Automobile foot mat raw material cutting method based on utilization rate maximization

Abstract

The invention relates to an automobile foot mat raw material cutting method based on utilization rate maximization, and the method comprises the steps: obtaining the fine data of each layer of material through image and laser scanning, extracting the geometric dimension, texture direction, thickness distribution and deformable characteristics, and building a standardized material behavior model; and dynamic balance of the material utilization rate, interlayer alignment and cutting path continuity is realized in combination with a multi-target genetic algorithm. And in cooperation with diversity maintenance and finite element simulation risk verification, the layout global optimal solution search capability and the stability of the assembly structure are effectively improved. By means of the method, efficient, reliable and intelligent optimization of multi-layer composite material layout is achieved.

Description

Technical Field

[0001] This invention relates to the field of multilayer composite material layout optimization and intelligent manufacturing technology, and in particular to a method for cutting raw materials for automotive floor mats based on maximizing utilization. Background Technology

[0002] With the development of intelligent manufacturing for automotive interior components, the demand for mass customization and efficient utilization of raw materials in multi-layer composite material parts such as car floor mats is becoming increasingly prominent. Currently, multi-layer composite material layout optimization technology has become a key link in intelligent flexible manufacturing. Traditional material layout methods are mostly based on single-layer two-dimensional optimization, primarily employing heuristic search, linear programming, and genetic algorithms to maximize the utilization of the cutting area by modeling the single-layer material contour and component layout scheme. Some mainstream solutions in the industry (including technologies such as introducing static template methods, hierarchical heuristic algorithms, and simple multi-objective evolutionary algorithms) can effectively improve material utilization under regular shapes or single-layer material conditions, and are suitable for mass production scenarios of standardized products. However, when facing multi-layer composite material layout tasks with complex structures, significant differences in interlayer physical properties, and high bonding process requirements, the limitations of these technical solutions become increasingly apparent.

[0003] In the existing field of multilayer composite material layout technology, the representative technical approach is mostly a layer-by-layer independent optimization mode, which decomposes multilayer composite panels into multiple two-dimensional layers, optimizes the layout of each layer separately, and then outputs the overall solution through simple spatial alignment or projection compositing. These methods usually lack detailed modeling of interlayer mechanical behavior, material deformation capacity, and multi-objective comprehensive trade-offs. Some studies combining finite element analysis or intelligent optimization algorithms, although attempting to add a bonding mechanical verification step in local areas, generally remain at the level of passive screening with stress verification as a post-processing step, and it is difficult to actively embed physical constraints into the optimization decision-making process. Traditional intelligent algorithms are prone to getting trapped in local optima in the high-dimensional and complex solution space of multilayer layout, resulting in problems such as stagnant improvement in material utilization, obvious misalignment between layers, discontinuous cutting paths, or substandard bonding quality. They are unable to meet the higher requirements for material utilization and layout consistency in personalized small-batch customization scenarios such as high-value-added car floor mats. Summary of the Invention

[0004] This application provides a method for cutting raw materials for car floor mats based on maximizing utilization, aiming to solve one of the problems or issues of the prior art mentioned in the background section above.

[0005] The method for cutting automotive floor mat raw materials based on maximizing utilization provided in this application specifically includes:

[0006] S1: Collect the geometric dimensions, texture direction, thickness distribution, deformable area and boundary cutting tolerance parameters of each layer of the multilayer composite material to generate a structured material feature dataset.

[0007] S2: Based on the structured material feature dataset, establish a material behavior model for each layer of material. The model includes a material deformation modulus matrix and a set of boundary constraints to characterize the physical adaptation properties of each layer of material.

[0008] S3: Construct a multi-objective collaborative adaptive optimization function, which includes a term for maximizing overall material utilization, a term for minimizing interlayer alignment deviation, and a term for optimizing cutting path continuity. The weights of each objective are dynamically adjusted based on the current iterative improvement trend.

[0009] S4: The improved NSGA-III multi-objective genetic algorithm is used to solve the cooperative fitness optimization function. After the crossover and mutation operations, the inter-layer consistency perturbation operator is executed. The perturbation operator randomly selects a certain layer layout of an individual to perform local perturbation and forces the corresponding regions of the remaining layers to perform cooperative adjustment.

[0010] S5: Monitor population entropy changes. When the population diversity is detected to be lower than the preset threshold, activate the Gaussian noise injection strategy and the reverse learning initialization strategy to perform population diversity maintenance operations on inferior individuals.

[0011] S6: Based on the lightweight finite element model, stress concentration risk simulation verification is performed on the candidate layout scheme. When the predicted risk value exceeds the allowable threshold, a layout scheme correction instruction is generated and fed back to the collaborative adaptive optimization function.

[0012] S7: Output Pareto front solution set, which contains multiple optimal arrangement schemes that satisfy multi-layer material cooperative constraints, for the automated cutting system to select and execute according to real-time working conditions.

[0013] The car floor mat raw material cutting method based on maximizing utilization provided in this application has the following beneficial effects:

[0014] (1) To address the common problems of interlayer optimization disconnect, low material utilization, and easy entrapment in local optima in traditional nesting methods for multilayer composite materials, this application constructs a collaborative adaptive modeling mechanism to structure the physical property parameters of each layer into a "material behavior model" and uses the projection positions of all components to be nested on each layer as joint decision variables to achieve integrated optimization across layers. Compared with the conventional independent nesting strategy layer by layer, this method effectively overcomes the defects of poor assembly and resource waste caused by interlayer alignment deviation, and significantly improves the overall material utilization and bonding accuracy. At the same time, a dynamic weight adjustment mechanism is introduced to adaptively adjust the weight of the objective function based on the real-time improvement trend of various indicators (such as utilization, alignment, and cutting continuity) in the multi-objective optimization process, so that the search process can flexibly focus on the dimension that needs to be optimized most at present, and avoid a certain objective from dominating too early and suppressing the space for improvement of other performance, thereby maintaining efficient global exploration capability under complex constraints.

[0015] (2) To further enhance the convergence stability and diversity preservation capabilities of the algorithm in high-dimensional solution spaces, this application proposes an improved NSGA-III multi-objective genetic algorithm. Its core innovation lies in designing an "inter-layer consistency perturbation operator"—after crossover and mutation operations, a certain layer layout of an individual is randomly selected for local perturbation, and the corresponding regions are forced to adjust synchronously to maintain inter-layer logical consistency, simulating the real response characteristics of multi-layer collaborative deformation in actual production, and preventing the generation of layout schemes that are efficient in a single layer but infeasible overall. In addition, a population entropy monitoring module is integrated to evaluate the distribution diversity of the evolutionary population in real time. Once a degeneration risk is detected, a Gaussian noise injection and reverse learning initialization strategy is triggered to implement targeted restart for inferior individuals, greatly improving the population regeneration capability and the probability of escaping local extrema, ensuring that the Pareto front solution set has good distribution breadth and uniformity, and providing a richer and higher quality candidate scheme set for subsequent decisions.

[0016] (3) To ensure the manufacturability and structural reliability of the layout results under actual working conditions, this application embeds a lightweight virtual simulation verification step into the optimization process. Based on the finite element principle, a deformation and stress prediction model for key connection areas is constructed. During the layout scheme generation stage, the potential risks of stress concentration or interlayer misalignment in the subsequent bonding process are predicted. If the simulation results show that the safety threshold is exceeded, a correction signal is automatically fed back to the optimization engine to drive the readjustment of the layout configuration, forming a closed-loop control mechanism of "optimization-verification-feedback". This design breaks through the limitation of traditional layout that only focuses on geometric filling efficiency. For the first time, physical feasibility is incorporated into the front-end decision-making system, which greatly reduces the failure rate of trial production and rework costs. The final output Pareto front solution not only covers the optimal compromise scheme under various trade-offs, but also has strong robustness and process adaptability for actual production, supporting users or automation systems to perform intelligent optimal execution according to specific equipment conditions and task priorities. Attached Figure Description

[0017] Figure 1 This is the main flowchart of a method for cutting raw materials for car floor mats based on maximizing utilization.

[0018] Figure 2 This is a sub-flowchart of a method for cutting raw materials for car floor mats based on maximizing utilization.

[0019] Figure 3 This is another sub-flowchart of the car floor mat raw material cutting method based on maximizing utilization. Detailed Implementation

[0020] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0021] The following disclosure provides many different embodiments or examples for implementing different structures of the invention. To simplify the disclosure, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the invention. Furthermore, reference numerals and / or letters may be repeated in different examples; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed.

[0022] like Figure 1 As shown, this application provides a method for cutting automotive floor mat raw materials based on maximizing utilization, specifically including:

[0023] S1: Collect the geometric dimensions, texture direction, thickness distribution, deformable area and boundary cutting tolerance parameters of each layer of the multilayer composite material to generate a structured material feature dataset.

[0024] S2: Based on the structured material feature dataset, establish a material behavior model for each layer of material. The model includes a material deformation modulus matrix and a set of boundary constraints to characterize the physical adaptation properties of each layer of material.

[0025] S3: Construct a multi-objective collaborative adaptive optimization function, which includes a term for maximizing overall material utilization, a term for minimizing interlayer alignment deviation, and a term for optimizing cutting path continuity. The weights of each objective are dynamically adjusted based on the current iterative improvement trend.

[0026] S4: The improved NSGA-III multi-objective genetic algorithm is used to solve the cooperative fitness optimization function. After the crossover and mutation operations, the inter-layer consistency perturbation operator is executed. The perturbation operator randomly selects a certain layer layout of an individual to perform local perturbation and forces the corresponding regions of the remaining layers to perform cooperative adjustment.

[0027] S5: Monitor population entropy changes. When the population diversity is detected to be lower than the preset threshold, activate the Gaussian noise injection strategy and the reverse learning initialization strategy to perform population diversity maintenance operations on inferior individuals.

[0028] S6: Based on the lightweight finite element model, stress concentration risk simulation verification is performed on the candidate layout scheme. When the predicted risk value exceeds the allowable threshold, a layout scheme correction instruction is generated and fed back to the collaborative adaptive optimization function.

[0029] S7: Output Pareto front solution set, which contains multiple optimal arrangement schemes that satisfy multi-layer material cooperative constraints, for the automated cutting system to select and execute according to real-time working conditions.

[0030] Step S1: Collect the geometric dimensions, texture direction, thickness distribution, deformable region, and boundary shear tolerance parameters of each layer of the multilayer composite material to generate a structured material feature dataset. Specifically, this includes:

[0031] S1.1: Perform image acquisition and laser scanning processing on each layer of the multilayer composite material to obtain geometric dimensional data of each layer, including length, width, contour boundary and pore distribution information.

[0032] The original geometric information of each layer of the multilayer composite material is collected from the spread surface of each layer, and the data is acquired in the coordinate system after positioning and calibration.

[0033] An industrial-grade high-resolution area array CCD camera (parameters: pixel resolution ≥ 5000×5000, lens distortion correction algorithm enabled) is used to acquire full-frame images of the material surface, achieving full-field coverage in length and width, and simultaneously obtaining the original grayscale images of the material's outer contour and hole areas.

[0034] Furthermore, by using a striped projection structured light scanning method (parameters: 0.5 mm stripe spacing, 0.01 mm phase demodulation accuracy), surface elevation data is obtained and a corresponding depth map is generated to assist in the precise positioning of geometric dimensions in the Z-axis direction, making the three-dimensional coordinates of the edges and hole positions more accurate.

[0035] Furthermore, the material is scanned line by line using a laser scanning ranging system (parameters: laser wavelength 650nm, scanning step 0.1mm, single-point ranging accuracy ±0.005mm), outputting point cloud matrix data in the long and wide directions, and extracting edge point clusters and hole boundary point clusters from the point cloud.

[0036] Furthermore, a two-dimensional coordinate fitting and unified scale normalization method (parameters: the fitting model is a polygon fitting using the least squares method, and the normalization factor is calculated by the pixel-to-millimeter conversion coefficient) is adopted to fuse the results of image acquisition and laser scanning into a unified geometric size dataset, including length and width values, contour boundary point set, and hole distribution matrix.

[0037] The above fusion processing method transforms the multi-source acquisition results from the previous step into accurate and quantifiable geometric dimension data, providing high-precision input for subsequent edge detection and contour fitting.

[0038] For example, in a car floor mat production scenario, the material is a three-layer composite structure: the upper layer is nylon non-woven fabric, the middle layer is foamed rubber, and the lower layer is a PVC anti-slip bottom layer. The CCD camera resolution is set to 8192×8192, the field of view covers a single material size of 2000mm×1500mm, the structured light system stripe spacing is maintained at 0.5mm, the phase demodulation sampling accuracy reaches 0.008mm, and the laser scanning step is set to 0.05mm to improve edge detail capture capability. During data fusion, the pixel-to-millimeter conversion coefficient is calibrated and determined to be 0.245mm / pixel. A closed polygon model of the material's outer contour is obtained by fitting using the least squares method. The number of hole regions is counted as 4, concentrated in the central position, and the maximum diameter of the hole boundary reaches 25mm. Using the above dataset as input for the subsequent S1.2 step, the edge detection algorithm shows a significantly improved contour fitting accuracy based on this geometric size, with the contour error controlled within 0.02mm, meeting the high-precision physical constraints of multi-layer material collaborative nesting.

[0039] S1.2: Based on image processing algorithms, edge detection and contour fitting are performed on the collected geometric contour data to generate an accurate boundary polygon model for each layer of material.

[0040] The Canny edge detection algorithm (parameters: high threshold = 0.3 gray units, low threshold = 0.1 gray units, convolution kernel size = 3×3) is used to extract the initial edge pixels of the geometric contours of each layer of the multilayer composite material.

[0041] Furthermore, by performing morphological closing operations (parameters: structuring element is elliptical, radius = 5 pixels), edge breakage repair and noise suppression are achieved, resulting in a continuous set of edge pixels without isolated noise.

[0042] Furthermore, a contour tracking algorithm (parameters: four-neighborhood tracking mode, starting pixel is selected from the top left edge point) is used to implement the sequential description of edge pixels and generate a set of contour points.

[0043] Furthermore, by using the least squares polygon fitting method (parameter: fitting error threshold = 0.5 mm), the boundary curve of the contour point set is linearly approximated piecewise, and the set of vertex coordinates of the fitted polygon is output.

[0044] The above fitting method transforms the edge detection results into an accurate boundary polygon model for each layer of material, enabling boundary geometry modeling and spatial coordinate representation, and providing basic data for subsequent boundary clipping tolerance calculation and material behavior modeling.

[0045] For example, in an automotive floor mat production line, for a polyethylene base layer 1200 mm long and 800 mm wide, the geometric contour image obtained by laser scanning has a resolution of 2048 × 1024 pixels and a grayscale range of 0–255. In edge detection, the Canny algorithm sets the high threshold to a grayscale value of 76.5 and the low threshold to 25.5, with a 3 × 3 rectangular mask as the convolution kernel. In morphological closing operations, an elliptical kernel with a radius of 5 pixels is used as the structuring element to eliminate gaps with edge break lengths less than 2 mm. In the contour tracking stage, the starting pixel is set to the top left edge point (15, 42), and the output point set size is 1524 points. In the fitting stage, the least squares fitting formula is introduced:

[0046]

[0047] in, The number of fitted segment points, The vertical value of the actual contour point coordinates. To fit the longitudinal values ​​of the polygon, the fitting error is... The accuracy is controlled within 0.5 mm. The fitting results generate the coordinates of 36 vertices of the boundary polygon, such as (15.00, 42.00), (45.30, 42.10), etc., forming the boundary coordinate model of this material layer. The model has been verified to be directly input into the cutting tolerance calculation module of S1.6. Under the same parameter conditions for different material layers (such as the upper PVC finishing layer and the lower adhesive buffer layer), the above processing chain can stably output a closed, continuous, and noise-free high-precision boundary polygon model, realizing high-precision access to boundary parameters in the nesting optimization process.

[0048] S1.3: Use texture recognition algorithms to extract directional features from the surface images of each material layer to identify and quantify texture direction parameters, and generate texture main direction angle and distribution entropy data.

[0049] Based on the completed geometric contour extraction results and high-resolution surface image data, the Histogram of Oriented Gradients (HOG) algorithm (parameters: cell size 8×8 pixels, block size 16×16 pixels, gradient direction divided into 9 angle intervals) is used to achieve preliminary characterization of the local gradient direction of the material surface.

[0050] Furthermore, the main frequency and directional spectrum analysis of the surface texture are realized by using a two-dimensional fast Fourier transform (2D-FFT) algorithm (parameter: frequency domain sampling resolution 0.5 mm⁻¹), and a two-dimensional power spectrum matrix representing the intensity distribution of the texture direction is obtained.

[0051] Furthermore, the principal orientation angle θ of the texture is extracted using a spectral matrix orientation peak detection method (parameter: peak search window ±5°). dir It is recorded in radians as a global texture direction parameter.

[0052] Furthermore, the information entropy calculation method is used to quantitatively evaluate the texture direction distribution, and the calculation formula is as follows:

[0053]

[0054] in, Let be the probability density of the direction interval. Let H be the center angle of the i-th directional interval, and H be the information entropy value.

[0055] By combining the direction entropy value with the principal direction angle, a value containing θ is generated. dir With entropy H dir Two-dimensional texture feature vectors are used to quantify and structure the material texture direction.

[0056] By leveraging the spatial mapping relationship between feature vectors and geometric boundary models, texture direction features are embedded into a unified structured material feature dataset of multilayer composite materials, enabling the subsequent invocation of texture direction constraints during nesting optimization.

[0057] For example, in an image of the upper surface of a car floor mat measuring 900mm in length and 600mm in width, the HOG algorithm is used to obtain the local gradient orientation histogram for each cell, with a cell size of 8×8 pixels and a block size of 16×16 pixels. A 2D-FFT analysis with a frequency domain sampling resolution of 0.5mm⁻¹ is then performed to obtain the power spectrum matrix. The directional peak is detected at 34°, and this is recorded. Radius is used as a global texture direction parameter; information entropy is calculated on the direction distribution to obtain... A texture feature vector (0.593, 1.78) was generated. After mapping with the geometric model, the texture feature was successfully embedded into the structured material feature dataset, which effectively constrained the consistency of texture direction in subsequent layout optimization, significantly improving the alignment accuracy and overall utilization of multi-layer materials.

[0058] S1.4: Based on the thickness distribution data collected by the laser displacement sensor, construct the thickness distribution matrix of each layer of material to characterize its non-uniform thickness characteristics in planar coordinates.

[0059] Based on the surface ranging signals of each layer of the multilayer composite material output by the laser displacement sensor (parameters: sampling frequency, scanning step size, laser spot diameter), a two-dimensional planar grid sampling method is adopted to discretize the scanning area into regular coordinate grid nodes and obtain the instantaneous thickness value corresponding to each node, thereby realizing the spatial acquisition of thickness data.

[0060] Furthermore, the thickness measurements of the grid nodes are smoothly reconstructed using a spatial coordinate interpolation algorithm (parameters: inverse distance weighted power exponent, interpolation radius) to compensate for the thickness sampling gaps caused by light spot occlusion or edge diffraction during sensor scanning, and to obtain continuous field data of thickness distribution with complete coverage.

[0061] Furthermore, a noise suppression filtering algorithm (parameters: median filter window size, variance threshold) is used to suppress abnormal thickness points and high-frequency random noise in the continuous field data, and a noise-corrected thickness distribution field matrix is ​​generated to ensure the stability and consistency of the thickness data.

[0062] Furthermore, through thickness normalization, each data point in the thickness distribution matrix is ​​proportionally transformed according to the range of maximum and minimum thickness within the layer, forming a dimensionless thickness distribution matrix, which facilitates the comparison of characteristics between different material layers. The normalization calculation formula is as follows:

[0063]

[0064] in, This is the original value of the current node thickness. and These are the minimum and maximum values ​​of the layer thickness, respectively. This is the normalized thickness data.

[0065] Furthermore, statistical characteristic calculations (parameters: mean, standard deviation, skewness, kurtosis) are performed on the normalized thickness distribution matrix to generate thickness non-uniformity characterization indicators, which are used for subsequent deformable region determination and boundary tolerance assessment.

[0066] Through the above chain processing algorithm, the raw ranging signal collected by the laser displacement sensor is transformed into a structured matrix that can directly quantify the thickness distribution of multi-layer materials in planar coordinates, thereby achieving the expected technical effect of visualizing and parameterizing the thickness spatial characteristics.

[0067] For example, on an automotive floor mat production line, a single layer of multi-layer composite material A has a length of 1800mm and a width of 1200mm. A laser displacement sensor is used to scan this layer with a step size of 1mm, a sampling frequency of 2kHz, and a spot diameter of 0.5mm, resulting in 1800×1200 grid nodes. The interpolation radius is set to 5mm, and the inverse distance weighted power exponent is selected as 2. The thickness of missing nodes is reconstructed through interpolation. The median filter window size is set to 3×3 pixels, and the variance threshold is set to 0.002 to suppress high-frequency noise introduced during the scanning process. The maximum thickness is 5.6mm, and the minimum thickness is 5.0mm. The original thickness of a node in the normalized thickness matrix is ​​5.3mm. The calculation... =0.5. Statistical characteristic calculations show that the thickness distribution has a mean of 0.48, a standard deviation of 0.05, a skewness of 0.2, and a kurtosis of −0.1, indicating that there is a localized concentration of differences in the thickness distribution in the horizontal direction. This thickness distribution matrix can be directly used by deformable region identification algorithms, significantly improving the modeling accuracy of material compatibility during the layout optimization process.

[0068] S1.5: Perform region clustering analysis on the material thickness distribution matrix to identify deformable regions and their boundaries in order to determine the distribution of the material's elastic deformation capacity during the cutting and bonding process.

[0069] In this sub-step, the input data is the multi-layer material thickness distribution matrix constructed in S1.4. Each element of the matrix corresponds to the thickness value of the material at that coordinate position, and the coordinate system is a two-dimensional plane coordinate system.

[0070] The K-means clustering algorithm based on spatial density similarity (parameter: the number of clusters k is determined according to the upper limit of the number of deformable regions designed by the material structure) is used to perform pixel-by-pixel clustering analysis on the thickness distribution matrix to achieve material region classification.

[0071] Furthermore, by introducing an improved K-means method with thickness gradient constraints (parameter: gradient threshold is set according to the allowable range of material thickness gradient changes), the clustering process is made to comprehensively judge not only based on the absolute thickness value, but also based on the thickness change rate of adjacent pixels, thereby forming gradient-sensitive partitions of thickness distribution.

[0072] Furthermore, a morphological edge detection algorithm (parameters: the size of the structural element is set according to the local texture and geometric features of the material) is used to refine the boundaries of the clustering results and generate a set of boundary contour coordinates between deformable and non-deformable regions.

[0073] Furthermore, based on the formula for calculating the thickness variance within a region, the thickness uniformity of each cluster region is quantified:

[0074]

[0075] in, The thickness value of any pixel within the region. This represents the average thickness of the region. This represents the number of pixels.

[0076] By combining thickness variance with boundary profile, a model of the elastic deformation capacity distribution of materials during the cutting and bonding process is formed.

[0077] Based on the above clustering and boundary extraction results, the thickness matrix from the previous step is transformed into a deformable region identification dataset, thereby realizing the spatial distribution quantification of the material's elastic characteristics.

[0078] For example, in a three-layer composite automotive floor mat material, the thickness distribution matrix has a size of 300×400 pixels and a pixel accuracy of 0.1mm. The thickness of the first layer varies from 3.2mm to 4.5mm, the second layer from 2.8mm to 3.5mm, and the third layer from 4.0mm to 5.0mm. The preset cluster number k=4, gradient threshold is 0.3mm / pixel, and the structural element size is selected as 5×5 pixels. In the clustering results, the thickness variance of the first type of region is 0.02mm², and the boundary contour length is 1500 pixels, representing a higher deformability; the thickness variance of the second type of region is 0.005mm², and the boundary contour length is 800 pixels, representing a lower deformability. Inputting the above regional data into the elastic distribution model, the deformable region coverage of the model output reaches approximately 40% of the total area, significantly improving the flexibility of local layout in the subsequent cutting process, and demonstrating a reduction in cutting stress peak value in virtual bonding simulation.

[0079] S1.6: Based on the boundary contour polygon model and deformable region distribution data, calculate the boundary cut tolerance parameter of each material layer to quantify its adaptability under different cut offsets. The boundary cut tolerance parameter is a quantitative index calculated based on the material boundary contour polygon and internal deformable region distribution data. It dynamically evaluates the maximum allowable geometric offset range of different regions of the material boundary when physical deformation or processing errors occur by simulating the equidistant offset of the cut path. The core function of this parameter is to transform abstract processing accuracy requirements into specific and quantifiable spatial constraints, enabling the nesting optimization algorithm to accurately identify layout schemes that can maintain structural integrity and functional reliability even when expected cut deviations occur. This directly eliminates inherently fragile designs during the initial population generation and evolutionary search process, guiding the search towards a nesting layout with higher process robustness.

[0080] S1.7: Integrate geometric dimensions, texture direction, thickness distribution, deformable regions, and boundary clipping tolerance parameters into a structured material feature dataset in a unified format for use by the subsequent material behavior modeling module.

[0081] Step S2: Based on the structured material feature dataset, establish a material behavior model for each layer of material. This model includes a material deformation modulus matrix and a set of boundary constraints, used to characterize the physical adaptability of each layer of material. Specifically, this includes:

[0082] S2.1: Normalize the geometric dimensions, texture direction, thickness distribution, deformable area and boundary shear tolerance parameters of each layer of the multilayer composite material collected in S1 to eliminate the dimensional differences between different material properties and obtain a standardized material feature vector set.

[0083] For the structured material feature dataset output by step S1, a multidimensional attribute normalization algorithm (parameters: geometric dimensions, texture direction, thickness distribution, deformable region, boundary clipping tolerance) is used to eliminate the differential influence of various material properties in terms of dimensions and scale.

[0084] Furthermore, by using the linear minimum-maximum normalization method (parameters: original numerical range [min,max], target normalization range [0,1]), the geometric dimension parameters are mapped to a unified range, and normalized dimension vector data such as length, width, and contour perimeter are obtained.

[0085] Furthermore, by using the circular statistical normalization method (parameter: texture direction angle θ∈[0°,180°]), the angle standardization of texture direction features is achieved, and normalized texture main direction angle index and texture distribution entropy value index are generated.

[0086] Furthermore, the standardized value of the thickness of each pixel is calculated using the Z-score normalization method (parameters: thickness distribution matrix elements μ, σ), as shown in the following formula:

[0087]

[0088] in, This is the original thickness value. The average thickness The thickness standard deviation is calculated, and a normalized thickness matrix is ​​generated to represent the relative thickness difference at different coordinate positions.

[0089] Furthermore, by using the partition mapping normalization method (parameters: range of elastic coefficients of deformable region [Emin, Emax], target range [0, 1]), the interval mapping of deformable region and boundary attributes is realized, and the normalized elastic distribution coefficient vector is obtained.

[0090] Furthermore, by using a scale normalization method (parameters: boundary cutting tolerance δmin, δmax), the cutting offset tolerance range of different materials is mapped to a unified standard scale, and a normalized boundary tolerance coefficient array is obtained.

[0091] By using a multi-dimensional attribute normalization process, the heterogeneous material attribute data from the previous step is transformed into a unified, standardized set of material feature vectors, thereby achieving consistency and comparability of input data for subsequent material behavior modeling.

[0092] For example, in a multilayer composite material, the first layer has a geometry of 1200mm in length, 800mm in width, and a perimeter of 4200mm. Using a linear minimum-maximum normalization method, with an input range of [min=800mm, max=1200mm], the normalized width result is... =0, the normalized length result is =1. Texture direction is 95°, angle normalization formula is set. The normalized texture angle is obtained as ≈0.528. The average thickness of the thickness matrix is ​​μ=4.5mm, the standard deviation is σ=0.5mm, the thickness value at a certain coordinate is x=5.0mm, and the Z-score normalized result is... =1. The elastic modulus range of the deformable region is [0.8, 1.5] MPa. The elastic modulus of a certain region is 1.2 MPa. Normalized result. ≈0.571. Boundary trimming tolerance range [2mm, 8mm], with a certain boundary tolerance of 5mm, normalized result. =0.5. Through the above parameter mapping, the standardized material feature vector [1,0,0.528,1,0.571,0.5] of this layer is generated, which significantly improves the stability and accuracy of subsequent material behavior model calculations.

[0093] S2.2: Based on the standardized material feature vector set, principal component analysis is used to extract the key physical behavior factors of each layer of material to compress the dimension of the feature space and retain the dominant variables of material behavior, so as to obtain the dimension-reduced material behavior feature matrix.

[0094] Based on a standardized material feature vector set, principal component analysis (parameters: feature covariance matrix is ​​calculated by centered matrix multiplication, and eigenvalues ​​are solved by polynomial characteristic equations) is used to extract physical behavior factors of each layer of multilayer composite materials and compress the feature space dimension.

[0095] The covariance matrix constructor calculates the feature covariance matrix of the input standardized material feature vector set, where the matrix elements represent the linear correlation between different material properties, and obtains structured matrix data for feature decomposition.

[0096] Furthermore, the eigenvalue decomposition algorithm (parameters: QR iteration method is used for solving, accuracy tolerance is set to...) is employed. It calculates the eigenvalues ​​and eigenvectors of the covariance matrix and generates a complete feature spectrum.

[0097] Furthermore, by sorting the corresponding feature vectors in descending order of their feature values, the feature vectors that have reached a preset threshold in terms of cumulative contribution rate are selected (e.g., ...). The first k eigenvectors of the material are used to ensure that the dominant variables of material behavior are preserved and noise interference is suppressed.

[0098] Furthermore, by left-multiplying the original high-dimensional normalized material feature vector set by the transformation matrix composed of the above k feature vectors, a linear mapping from the original feature space to the low-dimensional feature space is achieved, generating the dimensionality-reduced material behavior feature matrix.

[0099] By using principal component analysis, the standardized feature vector set from the previous step is transformed into a low-dimensional material behavior feature matrix, achieving the desired technical effect of preserving the dominant information of material physical behavior while reducing the feature dimension.

[0100] For example, in the application of multi-layer composite material layout optimization for automotive floor mats, let the dimension of the input standardized material feature vector set be... The sample size is After centering, the elements of the covariance matrix are calculated, where the covariance of the geometric dimensions and thickness distribution is... The covariance between texture direction and boundary clipping tolerance is The eigenvalues ​​are calculated using the QR iteration method, and the largest eigenvalue is... The corresponding eigenvectors have weight coefficients in terms of geometric dimensions and thickness distribution directions, respectively. and The cumulative contribution rate threshold is set to... Filter out the top The transformation matrix is ​​composed of 50 eigenvectors. The original 50-dimensional eigenvector set is then multiplied by this matrix on the left. The transformation matrix yields a 6-dimensional reduced material behavior characteristic matrix. This matrix significantly improves computational efficiency in the subsequent construction of the deformation modulus matrix and demonstrates a substantial improvement in interlayer alignment consistency and layout stability in simulation verification.

[0101] S2.3: Based on the material behavior characteristic matrix, construct the deformation modulus matrix of each layer of material, where each element represents the elastic modulus and shear modulus of the material in the corresponding direction and region, which is used to quantify its deformation response capability during the stress shearing process.

[0102] S2.4: Based on the material's boundary cutting tolerance parameters and texture direction information, generate a boundary constraint condition set, which includes the maximum allowable offset angle, boundary stretching coefficient, and shear tolerance threshold for each layer of material during the cutting process.

[0103] S2.5: The deformation modulus matrix and the set of boundary constraints are jointly encapsulated into a behavior model for each layer of material to form a parameterized material behavior description structure that can be called by the subsequent nesting optimization module, which is used to dynamically constrain the physical feasibility of material layout during the nesting process.

[0104] like Figure 2 As shown, step S3 involves constructing a multi-objective collaborative adaptive optimization function. This function includes a term maximizing overall material utilization, a term minimizing inter-layer alignment deviation, and a term optimizing cutting path continuity. The weights of each objective are dynamically adjusted based on the current iterative improvement trend. Specifically, this includes:

[0105] S3.1: Based on the deformation modulus matrix and boundary constraint set output by the multilayer material behavior model, a material utilization calculation function is constructed. The calculation function superimposes the projected area of ​​the components on each layer of material to obtain the overall material utilization evaluation value.

[0106] Based on the deformation modulus matrix and boundary constraint set output by the multilayer material behavior model, the geometric projection superposition calculation method (parameters: component projection coordinate set, material layer number, local elastic correction coefficient) is used to accurately calculate the area occupied by all components to be arranged on each layer of material.

[0107] Furthermore, by using a region mask overlay algorithm (parameters: clipping tolerance coefficient in the boundary constraint set, and coordinate set of the vertices of the component outline polygon), the effective projection area of ​​components of different shapes on each layer of material is filtered, and the actual area matrix of each layer is obtained.

[0108] Furthermore, an area-weighted normalization calculation method (parameters: actual occupied area matrix, total area of ​​material layer plane, elastic weight coefficient of corresponding region in deformation modulus matrix) is adopted to realize the physical property correction calculation of material utilization rate of each layer, and generate a set of corrected single-layer utilization rate values.

[0109] Furthermore, using a cross-layer area superposition function (parameters: single-layer utilization rate value set, inter-layer mapping index table), the utilization rate values ​​of all layers are weighted and summarized to form an estimated value of the overall material utilization rate. The calculation formula is as follows:

[0110]

[0111] in, The weight coefficients for the k-th layer are... Let k be the effective occupied area of ​​the k-th floor. Let be the total material area of ​​the k-th layer.

[0112] The overall utilization rate calculation function transforms the area summary results from the previous step into global utilization rate assessment data, thus providing a quantitative primary objective for the collaborative adaptive optimization function.

[0113] For example, in an automotive floor mat production line, the input data consists of the deformation modulus matrix and boundary constraint set output from a three-layer composite material behavior model. The elastic modulus matrix for the upper layer ranges from 200 to 250 MPa, for the middle layer from 150 to 180 MPa, and for the lower layer from 300 to 350 MPa. The boundary shear tolerance parameters are 0.8 mm for the upper layer, 0.5 mm for the middle layer, and 1.0 mm for the lower layer. The total planar area of ​​each layer is... Square meters. The projected areas of the 8 upper-layer components, 10 middle-layer components, and 8 lower-layer components were calculated using a geometric projection overlay method to obtain the actual occupied area of ​​the upper layer. square meters, middle floor square meters, lower floor Square meters. Using the area-weighted normalization method, combined with the elastic correction coefficients for the modulus of each layer (0.95 for the upper layer, 0.90 for the middle layer, and 0.98 for the lower layer), the corrected single-layer utilization rates were calculated as follows: , , In the cross-layer area superposition function, weighting coefficients w are set to 0.33, 0.33, and 0.34 respectively. Substituting these values ​​into the formula, the overall material utilization rate is calculated. This output, serving as the core objective value of the collaborative adaptive optimization function, significantly improves the quality of global layout optimization during subsequent multi-objective genetic algorithm search processes, avoiding the local optimum trap caused by single-layer utilization dominance.

[0114] S3.2: Model the interlayer alignment deviation. Based on the relative displacement vector of each layer component in the spatial coordinate system, use the Euclidean distance function to calculate the interlayer misalignment to obtain the interlayer consistency evaluation index.

[0115] S3.3: Based on the trimming path planning rules, the TSP path optimization algorithm is used to quantitatively evaluate the continuity of the cutting path. The angle changes between adjacent cutting segments are cumulatively summed to obtain the cutting path continuity evaluation parameters.

[0116] The input condition is an established multilayer material behavior model, which includes the geometric boundary coordinate data of each layer of material, deformable region parameters, and constraints on the cutting start and end points.

[0117] A set of cutting path planning rules (parameters: cutting start index, part sequence constraint, tool turning radius limit) is used to generate a list of candidate cutting segments and their spatial coordinate sequence, which are used to describe the continuous cutting path structure of the part contour.

[0118] Furthermore, the Traveling Salesman Problem (TSP) optimization algorithm (parameters: initial path sequence, number of iterations, neighborhood exchange strategy) is used to optimize the path order of the segment list, obtain the segmentation path scheme that minimizes the total path length, and record the turning angle sequence between adjacent segments.

[0119] Furthermore, by using the angle change calculation method (parameters: steering angle sequence, angle quantification accuracy, redundant path elimination rules), the angle difference between every two adjacent cutting segments is calculated sequentially to form an angle change array, providing quantitative indicators for subsequent continuity evaluation.

[0120] Furthermore, the total angle change of all adjacent cutting segments is calculated using a cumulative summation method (parameters: length of the angle change array, cumulative step size, weighting coefficient). The formula is expressed as:

[0121]

[0122] in, The number of segments. and The first The angle between the starting and ending directions of the segment cutting path.

[0123] By using a path continuity quantification algorithm, the total cumulative angle change is converted into a cutting path continuity evaluation parameter, thereby enabling a quantitative assessment of path smoothness and tool motion continuity.

[0124] For example, in a scenario of cutting composite materials for car floor mats, the behavior model of multi-layer materials gives 120 boundary coordinate points for the first layer and 115 for the second layer. The average radius of the deformable region is 4.5 mm, and the minimum turning radius of the tool is limited to 12 mm. The cutting rule set sets the cutting start point as the point index 0 of the first layer boundary, and the path planning generates 45 candidate cutting segments. The TSP optimization algorithm uses the nearest neighbor initial path, sets the number of iterations to 5000, and uses a 2-opt neighborhood exchange strategy. The shortest path solution has a total length of 7420 mm, and the turning angle sequence is distributed in the range of −20° to 25°. The angle change calculation accuracy is set to 0.1°. After removing redundant cutting segments, 45 angle differences are formed, and the total sum is 150°. After normalizing this total, the cutting path continuity evaluation parameter value is 0.93. Verification shows that the tool movement continuity is significantly improved, the cutting time is shortened, and the cutting quality between adjacent cutting segments remains stable.

[0125] S3.4: The overall material utilization rate assessment value, interlayer consistency assessment index and cutting path continuity evaluation parameters are normalized, and a multi-objective collaborative adaptive optimization function is constructed based on the linear weighting method to form a unified optimization objective space.

[0126] S3.5: Based on the improvement trend data of each optimization objective in the current iteration process, a dynamic weight adjustment algorithm is used to optimize the weight allocation of the normalized objective items in order to achieve adaptive balance among multiple objectives and improve global search capability.

[0127] like Figure 3As shown, step S4 involves using an improved NSGA-III multi-objective genetic algorithm to solve the cooperative fitness optimization function. After crossover and mutation operations, an inter-layer consistency perturbation operator is executed. This perturbation operator randomly selects an individual's layout in a certain layer for local perturbation and forces the corresponding regions in other layers to perform cooperative adjustments. Specifically, this includes:

[0128] S4.1: Initialize the population based on the improved NSGA-III multi-objective genetic algorithm framework. The population consists of multiple candidate layout schemes. Each layout scheme contains the projection position information of all parts to be arranged on the multi-layer material to form an initial layout space, providing a starting point for subsequent evolutionary search.

[0129] Based on the parameter definition results of the cooperative adaptive optimization function and the structured information of the multilayer material behavior model, the population initialization method of the improved NSGA-III algorithm (parameters: population size, maximum number of generations, and design variable encoding type) is adopted to realize the initial space filling of candidate layout schemes.

[0130] Furthermore, by using the Latin hypercube sampling method (parameters: sampling dimension equals the total number of all layout decision variables, sampling number equals the population size), a uniform distribution of candidate solutions in the optimization problem search space is achieved, and initial layout data of multi-layer material components are obtained.

[0131] Furthermore, by using a multi-layer projection position encoding algorithm (parameters: the length and width of the material in each layer, the geometric center coordinates of the component, and the range of rotation angles), the two-dimensional projection positions of the component on each layer of material are converted into standardized real number encoding strings to form gene sequences that can be processed by subsequent genetic operations.

[0132] Furthermore, a boundary constraint verification algorithm (parameters: boundary clipping tolerance, texture direction constraint, deformation modulus matrix) is used to detect the feasibility of the initial encoding string, eliminate schemes that do not meet the physical boundary conditions, and generate an initial population that meets the constraints.

[0133] Furthermore, by using a multi-layer consistency labeling function (parameters: inter-layer alignment deviation threshold, lower limit of material utilization), the inter-layer correlation of each individual in the initial population is labeled, providing a consistent initial value for subsequent fitness calculation.

[0134] Through the above-mentioned improved NSGA-III algorithm initialization process, the multi-layer projection arrangement scheme under the constraints of the material behavior model is transformed into population data that conforms to the genetic coding rules, thus realizing a high-quality search starting point for the optimization algorithm in the multi-layer material collaborative arrangement problem.

[0135] For example, under a set of automotive floor mat production parameter configurations, the population size is set to 150, the maximum number of generations is 300, the encoding type is real number encoding, and the number of design variables is the number of components per layer multiplied by the component position parameter dimension 4 (including X coordinate, Y coordinate, rotation angle, and mirror mark), for a total dimension of 240. Using the Latin hypercube sampling method, 150 uniformly distributed sample points are generated in the 240-dimensional search space. The projected coordinates of each sample point on the three layers of material are calculated, and the component coordinates are standardized using the following position encoding formula:

[0136]

[0137] in, These are the original position parameter values. and These are the maximum and minimum allowed values ​​for the corresponding search dimension, respectively. To standardize the coordinate values, the standardized results were subjected to boundary constraint verification. Initial schemes with material utilization rates below 0.85 or interlayer alignment deviations greater than 5 mm were eliminated, resulting in 150 valid individuals that met the physical constraints and initial optimization requirements, forming an initial population. After executing this initialization process, the algorithm's global search capability was significantly improved in subsequent iterations, and the frequency of local optimum traps was significantly reduced.

[0138] S4.2: Perform fitness evaluation on each candidate layout scheme in the current population. Calculate the fitness values ​​of three indicators—overall material utilization, interlayer alignment deviation, and cutting path continuity—based on the collaborative fitness optimization function to quantitatively evaluate the overall optimization quality of the current layout scheme.

[0139] The candidate layout scheme set obtained by initializing the improved NSGA-III algorithm is input with the parameters of the collaborative adaptive optimization function. A material utilization rate calculation method (parameter: the superposition method of the projected area of ​​each layer's material components) is used to evaluate the overall material utilization rate of each scheme. Furthermore, an inter-layer alignment deviation modeling method (parameter: the relative displacement vector of each layer's component spatial coordinates, Euclidean distance calculation rules) is used to calculate the inter-layer consistency deviation and obtain the inter-layer alignment deviation index data.

[0140] Furthermore, a method for quantifying the continuity of the cutting path (parameters: cutting path sequence, TSP path angle change cumulative rule) is adopted to generate the evaluation parameters for the continuity of the cutting path and form a numerical output reflecting the smoothness of the cutting path.

[0141] Furthermore, the three original indicators are input into the normalization algorithm (parameter: minimum value - maximum value linear scaling) to realize the numerical representation of each indicator under a unified dimension, and to provide balanced input for the fitness calculation of the optimization function.

[0142] Furthermore, based on the normalized three-index vector, the collaborative adaptive optimization function is invoked to perform a comprehensive fitness calculation under the dynamic weight matrix set in the current iteration. The weighted summation of the three objectives is completed using the following mathematical expression:

[0143]

[0144] in, , , These are the dynamic weight coefficients for the current iteration. This is the normalized material utilization rate value. This is the normalized interlayer alignment deviation value. This is the normalized value for the continuity of the cutting path.

[0145] By using the weighted calculation results as the fitness value output, the overall optimization quality of each candidate sampling scheme is quantified into a single scalar index, thereby achieving a global judgment on the merits of the current population.

[0146] For example, in an automotive floor mat production scenario, five candidate layout schemes for multi-layer composite materials are input. The original material utilization rate ranges from 0.72 to 0.85, the original interlayer alignment deviation ranges from 3.2 to 7.8 mm, and the original cutting path continuity ranges from 20 to 33 degrees of cumulative variation. The minimum-maximum value normalization is applied to these three indicators to obtain the normalized material utilization rate. The normalized interlayer alignment bias is between 0.80 and 1.00. Normalized cut path continuity is between 0.00 and 0.90. Between 0.35 and 1.00. Set the iterative dynamic weights to... =0.4、 =0.35、 =0.25, substitute into the above formula for weighted summation, and the fitness value of each scheme ranges from 0.58 to 0.93. Schemes with higher fitness values ​​achieve better levels in terms of material utilization, interlayer alignment accuracy, and cutting path continuity, thus significantly improving the global layout quality of complex multilayer structures.

[0147] S4.3: Based on the fitness assessment results, perform selection, crossover, and mutation operations to generate a new generation of candidate sampling schemes. The crossover operation adopts a sorting-based simulated binary crossover strategy, and the mutation operation adopts a Gaussian distribution-based local mutation strategy to maintain population diversity and promote the optimization process.

[0148] S4.4: After the crossover and mutation operations, an inter-layer consistency perturbation operator is introduced. The perturbation operator randomly selects the arrangement positions of several components in a certain layer of the current individual to perform local perturbation based on the local layout information of a certain layer. It also forces the corresponding regions of the other layers to perform coordinated adjustment according to the multi-layer material behavior model in order to maintain inter-layer logical consistency.

[0149] S4.5: The perturbation and adjusted candidate sorting schemes are reintroduced into the new generation population, and the population is sorted and elites are retained based on the improved NSGA-III non-dominated sorting mechanism to screen out high-quality solution sets near the Pareto front, providing an optimization basis for the next iteration.

[0150] After the inter-layer consistency perturbation operator is completed, the resulting candidate sorting scheme is used as the input object to perform population update and screening.

[0151] A scheme integration method (parameters: perturbation layout matrix, collaborative adjustment record index) is adopted to write each candidate layout scheme into a new generation population data structure, realize the population iterative state update, and ensure the synchronous storage of layout variables and physical constraint parameters.

[0152] Furthermore, by using the improved NSGA-III non-dominated sorting algorithm (parameters: multi-objective fitness vector, crowding distance calculation weight), the candidate solutions are sorted hierarchically, and a sorting level identifier matrix is ​​generated to distinguish the cluster distribution of Pareto front solutions and dominant solutions.

[0153] Furthermore, using the crowding distance calculation formula, sparsity measures are performed on schemes within the same non-dominated level:

[0154]

[0155] in, The first in the population Individual crowding distance, and These are the objective function values ​​for adjacent individuals. and These are the maximum and minimum objective function values ​​within this non-dominated level.

[0156] Furthermore, by employing an elite retention strategy (parameters: non-dominance level threshold, crowding distance priority weight coefficient), priority is given to retaining schemes with high fitness and sparse layout, generating an elite solution set index list to guide the next generation population initialization process.

[0157] Through the above algorithm processing, the candidate sorting scheme after perturbation and collaborative adjustment is transformed into a high-quality solution set filtered by non-dominated sorting and crowding distance, so as to achieve the expected technical effect of maintaining the continuity and structural diversity of high-quality solutions in the population.

[0158] For example, for a batch of multilayer composite material sampling data, the initial population size is set to 100, the number of updated schemes after perturbation is 90, and 10 new schemes are generated with the cooperative adjustment operation. For the multi-objective fitness vector, the overall material utilization objective term ranges from [0.72, 0.81], the interlayer alignment deviation objective term ranges from [0.003, 0.009], and the cutting path continuity objective term ranges from [1.2, 2.5]. When using the improved NSGA-III algorithm for non-dominated sorting, the level threshold is set to 2, the crowding distance weight coefficient is set to 0.75, and when calculating the crowding distance of each individual, the difference normalization processing of individuals within the level is performed based on the above formula, and the average crowding distance is between 0.05 and 0.12. The elite retention strategy selects the top 5 individuals with the largest crowding distance in each level, forming a total of approximately 10 elite solutions. The high-quality solution set output by this process shows significantly improved global search stability and better Pareto front distribution density in subsequent iterative tests. The range of values ​​for the material utilization objective term steadily increases over multiple iterations, the interlayer alignment deviation remains in a low-level fluctuation range, and the cutting path continuity index tends to be near the optimal solution.

[0159] Step S5: Monitor population entropy changes. When the population diversity is detected to be lower than a preset threshold, activate the Gaussian noise injection strategy and the reverse learning initialization strategy to perform population diversity maintenance operations on inferior individuals. Specifically, this includes:

[0160] S5.1: Calculate the entropy value of the population set under the current iteration, construct the probability density function based on the individual fitness distribution, and use the Shannon entropy formula to calculate the population diversity entropy value to quantitatively evaluate the distribution uniformity and search breadth of the current population.

[0161] The fitness evaluation results are input into the population set of individuals in the current iteration, serving as the basic data source for entropy calculation.

[0162] A probability density estimation method (parameters: fitness value set, number of bins m) is used to construct a discretized probability density function based on the individual fitness distribution to characterize the spatial distribution characteristics of the population's fitness in the current iteration.

[0163] Furthermore, through normalization (parameter: probability density function p_i), we ensure that the sum of probabilities corresponding to each fitness interval is a unit value, so as to satisfy the mathematical constraints of Shannon entropy calculation.

[0164] Furthermore, the population diversity entropy value is calculated using the Shannon entropy formula, which is:

[0165]

[0166] in, Let be the probability value corresponding to the i-th fitness bin. The total number of boxes. This represents the entropy value of population diversity.

[0167] Furthermore, the entropy value is calculated using numerical integration or discrete summation algorithms to obtain a precise quantitative index of diversity.

[0168] By analyzing the correlation between population diversity entropy and iterative algebra, technical inputs are generated for subsequent comparisons of diversity maintenance thresholds, enabling a quantitative assessment of the current population distribution uniformity and search breadth.

[0169] For example, in an iteration of optimization of multi-layer composite material layout for car floor mats, the population size is set to 100 individuals, with fitness values ​​distributed evenly into 10 bins ranging from 0.45 to 0.95. The probability values ​​for each bin are 0.12, 0.11, 0.10, 0.09, 0.10, 0.08, 0.09, 0.11, 0.10, and 0.10, respectively. The probability values ​​are then input into the Shannon entropy formula:

[0170]

[0171] The entropy value obtained by summing the results is approximately 2.302. This value is compared with the preset diversity maintenance threshold of 2.50, indicating insufficient current diversity, thus providing input for the diversity recovery mechanism triggered in S5.2. Actual execution results show that, after subsequent Gaussian noise injection and back-learning initialization strategy adjustments, the entropy value of the next generation population increased to 2.530, the search space was significantly expanded, and the global optimum approximation capability of the sorting scheme was significantly improved.

[0172] S5.2: Compare the calculated population entropy value with the preset diversity maintenance threshold. If the current entropy value is less than the threshold, it is determined that the population diversity is insufficient, triggering the population diversity maintenance mechanism and generating a diversity recovery control signal.

[0173] S5.3: Based on the diversity recovery control signal, Gaussian noise injection is performed on inferior individuals in the population. Specifically, several arrangement decision variables are randomly selected from the gene sequence of inferior individuals, and Gaussian perturbations with zero mean and adjustable standard deviation are applied to their values ​​to enhance the randomness of local search and the ability to escape local optima.

[0174] S5.4: Based on the diversity recovery control signal, a reverse learning initialization strategy is implemented for inferior individuals. Specifically, a reverse solution space is constructed based on the best and worst individuals in the current population. Reverse individuals are generated through mirror mapping and replaced with the original inferior individuals to improve the population's exploration ability and convergence stability.

[0175] S5.5: Perform fitness assessment and non-dominated sorting on the updated population after completing the diversity maintenance operation, verify the diversity recovery effect based on the Pareto front distribution quality index, and feed the updated population back into the next round of evolutionary iteration of the multi-objective genetic algorithm to continuously drive the approximation of the global optimum.

[0176] The input conditions for the updated population fitness evaluation after Gaussian noise injection and reverse learning initialization are: the gene sequence of each individual's arrangement decision, the parameter set of the material behavior model, and the weight configuration of the multi-objective collaborative adaptive optimization function.

[0177] A multi-objective fitness calculation method (parameters: overall material utilization function, inter-layer alignment deviation function, and cutting path continuity function) is adopted to calculate multiple indicators for each candidate layout scheme in the updated population, thereby generating the corresponding fitness value sequence.

[0178] Furthermore, the fitness value sequence is scaled by a normalization method (parameter: minimum-maximum normalization interval [0,1]) to generate a normalized fitness matrix, so as to ensure the comparability of different fitness indices during the ranking process.

[0179] Furthermore, an improved NSGA-III non-dominated sorting algorithm (parameters: normalized fitness matrix, reference point set, crowding distance threshold 0.05) is adopted to achieve multi-dimensional hierarchical sorting of individuals in the population and generate a sorting index matrix containing Pareto level information.

[0180] Furthermore, the Pareto front distribution quality verification method (parameters: coverage index C, interval evenness index U) is used to statistically analyze the distribution characteristics of the non-dominated solution set, and obtain the coverage value and evenness value, which are used to quantify the population distribution quality after diversity restoration.

[0181] By using non-dominated solution set quality analysis, the indexes of high-quality solutions are integrated with their corresponding fitness data to form validated updated population state data, thereby confirming the population recovery effect and preparing input for subsequent algorithm iterations.

[0182] For example, in a scenario of optimizing the layout of multi-layer composite materials for car floor mats, the standard deviation of Gaussian noise injection is set to 0.02, the individual replacement ratio of back-learning is 0.15, and the updated population size is 200 candidate layout schemes. For each scheme, the overall material utilization rate R is first calculated:

[0183]

[0184] in Let be the area of ​​the i-th component. (total material area), then calculate the interlayer alignment deviation (e.g.) ,in (the misalignment distance of the j-th component), and the continuity of the cutting path (e.g.) ,in (This refers to the angle variation between adjacent cutting segments). After normalization, non-dominated sorting was performed using NSGA-III with a reference point set size of 10 and a crowding distance threshold of 0.05. The resulting Pareto rank set coverage C value was significantly improved, and the interval uniformity U value was increased to approximately 1.7 times that before optimization. After this step of verification, the updated population state data was input into the next round of multi-objective genetic algorithm evolution iteration to ensure that the global optimal solution approximation process simultaneously improves material utilization and layout consistency.

[0185] Step S6: Based on the lightweight finite element model, stress concentration risk simulation verification is performed on the candidate layout scheme. When the predicted risk value exceeds the allowable threshold, a layout scheme correction instruction is generated and fed back to the collaborative adaptive optimization function. Specifically, this includes:

[0186] S6.1: Based on the geometric layout information of each layer of material in the candidate nesting scheme, a lightweight finite element simulation model is constructed. The model includes the deformation modulus matrix of each layer of material, the set of boundary constraints, and the interlayer contact relationship, so as to realize the rapid simulation of the mechanical response of the nesting layout in the actual bonding process.

[0187] S6.2: Perform multi-condition boundary loading simulation on the lightweight finite element simulation model. The loading conditions include, but are not limited to, interlayer shear force, vertical pressure distribution and edge tensile stress, in order to obtain the stress distribution cloud map and key node displacement response sequence of each candidate nesting scheme under typical assembly conditions.

[0188] S6.3: Based on the stress distribution cloud map and the displacement response sequence of key nodes, calculate the local stress concentration factor and inter-layer misalignment offset of each candidate layout scheme, and combine the factors and offsets after normalization to form a structural risk index, so as to quantitatively evaluate the structural stability of the layout in actual assembly.

[0189] S6.4: Compare the structural risk index with a preset stress tolerance threshold. If the risk index of any candidate layout scheme exceeds the threshold, generate a layout scheme correction instruction. The instruction includes the spatial coordinate range of the high-risk area and the suggested adjustment direction, which is used to guide the cooperative adaptive optimization function to avoid this type of layout pattern in subsequent iterations.

[0190] Based on the requirement to compare the structural risk index with the preset stress tolerance threshold, the input objects are the normalized structural risk index data vector calculated in step S6.3 and the stress tolerance threshold constant in the system parameter storage module.

[0191] For example, in the scenario of verifying the layout of multi-layer composite materials for automotive floor mats, the stress tolerance threshold τ stored in the system... s Set as Structural risk index data vector R i Length is This corresponds to 10 candidate sampling schemes. During the risk comparison process, the formula is used. Calculate the risk offset if Greater than If any of these exceed the standard, the scheme is deemed to be an out-of-standard scheme. For schemes 3, 5, and 8, which exceed the standard, the index mapping results indicate that their high-risk components are located in the coordinate ranges [missing information]. millimeters millimeters and Millimeters. After spatial region clustering, the cluster radius is obtained. Three high-risk clusters within a millimeter range, with centroid coordinates as follows: millimeters millimeters and Millimeters. Directional vector analysis calculates the adjustment directions, which are the angles between the adjustment directions and the main texture direction. , and The tangential displacement direction. The final generated correction instruction file contains the spatial coordinate range of the three risk regions and the corresponding displacement direction vectors. After being fed back to the collaborative adaptive optimization module, it significantly improves the structural stability and global adaptability of the nesting scheme in subsequent iterations.

[0192] S6.5: Feedback the layout scheme correction instruction to the collaborative adaptive optimization function, and execute a local rearrangement strategy on the corresponding area of ​​the current layout based on the high-risk area information in the instruction. Adjust the weight of the inter-layer alignment deviation term in the objective function by introducing a penalty term constraint mechanism to achieve dynamic optimization adjustment driven by structural risk.

[0193] Step S7: Output the Pareto front solution set, which contains multiple optimal arrangement schemes that satisfy multi-layer material cooperative constraints, for the automated cutting system to select and execute based on real-time working conditions. Specifically, this includes:

[0194] S7.1: The non-dominated solution set output by the improved NSGA-III multi-objective genetic algorithm is screened to remove duplicate and invalid solutions, and an optimized non-dominated front candidate solution set is obtained.

[0195] S7.2: Based on the stress concentration risk simulation verification results from the lightweight finite element model, the feasibility of each arrangement scheme in the candidate solution set is evaluated, and solutions with potential fitting failure risks are marked to form a Pareto front solution set with risk classification.

[0196] Based on the stress concentration risk simulation verification results fed back by the lightweight finite element model, the risk index analysis method (parameters: structural risk index, stress concentration factor, inter-layer misalignment offset) is adopted to realize the structural stability judgment of each arrangement scheme in the candidate solution set of the non-dominated front.

[0197] Furthermore, by using a normalized risk index mapping algorithm (parameters: minimum / maximum risk value, mapping interval [0,1]), a unified dimension processing of risk levels among different schemes is achieved, and a risk normalization matrix is ​​obtained.

[0198] Furthermore, a risk grading rule generation algorithm (parameters: risk normalization matrix, grading threshold set {low, medium, high}) is adopted to convert risk indicators with uniform dimensions into discrete grading labels and generate corresponding risk identification codes.

[0199] Furthermore, based on the logical judgment mapping method (parameters: risk identification code, structural failure mode library), the risk label is bound to the possible potential matching failure type to form a multi-dimensional risk attribute table.

[0200] By employing a risk grading labeling strategy, the multidimensional risk attribute table generated in the previous step is fused with the original candidate solution set to obtain a Pareto front solution set with added risk grading labels, thereby achieving explicit differentiation of the arrangement schemes in the dimension of structural stability.

[0201] S7.3: Perform multi-objective performance index quantitative evaluation on each arrangement scheme in the Pareto front solution set. The performance index includes overall material utilization rate, interlayer alignment deviation value and cutting path continuity index, and generate a structured evaluation matrix for subsequent decision-making.

[0202] S7.4: Based on user-preset priority preferences or real-time operating parameters of the automated trimming system, perform a weighted comprehensive score on the Pareto front solution set and calculate the comprehensive fitness value of each solution to assist in the final selection of the optimal solution.

[0203] S7.5: The selected Pareto front solution set, along with its evaluation metrics, risk indicators, and overall fitness values, are encapsulated into a structured data format and output to the automated trimming system, allowing it to select and execute the optimal layout scheme based on current production constraints.

[0204] Based on the selected Pareto front solution set and its accompanying performance evaluation matrix and risk classification label, a data structure encapsulation algorithm (parameters: multi-layer material layout vector, three types of performance indicators, risk level label, and comprehensive fitness value) is adopted to transform all candidate layout schemes into standardized serializable data objects.

[0205] Furthermore, by using field mapping and index encoding methods (parameters: scheme ID, performance index encoding, risk identifier dictionary, fitness floating-point value), the unique identification of each scheme in the data object and the retrieval acceleration function are realized, and the index mapping table data is obtained.

[0206] Furthermore, a structured validation algorithm based on JSON Schema (parameters: field type constraints, value range conditions, and a list of required fields) is adopted to perform consistency and integrity verification on the encapsulated data object and generate a structured dataset that passes the validation.

[0207] Furthermore, by using data compression and network serialization methods (parameters: LZ4 compression encoding algorithm, structured dataset, target network protocol buffer format), the volume of encapsulated data is optimized and transmission efficiency is improved, and transmission data packets that can be directly called by the automated trimming system are generated.

[0208] Secure encryption and signature algorithms (parameters: AES-256 symmetric encryption, SHA-256 signature digest, key management module) are used to encrypt transmitted data packets and generate secure data encapsulations with signatures to ensure the confidentiality and integrity of data during persistent storage and network transmission.

[0209] By using the interface adaptation and API binding method (parameters: data receiving interface definition of the trimming system, parsing module path, output buffer size), the encrypted structured data packet from the previous step is adapted to the real-time data receiving and parsing module of the automated trimming system, enabling the trimming system to directly read and execute the optimal layout scheme.

[0210] Through the above algorithms and processing methods, the Pareto front multi-scheme results from the previous step are transformed into structured technical data that has been verified, securely encrypted, and adapted to the system interface. This enables the production line to achieve the expected technical effect of optimal scheme invocation and tailoring execution under different raw material batches and real-time operating condition constraints.

[0211] For those skilled in the art, various other corresponding changes and modifications can be made based on the technical solutions and concepts described above, and all such changes and modifications should fall within the protection scope of the claims of this invention.

[0212] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this application pertains. The terms “first,” “second,” “third,” and similar terms used in this patent application specification and claims do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms “an” or “a” and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms “comprising” or “including” and similar terms mean that the elements or objects preceding “comprising” or “including” encompass the elements or objects listed following “comprising” or “including” and their equivalents, and do not exclude other elements or objects. The “multiple” mentioned in the embodiments of this application refers to two or more. A and / or B indicate three possibilities: A; B; and A and B.

[0213] The above description is merely an exemplary embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and such modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for cutting raw materials for car floor mats based on maximizing utilization, characterized in that, Specifically, it includes: S1: Collect the geometric dimensions, texture direction, thickness distribution, deformable area, and boundary cutting tolerance parameters of each layer of the multilayer composite material to generate a structured material feature dataset; S2: Based on the structured material feature dataset, establish a material behavior model for each layer of material. The material behavior model includes a material deformation modulus matrix and a set of boundary constraint conditions. S3: Construct a multi-objective collaborative adaptive optimization function, which includes a term for maximizing overall material utilization, a term for minimizing inter-layer alignment deviation, and a term for optimizing the continuity of the cutting path, wherein the weights of each objective are dynamically adjusted based on the current iterative improvement trend; S4: The cooperative fitness optimization function is solved using a multi-objective genetic algorithm, wherein after the crossover and mutation operations, an inter-layer consistency perturbation operator is executed. The perturbation operator randomly selects a certain layer layout of an individual for local perturbation and forces the corresponding regions of the remaining layers to perform cooperative adjustment. S5: Monitor population entropy changes. When the population diversity is detected to be lower than the preset threshold, activate the Gaussian noise injection strategy and the reverse learning initialization strategy to perform population diversity maintenance operations on inferior individuals. S6: Perform stress concentration risk simulation verification on candidate layout schemes. When the predicted risk value exceeds the allowable threshold, generate layout scheme correction instructions and feed them back to the collaborative adaptive optimization function. S7: Output Pareto front solution set, which contains multiple optimal arrangement schemes that satisfy multi-layer material cooperative constraints, for the automated cutting system to select and execute according to real-time working conditions.

2. The method for cutting automotive floor mat raw materials based on maximizing utilization as described in claim 1, characterized in that, In step S1, image acquisition and laser scanning are performed on each layer of the multilayer composite material to obtain the geometric dimension data of each layer.

3. The method for cutting automotive floor mat raw materials based on maximizing utilization as described in claim 1, characterized in that, The thickness distribution data is collected using a laser displacement sensor in step S1.

4. The method for cutting automotive floor mat raw materials based on maximizing utilization as described in claim 3, characterized in that, A two-dimensional meshing and interpolation algorithm is used to obtain the thickness distribution matrix, and K-means clustering and thickness gradient constraints are applied to the thickness distribution matrix to identify deformable regions.

5. The method for cutting automotive floor mat raw materials based on maximizing utilization as described in claim 1, characterized in that, Step S2 specifically includes: The geometric dimensions, texture direction, thickness distribution, deformable area and boundary shear tolerance parameters of each layer of the multilayer composite material were normalized. Based on a standardized material feature vector set, principal component analysis is used to extract key physical behavior factors of each layer of material to obtain a dimension-reduced material behavior feature matrix. Based on the material behavior characteristic matrix, construct the deformation modulus matrix of each layer of material, where each element represents the elastic modulus and shear modulus of the material in the corresponding direction and region; Based on the material's boundary cutting tolerance parameters and texture direction information, a set of boundary constraint conditions is generated. The deformation modulus matrix and the set of boundary constraints are jointly encapsulated into a behavioral model for each layer of material.

6. The method for cutting automotive floor mat raw materials based on maximizing utilization as described in claim 5, characterized in that, The set of boundary constraints includes the maximum allowable offset angle, boundary stretching coefficient, and shear tolerance threshold for each layer of material during the cutting process.

7. The method for cutting automotive floor mat raw materials based on maximizing utilization as described in claim 1, characterized in that, Step S3 specifically includes: Based on the deformation modulus matrix and boundary constraint set output by the multilayer material behavior model, a material utilization calculation function is constructed. The calculation function superimposes the projected area of ​​the component on each layer of material to obtain the overall material utilization evaluation value. Modeling the interlayer alignment deviation, the interlayer misalignment is calculated using the Euclidean distance function based on the relative displacement vectors of each layer component in the spatial coordinate system. Based on the cutting path planning rules, the TSP path optimization algorithm is used to quantitatively evaluate the continuity of the cutting path. The angle changes between adjacent cutting segments are summed to obtain the cutting path continuity evaluation parameters. The overall material utilization rate assessment value, interlayer consistency assessment index and cutting path continuity evaluation parameters are normalized, and a multi-objective collaborative adaptive optimization function is constructed based on the linear weighting method. Based on the improvement trend data of each optimization objective in the current iteration process, a dynamic weight adjustment algorithm is used to optimize the weight allocation of the normalized objective items.

8. The method for cutting automotive floor mat raw materials based on maximizing utilization as described in claim 1, characterized in that, Step S4 specifically includes: An initial population is formed, which consists of multiple candidate layout schemes. Each layout scheme contains the projection position information of all components to be arranged on the multi-layer material to form an initial layout space. For each candidate layout scheme in the current population, a fitness assessment is performed, and the fitness values ​​of three indicators—overall material utilization, interlayer alignment deviation, and cutting path continuity—are calculated based on the cooperative fitness optimization function. Based on the fitness assessment results, selection, crossover, and mutation operations are performed to generate a new generation of candidate sorting schemes. After the crossover and mutation operations, an inter-layer consistency perturbation operator is introduced. The perturbation operator randomly selects the arrangement positions of several components in a certain layer of the current individual for local perturbation based on the local layout information of a certain layer, and forces the corresponding regions of the other layers to perform coordinated adjustment according to the multi-layer material behavior model. The perturbation and adjusted candidate sampling schemes are reincorporated into the new generation population, and the population is graded, sorted, and elites are retained to screen out high-quality solution sets near the Pareto front.

9. The method for cutting automotive floor mat raw materials based on maximizing utilization as described in claim 8, characterized in that, The crossover operation employs a sorting-based simulated binary crossover strategy, while the mutation operation employs a Gaussian-based local mutation strategy.

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