representation errors and possesses good versatility and independence.

[0039] After obtaining the theoretical prediction value, it is subtracted from the actual observation value of the sensor at the current moment, and the absolute value is taken to obtain the prediction deviation. Then, the deviation is compared with the preset deviation allowable threshold. If the deviation exceeds the threshold, the spatiotemporal data point is marked as a cross-domain deviation point, and the sensor type, spatiotemporal coordinates, and direction sign of the deviation are recorded at the same time (i.e., whether the actual observation value is larger or smaller than the theoretical prediction value).

[0040] To avoid misjudgments caused by transient noise or occasional interference, preferably, a temporal consistency check is further performed on multiple consecutive time frames: only when multiple consecutive frames (e.g., three consecutive frames) of the same sensor at the same spatial location are all identified as cross-domain deviation points are they confirmed as valid cross-domain deviation points; otherwise, they are filtered out as transient noise. All valid cross-domain deviation points are then merged according to sensor type and spatiotemporal location to form a cross-domain deviation point identifier set. This identifier set reflects the measurement consistency of each sensor in the time dimension. If a sensor's observation value undergoes a significant jump in a short period that does not conform to its historical variation pattern, it indicates that the sensor's measurement may have failed or been subject to strong interference. This judgment, along with the logical confidence vector obtained using multi-sensor spatial redundancy and the difference attribution result obtained through logical reasoning in step S3, forms three independent and complementary information sources, laying a solid data foundation for subsequent consistency comparison and adaptive correction.

[0041] Step S5: Perform a consistency comparison on the logical confidence vector, the difference attribution result, and the cross-domain deviation point identifier set. If the consistency comparison points to the same value, output a high comprehensive confidence label; if the consistency comparison points to different values, output a low confidence label. Then, based on the type of inconsistency, correct the preset sensor failure feature mapping rule in step S2 and the preset deviation threshold in step S4 to generate the corrected failure feature mapping rule and the corrected deviation allowable threshold.

[0042] In step S5, the logical confidence vector, the difference attribution result, and the cross-domain deviation point identifier set are compared for consistency. If the consistency comparison points to the same value, a high overall confidence label is output; if the consistency comparison points to different values, a low confidence label is output. Based on the type of inconsistency, the preset sensor failure feature mapping rule in step S2 and the preset deviation threshold in step S4 are corrected to generate the corrected failure feature mapping rule and the corrected deviation allowable threshold. Specifically, the steps include the following: The logical confidence vector and the difference attribution results are compared sensor by sensor to determine whether the confidence level of the same sensor in the logical confidence vector and the fault type in the difference attribution results support each other, so as to obtain the first comparison result. The logical confidence vector is compared with the cross-domain deviation point identifier set sensor by sensor to determine whether the number of cross-domain deviation points corresponding to sensors whose logical confidence is lower than the preset confidence threshold exceeds the preset proportion threshold of the total number of deviation points in the cross-domain deviation point identifier set, so as to obtain the second comparison result. The difference attribution results are compared with the identified deviation points in the cross-domain deviation point identification set on a sensor-by-sensor basis to determine whether the sensor marked as fault in the difference attribution results is consistent with the source sensor of the identified deviation point in the cross-domain deviation point identification set, so as to obtain the third comparison result. If the first comparison result, the second comparison result, and the third comparison result all point to the same direction, then the overall consistency is determined to be consistent, a high comprehensive confidence label is output, and the current sensor failure feature mapping rule and deviation allowable threshold are used as the corrected failure feature mapping rule and the corrected deviation allowable threshold. If there is inconsistency among the first, second, and third comparison results, the overall comparison is determined to be inconsistent, and the object to be corrected is determined according to the specific type of inconsistency. Specifically, determining the object to be corrected according to the specific type of inconsistency includes: if the first comparison result is inconsistent, correcting the preset sensor failure feature mapping rule in step S2; if the second comparison result is inconsistent, simultaneously correcting the preset sensor failure feature mapping rule in step S2 and the deviation allowable threshold in step S4; if the third comparison result is inconsistent, correcting the deviation allowable threshold in step S4. Based on the identified objects requiring correction, the preset sensor failure feature mapping rules and deviation allowable thresholds are adjusted to generate corrected failure feature mapping rules and corrected deviation allowable thresholds. The adjustment of the preset sensor failure feature mapping rules and deviation allowable thresholds includes: adjusting the mapping relationship between the residual direction sign and the failure mode for the failure feature mapping rules; and increasing or decreasing the threshold value for the deviation allowable thresholds.

[0043] In this embodiment of the invention, the logical confidence vector, the difference attribution result, and the cross-domain deviation point identifier set are compared pairwise on a sensor-by-sensor basis. The first comparison checks whether the confidence level and the fault type support each other; the second comparison checks whether sensors with low confidence levels account for a major proportion of cross-domain deviation points; and the third comparison checks whether the sensors marked with faults are consistent with the source of the deviation point. If all three groups are consistent, a high comprehensive confidence label is output, and the rules and thresholds remain unchanged. If inconsistencies occur, a low confidence label is output, and the correction object is determined according to the specific type of inconsistency: when the first group is inconsistent, the failure feature mapping rule in step S2 is corrected (e.g., adjusting the correspondence between direction symbols and failure modes); when the second group is inconsistent, both the failure feature mapping rule and the deviation allowable threshold in step S4 are corrected (increasing or decreasing the threshold); when the third group is inconsistent, only the deviation allowable threshold is corrected. This differentiated correction mechanism can accurately locate the source of deviation, avoid over-adjustment of normal modules, and thus form a closed-loop self-optimization.

[0044] Step S6: Based on the high comprehensive confidence label, low confidence label, the corrected failure feature mapping rule, and the corrected deviation allowable threshold, generate the final vehicle detection analysis result.

[0045] In step S6, based on the high-confidence label, low-confidence label, the corrected failure feature mapping rule, and the corrected deviation allowable threshold, the final vehicle detection analysis result is generated, specifically including the following steps: If the high overall confidence label is the output label, the logical confidence vector, the difference attribution results, and the cross-domain deviation point identifier set are used as the fusion input data; If the low confidence label is the output label, steps S2 and S4 are re-executed using the corrected failure feature mapping rule and the corrected deviation allowance threshold, respectively, to obtain the updated logical confidence vector and the updated cross-domain deviation point identifier set. The difference attribution result, the updated logical confidence vector, and the updated cross-domain deviation point identifier set are used as the fusion input data. The confidence values ​​of each sensor in the logical confidence vector of the fused input data are normalized, and the normalized values ​​are used as the fusion weights of the target sensor to obtain the fusion weight vector of each sensor. Based on the fusion weight vector of each sensor, the observations of each sensor at the same spatiotemporal point are weighted and summed to obtain the initial result of vehicle detection after fusion. Using the fused initial vehicle detection results and combining the fault severity rating in the differential attribution results, the parts of the detection results with confidence levels below the preset output threshold are labeled or removed to obtain the corrected fused detection results. The corrected fusion detection results are structured according to time sequence and spatial location to generate the final vehicle detection and analysis results.

[0046] The confidence values ​​of each sensor in the logical confidence vector of the fused input data are normalized, and the normalized values ​​are used as the fusion weights of the target sensors to obtain the fusion weight vector of each sensor. The specific steps include the following: The maximum value of each confidence value in the logical confidence vector is normalized. The normalized confidence coefficient of each sensor is obtained by dividing the confidence value of each sensor by the maximum value in the vector. The normalized confidence coefficient of each sensor is multiplied by a preset sensor physical characteristic correction factor to obtain the weighted fusion weight coefficient; wherein the preset sensor physical characteristic correction factor is: pre-calibrated based on the sensor's measurement accuracy, noise level and reliability. The weighted fusion weight coefficients of all sensors are summed and normalized so that the sum of each weight coefficient is 1, thus obtaining the fusion weight vector of each sensor.

[0047] In this embodiment of the invention, a fusion path is selected based on the comprehensive confidence level label. If the label is high, the original outputs of steps S2, S3, and S4 are directly used as the fusion input data; if the label is low, steps S2 and S4 are re-executed using the corrected rules and thresholds to obtain an updated logical confidence vector and a cross-domain deviation point identifier set, which are then combined with the difference attribution results to form the fusion input data. Subsequently, the logical confidence vector in the fusion input data is double-normalized: first, maximum value normalization is performed to obtain the normalized confidence coefficient, then multiplied by a physical characteristic correction factor pre-calibrated based on sensor measurement accuracy, noise level, and reliability, and finally sum-normalization is performed to make the sum of weights equal to 1, thereby obtaining the fusion weights of each sensor.

[0048] The sensor observations at the same spatiotemporal point are weighted and summed based on this weight to obtain the initial fused detection result. Next, combined with the fault severity rating, portions of the initial result with confidence levels below a preset output threshold are labeled or removed, resulting in a corrected fused detection result. Finally, the data is organized into structured output according to time sequence and spatial location. The mathematical modeling of the entire process is reflected in the multi-stage normalization operator of the weights, the linear combination of weighted summations, and the nonlinear decision rules based on thresholds and ratings, transforming the model outputs of the aforementioned steps into vehicle detection and analysis information that can be directly used by downstream systems.

[0049] Please refer to 2. This invention also proposes a vehicle detection data analysis system based on mathematical modeling, the system comprising: The data acquisition and alignment module is used for: Acquire raw data from multiple sensors and perform spatiotemporal alignment to obtain an aligned multi-source data tensor set; The sensor status diagnostic module is used for: Numerical consistency comparison is performed on the modal data at the same spatiotemporal point in the aligned multi-source data tensor set. Based on the preset sensor failure feature mapping rules, the failure mode of each sensor is inferred from the inconsistent amplitude and direction signs, and a logical confidence vector is generated. Based on the logical credibility vector and the preset sensor behavior rule library, logical reasoning is performed to attribute the differences in sensor observations, and the difference attribution results are output. The cross-domain deviation detection module is used for: For each sensor, a local prediction model is constructed using the sensor's observation sequence within a historical time window through mathematical fitting to calculate the theoretical prediction value at the current moment. The deviation between the theoretical prediction value and the actual observation value of the sensor at the current moment is compared with a preset deviation threshold, and spatiotemporal data points with deviations exceeding the preset deviation threshold are marked as cross-domain deviation points, thus obtaining a cross-domain deviation point identifier set. The consistency comparison and adaptive correction module is used for: The logical confidence vector, the difference attribution result, and the cross-domain deviation point identifier set are compared for consistency. If the consistency comparison points to the same value, a high comprehensive confidence label is output. If the consistency comparison points to different values, a low confidence label is output. The sensor failure feature mapping rule preset in step S2 and the preset deviation threshold in step S4 are modified according to the type of inconsistency to generate the modified failure feature mapping rule and the modified deviation allowable threshold. The fusion output module is used for: Based on high-confidence labels, low-confidence labels, corrected failure feature mapping rules, and corrected deviation allowable thresholds, the final vehicle detection and analysis results are generated.

[0050] It should be understood that although the steps in the flowcharts of the various embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the various embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0051] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0052] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A vehicle detection data analysis method based on mathematical modeling, characterized in that, The method includes the following steps: S1. Acquire raw data from multiple sources and perform spatiotemporal alignment to obtain an aligned multi-source data tensor set; S2. Perform numerical consistency comparison on the modal data at the same spatiotemporal point in the aligned multi-source data tensor set. Based on the preset sensor failure feature mapping rules, infer the failure mode of each sensor from the inconsistent amplitude and direction signs, and generate a logical confidence vector. S3. Based on the logical credibility vector and the preset sensor behavior rule library, perform logical reasoning and attribution on the differences in sensor observations, and output the difference attribution results; S4. For each sensor, a local prediction model is constructed using the sensor's observation sequence within a historical time window through mathematical fitting to calculate the theoretical prediction value at the current moment; the deviation between the theoretical prediction value and the actual observation value of the sensor at the current moment is compared with a preset deviation threshold, and spatiotemporal data points with deviations exceeding the preset deviation threshold are marked as cross-domain deviation points to obtain a cross-domain deviation point identifier set. S5. Perform a consistency comparison on the logical confidence vector, the difference attribution result, and the cross-domain deviation point identifier set. If the consistency comparison points to the same value, output a high comprehensive confidence label. If the consistency comparison points to different values, output a low confidence label. Then, based on the type of inconsistency, correct the preset sensor failure feature mapping rule in step S2 and the preset deviation threshold in step S4 to generate the corrected failure feature mapping rule and the corrected deviation allowable threshold. S6. Based on high-confidence labels, low-confidence labels, corrected failure feature mapping rules, and corrected deviation allowable thresholds, the final vehicle detection and analysis results are generated.

2. The vehicle detection data analysis method based on mathematical modeling according to claim 1, characterized in that, In step S1, the raw data from the multi-source sensors are acquired and spatiotemporally aligned to obtain an aligned multi-source data tensor set. This specifically includes the following steps: Raw data frames are collected from cameras, millimeter-wave radar, and lidar respectively to obtain a multi-source raw data stream containing image, point cloud, and distance and velocity information; Each frame of data in the multi-source raw data stream containing image, point cloud and distance and velocity information is timestamped, and linear interpolation alignment is performed with reference to a preset reference time axis to obtain time-synchronized multi-source frame data; The coordinates of the lidar point cloud and the coordinates of the millimeter-wave radar detection points in the time-synchronized multi-source frame data are transformed to the camera image coordinate system through the extrinsic parameter matrix to obtain spatially aligned modal data. After spatial alignment, the modal data are tensorized and recombined according to the same spatiotemporal grid to generate a multi-source data tensor containing multiple dimensions of position, velocity, and reflection intensity. The multi-source data tensor containing multiple dimensions of position, velocity, and reflection intensity is then used as the aligned multi-source data tensor set.

3. The vehicle detection data analysis method based on mathematical modeling according to claim 2, characterized in that, In step S2, numerical consistency comparison is performed on the modal data at the same spatiotemporal point in the aligned multi-source data tensor set. Based on the preset sensor failure feature mapping rules, the failure mode of each sensor is inferred from the inconsistent amplitude and direction signs, and a logical confidence vector is generated. Specifically, the steps are as follows: The observations of each sensor at the same spatiotemporal point are extracted from the aligned multi-source data tensor set. Based on the differences in the physical measurement principles of the sensors, the observations are grouped to construct redundant sensor equations, resulting in multiple sets of redundant observation equations. Substitute each set of equations in the multiple sets of redundant observation equations into the corresponding sensor observation values ​​to solve the problem, calculate the absolute value of the residual between different equations in the same set, and arrange all the absolute values ​​of the residual in the order of sensor combination to obtain the analytical redundant residual vector. Traverse all non-zero elements in the parsed redundant residual vector, and match the direction sign and magnitude of each residual vector with the standard failure mode features in the rule library according to the preset sensor failure feature mapping rule library, and generate the failure mode identifier of each sensor at the current time and space point in turn. Based on the failure mode identifier of each sensor at the current spatiotemporal point, a corresponding initial logical confidence value is marked for each sensor to obtain the initial logical confidence value vector of each sensor; wherein, if there is a failure among the sensors, the initial confidence value corresponding to the failed sensor is set to be lower than the preset fault-free benchmark value; if the sensor does not fail, the initial confidence value corresponding to the non-failed sensor is set to be higher than the preset fault-free benchmark value. Each element in the initial logical confidence value vector of each sensor is normalized and weighted according to the differences in the physical characteristics of the sensors, so that the logical confidence values ​​output by different sensors under the same failure degree are comparable, thus obtaining the logical confidence vector.

4. The vehicle detection data analysis method based on mathematical modeling according to claim 3, characterized in that, The pre-defined sensor failure feature mapping rule base includes the construction of the sensor failure feature mapping rule base; specifically, the construction of the sensor failure feature mapping rule base includes the following steps: For camera sensors, deviation data are collected under three failure modes: strong light glare, lens damage, and motion blur. The directional sign features of the deviations under these three failure modes are extracted to form a subset of camera failure feature maps. The directional sign features of the deviations under the three failure modes include: strong light glare produces a systematic positive offset along the image row direction; lens damage produces a radial divergence vector from the image center to the edge; and motion blur produces a trailing offset vector along the tangent direction of the target motion trajectory. For millimeter-wave radar sensors, ranging deviation data under two failure modes—rain and snow attenuation and metal multipath reflection—are collected. The directional sign features of the deviations under these two failure modes are extracted to form a subset of millimeter-wave radar failure feature maps. Specifically, the extracted directional sign features of the deviations under these two failure modes include: rain and snow attenuation causing a monotonically positive expansion of the ranging value radially, and metal multipath reflection causing a periodic alternating positive and negative shift of the ranging value along the azimuth direction. For lidar sensors, point cloud deviation data are collected under two failure modes: long-range sparsity and glass mirror reflection. The directional sign features of the deviation under these two failure modes are extracted to form a lidar failure feature mapping subset. The extracted directional sign features of the deviation under the two failure modes include: long-range sparsity causes the centroid of the point cloud to drift radially outward with an amplitude proportional to the square of the distance, and glass mirror reflection causes the point cloud to produce a completely opposite virtual mirror offset along the normal direction. The camera failure feature mapping subset, the millimeter-wave radar failure feature mapping subset, and the lidar failure feature mapping subset are merged into a multimodal failure feature mapping rule library. Each mapping rule in the multimodal failure feature mapping rule library is associated with a corresponding sensor failure degree quantification function to obtain the associated failure feature mapping rule library. The associated failure feature mapping rule library is then used as the preset sensor failure feature mapping rule.

5. The vehicle detection data analysis method based on mathematical modeling according to claim 4, characterized in that, In step S3, based on the logical confidence vector and a preset sensor behavior rule base, logical reasoning is performed to attribute the differences in sensor observations, and the difference attribution results are output. Specifically, this includes the following steps: Based on the logical confidence vector, the observation values ​​of all sensors at the same spatiotemporal point in the current frame are extracted from the aligned multi-source data tensor set to obtain the original observation data set of each sensor. Each observation data point in the raw observation data set of each sensor is compared with the corresponding theoretical prediction value point by point to calculate the observation difference vector of each sensor at each observation point, thus obtaining a set of sensor observation difference vectors; wherein, the observation difference vector includes: difference amplitude, difference direction sign and time location information of the difference occurrence; Based on the logical confidence vector, each observation difference vector in the sensor observation difference vector set is weighted by confidence. The observation differences corresponding to low confidence sensors are marked as unverified states, and the observation differences corresponding to high confidence sensors are directly used as valid differences, so as to obtain the set of observation differences after confidence screening. Each observation difference vector in the set of observation differences filtered by confidence is input into the preset sensor behavior rule base for pattern matching. The similarity between the difference amplitude, difference direction sign and the time and location information of the difference occurrence of the observation difference vector and the condition part of each rule entry in the rule base is calculated, and the rule entry with the highest similarity and exceeding the preset matching threshold is selected to obtain the matching rule identifier and associated fault type corresponding to the observation difference vector. Based on the matching rule identifier and associated fault type corresponding to the observed difference vector, the attribution conclusion corresponding to the observed difference is determined; wherein, the attribution conclusion includes: fault source sensor identifier, fault type classification, and fault severity rating; The attribution conclusions corresponding to all observed difference vectors are summarized according to the sensor dimension and the time dimension to generate a structured set of difference attribution results, and the structured set of difference attribution results is used as the difference attribution result.

6. The vehicle detection data analysis method based on mathematical modeling according to claim 5, characterized in that, The preset sensor behavior rule base includes the construction of the sensor behavior rule base; wherein the construction of the sensor behavior rule base specifically includes the following steps: For typical sensor observation difference types in vehicle detection, conditional attribute dimensions are defined in rule entries to obtain a conditional attribute definition set; wherein, the conditional attribute dimensions include: the numerical range of the difference amplitude, the positive or negative polarity of the difference direction sign, the duration of the difference, and the distribution pattern of the difference in the spatiotemporal domain. For each type of sensor observation difference, a corresponding conclusion section is set to obtain a conclusion definition set; wherein, the conclusion section includes: the sensor fault type code corresponding to the difference, the fault risk level number, and the recommended preprocessing operation identifier; Each condition attribute in the condition attribute definition set and the corresponding conclusion in the conclusion definition set are associated as a set of rule entries according to the IF-THEN logic. A matching priority weight is preset for each set of rule entries to form a set of rule entries with matching weight. All the rule entries with matching weight are merged to form a merged sensor behavior rule library. The merged sensor behavior rule library is used as the preset sensor behavior rule library.

7. The vehicle detection data analysis method based on mathematical modeling according to claim 6, characterized in that, In step S4, for each sensor, a local prediction model is constructed using the sensor's observation sequence within a historical time window through mathematical fitting to calculate the theoretical prediction value at the current moment. The deviation between the theoretical prediction value and the actual sensor observation value at the current moment is compared with a preset deviation threshold, and spatiotemporal data points with deviations exceeding the preset deviation threshold are marked as cross-domain deviation points, resulting in a cross-domain deviation point identifier set. Specifically, this includes the following steps: For each sensor, the sequence of observations of that sensor at multiple consecutive historical moments is extracted from the aligned multi-source data tensor set to form a historical observation window; A mathematical fitting method is used to locally model the observation sequence within the historical observation window to obtain the theoretical prediction value at the current moment; wherein, the mathematical fitting method includes: linear regression or quadratic polynomial fitting or locally weighted regression or autoregressive model; Calculate the absolute value of the deviation between the theoretical prediction value and the actual observation value at the current moment, and compare the absolute value of the deviation with a preset allowable deviation threshold. If the absolute value of the deviation exceeds the preset allowable deviation threshold, mark the data point as a cross-domain deviation point, and record the sensor type, spatiotemporal coordinates and deviation direction sign corresponding to the data point. Then, merge all the data points marked as cross-domain deviation points according to sensor type and spatiotemporal coordinates to form a preliminary cross-domain deviation point identification set. For each identified deviation point in the preliminary set of cross-domain deviation points, a time sequence consistency check is performed. If the same sensor continuously produces cross-domain deviation points at the same spatial location in multiple consecutive time frames, the deviation point is confirmed as a valid cross-domain deviation point. Otherwise, the deviation point is marked as instantaneous noise and filtered out to form a set of cross-domain deviation point identifiers.

8. The vehicle detection data analysis method based on mathematical modeling according to claim 7, characterized in that, In step S5, the logical confidence vector, the difference attribution result, and the cross-domain deviation point identifier set are compared for consistency. If the consistency comparison points to the same value, a high overall confidence label is output; if the consistency comparison points to different values, a low confidence label is output. Based on the type of inconsistency, the preset sensor failure feature mapping rule in step S2 and the preset deviation threshold in step S4 are corrected to generate a corrected failure feature mapping rule and a corrected deviation allowable threshold. Specifically, the steps include the following: The logical confidence vector and the difference attribution results are compared sensor by sensor to determine whether the confidence level of the same sensor in the logical confidence vector and the fault type in the difference attribution results support each other, so as to obtain the first comparison result. The logical confidence vector is compared with the cross-domain deviation point identifier set sensor by sensor to determine whether the number of cross-domain deviation points corresponding to sensors whose logical confidence is lower than the preset confidence threshold exceeds the preset proportion threshold of the total number of deviation points in the cross-domain deviation point identifier set, so as to obtain the second comparison result. The difference attribution results are compared with the identified deviation points in the cross-domain deviation point identification set on a sensor-by-sensor basis to determine whether the sensor marked as fault in the difference attribution results is consistent with the source sensor of the identified deviation point in the cross-domain deviation point identification set, so as to obtain the third comparison result. If the first comparison result, the second comparison result, and the third comparison result all point to the same direction, then the overall consistency is determined to be consistent, a high comprehensive confidence label is output, and the current sensor failure feature mapping rule and deviation allowable threshold are used as the corrected failure feature mapping rule and the corrected deviation allowable threshold. If there are inconsistencies in the first, second, and third comparison results, the overall comparison is determined to be inconsistent, and the objects that need to be corrected are determined according to the specific type of inconsistency. Based on the identified objects requiring correction, the preset sensor failure feature mapping rules and deviation allowable thresholds are adjusted to generate corrected failure feature mapping rules and corrected deviation allowable thresholds. The adjustment of the preset sensor failure feature mapping rules and deviation allowable thresholds includes: adjusting the mapping relationship between the residual direction sign and the failure mode for the failure feature mapping rules; and increasing or decreasing the threshold value for the deviation allowable thresholds.

9. The vehicle detection data analysis method based on mathematical modeling according to claim 8, characterized in that, In step 6, based on the high-confidence labels, low-confidence labels, the corrected failure feature mapping rules, and the corrected deviation allowable threshold, the final vehicle detection analysis result is generated, specifically including the following steps: If the high overall confidence label is the output label, the logical confidence vector, the difference attribution results, and the cross-domain deviation point identifier set are used as the fusion input data; If the low confidence label is the output label, steps S2 and S4 are re-executed using the corrected failure feature mapping rule and the corrected deviation allowance threshold, respectively, to obtain the updated logical confidence vector and the updated cross-domain deviation point identifier set. The difference attribution result, the updated logical confidence vector, and the updated cross-domain deviation point identifier set are used as the fusion input data. The confidence values ​​of each sensor in the logical confidence vector of the fused input data are normalized, and the normalized values ​​are used as the fusion weights of the target sensor to obtain the fusion weight vector of each sensor. Based on the fusion weight vector of each sensor, the observations of each sensor at the same spatiotemporal point are weighted and summed to obtain the initial result of vehicle detection after fusion. Using the fused initial vehicle detection results and combining the fault severity rating in the differential attribution results, the parts of the detection results with confidence levels below the preset output threshold are labeled or removed to obtain the corrected fused detection results. The corrected fusion detection results are structured according to time sequence and spatial location to generate the final vehicle detection and analysis results.

10. The vehicle detection data analysis method based on mathematical modeling according to claim 9, characterized in that, The confidence values ​​of each sensor in the logical confidence vector of the fused input data are normalized, and the normalized values ​​are used as the fusion weights of the target sensors to obtain the fusion weight vector of each sensor. The specific steps include the following: The maximum value of each confidence value in the logical confidence vector is normalized. The normalized confidence coefficient of each sensor is obtained by dividing the confidence value of each sensor by the maximum value in the vector. The normalized confidence coefficient of each sensor is multiplied by a preset sensor physical characteristic correction factor to obtain the weighted fusion weight coefficient; wherein the preset sensor physical characteristic correction factor is: pre-calibrated based on the sensor's measurement accuracy, noise level and reliability. The weighted fusion weight coefficients of all sensors are summed and normalized so that the sum of each weight coefficient is 1, thus obtaining the fusion weight vector of each sensor.

11. A vehicle detection data analysis system based on mathematical modeling, characterized in that, The system employs the vehicle detection data analysis method based on mathematical modeling as described in any one of claims 1-10, and the system comprises: The data acquisition and alignment module is used for: Acquire raw data from multiple sensors and perform spatiotemporal alignment to obtain an aligned multi-source data tensor set; The sensor status diagnostic module is used for: Numerical consistency comparison is performed on the modal data at the same spatiotemporal point in the aligned multi-source data tensor set. Based on the preset sensor failure feature mapping rules, the failure mode of each sensor is inferred from the inconsistent amplitude and direction signs, and a logical confidence vector is generated. Based on the logical credibility vector and the preset sensor behavior rule library, logical reasoning is performed to attribute the differences in sensor observations, and the difference attribution results are output. The cross-domain deviation detection module is used for: For each sensor, a local prediction model is constructed using the sensor's observation sequence within a historical time window through mathematical fitting to calculate the theoretical prediction value at the current moment. The deviation between the theoretical prediction value and the actual observation value of the sensor at the current moment is compared with a preset deviation threshold, and spatiotemporal data points with deviations exceeding the preset deviation threshold are marked as cross-domain deviation points, thus obtaining a cross-domain deviation point identifier set. The consistency comparison and adaptive correction module is used for: The logical confidence vector, the difference attribution result, and the cross-domain deviation point identifier set are compared for consistency. If the consistency comparison points to the same value, a high comprehensive confidence label is output. If the consistency comparison points to different values, a low confidence label is output. The sensor failure feature mapping rule preset in step S2 and the preset deviation threshold in step S4 are modified according to the type of inconsistency to generate the modified failure feature mapping rule and the modified deviation allowable threshold. The fusion output module is used for: Based on high-confidence labels, low-confidence labels, corrected failure feature mapping rules, and corrected deviation allowable thresholds, the final vehicle detection and analysis results are generated.

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