A printing flat screen multi-reel thickness difference detection system

Abstract

The application provides a printing flat net multi-roll belt thickness difference detection system and relates to the technical field of thickness detection. The method comprises the following steps: a detection bridge construction module is used to construct a hollow cover type detection bridge which crosses the multi-roll parallel printing belt and forms a floating detection area with double curvature constraints in the belt splicing area; a solving module is used to solve a first virtual anchor point located on the geometric center line of the floating detection area and a second virtual anchor point located on the top symmetric axis of the hollow cover type detection bridge, so as to construct a U-shaped equidistant line cluster extending along the longitudinal direction of the floating detection area and an outer convex arc-shaped equipotential surface cluster extending along the transverse direction of the hollow cover type detection bridge. The application realizes global quantitative detection of the thickness difference of the multi-roll parallel printing belt, improves the accuracy, standardization and efficiency of the thickness detection, and solves the technical problem that the thickness difference of the multi-roll belt is difficult to accurately quantify.

Description

Technical Field

[0001] This invention relates to the field of thickness detection technology, and in particular to a system for detecting the thickness difference of multiple rolls of printed flat screen tape. Background Technology

[0002] In the production process of halftone printing, multiple rolls of substrate (such as film, paper, foil, etc.) are mostly unrolled in parallel and fed into the printing unit simultaneously. The consistency of thickness between each roll is one of the key factors to ensure printing registration accuracy, color uniformity, and post-processing quality. However, due to raw material cutting errors, winding tension fluctuations, and batch differences in substrates, slight thickness deviations are inevitable between multiple rolls of substrate. If these deviations are not detected and corrected in time, they may lead to quality problems such as local color differences, dot distortion, or even tape breakage in the printed pattern. In the existing technology, the thickness of the substrate is usually detected using offline thickness gauges (such as beta-ray or laser thickness gauges) or online single-point thickness sensors. These methods are relatively mature in detecting the absolute thickness of a single roll of substrate, but when applied to scenarios with multiple rolls running in parallel and splicing areas, they may reveal some shortcomings.

[0003] For example, in multi-roll printing, three rolls of polyester film (PET) from different batches are connected end-to-end by a splicing tape and simultaneously enter the flexographic printing unit at a speed exceeding 60 meters per minute. Because the film in the middle roll is approximately 2 micrometers thicker than the films on the sides, the printing pressure distribution is uneven, resulting in transverse color streaks on the finished product. However, existing online thickness detection devices can only sample a single point in the central area of ​​each roll, which may not effectively characterize the local thickness differences caused by tension redistribution near the splicing area, and is even less capable of quantifying the thickness deviation distribution between multiple rolls in the width and travel directions. Furthermore, traditional detection methods are easily affected by roll vibration, stress distortion in the splicing area, and equipment vibration, resulting in test results that often contain significant uncertainty. Summary of the Invention

[0004] This invention provides a multi-roll thickness difference detection system for printed flat screen tape, which enables high-precision and highly interference-resistant quantitative detection of thickness differences among multiple rolls of tape.

[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0006] A system for detecting thickness differences in multiple rolls of printed flat screen tape includes:

[0007] The detection cable tray construction module is used to construct a hollow cover-type detection cable tray spanning multiple rolls of parallel printed tape. The inner wall of the hollow cover-type detection cable tray is sequentially provided with a first arc-shaped protrusion array and a second arc-shaped protrusion array along the longitudinal extension direction. The first arc-shaped protrusion array is used to apply a first preload force in the normal direction of the reference surface of the printed tape, and the second arc-shaped protrusion array is used to apply a second preload force in the opposite direction. The first preload force and the second preload force work together in the splicing area of ​​two adjacent rolls of printed tape, so that the surface of the printed tape in the splicing area is subjected to normal opposing compression and normal opposing tension, respectively, to form a floating detection domain with double curvature constraint characteristics in the splicing area.

[0008] The solution module is used to solve the first virtual anchor point located on the geometric center line of the floating detection domain and the second virtual anchor point located on the axis of symmetry at the top of the hollow cover-type detection bridge, so as to construct a U-shaped equidistant line cluster extending longitudinally along the floating detection domain and an outwardly convex arc-shaped equipotential surface cluster extending laterally along the hollow cover-type detection bridge.

[0009] The cross-section segmentation module is used to interleave U-shaped equidistant line clusters and convex arc-shaped equipotential surface clusters in three-dimensional space to form a composite reference body composed of hollow rhombic meshes. The composite reference body is divided into several continuous trapezoidal cross-section segments with the common vertex of two adjacent hollow rhombic mesh units as the boundary.

[0010] The difference calculation module is used to select the first set of sensing nodes and the second set of sensing nodes within each trapezoidal cross section and connect them to form a spatial diagonal; it extracts the cumulative wall thickness of each spatial diagonal passing through the hollow rhomboid grid unit as the local thickness difference value of the corresponding cross section.

[0011] The results output module is used to weight and fuse all local thickness difference values ​​to obtain a multidimensional thickness deviation tensor, and then map the multidimensional thickness deviation tensor to a multidimensional thickness deviation output matrix as a quantitative detection result of the thickness difference between each roll of printing tape.

[0012] The above-described solution of the present invention has at least the following beneficial effects:

[0013] By constructing a hollow, dome-shaped inspection bridge spanning multiple rolls of parallel-printed strip and forming a floating inspection domain with double curvature constraints in the strip splicing area, interference from strip running vibration, tension fluctuations, and equipment vibration on the inspection area can be effectively suppressed. This stabilizes the spatial morphology of the strip in the critical splicing area, improving the stability and anti-interference capability of the thickness difference inspection process. Based on dual virtual anchor points, longitudinal U-shaped equidistant line clusters and transversely convex arc-shaped equipotential surface clusters are constructed respectively, forming a regular and uniform composite reference system in three-dimensional space. Compared with single-point inspection methods, this can completely cover the thickness distribution characteristics in both the width and travel directions, accurately characterizing the local thickness variation patterns in the splicing area of ​​multi-roll strips. By superimposing equidistant line clusters and equipotential surface clusters to form a hollow rhombic grid composite reference body and dividing it into continuous trapezoidal cross-section segments for segmented inspection, regional and refined analysis of thickness differences is achieved. This distinguishes local thickness deviations at different locations, avoids feature loss caused by overall averaging calculations, and improves the accuracy of thickness difference characterization. By constructing a spatial diagonal within a trapezoidal cross-section and calculating the cumulative wall thickness, the thickness difference of the strip is transformed into a quantifiable spatial geometric feature, enabling non-contact, high-response online detection. Weighted fusion of local thickness difference values ​​from each segment generates a multi-dimensional thickness deviation output matrix, which can intuitively and quantitatively reflect the thickness difference distribution among multiple rolls of printed strip. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of a multi-roll thickness difference detection system for printing flat screen provided in an embodiment of the present invention.

[0015] Figure 2 This is a statistical diagram of the first virtual anchor point calculation process provided in an embodiment of the present invention.

[0016] Figure 3 This is a trend diagram of the area distribution of the trapezoidal cross-section provided in an embodiment of the present invention. Detailed Implementation

[0017] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0018] like Figure 1 As shown, an embodiment of the present invention proposes a multi-roll thickness difference detection system for printed flat screens, comprising:

[0019] The detection cable tray construction module is used to construct a hollow cover-type detection cable tray spanning multiple rolls of parallel printed tape. The inner wall of the hollow cover-type detection cable tray is sequentially provided with a first arc-shaped protrusion array and a second arc-shaped protrusion array along the longitudinal extension direction. The first arc-shaped protrusion array is used to apply a first preload force in the normal direction of the reference surface of the printed tape, and the second arc-shaped protrusion array is used to apply a second preload force in the opposite direction. The first preload force and the second preload force work together in the splicing area of ​​two adjacent rolls of printed tape, so that the surface of the printed tape in the splicing area is subjected to normal opposing compression and normal opposing tension, respectively, to form a floating detection domain with double curvature constraint characteristics in the splicing area.

[0020] The solution module is used to solve the first virtual anchor point located on the geometric center line of the floating detection domain and the second virtual anchor point located on the axis of symmetry at the top of the hollow cover-type detection bridge, so as to construct a U-shaped equidistant line cluster extending longitudinally along the floating detection domain and an outwardly convex arc-shaped equipotential surface cluster extending laterally along the hollow cover-type detection bridge.

[0021] The cross-section segmentation module is used to interleave U-shaped equidistant line clusters and convex arc-shaped equipotential surface clusters in three-dimensional space to form a composite reference body composed of hollow rhombic meshes. The composite reference body is divided into several continuous trapezoidal cross-section segments with the common vertex of two adjacent hollow rhombic mesh units as the boundary.

[0022] The difference calculation module is used to select the first set of sensing nodes and the second set of sensing nodes within each trapezoidal cross section and connect them to form a spatial diagonal; it extracts the cumulative wall thickness of each spatial diagonal passing through the hollow rhomboid grid unit as the local thickness difference value of the corresponding cross section.

[0023] The results output module is used to weight and fuse all local thickness difference values ​​to obtain a multidimensional thickness deviation tensor, and then map the multidimensional thickness deviation tensor to a multidimensional thickness deviation output matrix as a quantitative detection result of the thickness difference between each roll of printing tape.

[0024] In this embodiment of the invention, by constructing a hollow cover-type detection bridge spanning multiple rolls of parallel printed strip and forming a floating detection domain with double curvature constraints in the strip splicing area, the interference of strip running vibration, tension fluctuation, and equipment vibration on the detection area can be effectively suppressed, stabilizing the spatial morphology of the strip in the key splicing area and improving the stability and anti-interference capability of the thickness difference detection process. Based on dual virtual anchor points, longitudinal U-shaped equidistant line clusters and transverse outward convex arc-shaped equipotential surface clusters are constructed respectively, which can form a regular and uniform composite reference system in three-dimensional space. Compared with the single-point detection method, it can completely cover the thickness distribution characteristics in the width direction and the strip travel direction, and accurately characterize the local thickness variation law in the splicing area of ​​multi-roll strips. By using the equidistant line clusters and equipotential surface clusters to form a hollow rhombic grid composite reference body, and dividing it into continuous trapezoidal cross-section segments for segmented detection, regional and refined analysis of thickness differences is achieved. It can distinguish local thickness deviations at different locations, avoid feature loss caused by overall averaging calculation, and improve the accuracy of thickness difference characterization. By constructing a spatial diagonal within a trapezoidal cross-section and calculating the cumulative wall thickness, the thickness difference of the strip is transformed into a quantifiable spatial geometric feature, enabling non-contact, high-response online detection. Weighted fusion of local thickness difference values ​​from each segment generates a multi-dimensional thickness deviation output matrix, which can intuitively and quantitatively reflect the thickness difference distribution among multiple rolls of printed strip.

[0025] In a preferred embodiment of the present invention, step 1 involves constructing a hollow-shell type inspection bridge spanning multiple rolls of parallel printing tape. The inner wall of the hollow-shell type inspection bridge is sequentially provided with a first arc-shaped protrusion array and a second arc-shaped protrusion array along its longitudinal extension direction. The first arc-shaped protrusion array applies a first preload force in the normal direction of the reference surface of the printing tape, and the second arc-shaped protrusion array applies a second preload force in the opposite direction. The first and second preload forces work together in the splicing area of ​​adjacent rolls of printing tape, causing the surface of the printing tape in the splicing area to be subjected to opposing normal compression and opposing normal tension, respectively, to form a floating inspection domain with double curvature constraint characteristics in the splicing area. Specifically, this includes:

[0026] First, a hollow-shell type inspection cable tray is constructed for testing. This cable tray adopts a portal frame structure, spanning across multiple rolls of parallel-fed printed tape. The transverse span of the cable tray is greater than the total width of all parallel printed tapes, completely covering the transverse extension range of each roll of tape along the tape width direction, avoiding blind spots in the inspection. The length of the cable tray along the tape's travel direction covers the transition area before and after the tape splice joint, completely enclosing the splice position and forming a closed inspection space. This effectively blocks external disturbances such as airflow, dust, and equipment vibration. Simultaneously, the cable tray itself uses rigid positioning installation to ensure that the overall geometric datum remains stable during high-speed tape movement. On the inner wall of the hollow-shell type inspection cable tray, along the longitudinal extension direction of the tape travel, a first arc-shaped protrusion array and a second arc-shaped protrusion array are installed sequentially. Both sets of protrusion arrays consist of multiple continuously arranged arc-shaped protrusions, uniformly distributed at equal intervals along the longitudinal direction. The first arc-shaped protrusion array corresponds to the upper surface area of ​​the substrate, and the second arc-shaped protrusion array corresponds to the lower surface area. The two arrays are symmetrically arranged in the thickness direction, ensuring that the preload applied to the substrate is symmetrically transmitted along the thickness direction, guaranteeing balanced force distribution during operation and preventing lateral tilting or vertical displacement. The first arc-shaped protrusion array continuously applies a first preload force to the reference plane of the substrate. This preload force acts perpendicularly to the surface of the substrate and points inward. Its value is determined based on the material stiffness, operating tension, and normal deformation range of the substrate, specifically 50 × 10⁻⁶. 6 Pa to 150×10 6 Pa, the range of values ​​is determined based on the elastic modulus and allowable stress range of mainstream flexible printing substrates, such as polyester film and aluminum foil, with the lower limit being 50 × 10⁻⁶. 6 Pa ensures effective clamping and damping of the high-speed strip, offsetting the slight vibrations caused by tension fluctuations, with an upper limit of 150×10. 6 Pa avoids exceeding the elastic yield limit of the strip material to prevent irreversible indentation or plastic deformation on the strip surface. A second preload, opposite in direction to the first preload, is applied to the substrate through the second arc-shaped protrusion array. This preload acts perpendicularly to the strip surface and away from the interior of the strip; its specific value range is also set to 50 × 10⁻⁶. 6 Pa to 150×10 6 The value of Pa is determined in accordance with the first preload, and the amplitude difference between the two sets of preloads is controlled within 30 × 10. 6 Within Pa, to ensure that the bidirectional force forms a balanced mechanical environment in the thickness direction of the strip, avoid the strip skewing, wrinkling or belt deviation caused by unilateral force imbalance, and ensure that the strip maintains a stable running posture in the detection area.

[0027] In the splicing area of ​​two adjacent rolls of printed tape, the first preload and the second preload together form a stable superimposed force field, which simultaneously applies normal opposing compression and normal opposing tension to the surface of the tape in the splicing area. The opposing compression is applied by the first arc-shaped protrusion array, causing the tape to locally produce inward curvature deformation, while the opposing tension is applied by the second arc-shaped protrusion array, causing the tape to locally produce outward curvature deformation. The two curvature deformations are coupled to each other in the splicing area to form a stable bidirectional bending shape. To quantify the effect of double curvature constraint, the curvature of any point in the strip splicing area along the direction of the first preload is defined as C1, and the curvature along the direction of the second preload is defined as C2. The double curvature constraint state is determined by jointly using the curvature ratio and the curvature sum. The curvature ratio = C1 / C2. Considering the stability requirements of multi-roll strip operation, the preset constraint range for the curvature ratio is [0.8, 1.2]. This range ensures that the curvature deformation of the upper and lower surfaces is in a relatively balanced state, avoiding excessive deformation in one direction that could lead to strip warping. The curvature sum = C1 + C2, and the preset allowable deformation range for the curvature sum is [0.002, 0.005] (unit: This range ensures that the strip forms a stable constraint shape in the splicing area, and avoids the strip from becoming permanently bent due to excessive curvature and value. When the curvature ratio is stably within the preset ratio range [0.8, 1.2], and the curvature and value are kept within the allowable deformation range [0.002, 0.005], it is determined that a floating detection domain with double curvature constraint characteristics has been formally formed in the splicing area of ​​the strip. The spatial shape of the strip in this area is constrained by the bidirectional curvature, which can continuously offset the tension fluctuation, lateral movement and normal offset during the operation of the strip.

[0028] This embodiment utilizes a hollow-shell-type detection cable tray and a double-arc protrusion array to form a double-curvature-constrained floating detection domain. This effectively suppresses morphological distortion caused by strip movement vibration, tension fluctuations, and equipment vibration, ensuring the stability of the strip's spatial shape in the splicing area and reducing the impact of external interference on thickness difference detection. The bidirectional pre-tightening effect of opposing compression and back-to-back tension evens out stress distribution at the splicing points of multiple strip rolls, preventing strip deformation caused by localized stress concentration and ensuring accurate reflection of thickness difference characteristics. The quantitative determination method of double-curvature constraint defines the effective detection area, ensuring that the detection space has uniform and stable benchmark conditions.

[0029] In a preferred embodiment of the present invention, the calculation of a first virtual anchor point located on the geometric center line of the floating detection domain and a second virtual anchor point located on the axis of symmetry at the top of the hollow-shell detection bridge is used to construct a U-shaped equidistant line cluster extending longitudinally along the floating detection domain and a convex arc-shaped equipotential surface cluster extending laterally along the hollow-shell detection bridge, including:

[0030] Step 200a: Discretize the floating detection domain at equal intervals along the longitudinal central axis to obtain the bidirectional curvature radius values ​​at each sampling point along the first and second preload directions, respectively; perform ratio calculation on the bidirectional curvature radius values ​​to obtain the bidirectional curvature ratio distribution sequence at each sampling point, and extract the sampling point with the largest rate of change in the bidirectional curvature ratio distribution sequence as the first candidate point; using the first candidate point as the search center, extend a preset distance in both forward and backward directions along the longitudinal central axis of the floating detection domain to form a first search window area; calculate the local root mean square error of the bidirectional curvature radius values ​​within the first search window area, and mark the position with the smallest local root mean square error as the first virtual anchor point, specifically including:

[0031] Using the longitudinal centerline of the floating detection domain as the sampling baseline, discrete sampling is performed along this centerline at equal intervals with a fixed step size of 0.5 mm to obtain multiple uniformly distributed sampling points. For each sampling point, the radius of curvature along the first preload direction and the radius of curvature along the second preload direction are measured and extracted. The ratio of the bidirectional radius of curvature values ​​corresponding to each sampling point is calculated as follows: Bicurvature ratio = radius of curvature along the first preload direction / radius of curvature along the second preload direction. All sampling points are arranged sequentially according to the conveyor belt order to form a continuous bicurvature ratio distribution sequence. The rate of change of this sequence is calculated using the following formula: Where vi is the rate of change of the hypercurvature ratio at the i-th sampling point. The hypercurvature ratio at the i-th sampling point For the first The hypercurvature ratio of each sampling point is used to determine the sampling point corresponding to the maximum rate of change as the first candidate point. A continuous first search window region with a total length of 10mm is defined by extending a preset distance of 5mm forward and backward along the longitudinal central axis from the first candidate point. Within this window region, the local root mean square error of the bidirectional curvature radius values ​​for all sampling points is calculated.

[0032] Right now = ,in This represents the local root mean square error of the bidirectional radius of curvature within the first search window region. It characterizes the degree of fluctuation of the radius of curvature within this region; the smaller the root mean square error, the more stable the curvature distribution. Indicates the first [number] in the window area The radius of curvature values ​​of each sampling point along the direction of the first preload. Indicates the first [number] in the window area The radius of curvature values ​​of each sampling point along the direction of the second preload. , Within the window area , The arithmetic mean, Given the total number of sampling points within the window, the location with the smallest local mean square error is designated as the first virtual anchor point.

[0033] Step 201a: Discretize the top axis of symmetry of the hollow-shell type testing cable tray along the transverse direction using equal arc length sampling to obtain the transverse vibration mode amplitude at each sampling point on the top axis of symmetry; perform zero-crossing point detection on the transverse vibration mode amplitude, extract all zero-crossing positions where the sign of the mode amplitude changes, and extract the zero-crossing position with the smallest arc length distance from the geometric center of the top axis of symmetry as the second candidate point; using the second candidate point as the search center, extend the search area by a preset arc length in both the front and rear directions along the top axis of symmetry to form a second search window area; calculate the sum of the absolute values ​​of the mode amplitude differences between adjacent sampling points within the second search window area, and mark the position with the smallest sum of absolute values ​​as the second virtual anchor point, specifically including:

[0034] The top axis of symmetry of the hollow-shell type testing cable tray is sampled using equal arc length discretization. The sampling arc length interval is set to 0.5mm to 1mm, and the sampling range covers the entire top axis of symmetry, ensuring that each sampling point is evenly distributed and without omission, with a total number of sampling points of no less than 50. The transverse vibration mode amplitude at each sampling point is collected one by one using vibration detection equipment (such as piezoelectric vibration sensor). The transverse vibration mode amplitude of all sampling points is traversed and detected, and all zero-crossing positions where the amplitude sign changes from positive to negative (i.e., the sampling point position where the amplitude changes from positive to negative or from negative to positive) are screened out, and the arc length coordinates of each zero-crossing position are recorded. According to the geometric parameters of the top axis of symmetry, the arc length distance between each zero-crossing position and the geometric center of the top axis of symmetry is calculated. By comparing the arc length distances of all zero-crossing positions, the zero-crossing position with the smallest distance is selected as the second candidate point, ensuring that this candidate point is closest to the center of the axis of symmetry. Using the second candidate point as the search center, a pre-set arc length is extended in both the front and rear directions along the top axis of symmetry (the pre-set arc length is set according to the length of the top axis of symmetry of the hollow-shell type detection cable tray, usually 5mm to 10mm) to form a closed second search window area, ensuring that the window area can cover the key vibration characteristic areas around the candidate point. Within the second search window area, the difference in mode amplitude between two adjacent sampling points is calculated one by one. The absolute value of each difference is taken and then summed to obtain the sum of the absolute values ​​of adjacent amplitude differences within the window area. This reflects the degree of fluctuation of mode amplitude within the window area. The smaller the sum, the smaller the difference in mode amplitude between adjacent sampling points, the smoother the mode fluctuation, and the stronger the stability. The larger the sum, the greater the difference in mode amplitude between adjacent sampling points, the more violent the mode fluctuation, and the weaker the stability, clearly presenting the fluctuation state of mode amplitude within the window area. By comparing the sum of the absolute values ​​of adjacent amplitude differences corresponding to all sampling points within the second search window area, the position with the smallest value (i.e., the position with the smallest and most stable mode amplitude fluctuation) is marked as the second virtual anchor point.

[0035] Step 200b: Acquire the spatial coordinates of the first virtual anchor point on the longitudinal central axis of the floating detection domain, and extract the stress interference fringe image frame by frame along the longitudinal direction within the floating detection domain, which is jointly excited by the first preload and the second preload; perform binarization processing on the stress interference fringe image, calculate the ratio of the fringe line density in the upstream half region to the downstream half region in each frame image, and when the ratio is greater than the preset dense-sparse discrimination coefficient for three consecutive frames or more, it is determined that the stress interference fringe distribution presents a state of dense upstream and sparse downstream, specifically including:

[0036] The spatial coordinates of the first virtual anchor point on the longitudinal central axis of the floating detection domain are obtained using a 3D positioning device (such as a laser positioning instrument), denoted as (x1, y1, z1). This clarifies the specific spatial location of the anchor point within the floating detection domain. Within the floating detection domain, stress interference fringe images excited by the first and second preload forces are acquired frame by frame along the longitudinal direction at a fixed frame rate (30 frames / second). During the acquisition process, the ambient lighting is kept uniform to avoid interference from reflections, shadows, etc., ensuring that each frame is clear, free of significant noise, and has a complete fringe outline. An adaptive binarization algorithm is used to process each frame of the stress interference fringe image, setting a reasonable grayscale threshold (usually 128 to 150) to remove redundant pixels and background noise, while retaining a clear fringe outline. Each frame of the image is divided into an upstream half and a downstream half, with the vertical centerline of the floating detection domain as the boundary. The total pixel length of the stripe center line in each half is counted, and the effective pixel area of ​​each half is calculated (excluding blurred edges and invalid areas). The line density of the upstream half and the downstream half is calculated according to the formula: line density = total pixel length of stripe center line / effective pixel area of ​​corresponding area. The linear density ratio is calculated as: Linear density ratio = Linear density of the upstream half-zone / Linear density of the downstream half-zone, to quantify the difference in stripe density between the upstream and downstream regions. The dense-sparse discrimination coefficient is set to 1.8. This coefficient is determined as follows: First, sample data of the linear density ratio under different working conditions are collected. These conditions include three categories: stable stress conditions, slight vibration conditions, and tension fluctuation conditions. Stable stress conditions are characterized by smooth strip operation without significant vibration, tension fluctuations controlled within ±5%, and uniform stress stripe distribution. Slight vibration conditions are characterized by minor strip swaying, tension fluctuations within ±10%, and only slight stripe disorder. Tension fluctuation conditions are characterized by strip speed fluctuations exceeding ±10% or preload deviations exceeding ±15%, and disordered stripe distribution. The data for stable stress conditions and disturbed conditions are then statistically analyzed separately. The distribution of linear density ratios under various operating conditions (slight shaking, tension fluctuations) is calculated by taking the average of all linear density ratios under stable stress conditions and the average of all linear density ratios under disturbed conditions. The median of these two averages is taken as the dense-sparse discrimination coefficient, assumed to be 1.8. This calculation process involves statistical analysis of a large amount of sample data (covering commonly used printing substrates such as PET, PP, and PVC, as well as different thicknesses from 0.1mm to 0.5mm) to ensure that the coefficient can clearly distinguish between stable and disturbed states. The linear density ratios of multiple consecutive frames are monitored in real time, with no fewer than 3 frames monitored. When the linear density ratios of 3 or more consecutive frames are all greater than 1.8, the system determines that the current stress interference fringes exhibit a characteristic state of being dense upstream and sparse downstream.

[0037] Step 201b: After determining the upstream dense and downstream sparse state, using the spatial coordinates of the first virtual anchor point as the cluster center, a set of U-shaped curves with radii increasing in an arithmetic sequence are generated in the longitudinal plane of the floating detection domain. The opening direction of each U-shaped curve points to the upstream boundary of the floating detection domain, and the two endpoints of each U-shaped curve fall on the longitudinal boundary of the floating detection domain, thereby forming a cluster of U-shaped equidistant lines extending longitudinally along the floating detection domain, specifically including:

[0038] After completing step 200b and determining that the current stress interference fringes exhibit a dense upstream and sparse downstream distribution, the construction process of the U-shaped equidistant line cluster is initiated. First, the spatial coordinates (x1, y1, z1) of the first virtual anchor point on the longitudinal central axis of the floating detection domain are used as the fixed cluster center. Within the longitudinal plane of the floating detection domain, a set of U-shaped curves is generated according to preset geometric parameters. These preset geometric parameters specifically include the radial dimension parameters, opening direction parameters, and endpoint positioning parameters of the U-shaped curves. The radial dimension increases sequentially in an arithmetic progression, with the first term's radius set to 5mm. This value is determined based on the minimum effective analysis size of the floating detection domain, ensuring that the innermost curve completely encloses the core fringe area near the cluster center. The tolerance of the arithmetic progression is set to 2mm, which can be adjusted according to actual detection accuracy requirements. Fine-tuning is performed to maintain a uniform spacing between adjacent curves, ensuring that excessive spacing prevents feature omissions and insufficient spacing prevents curve overlap, thus guaranteeing a neat and orderly distribution of the line cluster. The opening direction parameter is set to uniformly face the upstream boundary of the floating detection domain, matching the distribution direction of denser fringes upstream and sparser fringes downstream. The endpoint positioning parameter is set so that both endpoints of each U-shaped curve precisely fit the longitudinal boundary of the floating detection domain, with endpoint positioning deviation controlled within ±0.1mm to avoid distortion of the line cluster coverage due to boundary offset. Finally, through the above continuous construction operations, a set of U-shaped equidistant line clusters extending along the longitudinal direction of the floating detection domain is formed. This line cluster completely covers the entire effective longitudinal area of ​​the floating detection domain, enabling it to capture the stress interference fringe distribution characteristics in different radial ranges in a layered and orderly manner.

[0039] Step 202b: Acquire the arc length coordinates of the second virtual anchor point on the axis of symmetry at the top of the hollow-shell type detection cable tray, and arrange a vibration sensor array in the width direction of the hollow-shell type detection cable tray to acquire vibration modal spectra in real time; perform energy integration on the vibration modal spectra, calculate the ratio of energy density in the middle section to that in both ends of the width direction, and when the ratio is lower than the preset energy concentration-dispersion discrimination coefficient for three consecutive frames or more, it is determined that the vibration energy distribution is dense in the middle section and sparse at both ends, specifically including:

[0040] Using an arc length measuring instrument, the arc length coordinates of the second virtual anchor point on the axis of symmetry at the top of the hollow-shell-type inspection cable tray are obtained and denoted as L (where L represents the arc length coordinate value of the second virtual anchor point on the axis of symmetry at the top, in mm). A vibration sensor array is evenly arranged along the width direction of the hollow-shell-type inspection cable tray, with the sensor spacing set to 1mm to 2mm, which can be adaptively adjusted according to the actual width of the cable tray to ensure that the sensors can comprehensively capture vibration signals in the width direction without any blind spots. Simultaneously, the sensor sampling frequency is not lower than 1000Hz to avoid issues caused by low sampling frequency. Insufficient signal strength leads to signal loss. Vibration data from the cable tray is acquired in real-time using a vibration sensor array. The raw vibration signals are then subjected to high-pass filtering and low-noise amplification to effectively remove environmental interference signals (such as external noise) and high-frequency noise, generating a clear vibration modal spectrum. This spectrum accurately reflects the vibration amplitude distribution at different locations along the width of the cable tray. Each point in the spectrum corresponds to a specific location along the width of the cable tray; a larger amplitude value indicates stronger vibration at that location, while a smaller amplitude value indicates smoother vibration. Energy integration is then performed on the vibration modal spectrum, i.e., E= dt, where E represents the integral value of vibrational energy (in J). The amplitude of vibration at a certain moment (in mm). The unit of time is s, and dt represents the integration time interval, set to 0.001s to match the sensor's 1000Hz sampling frequency, i.e., the sampling period is 1 / 1000s = 0.001s. The energy integral values ​​for the middle section (preset middle section range is the middle 1 / 3 of the width) and the two end sections (preset end sections are the two ends of the width, each 1 / 3 of the width) in the width direction are calculated respectively and denoted as follows: and (in This represents the integral value of vibration energy in the middle section region. (Represents the integral value of vibration energy at both ends, in J); calculate the energy density ratio of the two regions, i.e., the energy density ratio of the two regions. = / Calculate the energy concentration-dispersion discrimination coefficient, which involves first collecting multiple sets of energy density ratios under stable, undisturbed operating conditions and under vibration-disturbed operating conditions. The data is categorized into two conditions: Stable, interference-free operation refers to the hollow-shell type cable tray operating smoothly without external vibration interference, structural loosening, or constant tension (fluctuation range controlled within ±5%). Vibration amplitudes collected by vibration sensors are all below 0.01 mm, and the vibration signal is stable with no significant fluctuations. Under this condition, the vibration energy distribution along the width of the cable tray is uniform, without obvious concentrated or sparse areas. Vibration interference operation refers to the cable tray being subjected to slight shaking, tension fluctuations, etc. (tension fluctuations exceeding ±10% or slight external vibration interference), but without severe vibration or structural abnormalities. Vibration amplitudes collected by vibration sensors are between 0.01 mm and 0.1 mm, and the vibration signal exhibits significant fluctuations. Under this condition, the vibration energy along the width of the cable tray is prone to localized concentration. The calculation is performed under the stable, interference-free operation condition. The average value (denoted as) ) and vibration disturbance conditions The average value (denoted as) ), taking these two types of working conditions The boundary value of the value distribution is used as the discriminant coefficient, assumed to be 0.8. The energy density ratio over multiple consecutive frames (at least 3 frames) is also considered. Real-time monitoring is performed when 3 or more consecutive frames are detected. When all values ​​are below 0.8, the vibration energy distribution is determined to be dense in the middle and sparse at both ends.

[0041] Step 203b: After determining the state as dense in the middle and sparse at both ends, using the arc length coordinates of the second virtual anchor point as the cluster center, a set of convex arc-shaped curves with increasing potential energy values ​​in an arithmetic progression are generated within the transverse section of the hollow-cover type testing cable tray. The convex direction of each convex arc-shaped curve is away from the inner wall surface of the hollow-cover type testing cable tray, and the two endpoints of each convex arc-shaped curve fall on the inner walls on both sides of the hollow-cover type testing cable tray. This forms a cluster of convex arc-shaped equipotential surfaces extending transversely along the hollow-cover type testing cable tray, specifically including:

[0042] After clearly determining the vibration energy distribution as dense in the middle and sparse at both ends through step 202b (vibration energy distribution determination step), the arc length coordinate L of the second virtual anchor point is taken as the cluster center (this coordinate is the arc length coordinate calculated in step 202b, corresponding to the core area where the cable tray vibration energy is most concentrated). Within the transverse section of the hollow cover type testing cable tray, a set of convex arc curves with increasing potential energy values ​​in an arithmetic sequence are generated. The first term of the arithmetic sequence is set to 10J. The determination of this value combines the material stiffness of the hollow cover type testing cable tray (such as the bending and vibration resistance of commonly used cable tray materials such as steel and aluminum alloy) and the actual vibration energy level to ensure that the first curve can cover the basic potential energy area within the section. The tolerance of the arithmetic sequence is set to 5J, which can be flexibly adjusted according to the actual detection accuracy requirements. This ensures that the potential energy difference between adjacent curves is uniform and avoids curve overlap, clearly presenting the gradient distribution of potential energy from low to high within the section, so that the potential energy state corresponding to each curve can be quantified and traced. It is ensured that the convex direction of all outwardly convex arc curves is opposite to the inner wall of the hollow-shell-type testing cable tray, and the curvature of the convex surface must match the curvature parameter of the inner wall of the cable tray (e.g., if the curvature of the inner wall of the cable tray is 500mm, then the curvature of the convex surface of the curve must be consistent with it). The endpoint positions of each outwardly convex arc curve are controlled to ensure that both endpoints of all curves accurately fall on the inner walls of both sides of the hollow-shell-type testing cable tray, with the fitting error between the endpoints and the inner wall controlled within ±0.1mm, without offset or misalignment. Simultaneously, the endpoint positions must correspond to the mounting holes and support structures on the inner wall of the cable tray to avoid the curve failing to accurately reflect the potential energy distribution due to endpoint offset, ensuring that the curve and the cable tray structure are perfectly matched and meet the geometric constraints of the testing. Through the above orderly construction operations, a cluster of outwardly convex arc equipotential surfaces extending laterally along the hollow-shell-type testing cable tray is finally formed. This cluster of equipotential surfaces completely covers the entire transverse section of the cable tray, and the potential energy value corresponding to each curve is clearly visible.

[0043] This embodiment, through sampling and numerical iterative calculation of the floating detection domain and the cable tray's axis of symmetry, can locate the first and second virtual anchor points, effectively eliminating interference factors such as vibration and tension fluctuations, and ensuring the stability and uniqueness of the detection benchmark. Based on the stripe distribution and energy distribution state, a U-shaped equidistant line cluster and an outwardly convex arc-shaped equipotential surface cluster are constructed, forming a three-dimensional spatial benchmark adapted to the actual operating form of the strip, avoiding detection deviations caused by using a fixed geometric benchmark. The segmented stability judgment condition and the arithmetic sequence curve construction method ensure that the spatial benchmark has uniformity and continuity, and can completely cover the thickness variation characteristics of the splicing area.

[0044] In a preferred embodiment of the present invention, U-shaped equidistant line clusters and convex arc-shaped equipotential surface clusters are interleaved and superimposed in three-dimensional space to form a composite reference body composed of hollow rhombic meshes. The composite reference body is divided into several continuous trapezoidal cross-sectional segments, using the common vertex of two adjacent hollow rhombic mesh units as boundaries, including:

[0045] Step 300a: Orthogonally project the longitudinal plane containing the U-shaped equidistant line cluster and the transverse section containing the convex arc-shaped equipotential surface cluster into three-dimensional space, so that each U-shaped curve in the U-shaped equidistant line cluster intersects with each convex arc-shaped curve in the convex arc-shaped equipotential surface cluster in space, generating a series of three-dimensional spatial intersection points, specifically including:

[0046] Using the spatial coordinates (x1, y1, z1) of the first virtual anchor point determined in step 200b as the core positioning reference, the longitudinal plane containing the U-shaped equidistant line cluster is locked. This plane serves as the core longitudinal analysis plane of the floating detection domain and is completely coplanar with the image acquisition plane of the stress interference fringes in step 200b, ensuring that the projection operation remains consistent with the reference of the previous stress analysis. Simultaneously, using the arc length coordinates of the second virtual anchor point on the axis of symmetry at the top of the hollow-shell-type detection cable tray in step 201a as a reference, the transverse section range containing the convex arc-shaped equipotential surface cluster is defined. The effective range of this transverse section along the width of the cable tray is 30mm to 120mm, and the effective range along the height of the section is 15mm to 45mm, perfectly matching the internal cross-sectional dimensions of the hollow-shell-type detection cable tray, ensuring that all convex arc-shaped equipotential curves are constrained within this section range. The spatial positions of the two planes are calibrated using a coordinate calibration tool to eliminate positioning deviations.

[0047] A three-dimensional rectangular coordinate system is established with the first virtual anchor point (x1, y1, z1) as the origin. The x-axis is parallel to the direction of the printed tape, the y-axis extends laterally along the detection domain, and the z-axis is perpendicular to the detection plane (vertical direction). This coordinate system serves as the unified reference for projection calculation. Orthogonal projection is performed on the longitudinal plane containing the U-shaped equidistant line cluster and the transverse section containing the convex arc equipotential surface cluster. The longitudinal plane containing the U-shaped equidistant line cluster is projected along the normal direction of the transverse section of the convex arc equipotential surface, and the transverse section containing the convex arc equipotential surface cluster is projected along the normal direction of the longitudinal plane of the U-shaped line cluster. The projection direction is strictly perpendicular to the corresponding plane to ensure that the two planes are orthogonal and without any offset. After completing orthogonal projection and ensuring the orthogonality of the two planes, a one-to-one pairing and traversal calculation is performed on all U-shaped curves within the U-shaped equidistant line cluster and all convex arc curves within the convex arc equipotential surface cluster. The number of U-shaped curves is set to 5 to 8 based on the required detection accuracy, and the number of convex arc curves corresponds one-to-one with the number of U-shaped curves to ensure complete coverage without omissions. A spatial curve intersection analytical algorithm is used to solve for the intersection points. First, the parameterized spatial coordinate equations of the two curves are established. The parameterized equation of the U-shaped curve (based on the longitudinal plane, parameters...) is... ∈[0,1]): ;

[0048] In the formula, , , Let x, y, and z be the x, y, and z coordinates of any point on the U-shaped curve in the three-dimensional coordinate system, respectively, and let x1, y1, and z1 be the coordinates of the first virtual anchor point. For the U-shaped curve along The total length of the shaft (in the belt feeding direction), This is the lateral profile function for the U-shaped curve (set according to the curvature of the U-shaped curve). =4R ), The parameter variable has a value range of [0,1], which corresponds to the complete outline of the U-shaped curve. R is the preset radius of curvature of the U-shaped curve, in mm.

[0049] Parametric equations for convex arc curves (based on the transverse section, parameters) ∈[0,1]): ;

[0050] In the formula, , , Let x, y, and z be the x, y, and z coordinates of any point on the convex arc curve in the three-dimensional coordinate system, respectively. Let be the contour function of the convex arc curve along the y-axis. =B , Let be the profile function of the convex arc curve along the z-axis. =H , The parameter variable has a value range of [0,1], which corresponds to the complete outline of the convex arc curve. x1, y1, and z1 are also the coordinates of the first virtual anchor point to ensure consistency with the reference of the U-shaped curve.

[0051] By simultaneously solving the two parameterized equations, the common solution of the system of equations is obtained using Newton's iteration method. The iteration accuracy is controlled within 0.001 mm. Invalid solutions exceeding the transverse cross-section (width 30 mm to 120 mm, height 15 mm to 45 mm) and the longitudinal range of the U-shaped curve cluster are discarded. Finally, a unique common solution is obtained, which is the spatial intersection coordinate of a single set of paired curves. Following this method, all U-shaped curves and convex arc curves are paired and calculated one by one. The coordinate calculation error of all intersection points is controlled within ±0.01 mm. Finally, all intersection points are sorted according to their spatial position to form a continuous and ordered three-dimensional spatial intersection point set, and the (x, y, z) three-dimensional coordinates of each intersection point are completely stored.

[0052] Step 301a: Each 3D spatial intersection point is used as a mesh vertex. Adjacent intersection points on adjacent U-shaped curves and adjacent intersection points on adjacent convex arc curves are connected sequentially to form an initial mesh shell composed of multiple quadrilateral mesh patches. Specifically, this includes: using all 3D spatial intersection points as the basic vertices of the initial mesh shell, and supplementing them with floating detection domain boundary feature points and convex arc equipotential surface contour feature points. There are 4 floating detection domain boundary feature points, corresponding to the four corner vertices of the detection domain (upper left, lower left, upper right, and lower right). The coordinates of each vertex are obtained by actual measurement using a 3D positioning instrument, and the coordinate measurement accuracy is controlled within ±0.05mm. The convex arc equipotential surface contour feature points are the two endpoints and the midpoint of each convex arc curve, with a total of 2m points, where m is the total number of convex arc curves, and the points are arranged one-to-one with the number of curves. All vertices are uniformly included in the vertex dataset to ensure complete spatial coverage, no omission of key feature points, and that the accuracy of all vertex coordinates is consistent with the accuracy of the intersection point calculation in step 300a.

[0053] Using all three-dimensional spatial intersections, floating detection domain boundary feature points, and convex arc equipotential surface contour feature points as the basis for mesh construction, vertex connections are completed sequentially according to spatial topological adjacency relationships. First, adjacent spatial intersections on the same U-shaped curve are connected sequentially, and then adjacent intersections on the same convex arc curve are connected sequentially. At the same time, the convex arc equipotential surface boundary contour points are closedly connected with the corresponding boundary feature points of the floating detection domain, generating regular quadrilateral mesh patches one by one. The single-side length of all quadrilateral mesh patches is controlled within the range of 0.5mm to 1mm, matching the line density detection accuracy set in step 200b, so that each patch can correspond to an independent stress interference fringe distribution area. Adjacent quadrilateral mesh patches are seamlessly connected, and the overlap error of the common edge of the patches does not exceed ±0.02mm. There are no patch overlaps or area gaps. The spatial coverage of the overall initial mesh shell is completely consistent with the longitudinal range of the U-shaped equidistant line cluster and the lateral range of the convex arc equipotential surface cluster, forming an initial mesh shell with complete structure and regular topology.

[0054] Step 302a: For each quadrilateral mesh facet, connect the intersection points of the diagonals of the quadrilateral mesh facet, generate a hollow node at the center of the quadrilateral mesh facet, and delete the original four edges of the quadrilateral mesh facet, so that each quadrilateral mesh facet evolves into a hollow rhombic mesh unit enclosed by four triangular facets; splice all the hollow rhombic mesh units according to the three-dimensional space intersection coordinates to form a composite reference body, specifically including:

[0055] A global geometric check is performed on the initial mesh shell constructed in step 301a. Quadrilateral faces with side lengths exceeding the allowable range of 0.5mm to 1mm are adaptively adjusted. Faces with side lengths greater than 1mm are divided into equal parts, and faces with side lengths less than 0.5mm are merged to ensure all mesh face lengths meet accuracy requirements. Simultaneously, the entire mesh shell undergoes surface smoothing to eliminate edge burrs, sharp corners, and locally distorted faces, ensuring the overall surface flatness deviation is controlled within ±0.01mm. For each pre-processed quadrilateral mesh face, its two diagonal edges are connected. The geometric intersection of these two diagonals is the center position of the quadrilateral face. The three-dimensional coordinates of the center are calculated using the arithmetic mean method. , , )= Where (x1,y1,z1), (x2,y2,z2), (x3,y3,z3), and (x4,y4,z4) are the spatial coordinates of the four vertices of the quadrilateral facet; hollow nodes are generated using these central coordinates as the positioning reference, with the diameter of the hollow nodes uniformly set to 0.3mm and the spatial positioning error of the nodes not exceeding ±0.03mm; after the hollow nodes are generated, the four contour edges of the original quadrilateral facet are deleted, leaving only the four vertices and the central hollow node, thus completing the geometric reconstruction of a single facet.

[0056] Using the hollow node at the center of the facet as the core, the four vertices of the original quadrilateral facet are connected to the hollow node with straight lines to form four triangular facets that are adjacent to each other and share a vertex. The four triangular facets together form a hollow rhomboid mesh unit. After reconstruction, the side length error of each triangular facet is controlled within ±0.05mm and the interior angle deviation does not exceed ±1°, ensuring that the mesh unit is geometrically regular and structurally stable. The reconstructed hollow rhombic mesh units are assembled in an orderly manner according to their original three-dimensional spatial coordinates. During assembly, it is ensured that adjacent mesh units share vertices that coincide and common edges that match perfectly. The connection error between adjacent units does not exceed ±0.05mm. The resulting composite reference body extends continuously longitudinally along the floating detection domain, while completely covering the transverse cross-sectional area of ​​the convex arc-shaped equipotential surface cluster. It retains the longitudinal stress distribution characteristics represented by the U-shaped equidistant line cluster and also bears the transverse vibration potential energy distribution characteristics represented by the convex arc-shaped equipotential surface cluster. It can truly reflect the distribution law of stress and vibration coupling in three-dimensional space. The spacing and density of the longitudinally arranged mesh nodes correspond to the U-shaped equidistant line cluster. The stress gradient variation is characterized by a dense grid, specifically defined as having ≥3 grid nodes and a node spacing ≤0.33mm within a unit longitudinal length (1mm). Areas with such dense nodes exhibit more significant stress variations. The transverse grid outline and curvature variation correspond to the vibration potential energy distribution trend represented by the convex arc-shaped equipotential surface cluster. Areas with higher potential energy exhibit greater grid curvature. Through the mutual constraint and spatial superposition of longitudinal stress characteristics and transverse potential energy characteristics within the grid structure, the composite reference body can synchronously present the coupling relationship between stress intensity and vibration energy magnitude in three-dimensional space, intuitively and quantitatively reflecting the coordinated change law of stress distribution and vibration modes within the detection area.

[0057] Step 300b: Along the tape travel direction, perform a longitudinal scan of the composite reference body to extract the coordinates of the common vertices of all hollow rhombic mesh elements in the composite reference body; use the projection points of two adjacent common vertices in the tape travel direction as segment boundaries, and make cutting planes perpendicular to the tape travel direction on the composite reference body. The region between two adjacent cutting planes is defined as a trapezoidal cross-section segment; for each trapezoidal cross-section segment, calculate the first cross-sectional area at the upstream boundary and the second cross-sectional area at the downstream boundary. If the first cross-sectional area and the second cross-sectional area are not equal, determine that the corresponding cross-section segment has trapezoidal geometric features and mark the corresponding cross-section segment as a trapezoidal cross-section segment. Specifically, this includes:

[0058] Along the tape travel direction, using the longitudinal central axis of the composite reference body as a spatial reference, a continuous straight-line scanning path is planned and set. The scanning frequency is set to 30 times per second, ensuring it is completely consistent with the image acquisition frame rate of the stress interference fringes in step 200b. This guarantees that the scanning sequence and spatial position correspond one-to-one with the previously acquired stress and vibration data, achieving synchronous matching of multi-source detection data. Through continuous longitudinal scanning along the tape travel direction, the vertex coordinates shared by all hollow rhombic mesh units inside the composite reference body are traversed and extracted. Only valid common vertices belonging to two or more adjacent mesh units are retained, while isolated boundary vertices and non-shared vertices are removed. Each common vertex is vertically projected onto the normal plane of the tape travel direction. Using the resulting projection point as the segmentation boundary reference, a series of parallel cutting planes perpendicular to the tape travel direction are generated on the composite reference body. The spacing between each cutting plane is consistent with the length of the preset trapezoidal section segment, ensuring that each cutting plane can pass through the vertex position of the corresponding mesh unit, achieving precise segmentation and cutting of the mesh structure. For each trapezoidal cross-sectional segment enclosed by adjacent cutting planes, its cross-sectional area is calculated using the coordinate analytical method, i.e., the cross-sectional area of ​​each trapezoidal cross-sectional segment = In the formula, a is the length of the intersection line between the upstream cutting plane and the composite reference body contour, and b is the length of the intersection line between the downstream cutting plane and the composite reference body contour. The vertical distance between two adjacent cutting planes is expressed in mm, and the calculation result is in mm². The formula is used to calculate the first cross-sectional area (upper) of the upstream boundary and the second cross-sectional area (lower) of the downstream boundary of the same trapezoidal cross-section segment. The upstream and downstream cross-sectional areas of the same segment are compared numerically. If the upper and lower values ​​are not equal, and the absolute difference is greater than or equal to 0.5 mm², the segment is determined to have obvious trapezoidal geometric features. The system then uniformly identifies the trapezoidal cross-section segment and records its spatial location and cross-sectional parameters, completing the identification and marking of all cross-section segments.

[0059] This embodiment constructs spatial intersections and generates a quadrilateral mesh shell through orthogonal projection, enabling the rapid establishment of a three-dimensional geometric model of stress and vibration characteristic regions, and achieving precise fusion of the two types of feature spaces. Optimizing the quadrilateral facets into hollow rhombic mesh units reduces mesh redundancy while ensuring structural strength, improving the efficiency of subsequent data calculation and feature extraction. Dividing the cross-section into trapezoidal segments based on common vertices and using area differences to determine geometric features allows for the identification of the cross-sectional deformation state of the printed strip during operation, providing a reliable quantitative basis for the joint analysis of stress distribution and vibration modes.

[0060] In a preferred embodiment of the present invention, within each trapezoidal cross-section segment, a first set of sensing nodes and a second set of sensing nodes are selected and intersected to construct a spatial diagonal; the cumulative wall thickness of each spatial diagonal passing through the hollow rhombic grid unit is extracted as the local thickness difference value of the corresponding cross-section segment, including:

[0061] Step 400a: For each trapezoidal cross-section segment, locate the vertices of all hollow rhombic mesh units within the projection area of ​​the first arc-shaped protrusion array as the first set of sensing nodes, and locate the vertices of all hollow rhombic mesh units within the projection area of ​​the second arc-shaped protrusion array as the second set of sensing nodes. Specifically, this includes: for each independent trapezoidal cross-section segment that has undergone feature determination, using the projection area formed by the first arc-shaped protrusion array on the composite reference body as the spatial constraint range, specifically, the nodes must simultaneously be located inside the boundary of the trapezoidal cross-section segment and within the effective contour range of the composite reference body, and the node coordinates must fall within the three-dimensional spatial interval covered by the normal projection of the first arc-shaped protrusion array. Within this constraint range, all vertices of the hollow rhombus mesh cells are traversed, and all vertices satisfying the above spatial coordinate constraints are uniformly marked as the first group of sensing nodes. Simultaneously, the projection area formed by the second arc-shaped protrusion array on the composite datum body is used as the spatial constraint range. Specifically, the nodes must belong to the current trapezoidal section segment, be located within the outline of the composite datum body, and their coordinates must be within the spatial area covered by the projection of the second arc-shaped protrusion array, and must not overlap with the section segment boundary or the outer area of ​​the mesh. Within this constraint range, all vertices of the hollow rhombus mesh cells within the same trapezoidal section segment are traversed, and all vertices satisfying the above spatial coordinate constraints are uniformly marked as the second group of sensing nodes. Both groups of sensing nodes are confined to the spatial range of the corresponding trapezoidal section segment, not exceeding the section segment boundary and the outline of the composite datum body. The node coordinates use the three-dimensional coordinate data from the previous mesh construction, with a coordinate accuracy maintained at ±0.01mm.

[0062] Step 401a involves pairing each node in the first group of sensing nodes with the node in the second group of sensing nodes that is located within the same trapezoidal cross-section and has the largest spatial distance, generating several pairs of cross-paired node pairs. Specifically, for each independent node in the first group of sensing nodes, all valid nodes belonging to the current trapezoidal cross-section are selected in the second group of sensing nodes, and the Euclidean distance between the node and all sensing nodes in the second group is calculated using the three-dimensional spatial distance formula. The node with the largest distance value is selected from all the calculation results as the pairing target, and the two groups of nodes are matched one-to-one to form cross-paired node pairs. After traversal, a set of all cross-paired node pairs under the current trapezoidal cross-section is obtained.

[0063] Step 402a: For each pair of intersecting nodes, connect the two nodes to form a straight line segment, treating this segment as a spatial diagonal, ensuring that each spatial diagonal passes through the geometric centroid of the trapezoidal cross-section segment. Specifically, this includes: for each pair of intersecting nodes, connecting the two nodes with a straight line to form a spatial straight line segment, defining this segment as a spatial diagonal; during the construction process, first calculate the geometric centroid coordinates of the trapezoidal cross-section segment, where the centroid coordinates (xc, yc, zc) = , , Where (x1,y1,z1) to (x4,y4,z4) are the coordinates of the four boundary corner points of the trapezoidal cross section. By fine-tuning the coordinates, each spatial diagonal is made to pass through the geometric centroid. That is, firstly, the coordinate deviation components between the node pair connection line and the geometric centroid are calculated, and then the coordinates of the two paired nodes are corrected by the same direction offset. The offset amount is no more than ±0.02mm. Under the premise of ensuring that the node still belongs to the corresponding sensing node group, the corrected connection line passes through the geometric centroid, ensuring that all spatial diagonals are symmetrically distributed with the centroid as the center and do not interfere with the edge of the grid cell.

[0064] Step 400b involves discretizing and sampling each spatial diagonal along its extension direction, recording the cell number and the coordinates of the entry and exit points of each hollow rhombus grid cell that the spatial diagonal sequentially passes through. Specifically, this includes: for each constructed spatial diagonal, performing equally spaced discretized sampling along its extension direction, with the sampling interval set to 0.1 mm to maintain consistency with the grid cell precision. During the sampling process, each hollow rhombus grid cell that the spatial diagonal sequentially passes through is identified and recorded segment by segment, simultaneously recording the unique cell number of each passed grid cell, and acquiring the coordinates of the entry point and exit point of the spatial diagonal entering the corresponding grid cell.

[0065] Step 401b involves creating a cumulative variable for each spatial diagonal and setting its initial value to zero. For each hollow rhombus mesh cell that is penetrated, the wall thickness value of the corresponding hollow rhombus mesh cell along the line connecting the penetration point and the exit point is obtained, and the wall thickness value is accumulated into the cumulative variable corresponding to the spatial diagonal. Specifically, this includes: creating a floating-point cumulative variable for each independent spatial diagonal and setting its initial value to 0; for each hollow rhombus mesh cell penetrated by a spatial diagonal, calculating the wall thickness value of the cell according to the line connecting the penetration point and the exit point, specifically using the three-dimensional Euclidean distance formula. = Where (x3, y3, z3) are the coordinates of the entry point, and (x4, y4, z4) are the coordinates of the exit point. The calculation results are... This is the actual wall thickness value of the hollow rhomboid grid cell in the current diagonal direction; the wall thickness value of each cell that is passed through is sequentially added to the cumulative variable of the corresponding spatial diagonal. The accumulation process is performed in the order in which the spatial diagonal passes through the grid cells, without repeated calculation or omission of cells, to ensure that the accumulation result truly reflects the wall thickness distribution on the path.

[0066] Step 402b involves taking the final value of the cumulative variable corresponding to each spatial diagonal as the cumulative wall thickness of the corresponding spatial diagonal, calculating the arithmetic mean of the cumulative wall thickness of all spatial diagonals within the same trapezoidal cross-section, and using the arithmetic mean as the local thickness difference value of the corresponding trapezoidal cross-section. Specifically, this includes:

[0067] After the wall thickness values ​​of all hollow rhombic grid units are accumulated, the final value of the accumulated variable corresponding to each spatial diagonal is defined as the cumulative wall thickness of that diagonal. The arithmetic mean of the cumulative wall thickness of all spatial diagonals within the same trapezoidal cross-section is calculated, and the calculated arithmetic mean is used as the local thickness difference value of the current trapezoidal cross-section. This value directly reflects the uniformity of the thickness distribution and the level of local deviation within the cross-section. The smaller the local thickness difference value, the closer the cumulative wall thickness of all spatial diagonals within the same trapezoidal cross-section is, meaning that the wall thickness distribution of hollow rhombic grid units at each position within the cross-section is more uniform and the local thickness deviation is smaller. The larger the local thickness difference value, the greater the difference in the cumulative wall thickness of each spatial diagonal is, indicating that the wall thickness difference of grid units in different areas within the cross-section is more obvious and the local thickness deviation is greater. When the value exceeds the preset threshold (the preset threshold is set according to the detection accuracy, ranging from 0.08mm² to 0.12mm², with 0.10mm² preferred under normal detection accuracy), it can be determined that there is a significant thickness non-uniformity problem in the cross-section.

[0068] This embodiment, by dividing the sensing nodes into dual-array projection areas and performing maximum-distance cross-pairing, can maximize the coverage of the internal space of the cross-section, improving the comprehensiveness and representativeness of thickness detection. Using the diagonal of the centroid space as the sampling path ensures a symmetrical and uniform detection path, avoiding calculation errors caused by local bias. Employing discrete sampling along the path and wall thickness accumulation reflects thickness changes at the grid cell level, resulting in higher quantification accuracy and effectively identifying minute thickness differences. Averaging the accumulated wall thickness along multiple diagonals yields the local thickness difference value, reducing random errors from a single sampling path and improving the stability and reliability of cross-section thickness evaluation.

[0069] In a preferred embodiment of the present invention, all local thickness difference values ​​are weighted and fused to obtain a multidimensional thickness deviation tensor, and the multidimensional thickness deviation tensor is mapped to a multidimensional thickness deviation output matrix as a quantitative detection result of the thickness difference between each roll of printing tape, including:

[0070] Step 500: Collect the local thickness difference values ​​of all trapezoidal cross-section segments and assign a spatial weight coefficient to each trapezoidal cross-section segment. The spatial weight coefficient is proportional to the longitudinal position coordinate of the corresponding trapezoidal cross-section segment in the composite reference body. Specifically, the system sequentially traverses and extracts all trapezoidal cross-section segment data that have completed feature determination and local thickness difference value calculation according to the longitudinal arrangement order of the trapezoidal cross-section segments. The local thickness difference value corresponding to each segment is uniformly stored in the global thickness feature dataset. The dataset is stored in order according to the cross-section segment number to ensure that the data corresponds one-to-one with the spatial position, without loss or error. A spatial weight coefficient adapted to its spatial position is assigned to each trapezoidal cross-section segment, i.e. =Normalization scaling factor × In the formula, For the first The spatial weighting coefficients corresponding to each trapezoidal cross-section segment The coordinates of the geometric centroid of the trapezoidal cross-section in the longitudinal coordinate system of the composite reference body are normalized by a scaling factor of 0.02. This factor is used to uniformly scale the longitudinal coordinate values ​​to a reasonable weight range between 0.1 and 1.0, preventing the coefficient from being too large or too small and affecting the stability of subsequent calculations. According to this formula, the larger the longitudinal coordinate of the cross-section, the higher the corresponding spatial weight coefficient, achieving a positive correlation between weight and longitudinal position. All spatial weight coefficients are non-negative real numbers, matched one-to-one with the trapezoidal cross-section, without redundancy or omission of any cross-section.

[0071] Step 501 involves multiplying the local thickness difference value of each trapezoidal cross-section segment with the corresponding spatial weight coefficient, and accumulating the values ​​in the row and column vectors according to the distribution position of each trapezoidal cross-section segment in the width direction to form a multidimensional thickness deviation tensor with rows and columns. Specifically, this includes: performing point-to-point multiplication of the local thickness difference value of each trapezoidal cross-section segment with the corresponding assigned spatial weight coefficient to obtain the thickness deviation characteristic value of the cross-section segment after spatial position weighting; dividing and classifying the actual spatial distribution interval of each trapezoidal cross-section segment in the width direction of the printing strip, dividing the width direction from left to right into several equally spaced intervals (each interval is 5mm wide, adapted to the width of the printing strip, ensuring that there is a corresponding trapezoidal cross-section segment in each interval), with each distribution interval corresponding to a fixed width position, clearly defining the affiliation of each trapezoidal cross-section segment, ensuring no overlap or omission. For each distribution interval, the weighted thickness deviation value of the corresponding trapezoidal cross-section segment is classified according to its affiliation, and then successively accumulated into the corresponding positions of the pre-constructed row vector and column vector. The row vector is set according to the interval numbering in the width direction, with a total of 8 equal intervals (corresponding to 8 row indices). Each row vector position corresponds to one width interval and is used to accumulate the weighted thickness deviation value of all trapezoidal cross-section segments in that interval. The column vector is set according to the segment number of the longitudinal trapezoidal cross-section segment, with a total of 10 longitudinal segments (corresponding to 10 column indices). Each column vector position corresponds to one longitudinal segment and is used to accumulate the weighted thickness deviation value of all trapezoidal cross-section segments in that segment. The pre-constructed row and column vectors are constructed as follows: First, initialize two vectors with all zeros. The length of the row vector is the same as the number of equal intervals in the width (8), and the length of the column vector is the same as the number of vertical segments (10). Traverse each trapezoidal section segment and, based on its distribution position in the width direction, accumulate its weighted thickness deviation value to the corresponding position of the corresponding row vector. At the same time, based on its vertical segment number, accumulate it to the corresponding position of the corresponding column vector to ensure that each weighted thickness deviation value can correspond to its own row and column position without errors, omissions, or repetitions.

[0072] Using the width-divided interval numbers as row indices (1 to 8) and the segment numbers of the longitudinal trapezoidal cross-section segments as column indices (1 to 10), the feature values ​​accumulated in the row and column vectors are substituted one by one into a preset tensor matrix according to the rule that the row index corresponds to the row and the column index corresponds to the column. This fills in the values ​​at the intersection of each row and column, thus constructing a multidimensional thickness deviation tensor with a fixed number of rows (8 rows) and columns (10 columns). The number of rows in this tensor is determined by the total number of width-divided intervals (8), and the number of columns is determined by the total number of longitudinal trapezoidal cross-section segments (10). The overall dimensional dimensions and composite... The number of segments along the width and the number of segments along the longitudinal direction of the reference volume are completely consistent, ensuring that the tensor corresponds one-to-one with the actual spatial segments. Each element in the tensor uniquely corresponds to an independent spatial sub-region (i.e., the intersection of a certain width division interval and a certain longitudinal segment). The larger the element value, the more significant the weighted thickness deviation after position weight correction in the spatial sub-region, and the worse the thickness uniformity. The smaller the element value, the more uniform the thickness distribution in the region, and the lower the degree of local deviation. By changing the size of the element values, the overall thickness deviation characteristics after position weight correction in the corresponding spatial region can be intuitively and quantitatively reflected.

[0073] Step 502: Fill each tensor element of the multidimensional thickness deviation tensor into the corresponding position of a pre-initialized output matrix according to the corresponding row index and column index to form a multidimensional thickness deviation output matrix. The multidimensional thickness deviation output matrix is ​​then used as the quantitative detection result of the thickness difference between each roll of printed tape. Specifically, based on the total number of equal intervals in the width direction and the total number of trapezoidal cross-section segments in the longitudinal direction of the composite reference body, a matrix with all zero elements is pre-initialized according to the principle of consistent row and column dimensions. The number of rows in this matrix is ​​exactly the same as the number of segments in the width direction, the number of columns is exactly the same as the number of segments in the longitudinal direction, and the matrix dimensions are consistent with the multidimensional thickness deviation tensor. This matrix serves as the initial carrier of the multidimensional thickness deviation output matrix. During the matrix filling process, each element in the multidimensional thickness deviation tensor is read sequentially, and the row index and column index information of the element are extracted. The row index corresponds to the interval number in the width direction, and the column index corresponds to the segment number in the vertical direction. According to the index matching rules, the tensor elements are assigned to the coordinate positions of the same row number and the same column number in the output matrix. The filling of all elements is completed row by row and column by column. The entire assignment process follows the one-to-one correspondence principle, and there are no cases of misalignment of rows and columns, missing values, duplicate assignments, or coordinate offsets. The multidimensional thickness deviation output matrix after filling retains the distribution pattern of thickness deviation in the two core dimensions. In the longitudinal direction of the tape, if the value of a column gradually increases from top to bottom, it indicates that the thickness deviation becomes more significant as the longitudinal position progresses, meaning that the thickness non-uniformity is more obvious closer to the downstream of the tape. If the value gradually decreases from top to bottom, it indicates that the thickness distribution is more uniform and the thickness deviation is smaller as the longitudinal position moves further downstream. In the width direction, if the value of a row is generally high, it indicates that the thickness deviation is generally large and the thickness uniformity is poor at that width position. If the value of a row is generally low and the fluctuation is small, it indicates that the thickness distribution at that width position is relatively uniform and the local deviation is not obvious.

[0074] The value at each position in the matrix can intuitively reflect the thickness deviation of the corresponding spatial region. The larger the value, the more significant the thickness deviation in that region, the worse the thickness uniformity, and there may even be obvious thickness anomalies. The smaller the value, the more uniform the thickness distribution in that region, and the smaller the thickness deviation. It can clearly and accurately reflect the thickness difference characteristics of the corresponding spatial sub-region, realize the full-domain quantitative expression of thickness difference, and make the thickness deviation of different rolls and different positions clear at a glance. The system finally outputs this multi-dimensional thickness deviation matrix as a standardized quantitative detection result of the thickness difference between different rolls of printed tape.

[0075] This embodiment constructs a multidimensional thickness deviation tensor through weighted accumulation, which integrates discrete local thickness features into structured spatial features, improving the integrity and readability of the data. The quantitative detection results are output in matrix form, enhancing system integration and detection efficiency.

[0076] The experimental data in this embodiment comes from the actual operation record of a flatbed printing production line of a large printing company. The experimental object is three rolls of polyester film (PET) printing tape running in parallel, with a thickness of 0.12mm and a running speed of 60 meters / minute. The experimental environment is the actual production condition.

[0077] Module 2: Dual Virtual Anchor Point Calculation and Isocentric Line Cluster Construction:

[0078] The floating detection domain was discretized along the longitudinal central axis with equal intervals and a sampling step size of 0.5 mm to obtain the bidirectional radius of curvature values ​​at each sampling point on the longitudinal central axis. The bidirectional radius of curvature values ​​were then ratio-calculated to obtain a bidirectional curvature ratio distribution sequence. The bidirectional curvature ratio distribution sequence was extracted in the experiment, and the sampling point with the largest rate of change (sampling point number 45) was selected as the first candidate point. Using the first candidate point as the center, a first search window area was formed with a total length of 10 mm, extending 5 mm forward and backward along the longitudinal central axis. The local root mean square error of the bidirectional radius of curvature values ​​was calculated within this window area, and the position with the smallest local root mean square error (sampling point number 48) was designated as the first virtual anchor point. The top axis of symmetry of the hollow-shell type detection bridge was discretized along the transverse direction with equal arc lengths and a sampling arc length interval of 0.5 mm to obtain the transverse vibration mode amplitude at each sampling point. Zero-crossing point detection was performed on the mode amplitudes, and all zero-crossing positions where the sign of the mode amplitude changed were extracted.

[0079] Figure 2 The process of solving the first virtual anchor point is shown, displaying the hypercurvature ratio distribution sequence (blue curve), the first candidate point (red dot, idx=45), the first search window area (green shading), and the first virtual anchor point (green asterisk, idx=48).

[0080] Module 3: Trapezoidal Section Segment Division:

[0081] The composite reference body is longitudinally scanned (scanning frequency 30Hz) along the tape travel direction to extract the coordinates of the common vertices of all hollow rhombic mesh elements. Using the projection points of two adjacent common vertices in the tape travel direction as segment boundaries, a cutting plane perpendicular to the tape travel direction is made on the composite reference body to divide the composite reference body into 10 continuous trapezoidal cross-sectional segments.

[0082] For each trapezoidal cross-section segment, calculate the first cross-sectional area at the upstream boundary and the second cross-sectional area at the downstream boundary. If the absolute difference between the two is greater than or equal to 0.5 mm², the cross-section segment is determined to have trapezoidal geometric characteristics. All 10 trapezoidal cross-section segments in the experiment met the trapezoidal determination criteria.

[0083] Figure 3The area distribution of the trapezoidal cross-section is shown, displaying the upstream boundary area (blue dots), downstream boundary area (red squares), and area difference (green bars) of each cross-section. The dashed line represents the trapezoidal determination threshold (0.5 mm²).

[0084] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A system for detecting thickness difference in multiple rolls of printed flat screen tape, characterized in that, include: The detection cable tray construction module is used to construct a hollow cover-type detection cable tray spanning multiple rolls of parallel printed tape. The inner wall of the hollow cover-type detection cable tray is sequentially provided with a first arc-shaped protrusion array and a second arc-shaped protrusion array along the longitudinal extension direction. The first arc-shaped protrusion array is used to apply a first preload force in the normal direction of the reference surface of the printed tape, and the second arc-shaped protrusion array is used to apply a second preload force in the opposite direction. The first preload force and the second preload force work together in the splicing area of ​​two adjacent rolls of printed tape, so that the surface of the printed tape in the splicing area is subjected to normal opposing compression and normal opposing tension, respectively, to form a floating detection domain with double curvature constraint characteristics in the splicing area. The solution module is used to solve the first virtual anchor point located on the geometric center line of the floating detection domain and the second virtual anchor point located on the axis of symmetry at the top of the hollow cover-type detection bridge, so as to construct a U-shaped equidistant line cluster extending longitudinally along the floating detection domain and an outwardly convex arc-shaped equipotential surface cluster extending laterally along the hollow cover-type detection bridge. The cross-section segmentation module is used to interleave U-shaped equidistant line clusters and convex arc-shaped equipotential surface clusters in three-dimensional space to form a composite reference body composed of hollow rhombic meshes. The composite reference body is divided into several continuous trapezoidal cross-section segments with the common vertex of two adjacent hollow rhombic mesh units as the boundary. The difference calculation module is used to select the first set of sensing nodes and the second set of sensing nodes within each trapezoidal cross section and connect them to form a spatial diagonal; it extracts the cumulative wall thickness of each spatial diagonal passing through the hollow rhomboid grid unit as the local thickness difference value of the corresponding cross section. The results output module is used to weight and fuse all local thickness difference values ​​to obtain a multidimensional thickness deviation tensor, and then map the multidimensional thickness deviation tensor to a multidimensional thickness deviation output matrix as a quantitative detection result of the thickness difference between each roll of printing tape.

2. The multi-roll thickness difference detection system for printed flat screens according to claim 1, characterized in that, Solving for the first virtual anchor point located on the geometric center line of the floating detection domain and the second virtual anchor point located on the axis of symmetry at the top of the hollow-shell detection cable tray includes: The floating detection domain is discretized at equal intervals along the longitudinal central axis to obtain the bidirectional curvature radius values ​​at each sampling point along the first and second preload directions, respectively. The bidirectional curvature radius values ​​are then ratio-calculated to obtain the bidirectional curvature ratio distribution sequence at each sampling point. The sampling point with the largest rate of change in the bidirectional curvature ratio distribution sequence is extracted as the first candidate point. Using the first candidate point as the search center, the domain is extended forward and backward by a preset distance along the longitudinal central axis to form a first search window. The local mean square error of the bidirectional curvature radius values ​​is calculated within the first search window, and the position with the smallest local mean square error is marked as the first virtual anchor point. The top axis of symmetry of the hollow-shell type testing cable tray is discretized along the transverse direction using equal arc length sampling to obtain the transverse vibration mode amplitude at each sampling point on the top axis of symmetry. Zero-crossing point detection is performed on the transverse vibration mode amplitude, and all zero-crossing positions where the sign of the mode amplitude changes are extracted. The zero-crossing position with the smallest arc length distance from the geometric center of the top axis of symmetry is extracted as the second candidate point. Using the second candidate point as the search center, a preset arc length is extended in both the front and rear directions along the top axis of symmetry to form a second search window area. Within the second search window area, the sum of the absolute values ​​of the mode amplitude differences between adjacent sampling points is calculated, and the position with the smallest sum of absolute values ​​is marked as the second virtual anchor point.

3. The multi-roll thickness difference detection system for printed flat screens according to claim 2, characterized in that, Constructing a cluster of U-shaped equidistant lines extending longitudinally along the floating detection domain and a cluster of outwardly convex arc-shaped equipotential surfaces extending laterally along the hollow-cover type detection bridge, including: The spatial coordinates of the first virtual anchor point on the longitudinal central axis of the floating detection domain are acquired, and the stress interference fringe image excited by the first preload and the second preload is extracted frame by frame along the longitudinal direction in the floating detection domain. The stress interference fringe image is binarized, and the ratio of the fringe line density of the upstream half region to the downstream half region in each frame image is calculated. When the ratio is greater than the preset dense-sparse discrimination coefficient for three consecutive frames, it is determined that the stress interference fringe distribution is dense upstream and sparse downstream. After determining that the upstream is dense and the downstream is sparse, a set of U-shaped curves with an arithmetic progression are generated in the longitudinal plane of the floating detection domain, with the spatial coordinates of the first virtual anchor point as the cluster center. The opening direction of each U-shaped curve points to the upstream boundary of the floating detection domain, and the two endpoints of each U-shaped curve fall on the longitudinal boundary of the floating detection domain, thus forming a U-shaped equidistant line cluster extending longitudinally along the floating detection domain. The arc length coordinates of the second virtual anchor point on the axis of symmetry at the top of the hollow-covered detection bridge are collected, and a vibration sensor array is arranged in the width direction of the hollow-covered detection bridge to acquire vibration modal spectra in real time. Energy integration is performed on the vibration modal spectra, and the ratio of energy density in the middle section to that in both ends of the width direction is calculated. When the ratio is lower than the preset energy concentration-dispersion discrimination coefficient for three consecutive frames or more, it is determined that the vibration energy distribution is dense in the middle section and sparse at both ends. After determining that the state is dense in the middle section and sparse at both ends, a set of convex arc curves with increasing potential energy values ​​are generated in the transverse section of the hollow cover-type detection cable tray, with the arc length coordinate of the second virtual anchor point as the cluster center. The convex surface direction of each convex arc curve is away from the inner wall surface of the hollow cover-type detection cable tray, and the two endpoints of each convex arc curve fall on the inner walls on both sides of the hollow cover-type detection cable tray, thereby forming a cluster of convex arc equipotential surfaces extending laterally along the hollow cover-type detection cable tray.

4. The multi-roll thickness difference detection system for printed flat screens according to claim 3, characterized in that, By interleaving and overlapping U-shaped equidistant line clusters and convex arc-shaped equipotential surface clusters in three-dimensional space, a composite reference body composed of hollow rhombic meshes is formed, including: The longitudinal plane containing the U-shaped equidistant line cluster and the transverse section containing the outwardly convex arc equipotential surface cluster are orthogonally projected in three-dimensional space, so that each U-shaped curve in the U-shaped equidistant line cluster intersects with each outwardly convex arc curve in the outwardly convex arc equipotential surface cluster in space, generating a series of three-dimensional spatial intersection points. Using the intersection points of each three-dimensional space as grid vertices, the adjacent intersection points on adjacent U-shaped curves and adjacent intersection points on adjacent convex arc curves are connected in sequence to form an initial grid shell composed of multiple quadrilateral grid patches. For each quadrilateral mesh facet, connect the intersection of the diagonals of the quadrilateral mesh facet to generate a hollow node at the center of the quadrilateral mesh facet, and delete the original four sides of the quadrilateral mesh facet, so that each quadrilateral mesh facet evolves into a hollow rhombus mesh unit enclosed by four triangular facets; splice all the hollow rhombus mesh units according to the three-dimensional space intersection coordinates to form a composite reference body.

5. The multi-roll thickness difference detection system for printed flat screens according to claim 4, characterized in that, Using the common vertex of two adjacent hollow rhombic mesh elements as boundaries, the composite reference volume is divided into several continuous trapezoidal cross-sectional segments, including: Along the tape travel direction, the composite reference body is longitudinally scanned to extract the coordinates of the common vertex of all hollow rhombic mesh units in the composite reference body; the projection points of two adjacent common vertices in the tape travel direction are used as segment boundaries, and a cutting plane perpendicular to the tape travel direction is made on the composite reference body. The area between two adjacent cutting planes is defined as a trapezoidal section segment. For each trapezoidal cross-section segment, calculate the first cross-sectional area at the upstream boundary and the second cross-sectional area at the downstream boundary. If the first cross-sectional area and the second cross-sectional area are not equal, the corresponding cross-section segment is determined to have trapezoidal geometric features and is marked as a trapezoidal cross-section segment.

6. The multi-roll thickness difference detection system for printed flat screens according to claim 5, characterized in that, Select the first group of sensing nodes and the second group of sensing nodes and connect them crosswise to construct a spatial diagonal, including: For each trapezoidal cross-section segment, the vertices of all hollow rhombic grid units located within the projection area of ​​the first arc-shaped protrusion array are positioned as the first set of sensing nodes, and the vertices of all hollow rhombic grid units located within the projection area of ​​the second arc-shaped protrusion array are positioned as the second set of sensing nodes. Each node in the first group of sensing nodes is paired one by one with the node in the second group of sensing nodes that is located in the same trapezoidal cross section and has the largest spatial distance, generating several pairs of cross-paired node pairs. For each pair of cross-paired nodes, connect the two nodes to form a straight line segment, treat the straight line segment as a spatial diagonal, and ensure that each spatial diagonal passes through the geometric centroid of the trapezoidal cross-section segment.

7. The multi-roll thickness difference detection system for printed flat screens according to claim 6, characterized in that, Extract the cumulative wall thickness of each spatial diagonal line passing through the hollow rhomboid grid cell, as the local thickness difference value of the corresponding cross-section segment, including: For each spatial diagonal, discretize and sample along the extension direction of the corresponding spatial diagonal, and record the cell number of each hollow rhomboid grid cell that the corresponding spatial diagonal passes through in sequence, as well as the coordinates of the entry point and the exit point. Create an accumulated variable for each spatial diagonal and set the initial value of the accumulated variable to zero; for each hollow rhombus grid cell that is pierced, obtain the wall thickness value of the corresponding hollow rhombus grid cell in the direction of the line connecting the entry point and the exit point, and accumulate the wall thickness value into the accumulated variable corresponding to the spatial diagonal. The final value of the cumulative variable corresponding to each spatial diagonal is taken as the cumulative wall thickness of the corresponding spatial diagonal. The arithmetic mean of the cumulative wall thickness of all spatial diagonals within the same trapezoidal section is calculated, and the arithmetic mean is taken as the local thickness difference value of the corresponding trapezoidal section.

8. The multi-roll thickness difference detection system for printed flat screens according to claim 7, characterized in that, All local thickness difference values ​​are weighted and fused to obtain a multidimensional thickness deviation tensor. This multidimensional thickness deviation tensor is then mapped to a multidimensional thickness deviation output matrix, serving as the quantitative detection result of thickness differences between rolls of printing tape, including: Collect the local thickness difference values ​​of all trapezoidal cross-section segments, and assign a spatial weight coefficient to each trapezoidal cross-section segment. The spatial weight coefficient is proportional to the longitudinal position coordinate of the corresponding trapezoidal cross-section segment in the composite reference body. The local thickness difference value of each trapezoidal section segment is multiplied with the corresponding spatial weight coefficient, and then accumulated into the row vector and column vector according to the distribution position of each trapezoidal section segment in the width direction, forming a multidimensional thickness deviation tensor with the number of rows and columns. Each element of the multidimensional thickness deviation tensor is filled into the corresponding position of a pre-initialized output matrix according to the corresponding row index and column index, forming a multidimensional thickness deviation output matrix. The multidimensional thickness deviation output matrix is ​​then output as the quantitative detection result of the thickness difference between each roll of printed tape.

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