High-frequency substrate material signal transmission loss evaluation method, device, equipment and medium

Abstract

This application discloses a method, apparatus, device, and medium for evaluating signal transmission loss of high-frequency substrate materials, relating to the field of next-generation information technology. The method includes: acquiring three-dimensional point cloud data of the interface and a broadband scattering parameter matrix of a sample high-frequency substrate material; performing multi-scale feature extraction on the interface three-dimensional point cloud data to obtain a multi-scale fractal dimension feature set; extracting the test frequency sequence corresponding to the scattering parameter matrix, and constructing a fractal interface impedance feature sequence based on the fractal dimension feature set, preset micro-polarization parameters, and the test frequency sequence; training a physical information neural network based on the impedance feature sequence and the scattering parameter matrix to obtain a full-band transmission loss evolution model; and predicting the transmission loss of the target high-frequency substrate material to be evaluated using this model to obtain a signal transmission loss evaluation result. This application can accurately evaluate the broadband signal transmission loss of high-frequency substrate materials caused by surface micromorphology.

Description

Technical Field

[0001] This application relates to the field of next-generation information technology, and in particular to methods, apparatus, equipment and media for evaluating signal transmission loss of high-frequency substrate materials. Background Technology

[0002] In ultra-high frequency (UHF) applications, the microscopic surface condition of high-frequency substrate materials (such as copper-clad laminates) has a significant impact on signal attenuation. The transmission loss of the substrate material not only directly determines signal integrity but also profoundly affects the power consumption and thermal management of the entire system. Currently, the evaluation of substrate material transmission loss mainly relies on purely empirical formula models and traditional numerical electromagnetic simulation software (Electronic Design Automation, EDA). Empirical formulas typically introduce two-dimensional parameters such as root mean square roughness (RMS) to perform simple weighted corrections for the standard skin effect; while numerical electromagnetic simulation mainly involves establishing simplified roughness geometry arrays (such as regular spherical or pyramidal protrusions) in EDA software to perform full-wave electromagnetic field calculations.

[0003] However, the aforementioned traditional evaluation methods face significant technical bottlenecks when dealing with the complex microstructures of millimeter-wave frequencies. First, purely empirical models are overly idealistic, using simple parameters that completely ignore the true three-dimensional topology and nonlinear fractal characteristics of the substrate surface, resulting in extremely low prediction accuracy at high frequencies, making it difficult to guide actual manufacturing processes. Second, EDA faces severe challenges in mesh generation when dealing with highly irregular real microstructures, resulting in a serious curse of dimensionality; the computational load of full-wave simulation explodes exponentially, often requiring enormous computing power and time costs to achieve convergence across the entire frequency band. Traditional pure physical modeling and pure empirical fitting can no longer balance computational efficiency and physical rigor, and the industry urgently needs to introduce artificial intelligence technology to break this deadlock between computing power and accuracy. Therefore, accurately evaluating the broadband signal transmission loss caused by the surface microstructure of high-frequency substrate materials has become a pressing problem to be solved. Summary of the Invention

[0004] The purpose of this application is to provide a method, apparatus, device and medium for evaluating signal transmission loss of high-frequency substrate materials, aiming to solve the technical problem of how to accurately evaluate the broadband signal transmission loss caused by the surface micromorphology of high-frequency substrate materials.

[0005] To achieve the above objectives, this application proposes a method for evaluating signal transmission loss of high-frequency substrate materials, the method comprising: Acquire the three-dimensional point cloud data of the interface and broadband scattering parameter matrix of the sample high-frequency substrate material; Multi-scale feature extraction is performed on the three-dimensional point cloud data of the interface to obtain a multi-scale fractal dimension feature set; Extract the test frequency sequence corresponding to the broadband scattering parameter matrix, and construct a fractal interface impedance feature sequence based on the multi-scale fractal dimension feature set, the preset micro-polarization parameters, and the test frequency sequence; Based on the fractal interface impedance characteristic sequence and the broadband scattering parameter matrix, the physical information neural network is trained to obtain a full-band transmission loss evolution model. The transmission loss is predicted using the full-band transmission loss evolution model for the target high-frequency substrate material to be evaluated, and the signal transmission loss evaluation result is obtained.

[0006] Furthermore, to achieve the above objectives, this application also proposes a signal transmission loss evaluation device for high-frequency substrate materials, the device comprising: The data acquisition module is used to acquire the interface three-dimensional point cloud data and broadband scattering parameter matrix of the sample high-frequency substrate material; The feature extraction module is used to perform multi-scale feature extraction on the interface 3D point cloud data to obtain a multi-scale fractal dimension feature set; The impedance construction module is used to extract the test frequency sequence corresponding to the broadband scattering parameter matrix, and construct the fractal interface impedance feature sequence based on the multi-scale fractal dimension feature set, the preset micro-polarization parameters and the test frequency sequence. The model training module is used to train the physical information neural network based on the fractal interface impedance characteristic sequence and the broadband scattering parameter matrix to obtain a full-band transmission loss evolution model. The evaluation and prediction module is used to predict the transmission loss of the target high-frequency substrate material to be evaluated using the full-band transmission loss evolution model, and obtain the signal transmission loss evaluation result.

[0007] In addition, to achieve the above objectives, this application also proposes a signal transmission loss evaluation device for high-frequency substrate materials, the device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the signal transmission loss evaluation method for high-frequency substrate materials as described above.

[0008] In addition, to achieve the above objectives, this application also proposes a storage medium, which is a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the steps of the high-frequency substrate material signal transmission loss evaluation method described above.

[0009] In addition, to achieve the above objectives, this application also provides a computer program product, which includes a computer program that, when executed by a processor, implements the steps of the high-frequency substrate material signal transmission loss evaluation method described above.

[0010] One or more technical solutions proposed in this application have at least the following technical effects: First, the interface three-dimensional point cloud data and broadband scattering parameter matrix of the sample high-frequency substrate material are acquired. Microscopic spatial coordinate information and macroscopic broadband electromagnetic response data of the material surface are collected, providing fundamental real data support for subsequent feature mining and model construction. Second, multi-scale feature extraction is performed on the interface three-dimensional point cloud data to obtain a multi-scale fractal dimension feature set, which can deeply and quantitatively characterize the complex undulating geometric state of the surface micromorphology. Next, the test frequency sequence corresponding to the broadband scattering parameter matrix is ​​extracted, and a fractal interface impedance feature sequence is constructed based on the multi-scale fractal dimension feature set, preset micro-polarization parameters, and the test frequency sequence. This paper presents a method to effectively map purely geometric morphological features into frequency-domain equivalent electromagnetic features with physical computational significance. Subsequently, based on the fractal interface impedance feature sequence and the broadband scattering parameter matrix, a physical information neural network is trained to obtain a full-band transmission loss evolution model. This process combines impedance features with broadband data, ensuring that the trained prediction model not only conforms to measured patterns but also possesses rigorous physical evolution rationality. Finally, the transmission loss of the target high-frequency substrate material to be evaluated is predicted using the full-band transmission loss evolution model, yielding a signal transmission loss assessment result. This makes the performance extrapolation process for unknown target materials more efficient and reliable. This application can accurately assess the broadband signal transmission loss of high-frequency substrate materials caused by surface micromorphology. Attached Figure Description

[0011] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0012] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a flowchart illustrating an embodiment of the signal transmission loss assessment method for high-frequency substrate materials in this application. Figure 2 This is a schematic diagram of spatial coordinate system transformation provided in Embodiment 1 of the method for evaluating signal transmission loss of high-frequency substrate materials in this application; Figure 3 This is a schematic diagram of the physical modeling of the equivalent impedance of the fractal interface provided in Embodiment 1 of the method for evaluating signal transmission loss of high-frequency substrate materials in this application. Figure 4 This is a flowchart illustrating Embodiment 2 of the method for evaluating signal transmission loss of high-frequency substrate materials in this application. Figure 5 This is a schematic diagram of the module structure of the high-frequency substrate material signal transmission loss evaluation device according to an embodiment of this application; Figure 6 This is a schematic diagram of the equipment structure of the hardware operating environment involved in the signal transmission loss assessment method for high-frequency substrate materials in the embodiments of this application.

[0014] The purpose, features, and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0015] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0016] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0017] It should be noted that the executing entity of this application embodiment can be a computing service device with data processing, network communication, and program execution functions, such as a tablet computer, personal computer, or mobile phone, or an electronic device or transmission loss assessment system capable of realizing the above functions. The following description uses a transmission loss assessment system as an example to illustrate this embodiment and the subsequent embodiments.

[0018] The user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data comply with the relevant laws, regulations and standards of the relevant countries and regions.

[0019] Based on this, embodiments of this application provide a method for evaluating signal transmission loss of high-frequency substrate materials, referring to... Figure 1 , Figure 1 This is a flowchart illustrating the first embodiment of the signal transmission loss assessment method for high-frequency substrate materials in this application.

[0020] In this embodiment, the signal transmission loss evaluation method for high-frequency substrate materials includes steps S10 to S50: Step S10: Obtain the three-dimensional point cloud data of the interface and the broadband scattering parameter matrix of the sample high-frequency substrate material; It should be noted that the sample high-frequency substrate material refers to the standardized circuit board material used to establish the basic database, which typically possesses known physical properties and electromagnetic characteristics. The interface 3D point cloud data can be a set of spatial coordinates of the conductor surface obtained using high-precision scanning equipment, used to characterize the undulations of the microstructure. The broadband scattering parameter matrix refers to a complex data set reflecting the reflection and transmission characteristics of electromagnetic signals within a preset frequency range. In this embodiment, the preset frequency range refers to a broadband frequency domain covering the microwave to millimeter-wave band, typically set to 1 GHz to 110 GHz. This frequency band covers the core operating frequency band of mainstream high-frequency communication and radar systems, and can completely map the transmission loss evolution trajectory of the substrate material under skin effect and intensified dielectric polarization conditions.

[0021] Understandably, a non-contact scanning method using a confocal microscope or white-light interferometer is employed to capture the microscopic undulations at the conductor-dielectric interface, generating a digital model containing millions of spatial coordinate points. Simultaneously, the same material sample is fabricated into a standard test transmission line and connected to a Vector Network Analyzer (VNA) for frequency sweep testing in a broadband frequency domain at the GHz level. Scattering parameters containing amplitude and phase information are obtained through measurement and organized into a standard matrix format, serving as electromagnetic label data for subsequent training. This step, by simultaneously acquiring physical morphological features and electromagnetic response features, establishes an accurate "morphology-performance" correspondence for the subsequent model, ensuring the authenticity and completeness of the underlying data.

[0022] Step S20: Perform multi-scale feature extraction on the three-dimensional point cloud data of the interface to obtain a multi-scale fractal dimension feature set; It should be noted that the multi-scale fractal dimension feature set refers to a set of quantitative indicators that characterize the complexity and self-similarity of morphology at different spatial observation scales.

[0023] Understandably, box-counting or other fractal algorithms are used to divide the scanned spatial coordinate data into grid cells of different sizes. By statistically analyzing the number of grid cells required to cover the surface at different scales, the slope is calculated and the fractal dimension is extracted. This process not only calculates roughness at a global scale but also delves into micrometer-level local details, ultimately forming a vector set containing multi-dimensional features to describe the ruggedness and space-filling ability of the surface morphology at different observation scales. Multi-scale feature extraction effectively uncovers the complex geometric information hidden in the morphology, solving the problem that traditional single roughness parameters cannot accurately describe the tortuosity of high-frequency current paths, and significantly improving the depth of feature expression.

[0024] Step S30: Extract the test frequency sequence corresponding to the broadband scattering parameter matrix, and construct the fractal interface impedance feature sequence based on the multi-scale fractal dimension feature set, the preset micro-polarization parameters, and the test frequency sequence. It should be noted that the test frequency sequence refers to an ordered set of discrete frequency points selected during electromagnetic simulation or actual measurement. The preset micro-polarization parameter refers to the physical constant that quantifies the polarization response capability of a material under an alternating electric field. This parameter should be derived based on the complex permittivity (including relative permittivity and loss tangent) of the specific high-frequency substrate dielectric material (such as PTFE, LCP, or FR4). Specifically, the fundamental relative permittivity of the substrate material under static or low-frequency conditions is extracted. With loss tangent The preset micro-polarization parameters are derived based on the complex permittivity formula. Its mathematical expression is: in, The vacuum permittivity, This refers to the imaginary unit. This parameter rigorously quantifies the ratio of electrical energy storage to thermal energy dissipation caused by dipole polarization rearrangement under an alternating electric field. For example, for a millimeter-wave radar substrate with extremely low loss, the corresponding fundamental relative permittivity typically ranges from 2.1 to 3.5, and the loss tangent is between 0.001 and 0.005. The fractal interface impedance characteristic sequence refers to a frequency-dependent equivalent impedance data stream that integrates geometric features and polarization physical properties.

[0025] Understandably, the frequency sweep range and step size are set according to the testing requirements. The extracted fractal dimension is combined with the inherent dielectric polarization constant of the material and substituted into the preset equivalent circuit equation. At each frequency point, the skin effect is corrected according to the fractal dimension, and the additional loss contribution caused by micro-polarization is calculated. The preset equivalent circuit equation refers to the physical mapping function used to derive the dynamic capacitance component affected by surface geometric distortion. Specifically, the calculation formula for the capacitance component at each frequency point in the fractal equivalent capacitance sequence is as follows: In the formula, This represents the basic polarization capacitance component under an ideal smooth state, derived from preset micro-polarization parameters. Represents the fundamental fractal dimension; This represents the preset dielectric edge effect attenuation constant, which ranges from 0.15 to 0.35 in this example. This equation quantifies the nonlinear attenuation effect of polarization contact area scaling and spatial electric field edge distortion caused by microsurface ruggedness on the material's capacitive reactance.

[0026] This mapping process transforms abstract geometric features into frequency-dependent resistance, inductance, and capacitance components, ultimately synthesizing a complex impedance sequence reflecting the physical state of the interface. This step, through physical mapping, converts topographic information into feature quantities that can be directly processed by electromagnetic calculations, achieving a cross-dimensional transformation from physical geometric features to electromagnetic mechanism features, thus enhancing the physical interpretability of the model.

[0027] Step S40: Based on the fractal interface impedance characteristic sequence and the broadband scattering parameter matrix, train the physical information neural network to obtain a full-band transmission loss evolution model. It should be noted that Physics-Informed Neural Networks (PINN) refers to a deep learning network architecture that embeds physical evolution equations as constraints into the loss function. The full-band transmission loss evolution model refers to an intelligent mathematical mapping logic model capable of predicting signal attenuation at any frequency.

[0028] Understandably, a multilayer perceptron structure is constructed, using the constructed impedance sequence as input layer data. During training, in addition to calculating the mean square error between the predicted values ​​and the measured scattering parameters, the simplified transmission line equations (such as the telegraph equations) from Maxwell's equations are used as internal physical constraints. The network weights are adjusted using the backpropagation algorithm, ensuring that the model output not only numerically fits the experimental data but also physically follows the fundamental laws of electromagnetic wave propagation. Through continuous iterative optimization, the model grasps the underlying laws governing loss evolution with frequency. This step, introducing a physically-informed neural network, significantly reduces the dependence on large-scale pure experimental data, effectively avoiding the physical distortion problem that traditional neural networks easily encounter when predicting broadband evolution, and improving the model's generalization ability and robustness.

[0029] Step S50: The transmission loss of the target high-frequency substrate material to be evaluated is predicted using the full-band transmission loss evolution model to obtain the signal transmission loss evaluation result.

[0030] It should be noted that the target high-frequency substrate material refers to a sample of a new type of substrate whose loss performance is to be tested in actual production or design. The signal transmission loss assessment result refers to quantitative evaluation data reflecting the attenuation of signal strength with frequency.

[0031] The process involves placing a sample of the new material to be evaluated into a topographic scanning device to acquire point cloud data. Using a trained full-band transmission loss evolution model, the point cloud characteristics of the new material and the target test frequency are input into the system. Based on the learned physical evolution laws, the model quickly calculates and outputs key indicators such as insertion loss and return loss for the material over a wide bandwidth. The evaluation results can be presented as loss curves or loss level reports, providing direct reference for process improvement or circuit design. This step achieves non-destructive and rapid detection, significantly shortening the cycle from R&D to performance verification of new materials and reducing the cost of repeated experiments.

[0032] As an example, the steps of acquiring the interface three-dimensional point cloud data and broadband scattering parameter matrix of the sample high-frequency substrate material include: scanning the surface morphology of the sample high-frequency substrate material to obtain an initial interface morphology image; performing three-dimensional reconstruction and point cloud sampling on the initial interface morphology image to obtain interface three-dimensional point cloud data; performing multi-frequency electromagnetic excitation on the sample high-frequency substrate material to obtain a reflection transmission test signal; performing de-embedding processing and parameter transformation on the reflection transmission test signal to obtain a broadband scattering parameter matrix; and spatially associating the interface three-dimensional point cloud data and the broadband scattering parameter matrix.

[0033] It should be noted that the initial interface topography image refers to a two-dimensional or three-dimensional original image file containing the original optical or interference information of the material surface's undulations. In this example, the interface three-dimensional point cloud data refers to a discrete data set containing a large number of microscopic undulation spatial coordinate points extracted from the reconstructed material surface digital model. The reflected transmission test signal can be the original electrical signal captured by the vector network analyzer at the receiving end, containing the electromagnetic wave reflection amplitude and transmission phase at different frequencies. De-embedding refers to the process of removing electromagnetic parasitic effects caused by test fixtures, connectors, and leads, etc., from the overall measurement results using mathematical algorithms and standard calibration data. Parameter conversion refers to the process of converting the de-embedded electromagnetic signal into a standard microwave network scattering parameter matrix (S-parameters). Spatial location correlation refers to the operation of establishing a mapping relationship between the microscopic topography digital model of a specific scanned area of ​​the material surface and the macroscopic frequency domain electromagnetic response data measured in the same physical area in a database.

[0034] Understandably, a white-light interferometric scanning device with nanometer-level longitudinal resolution is used. The high-frequency substrate material of the sample, after surface cleaning, is placed on a high-precision stage, and the focal length of the interferometric objective lens is adjusted and the scanning field of view is set. After the device is started, the physical property of the interference fringes generated by the broadband light source changing with height is utilized to scan the microscopic undulation contour of the substrate material surface layer by layer. The system automatically acquires the interference pattern of each pixel and performs phase unpacking, thereby outputting an initial interface morphology image containing rich elevation information and topographic details.

[0035] The acquired initial interface topography image is imported into 3D processing software. First, a filtering algorithm is used to remove high-frequency noise caused by environmental vibrations and low-frequency errors caused by the tilt of the reference surface. Then, coordinate points are extracted at equal intervals on the reconstructed continuous 3D surface at a fixed spatial sampling rate. The horizontal and vertical coordinates and corresponding elevation values ​​of each sampling point are recorded. These discrete spatial coordinate point sets are exported to finally generate interface 3D point cloud data that can be used for subsequent fractal geometric feature analysis.

[0036] A custom-designed high-frequency test fixture is connected to the test port of a vector network analyzer using a coaxial cable. The substrate material sample is fabricated into a standard microstrip or stripline structure and fixed in the fixture. The vector network analyzer is used to set the start frequency, end frequency, and the number of discrete sweep points. The instrument then automatically sends multi-frequency electromagnetic excitation signals covering the required broadband range to the substrate material sample. The receiving end synchronously records the electromagnetic wave energy and phase deflection information reflected from the material surface and penetrating the material at each frequency point, summarizing these data to generate a reflected transmission test signal.

[0037] For the acquired reflected transmission test signal, calibration and de-embedding algorithms such as the multi-line method (Thru, Reflect, Line, TRL) or open-circuit, short-circuit, load-through (Short, Open, Load, Thru, SOLT) are applied, combined with pre-measured calibration reference data, to accurately deduct attenuation and phase delay interference from coaxial connectors, test fixture adapters, and feeders from the total test signal. After removing non-material-related factors, the purified test device signal is transformed into a standard broadband scattering parameter matrix according to microwave network theory. This matrix contains core complex parameters characterizing the high-frequency properties of the material, such as return loss and insertion loss.

[0038] A unified identification code is established for the same sample material in the database, recording the optical coordinate origin during the morphology scanning process and the physical probe contact position during the electromagnetic testing process. Through coordinate system translation and scaling matrix transformation, the interface 3D point cloud data acquired at the microscale and the broadband scattering parameter matrix measured at the macroscale are bound to the same global reference system, ensuring that the electromagnetic response data strictly corresponds to the local rough morphology that produces the response, and completing a high-precision mapping and correlation between morphological features and electromagnetic properties in space and logic.

[0039] This example successfully eliminates parasitic interference from the testing environment and fixtures by combining high-precision optical interferometry with microwave network frequency domain measurement, obtaining the purest underlying microstructure and macroscopic electromagnetic parameters of the material. Based on this, strict spatial correlation is implemented, breaking the limitation of the separation between morphological observation and electrical performance measurement in traditional material testing. An accurate one-to-one mapping relationship between rough interfaces and signal attenuation is established at the physical source level, laying a data foundation for subsequent deep feature mining and loss evolution learning using physical information neural networks.

[0040] As an example, the step of extracting multi-scale features from the interface 3D point cloud data to obtain a multi-scale fractal dimension feature set includes: transforming the interface 3D point cloud data into a spatial coordinate system to obtain a horizontal projection height matrix; dividing the horizontal projection height matrix into blocks using a preset sliding window to obtain multiple local height matrices; calculating the surface area of ​​the multiple local height matrices at different preset scale steps; mapping the surface area to a double logarithmic coordinate system based on the preset scale step and the surface area to obtain a multi-scale logarithmic scatter set; and performing regression fitting calculation on the multi-scale logarithmic scatter set using the least squares method to obtain the multi-scale fractal dimension feature set.

[0041] It should be noted that the horizontal projection height matrix refers to a two-dimensional mathematical feature data structure formed by arranging the elevation values ​​of each grid node according to row and column rules after projecting discrete coordinate points in three-dimensional space onto a two-dimensional reference plane. The preset sliding window can be a sampling range mask frame of fixed size that slides row by row and column by column on the two-dimensional data matrix according to a specific step size, used to achieve localized truncation and segmentation of global environmental data. The window size should be set larger than the spatial correlation length of the micro-roughness of the copper foil surface morphology to ensure that each local matrix contains complete fractal geometric features, while not being too large to cause local features to be averaged. In this example, it is between 64×64 pixels and 256×256 pixels. The local height matrix refers to a two-dimensional sub-matrix containing extremely small-range micro-undulation topological information extracted from the globally continuous height data through masking operations.

[0042] The preset scale step size refers to the reference scale value used to discretize and cover the three-dimensional surface topography when calculating fractal geometry properties. Its lower limit depends on the maximum lateral optical resolution of the white light interferometer or scanning device, and its upper limit depends on the physical size boundary of the preset sliding window. In this example, the value ranges from 0.1 μm to 50 μm in a logarithmically increasing sequence. The multi-scale logarithmic scatter set refers to a series of discrete coordinate points generated by taking the logarithm of different spatial measurement scales and their corresponding equivalent surface area values ​​and mapping them to a Cartesian coordinate system. In this example, the multi-scale fractal dimension feature set refers to the collection of fractal dimension values ​​derived from various local regions of the material surface under continuous scale transformations, used to comprehensively characterize the ruggedness and self-similarity properties of the interface.

[0043] Understandably, the high-precision 3D point cloud data of the interface collected in the early stage is imported into the processing system, and a Cartesian coordinate system is established using the macroscopically flat surface of the material as a 2D reference plane. Along the Z-axis direction perpendicular to the reference plane, the discrete coordinate points scattered in space are vertically projected onto the grid intersection nodes on the reference plane. If some grid nodes have multiple projected height values, the unique effective height of the node is determined by a cubic spline interpolation algorithm or by calculating the local mean. Finally, the elevation values ​​of all grid nodes are arranged according to the row and column order of the original coordinates to generate a horizontal projected height matrix that reflects the overall topographical undulations.

[0044] Please refer to Figure 2 , Figure 2 This is a schematic diagram of spatial coordinate system transformation provided in Embodiment 1 of the signal transmission loss assessment method for high-frequency substrate materials of this application. First, a set of discrete coordinate points on the micro-undulation surface reflecting the micro-morphology of the high-frequency substrate material is obtained. Then, vertical projection and interpolation operations are performed on this spatial point set along the vertical direction to map the scattered discrete coordinate points onto the grid nodes of the two-dimensional reference plane to determine the unique effective height. Finally, these obtained elevation values ​​are arranged in a standardized manner according to row and column order (as shown by the elements on the right side of the diagram). to By generating a horizontal projection height matrix from a two-dimensional mesh, a mathematical feature structure that can intuitively characterize the microscopic topological undulations of the substrate material surface is successfully constructed.

[0045] Then, a preset sliding window with fixed size characteristics (such as a pixel side length of M x N) is set in system memory, and the translation step size of this window in the horizontal and vertical directions is planned. The system controls the preset sliding window to start from the upper left corner of the horizontal projection height matrix and slide to the right and down sequentially according to the set step size. At each stop position, the system will crop and save all elevation values ​​within the window coverage area. In this way, the large and continuous global macroscopic topography data is safely segmented into a series of independent but overlapping local height matrices, so as to capture extremely fine topography features in small areas later.

[0046] For each local height matrix output by segmentation, a series of preset scale steps, gradually transitioning from coarse to fine, are configured for 3D surface mesh generation. Using the currently executed scale step as the baseline length, spatial polygonal units are constructed using four adjacent mesh nodes. The actual physical area of ​​each spatial polygonal unit is calculated using Heron's formula or the vector cross product algorithm. After completing the traversal at a single scale, the calculated areas of all small spatial polygons are summed to obtain the approximate equivalent surface area at the current measurement scale. The system will repeatedly execute this meshing and summation process until all preset scale steps are exhausted, thereby obtaining a set of surface area values ​​that increase or decrease nonlinearly with changes in the observation scale.

[0047] The series of preset scale step values ​​and their corresponding equivalent surface area values ​​obtained in the previous calculation are subjected to logarithmic operations with the natural constant as the base. A two-dimensional rectangular coordinate system is constructed in the processing software, with the logarithmic scale step values ​​as the x-axis and the logarithmic equivalent surface area values ​​as the y-axis. The paired data after logarithmic transformation are projected one by one into this rectangular coordinate system, forming a series of scattered data points on the map, thereby generating a multi-scale logarithmic scatter plot that intuitively shows the physical self-similarity of the morphology and the dependence on scale.

[0048] Finally, the algorithm selects effective data segments from the multi-scale logarithmic scatter plot that conform to the scale-free interval, establishes a least-squares mathematical evaluation model, and finds a globally optimal fitting line that minimizes the sum of the squares of the perpendicular distances from all discrete scatter points to this line (the scale-free interval refers to the scale range in a double logarithmic coordinate system where the equivalent surface area and the observation scale exhibit a strictly linear physical proportional relationship, characterizing the stable self-similar fractal features of the morphology within this range). The slope parameter of this optimal fitting line is extracted, and algebraic transformations are performed using the dimensional constant from fractal geometry theory to derive the fractal dimension value that characterizes the roughness complexity of the local region. All fractal dimensions derived from multi-scale transformations for each local region are summarized, ultimately constructing a multi-scale fractal dimension feature set that comprehensively characterizes the nonlinear geometric features of the substrate's micro-interface.

[0049] This example utilizes a sliding window mechanism to transform the massive and complex macroscopic substrate surface into a locally computable feature matrix, effectively reducing memory overhead when processing massive 3D point cloud data, significantly improving computational efficiency and reducing system costs. Simultaneously, by introducing a multi-scale measurement space and a double logarithmic fitting algorithm, it is possible to mine the self-similar physical laws and nonlinear fractal characteristics within the morphology from different spatial observation scale depths. This overcomes the information loss and distortion problems inherent in traditional root mean square roughness parameters when characterizing high-frequency microscopic tortuous current paths, extracting a set of microscopic geometric features with strong anti-interference capabilities, rich information dimensions, and significant physical support for the subsequent construction of a high-precision electromagnetic loss evolution model.

[0050] As an example, the step of calculating the surface area of ​​the multiple local height matrices at different preset scale steps includes: obtaining the grid nodes corresponding to each matrix element in the multiple local height matrices; determining the current preset scale step as the horizontal spacing between adjacent grid nodes; calculating the relative height difference between adjacent grid nodes based on the height values ​​of each element in the multiple local height matrices; constructing a spatial triangular patch network based on the relative height difference and the horizontal spacing; calculating the local patch area of ​​each triangular patch in the spatial triangular patch network according to Heron's formula; and summing the local patch areas at the same preset scale step to obtain the surface area of ​​the multiple local height matrices at different preset scale steps.

[0051] It should be noted that a grid node refers to a discrete coordinate point with a definite positional attribute formed by the intersection of row and column grid lines in a two-dimensional coordinate plane grid system. Horizontal spacing refers to the absolute physical distance between two adjacent grid nodes along the horizontal coordinate axis within a defined two-dimensional reference plane. Relative height difference can be the absolute value of the difference in elevation values ​​between two adjacent data points in three-dimensional space in a direction perpendicular to the reference plane. A spatial triangular patch network refers to a grid skeleton structure composed of multiple interconnected and non-overlapping spatial triangular geometric units, used to approximate the undulating topology of complex material surfaces. Local patch area refers to the absolute surface area occupied by a single triangular geometric unit in three-dimensional space within a spatial triangular patch network.

[0052] Understandably, the process begins by extracting multiple pre-processed local height matrices from the data storage unit. Based on the row and column index arrangements of the matrix data, a low-level Cartesian two-dimensional reference grid coordinate system is established. Following the absolute geometric position of each elevation element within the matrix rows and columns, each independent elevation element value is unidirectionally mapped to the corresponding intersection point within the two-dimensional reference grid system. This completes the binding of discrete elevation data with two-dimensional plane coordinate positions, obtaining the grid nodes corresponding to each matrix element in the multiple local height matrices. This provides a robust low-level two-dimensional positioning reference framework for subsequent three-dimensional spatial topology reconstruction.

[0053] Secondly, the specific observation scale constant value currently being executed by the computing system is extracted as the reference physical benchmark for the current round of calculation. The extracted current preset scale step value is assigned to the distance interval parameter between each node in the two-dimensional reference grid system. The current preset scale step is determined as the horizontal spacing between adjacent grid nodes, thereby establishing a quantitative proportional relationship between the virtual pixel position span inside the data matrix and the real microscopic physical straight-line distance on the substrate surface.

[0054] Then, for any two adjacent grid nodes in the two-dimensional reference grid coordinate system, the vertical elevation component values ​​recorded in the corresponding matrix positions of these two nodes are extracted. The absolute elevation values ​​corresponding to each grid node are extracted from the horizontal projection height matrix and mapped to the two-dimensional plane coordinates of the grid nodes. By traversing the entire matrix, a discrete coordinate point set containing three-dimensional spatial position information is established, realizing a preliminary quantitative expression of the undulating topological state of the material's micro-surface along the vertical axis.

[0055] Based on this, nodes obtained from the underlying 2D reference mesh are used as the basic vertices for 3D reconstruction. Combining the horizontal spacing parameters determined in the horizontal direction and the relative height difference parameters calculated in the vertical direction, the Pythagorean theorem is applied to calculate the actual spatial connection line length between any adjacent vertices in the 3D spatial coordinate system. A spatial rectangular region consisting of any four adjacent vertices is selected, and this rectangular region is divided along its diagonal in a fixed direction. Each rectangular region is then divided into two adjacent spatial triangular geometric units. After comprehensive diagonal line partitioning of the entire matrix coverage area, the discrete 3D elevation nodes are reconstructed into a network of interconnected spatial triangular facets covering the surface.

[0056] Next, the three physical side lengths of each independent spatial triangular unit within the constructed spatial triangular patch network are extracted. These three physical side lengths are added together and divided by 2 to obtain the semi-perimeter characteristic parameter of the corresponding spatial triangular unit. The three physical side lengths of the spatial triangular unit are then substituted into Heron's formula to calculate the local physical surface area of ​​each triangular patch. The local patch area of ​​each triangular patch in the spatial triangular patch network is then calculated to obtain the true physical area value of each tiny topological geometric unit in three-dimensional space.

[0057] Finally, the surface area at that scale is obtained by summing up all local surfaces at the same observation scale. By continuously changing the subsequent observation scale and repeating the above geometric subdivision calculation and summation process, the surface area of ​​multiple local height matrices at different preset scale steps is obtained.

[0058] This example constructs a spatial triangular patch network that closely matches the actual physical morphology of the substrate material by performing gridded benchmark positioning and three-dimensional spatial topology reconstruction on the local elevation matrix. Heron's formula is then used to accurately quantify the physical area of ​​the microscopically irregular undulating surface. This surface area evaluation logic based on scale transformation parameters and grid geometric partitioning effectively avoids the omission of morphological features caused by traditional two-dimensional roughness statistical parameters when measuring complex three-dimensional high-frequency electronic transmission interfaces. While ensuring the rigor of the electromagnetic geometric calculation logic, it also uncovers the microscopic topological fractal features hidden beneath the macroscopic substrate surface in a multi-dimensional and fine-grained manner. This provides high-quality microscopic feature input data with strong physical support for the subsequent extraction of fractal dimension datasets and the construction of signal transmission loss evolution evaluation models.

[0059] As an example, the step of constructing a spatial triangular patch network based on the relative height difference and the horizontal spacing includes: mapping the adjacent mesh nodes to discrete topological vertices in a three-dimensional coordinate space; constructing a two-dimensional rectangular topological boundary between every four adjacent discrete topological vertices according to the horizontal spacing; dividing the two-dimensional rectangular topological boundary according to a preset diagonal connection rule to obtain two-dimensional planar triangular topological units; injecting the relative height difference as a spatial offset in the vertical dimension into the two-dimensional planar triangular topological units to upgrade and reconstruct the two-dimensional planar triangular topological units into a three-dimensional spatial connected skeleton; and performing surface solidification encapsulation processing on each skeleton unit in the three-dimensional spatial connected skeleton to obtain a spatial triangular patch network.

[0060] It should be noted that discrete topological vertices refer to the geometrically fundamental connection endpoints within a virtual three-dimensional Cartesian coordinate system, where physical volume attributes have been removed and only absolute spatial coordinate information is retained. A two-dimensional rectangular topological boundary can be a closed quadrilateral geometric outline formed by connecting four adjacent and coplanar discrete topological vertices. Preset diagonal connection rules refer to the geometric judgment logic pre-defined during computer graphics meshing to guide how to connect two non-adjacent vertices within a quadrilateral using line segments to achieve polygon segmentation. Since the diagonal connection method (e.g., from top left to bottom right, or from top right to bottom left) affects the smoothness of the final mesh, it is usually based on the "shortest diagonal principle" or the "maximize minimum angle principle" (Delaunay triangulation criterion). In this example, the shortest diagonal principle from the Delaunay triangulation criterion is adopted, that is, selecting the shorter diagonal line within the rectangle for connection to avoid generating extremely long and distorted triangular patches.

[0061] A two-dimensional planar triangular topological unit refers to the smallest planar polygon structure located on the same horizontal reference plane and formed by three straight line boundaries connected end to end, generated by dividing a rectangular boundary by diagonals. The spatial offset in the vertical dimension can be the absolute coordinate distance constant required for each topological vertex to be translated in the direction of the normal vector orthogonal to the two-dimensional reference plane. A three-dimensional spatial connected skeleton refers to an irregular three-dimensional mesh support frame formed by the displacement and stretching of each vertex of the planar triangular unit in the height direction, and the interlocking of spatial line segments with tilt angles. The skeleton unit refers to the basic structure that constitutes the three-dimensional spatial connected skeleton, usually represented as a triangular wireframe closed loop in a tilted state in three-dimensional space. Surface solidification encapsulation processing refers to the calculation process of generating a continuous geometric surface with lossless topological properties on the spatial skeleton frame composed of multiple line segments, giving the frame model real physical area properties. In this example, the spatial triangular patch network refers to a continuous digital topology representation shell formed by splicing and fusing three-dimensional triangular patches after solidification processing according to the undulation law of the material's microscopic surface.

[0062] Understandably, the process begins by extracting adjacent mesh nodes in a two-dimensional structure and establishing a three-dimensional Cartesian coordinate space with height vector components within the computational system. Based on the row and column index relationships in the two-dimensional matrix, each adjacent mesh node is assigned to its corresponding projection position in the base plane coordinate system of this three-dimensional coordinate space. At this stage, the elevation components of all nodes are initialized to zero, allowing the original two-dimensional array nodes to undergo a dimensional migration to the lower dimensional level of the three-dimensional coordinate system while preserving their planar physical adjacency. This mapping transforms them into discrete topological vertices in the three-dimensional coordinate space.

[0063] Secondly, the extracted horizontal spacing values ​​are used as the base grid scale to define the physical span between each vertex. Within the base coordinate plane, four discrete topological vertices arranged in a crisscross pattern are locked. Using a line segment generation algorithm in a computer graphics engine, these four vertices are connected end-to-end with straight lines along both the horizontal and vertical axes, with a fixed horizontal spacing. Through this systematic connection operation that traverses all bottom-level vertices, orthogonal grid connections are established within the originally isolated geometric vertex group, thereby constructing a regularly arranged two-dimensional rectangular topological boundary between every four adjacent discrete topological vertices.

[0064] Next, the preset diagonal connection rules set in the graphics processing system are retrieved. For each independent two-dimensional rectangular topological boundary generated in the base plane, a virtual dividing line segment is drawn along the fixed cross-regional diagonal direction inside the rectangular boundary. With the topological partitioning effect applied by this diagonal dividing line segment, the structural symmetry and connectivity of the original rectangular quadrilateral are broken, dividing it into two right-angled triangle structures with equal areas and sharing a diagonal boundary. After performing this diagonal connection partitioning process on the entire rectangular mesh array, the two-dimensional rectangular topological boundary is structurally segmented, resulting in densely distributed two-dimensional planar triangular topological units.

[0065] Then, the absolute elevation values ​​corresponding to each grid node recorded in the local height matrix are extracted. For the three basic vertices contained in each two-dimensional planar triangular topological unit, the absolute elevation values ​​are injected into the three-dimensional coordinates of the basic vertices in the normal direction perpendicular to the reference plane. Relying on this assignment mechanism based on real physical elevation, the triangular vertices originally tiled on the basic plane are driven to shift, causing the original planar right-angled boundaries and diagonal boundaries to undergo spatial tilting and physical stretching. This transforms the two-dimensional planar triangular topological unit into a three-dimensional spatially connected skeleton that conforms to the real undulations of the material surface.

[0066] Finally, for the 3D spatially connected skeleton exhibiting a 3D wireframe structure, the surface skinning and filling function within the geometry rendering system is activated. Along the three spatially inclined boundaries within each skeleton unit, continuous polygonal thin-film geometric surfaces without physical thickness but possessing actual geometric area properties are rendered and generated within their closed regions. By traversing all the wireframe microstructures within the framework system and executing the skinning and filling instructions for these thin-film geometric surfaces, the originally hollow linear topology is transformed into a continuous geometric shape structure with closed surface physical properties. Each skeleton unit in the 3D spatially connected skeleton undergoes surface solidification encapsulation processing, ultimately obtaining a spatial triangular patch network that reflects the rough and undulating state of the real microscopic substrate.

[0067] This example introduces a graphics-based flow processing architecture of "dimensionality reduction planar mapping - 2D topological partitioning - spatial dimensionality upgrade reconstruction - skeleton entity encapsulation," overcoming the topological defects of mesh intersections or holes that are easily caused by directly performing spatial triangulation on 3D discrete points in traditional roughness evaluation schemes. This geometric reconstruction process first establishes stable right-angle and diagonal connectivity in the underlying 2D plane, and then achieves spatial dimensionality upgrade evolution of physical morphology features by injecting height differences. This significantly reduces the computational power consumption of computers when processing highly irregular complex microscopic high-frequency material morphologies for geometric deduction. The generated topological patch network with materialized surface properties retains the true geometric self-similarity and extremely high elevation continuity of the substrate material surface to the greatest extent, providing a solid and physically logically rigorous 3D digital spatial representation foundation for high-precision Heron's formula area integral calculation and the establishment of broadband electromagnetic skin effect boundary conditions.

[0068] As an example, the step of extracting the test frequency sequence corresponding to the broadband scattering parameter matrix and constructing a fractal interface impedance characteristic sequence based on the multi-scale fractal dimension feature set, preset micro-polarization parameters, and the test frequency sequence includes: weighting and averaging the fractal dimensions of multiple different scales in the multi-scale fractal dimension feature set to obtain the basic fractal dimension; extracting the test frequency sequence corresponding to the broadband scattering parameter matrix and converting the test frequency sequence into a multi-frequency angular frequency sequence; calculating the fractal equivalent capacitance sequence based on the basic fractal dimension, the multi-frequency angular frequency sequence, and preset micro-polarization parameters; calculating the fractal equivalent inductance value based on the basic fractal dimension and preset skin equivalent inductance value; and performing impedance synthesis with the fractal equivalent inductance value and each element in the fractal equivalent capacitance sequence to obtain the fractal interface impedance characteristic sequence, wherein the calculation formula for impedance synthesis is: In the formula, This represents the fractal interface impedance value in the fractal interface impedance characteristic sequence, in ohms. This represents the fractal equivalent inductance value, in Henry. This represents a fractal equivalent capacitance sequence, measured in farads. This represents the angular frequency values ​​in a multi-frequency angular frequency sequence, expressed in radians per second. It represents the imaginary unit.

[0069] It should be noted that the fundamental fractal dimension refers to a single, reduced-dimensional representative value used to characterize the global average roughness complexity of a material's microscopic surface, obtained by weighting and evaluating fractal geometric feature values ​​acquired at multiple different spatial observation scales. The multi-frequency angular frequency sequence refers to the set of cyclic frequency values ​​measured in radians per second obtained by mathematically transforming discrete test physical frequencies (conventionally measured in Hertz) by multiplying by 2π. The fractal equivalent capacitance sequence refers to the set of equivalent distributed capacitance values ​​calculated at various independent high-frequency alternating test frequencies, combining the material's inherent microscopic polarization properties with surface roughness fractal characteristics. The fractal equivalent inductance value refers to the inductance constant value reflecting the true rugged interface state, obtained by geometrically nonlinearly correcting the fundamental skin inductance value under ideal smooth conditions by introducing surface microscopic fractal roughness parameters.

[0070] The preset skin equivalent inductance value (i.e., the equivalent inductive reactance in an ideal plane) can be a theoretical inductance constant value derived in advance based on the current skin distribution effect on an ideal smooth conductor surface under the action of a high-frequency electromagnetic field. The specific calculation process is as follows: First, the absolute conductivity of the copper foil material on the high-frequency substrate is extracted. and the angular frequency values ​​in the test frequency sequence Combined with spatial permeability The theoretical skin depth under a specific high-frequency alternating magnetic field was calculated. Its formula is: Subsequently, based on the wave impedance characteristics of electromagnetic waves propagating on the surface of a good conductor, the unit internal surface impedance of an ideal smooth conductor surface is... Expressed as: in, This refers to skin resistance, also known as surface resistance, which is surface impedance. The real part represents the energy loss (i.e., the portion of electrical energy converted into Joule heat) caused by the skin effect when high-frequency electromagnetic waves enter the surface of a conductor.

[0071] Extract the imaginary inductive reactance component from the impedance equation above, and calculate the equivalent value of the inductive reactance in the ideal plane using algebraic transformation. ,Right now: This derivation process ensures strict consistency of the inductance reference parameters in terms of physical dimensions (Henry), laying an objective and verifiable physical foundation for subsequent introduction of fractal dimension for nonlinear geometric correction.

[0072] Understandably, the process begins by extracting a series of fractal dimension values ​​from the previously constructed multi-scale fractal dimension feature set. For each scale, a weighting coefficient is assigned based on its physical contribution to the overall morphology characterization, assigning higher weights to smaller scales that better reflect the microscopic tortuous paths of high-frequency currents. This weighting coefficient is then used to perform a weighted average of the fractal dimensions at multiple scales. Through this multi-dimensional feature dimensionality reduction evaluation mechanism, a weighted average of the fractal dimensions at multiple scales is calculated and output, resulting in a fundamental fractal dimension that reflects the combined macroscopic and microscopic ruggedness of the material surface.

[0073] Secondly, frequency configuration information strictly bound to the broadband scattering parameter matrix is ​​read from a database storing RF measurement parameters. A series of discrete test frequencies, with Hertz as the basic physical unit, are extracted to form a test frequency sequence. Each frequency value in the test frequency sequence is multiplied by 2π to perform a phase space transformation, converting the physical frequency, which originally represents the number of oscillations per second, into the phase space system. This transforms the test frequency sequence into a multi-frequency angular frequency sequence, ensuring that the discrete frequency points meet the requirements of the complex domain impedance calculation format for subsequent microwave equivalent circuits.

[0074] Next, the preset micro-polarization parameters characterizing the inherent properties of the substrate dielectric material and the basic fractal dimension obtained from the previous steps are retrieved and input into a preset rough interface dielectric response calculation model. At each discrete angular frequency node, the model performs nonlinear scaling correction on the effective polarized contact area under the high-frequency alternating electric field based on the basic fractal dimension, deriving the dynamic capacitance component affected by surface geometric distortion. By performing this polarization response calculation one by one at all independent nodes covering the test frequency domain, a series of capacitance value combinations that evolve with frequency and incorporate morphological features are generated. Based on the basic fractal dimension, multi-frequency angular frequency sequence, and preset micro-polarization parameters, the output fractal equivalent capacitance sequence is derived.

[0075] Then, the preset skin equivalent inductance value, determined based on an ideal smooth conductor surface model under high-frequency skin depth conditions, is read. The fundamental fractal dimension is introduced as a geometric compensation parameter to construct an inductive reactance fractal compensation function. The difference between the fundamental fractal dimension and the topological dimension of an absolutely smooth surface is used to quantitatively evaluate the parasitic flux linkage effect caused by the physical extension of the path when high-frequency current flows within a rugged profile. The calculated parasitic flux linkage compensation coefficient is multiplied by the preset skin equivalent inductance value to complete the geometric correction evolution from an ideal smooth state to a truly rough state. Based on the fundamental fractal dimension and the preset skin equivalent inductance value, a fractal equivalent inductance value that conforms to the physical morphology of the actual material is calculated and extracted.

[0076] Finally, within the framework of complex impedance calculation in microwave equivalent circuits, the fundamental fractal equivalent inductance value is locked as the inductive reactance constant characterizing the geometric topology. Simultaneously, paired frequency elements from the fractal equivalent capacitance sequence and the multi-frequency angular frequency sequence are extracted sequentially. Applying an AC impedance synthesis formula encompassing both real and imaginary parts, for each evaluation node in the angular frequency sequence, the fractal equivalent inductance value and the corresponding fractal equivalent capacitance element are algebraically concatenated to calculate the equivalent physical impedance response under that specific high-frequency state. Specifically, the physical logic of impedance synthesis lies in equating the fractal interface to a complex impedance circuit model. Based on microwave transmission line theory, the fractal interface at the microscale can be equivalent to a distributed parameter network, whose characteristic impedance is determined by the square root of the ratio of the fractal equivalent inductance value to the fractal equivalent capacitance sequence, constituting the real part of the impedance. Secondly, the irregular fluctuations of the fractal interface lead to a physical extension of the high-frequency current path, generating a magnetic field energy storage effect characterized by inductive reactance; simultaneously, microscopic polarization and geometric coupling generate an electric field energy storage effect characterized by capacitive reactance. The imaginary part of the impedance is formed by superimposing the inductive and capacitive reactance terms in the complex domain. By synthesizing the real part, which characterizes the intrinsic propagation characteristics, with the imaginary part, which characterizes the dynamic frequency response, the signal evolution state of the target high-frequency substrate material in a broadband environment can be accurately quantified. By traversing the entire frequency domain node matrix and performing this point-to-point independent operation process, the fractal equivalent inductance value and each element in the fractal equivalent capacitance sequence are synthesized one by one to output a fractal interface impedance characteristic sequence spanning a wide frequency range.

[0077] Please refer to Figure 3 , Figure 3 This is a schematic diagram of the physical modeling of the equivalent impedance of the fractal interface provided in Embodiment 1 of the signal transmission loss assessment method for high-frequency substrate materials of this application. In the microscopic cross-section of the substrate material presenting a rugged contour line and a current skin layer, the high-frequency alternating current is forced to flow along the undulating rugged contour line due to the skin effect. The system performs geometric correction on this path distortion phenomenon to extract the equivalent inductance feature L, thereby obtaining the fractal equivalent inductance used to characterize the magnetic field energy storage effect. Simultaneously, polarization mapping is performed by combining the microscopic geometric topological features of the rugged contour lines to extract the equivalent capacitance features. And at the multi-frequency angular points where external excitation is introduced. After parameterization, dynamic response calculations are performed, and a fractal equivalent capacitance sequence for characterizing micro-polarization and electric field energy storage effects is derived. Finally, the results obtained from the deduction will be... as well as In the common input impedance synthesis operation module, AC impedance superposition logic covering real and imaginary features is executed, and finally the fractal interface impedance feature sequence Z that can quantitatively evaluate the broadband electromagnetic evolution state of the substrate is calculated and generated.

[0078] This example establishes a rigorous mathematical mapping between microscopic nonlinear geometric topology and macroscopic broadband electromagnetic parameters in the underlying data link by extracting the dimensionality-reduced fundamental fractal dimension and combining it with the mechanisms of microscopic dielectric polarization and high-frequency skin effect. This computational architecture, which drives a broadband dynamic polarization capacitive reactance sequence with specific geometrically equivalent inductive reactance values, conforms to the dispersion laws and physical distribution characteristics of high-frequency signals, effectively avoiding the computational exhaustion and convergence difficulties encountered in directly solving the full-wave electromagnetic field differential equations under extremely complex morphologies. The calculated fractal interface impedance characteristic sequence possesses a high degree of physical causal relationship and consistent frequency domain data dimension, providing a high-quality feature dataset carrying prior physical laws for the subsequent training of physical information neural networks, thereby improving the data mining depth and generalization prediction capability of the evolutionary prediction model.

[0079] As an example, the step of calculating the fractal equivalent inductance value based on the basic fractal dimension and the preset skin equivalent inductance value includes: calculating the dimensionality difference between the basic fractal dimension and the preset smoothing dimension; subtracting a preset offset from the basic fractal dimension and inputting it into a preset gamma function to obtain a fractional scaling factor; performing a natural exponential mapping based on the dimensionality difference and the preset scaling constant to obtain a nonlinear compensation coefficient; and multiplying the fractional scaling factor, the nonlinear compensation coefficient, and the preset skin equivalent inductance value to obtain the fractal equivalent inductance value.

[0080] It should be noted that the preset smoothness dimension refers to the theoretical topological dimension constant representing an absolutely ideal smooth two-dimensional plane in fractal geometry theory. In this example, it is 2.0 because the standard dimension of an ideal, absolutely smooth plane in terms of geometric topology is two dimensions. The dimension difference is the algebraic result obtained by subtracting the fundamental fractal dimension of the material's actual physical surface from the dimension constant of the ideal, absolutely smooth plane. It is used to quantify the physical degree to which roughness deviates from the ideal plane. The preset offset can be a dimensionless constant pre-set in the mathematical calculation model to meet the convergence domain requirements of a specific distribution function. In this example, it is set to 1.0 to shift the fractal dimension to the optimal positive real-valued convergence integral interval of the preset gamma function.

[0081] The predefined gamma function is a special mathematical function used in the complex domain to extend the concept of factorial, to handle fractal dimension inputs containing decimal forms, and to derive the fractal convergence characteristics of surface complexity; its mathematical definition is: in, This refers to the independent variable of the function. In the physical modeling of this embodiment, the independent variable x corresponds to the translation value after subtracting the preset offset 1.0 from the basic fractal dimension D. is the internal variable of the integral; e is the natural constant.

[0082] By utilizing the continuous integral convergence property of this function in the positive real number domain, discrete fractal geometric features can be smoothly mapped to the adjustment ratio of the physical extension of the current path.

[0083] The fractional scaling factor refers to the dimensionless multiplier output after mapping the fundamental fractal dimension through a special algebraic function. It characterizes the dimensionality reduction adjustment ratio of the equivalent current path distribution by the multi-scale self-similarity characteristics of the micro-morphology. The preset scaling constant is an exponential nonlinear attenuation or amplification regulation parameter pre-calibrated based on the physical empirical laws of the interaction between microwave high-frequency electromagnetic fields and micro-rough surfaces. Its value range is set to 0.4 to 0.6 (0.5 in this example). Its physical basis lies in quantifying the intensity of parasitic eddy currents generated by the high-frequency alternating magnetic field within the micro-valleys of the rough surface. This constant limits the divergence boundary of the inductive reactance nonlinear compensation coefficient. The nonlinear compensation coefficient refers to the data weight generated based on dimensional difference characteristics and a specific exponential base, used to restore the nonlinear abrupt mapping relationship of the high-frequency parasitic inductance caused by morphological fluctuations in a broadband environment.

[0084] Understandably, the first step is to calculate the absolute difference between the basic fractal dimension and the preset smoothing dimension, thereby establishing a direct quantitative scale to measure the deviation of the actual surface undulation of the substrate from the absolute smoothing benchmark. The basic fractal dimension is then subtracted from a preset offset to complete a linear translation transformation of the data domain. The transformed value is then used as the sole independent variable input to a preset gamma function for integration, extending the discrete factorial to the continuous real number domain. This deeply explores the self-similar scaling properties of the fractal geometry of the dielectric surface, and subsequently calculates a fractional scaling factor, providing an adjustment base with fractal mathematical support for subsequent correction of the inductive impedance distribution.

[0085] Next, the product of the dimension difference and the preset scaling constant is used as the exponential parameter to perform natural exponential mapping. By taking advantage of the inherent nonlinear amplification and contraction physical characterization characteristics of the natural exponential function, the simple geometric dimension deviation feature is mapped into the change weight of electromagnetic response intensity. Based on the dimension difference and the preset scaling constant, natural exponential mapping is performed, and the output is a nonlinear compensation coefficient that can be used to adjust the strength of high-frequency parasitic flux linkage effect.

[0086] Finally, the preset skin equivalent inductance value calculated based on the smooth surface theoretical model, the fractional scaling factor characterizing the self-similar proportional characteristics, and the nonlinear compensation coefficient quantifying the degree of fluctuation deviation are retrieved sequentially. The preset skin equivalent inductance value is multiplied by the fractional scaling factor and the nonlinear compensation coefficient, respectively. This allows the basic inductance parameters, originally applicable only to ideal mirror conductors, to be simultaneously incorporated into the fractal scaling adjustment law and topological deviation law of the rough interface. Through this combined multiplication operation, the cross-domain correction of the physical parameters by the geometric parameters is achieved, yielding the fractal equivalent inductance value. This completes the accurate calculation and extraction of the equivalent inductive reactance for the tortuous path of high-frequency current on real complex surfaces.

[0087] Specifically, the formula for calculating the fractal equivalent inductance is: In the formula, This represents the fractal equivalent inductance value, measured in Henry. This indicates the preset skin equivalent inductance value, in Henry. denoted as the fundamental fractal dimension (dimensionless, and 2.0 ≤ D < 3.0). This represents the preset scaling constant (0.5, dimensionless). This indicates the default gamma function.

[0088] The derivation of this formula is based on the cross-mapping between microwave electromagnetic field theory and fractal geometry. First, it derives the inductance of an ideal smooth conductor based on the traditional skin effect. It cannot characterize the current path distortion caused by the rough surface; when there are micro-undulations on the substrate surface, its basic fractal dimension D will be greater than the smooth reference value of 2.0; as the high-frequency current is forced to flow along the rugged three-dimensional contour, the actual conduction path is physically elongated.

[0089] In the derivation process, on the one hand, we introduce... As a fractional scaling factor, the continuous integral property of the gamma function in the real domain is utilized to accurately quantify the adjustment ratio of the self-similar scaling property of the microstructure on the total length of the current path; on the other hand, a natural exponential term is introduced. As a nonlinear compensation coefficient, it is used to characterize the situation when the surface dimension deviates from absolute smoothness. At that time, the local parasitic flux linkage effect and energy loss induced by the peak-valley topology of the rough interface exhibit an exponentially amplified physical evolution law. Through the product of the above-mentioned geometric and physical dual correction terms, the pure geometric parameters characterizing the degree of topographic ruggedness are rigorously transformed into electromagnetic physical weights that adjust the strength of high-frequency parasitic induction.

[0090] This example constructs a nonlinear mathematical evolution logic that robustly transforms pure fractal geometric features into equivalent electromagnetic induction resistance correction weights by introducing a smooth dimensional benchmark difference comparison and gamma function mapping. Employing a multiplicative adjustment mechanism combining fractional scaling and natural exponential compensation, it successfully overcomes the boundary condition divergence problem of traditional empirical loss formulas when dealing with extremely rough materials, ensuring the physical continuity of the model as it degenerates towards smooth surfaces. Simultaneously, it reasonably characterizes the additional magnetic field energy storage effect induced by high-frequency current flowing in a microscopic rugged topological network, providing highly electromagnetically causal input features for subsequent broadband impedance sequence synthesis and artificial intelligence network training.

[0091] As an example, the construction steps of the physical information neural network include: constructing a basic multilayer perceptron network structure comprising an impedance feature input layer, a multidimensional fully connected hidden layer, and a scattering parameter output layer; adding an electromagnetic wave transmission line theory constraint layer at the output end of the scattering parameter output layer; constructing a composite loss function comprising data-driven error and physical law residuals; embedding the frequency domain wave equation residuals of Maxwell's equations into the physical law residual term in the composite loss function; and constructing the physical information neural network based on the basic multilayer perceptron network structure, the electromagnetic wave transmission line theory constraint layer, and the composite loss function.

[0092] It should be noted that the impedance feature input layer refers to the first neuron connection layer in the neural network used to receive the fractal interface impedance data sequence, and its number of neurons is consistent with the length and dimension of the input feature sequence. A multidimensional fully connected hidden layer can be a deep computational architecture located between the input and output layers, consisting of multiple neuron layers with nonlinear activation functions, used to extract high-dimensional feature mapping relationships. The scattering parameter output layer refers to the neuron layer at the end of the neural network used to map and generate predicted scattering parameter values, typically responsible for outputting complex components representing amplitude and phase. The electromagnetic wave transmission line theory constraint layer refers to a physical computation module that does not contain training parameters but internally encapsulates the mathematical logic of the transmission line analytical equation or telegraph equation, used to perform consistency checks on the original network output.

[0093] Data-driven error refers to an empirical error metric measured by the degree of deviation between the predicted value of a neural network and the known experimentally measured label value. Physical law residuals refer to the numerical deviation of the neural network's output from objective electromagnetic physical laws such as Maxwell's wave equation. A composite loss function is a comprehensive objective function used to guide the direction of network parameter updates after weighted summation of discrete data error terms and continuous physical residual terms. In this example, the physical information neural network refers to an intelligent modeling architecture that combines deep learning algorithms with fundamental electromagnetic physical laws, achieving dual-driven modeling based on both mechanism and data by embedding physical equation residuals into the network loss function.

[0094] Understandably, in this example, a multilayer perceptron with a specific number of neurons is configured as the basic computational skeleton. The complex values ​​of each frequency point in the fractal interface impedance feature sequence are used as the original driving source of the impedance feature input layer. The deep mapping of cross-frequency band features is achieved by setting up a multidimensional fully connected hidden layer with more than 3 layers and each layer containing at least 64 neurons. Finally, the high-dimensional hidden features are restored to a complex scattering parameter array that characterizes the electromagnetic transmission properties using the scattering parameter output layer.

[0095] Secondly, a theoretical constraint layer for electromagnetic wave transmission lines, specifically designed for physical rectification, is connected at the top of the basic network architecture. The preliminary prediction data generated by the scattering parameter output layer is injected into this constraint layer in real time. The prediction data is then processed for compliance using internally fixed transmission line impedance transformation and signal superposition functions, ensuring that each set of electromagnetic responses generated by the network can meet the basic physical boundary conditions for electromagnetic wave propagation in the transmission line.

[0096] Next, a target optimization strategy consisting of multiple error components is defined. The mean square error algorithm is selected to quantify the empirical deviation between the predicted scattering parameters and the measured sample data. At the same time, an evaluation term specifically used to capture physical logic violations is introduced. The two error components with different properties are assigned corresponding weight coefficients and then summed. Thus, a composite loss function that can simultaneously take into account the sample fitting accuracy and the rationality of the physical mechanism is established.

[0097] Then, starting from Maxwell's equations, the frequency domain wave differential equation describing the propagation of electromagnetic waves in the substrate medium is derived. The algebraic deviation of the wave equation is calculated based on the intermediate eigenvalues ​​produced by the network in the current training cycle. This deviation value is then embedded as a physical feedback signal into the physical law residual term of the composite loss function, so that the optimization process is not only limited by the known experimental data, but also subject to the strict constraints of the objective wave evolution law.

[0098] Finally, by integrating the nonlinear fitting capability provided by the multilayer perceptron basic network structure, the output physical constraints provided by the electromagnetic wave transmission line theory constraint layer, and the multi-dimensional optimization guidance provided by the composite loss function, the logical connections between the modules and the gradient flow are completed within the underlying algorithm framework. Through this modeling method that deeply couples data features and physical priors, a physical information neural network with cross-frequency band evolution prediction capability is finally constructed.

[0099] This example constructs a neural network architecture deeply coupled with physical logic, achieving collaborative modeling of data-driven features and electromagnetic physical laws. This effectively addresses the issues of physical distortion and poor generalization ability that traditional black-box models often exhibit when predicting broadband transmission loss. By introducing residuals from Maxwell's wave equations and a transmission line theory constraint layer, this example not only significantly improves the model's prediction stability and reliability under small sample conditions but also deeply explores the electromagnetic evolution laws of material interfaces through the introduction of physical residuals. This achieves higher-precision loss assessment and reduces reliance on numerical simulations of extremely complex electromagnetic fields.

[0100] As an example, the step of training a physical information neural network based on the fractal interface impedance feature sequence and the broadband scattering parameter matrix to obtain a full-band transmission loss evolution model includes: dividing the fractal interface impedance feature sequence into a training impedance set and a verification impedance set, and dividing the broadband scattering parameter matrix into a training parameter set and a verification parameter set; using the training impedance set as input features and the training parameter set as label data, inputting them into the physical information neural network for forward propagation prediction to obtain predicted scattering parameters; calculating the data prediction loss value based on the predicted scattering parameters and the training parameter set; inputting the predicted scattering parameters into a preset microwave transmission line telegraph equation to calculate the physical constraint residual, obtaining the physical residual loss value; calculating the total loss value based on the data prediction loss value and the physical residual loss value; and updating the network weights of the physical information neural network using a backpropagation algorithm based on the total loss value until a preset convergence condition is met to obtain a full-band transmission loss evolution model.

[0101] It should be noted that the training impedance set refers to a combination of data subsamples randomly selected from the overall fractal interface impedance feature sequence at a set ratio or truncated according to a specific frequency band, specifically used as input independent variables in the neural network optimization stage. The validation impedance set can be a combination of impedance feature test data independent of the training sample set, used to monitor the model's generalization ability boundary and prevent overfitting during the backpropagation iteration process. The training parameter set refers to the set of real measurements of broadband scattering parameters that are strictly physically aligned with the training impedance set in terms of frequency points, serving as a benchmark for comparison in the forward propagation of the neural network. Forward propagation prediction refers to the mathematical calculation process in which the input feature data, along a single direction from the input receiver to the final output, sequentially undergoes multidimensional spatial feature projection, node weight matrix multiplication, and nonlinear activation function mapping between neurons in each layer of the neural network, ultimately outputting the deduced parameters. The preset microwave transmission line telegraph equation refers to a second-order partial differential equation derived from the laws of classical electromagnetic field physics, used to rigorously describe the attenuation law of high-frequency voltage waves and current waves as they propagate along a guiding medium system with distributed characteristics, with the evolution of spatial ordinate and time.

[0102] The physical residual loss value refers to the numerical difference between the two sides of the equation obtained by substituting the virtual parameters predicted by the neural network into the objectively existing classical electromagnetic physics equations, and the resulting equation, indicating whether the equilibrium balancing condition is met. It is used to quantify the degree to which the network output violates the underlying physical laws. The backpropagation algorithm is a core optimization mechanism in deep learning. It calculates the gradient of the partial derivatives of the top-level loss function with respect to the weight parameters of each hidden layer within the network, and relies on the chain rule of calculus to propagate the error signal back from the output layer to the input layer, thereby guiding the downward updates of each weight. The preset convergence condition can be a pre-defined rule for stopping neural network iterations, such as the global total loss value steadily decreasing below a minimum preset threshold (e.g., 0.0001) or the total number of training iterations reaching a system-set upper limit (e.g., 5000).

[0103] Understandably, the fractal interface impedance feature sequence after preprocessing and reconstruction, along with the measured broadband scattering parameter matrix, are extracted. Following the classic deep learning data sample splitting and allocation ratio rules, the global dataset is segmented using a random data shuffling strategy or by truncating and isolating data according to continuous broadband frequency bands. The vast majority of the segmented core data is categorized and designated as the driving foundation for updating and evolving the model's internal parameters, corresponding to the generation of training impedance and training parameter sets. The remaining small portion of isolated data is reserved as a test sample library that does not participate in gradient partial derivative calculations but is only used for periodically and objectively monitoring the model's generalization state for unknown data, corresponding to the generation of validation impedance and validation parameter sets. This establishes a model training library and validation library where data boundaries do not interfere with each other.

[0104] Within the computing platform, a pre-built physical information neural network node architecture is instantiated. The complex features of the equivalent inductive and capacitive reactance of each sampling frequency band within the segmented training impedance set are mapped and loaded one by one onto the corresponding receiving terminals of the network input layer. The tensor forward propagation data stream of the network model is initiated, causing the loaded impedance feature data to undergo linear feature amplification, weight cross-combination pairing, and nonlinear spatial distortion operations of the activation function sequentially within the multi-dimensional fully connected hidden layer. The high-dimensional feature data stream continuously undergoes information compression and physical pattern extraction along a unidirectional data link from the bottom to the top layer within the network architecture. When it reaches the final scattering parameter output layer, it is transformed into a complex matrix representing the ratio of electromagnetic wave energy transmission and reflection, completing the computational loop and outputting the predicted scattering parameters.

[0105] For the predicted scattering parameters generated by the network's forward data flow and the training parameter set, which is strictly aligned with the physical characteristics of its corresponding frequency points, the mean square error (MSE) or absolute error assessment mathematical logic is retrieved in the error assessment module. At each discrete test frequency point across the entire frequency band, the pure algebraic deviations between the predicted values ​​and the measured label values ​​on the real and imaginary axes are extracted and compared. The collected deviation data undergoes square scaling to eliminate positive and negative sign cancellation interference, and the penalty for significantly severe error points is increased. After completing the comparison of all nodes, the arithmetic mean of the overall deviation matrix is ​​calculated to quantify the empirical difference distance between the current network output data and the actual experimental baseline curve, generating a data prediction loss value for the single scalar output state.

[0106] Based on the underlying physical mechanism of electromagnetic field propagation along microwave guiding structures, a tiny transmission line element with distributed parameter characteristics (i.e., a minimal axial length or element length along the propagation direction, denoted as dz) is extracted. According to Kirchhoff's law of circuit conservation, a structure containing distributed resistance R and distributed inductance is constructed for this element. Distributed conductance G and distributed capacitance The high-frequency equivalent series-parallel basic network is derived. Limit differentiation is performed on the high-frequency voltage V(z) and current I(z) across this infinitesimal element along the longitudinal propagation coordinate system, yielding the differential equation describing the first-order coupling relationship between the current and voltage. as well as Substituting these two first-order relations into each other and continuously taking the second-order spatial derivative with respect to the spatial coordinate z, we introduce the complex propagation constant. By integrating polynomial variables and decoupling, a predefined microwave transmission line telegraph equation describing the spatial evolution of the voltage wave is derived, and its computational expression is as follows: In the formula, z represents the spatial coordinates of the longitudinal propagation of the transmission line.

[0107] The predicted scattering parameters produced in the forward stage of the network are extracted and inverted into corresponding infinitesimal distributed voltage and current evolution state variables using the microwave equivalent network theory. The inverted physical state variables are directly substituted into the partial differential expression on the left side of the derived microwave transmission line telegraph equation to perform polynomial algebraic operations. Due to errors in the early stage of model training, the left side of the equation is difficult to strictly cancel to zero. The absolute difference between the partial differential operation result and the ideal zero-state equilibrium boundary is statistically analyzed. By performing a cumulative summation penalty on this distortion degree that deviates from the objective physical logic at the global frequency domain evaluation node, the physical residual loss value of the non-physical attributes of the quantified network output is obtained.

[0108] The data prediction loss value, which measures the approximation of the numerical fit, and the physical residual loss value, which constrains the compliance of macroscopic electrical logic, are extracted. Within the highest-level objective optimization decision layer of the neural network framework, independently operating weight hyperparameters are configured for these two loss scalars with completely different optimization attributes, based on the theoretical confidence level of prior physical knowledge and the signal-to-noise ratio environment of the actual input samples. According to the preset weight coefficients, the data prediction loss value and the physical residual loss value are weighted and summed to construct a global decision index that considers both the macroscopic data approximation and the microscopic evolution rationality, thus completing the final calculation and output of the total loss value. The empirical weight coefficients corresponding to the data prediction loss value and the physical weight coefficients corresponding to the physical residual loss value both range from [0,1], and their sum is 1. In the case of small sample data, the physical weight coefficients can be increased (e.g., set to 0.6 to 0.8) to enhance the guiding role of the objective laws of microwave evolution on model generalization.

[0109] The calculated total loss scalar is used as the starting point for tracing the source of network performance degradation, activating the backpropagation engine and parameter optimizer module built into the deep learning framework. Using the chain rule of calculus, the entire neural network hierarchy is reversed, progressing down the electromagnetic wave transmission line theory constraint layer to the multi-dimensional hidden layer. Gradient partial derivatives of the total loss function relative to the connection weight matrix of each neural node and the neuron bias parameters are calculated. Combined with the system's dynamic learning rate parameter decay anti-oscillation strategy, the complex weight values ​​in the hidden layer are proportionally reduced and corrected using gradient descent calculation logic. The system iteratively executes forward inference calculation and backward gradient correction iterations, and in each evaluation cycle, the network's boundary generalization index is rigorously monitored using a verification impedance set. When the slope of the global total loss value decreases gradually and falls below the set minimum tolerance threshold, or when the overall algebraic iteration reaches the safety protection upper limit and triggers termination, all updated network weight parameter matrices are frozen and solidified, outputting a full-band transmission loss evolution model with high-precision regular generalization capabilities.

[0110] This example employs a deep weighted coupling between the data prediction loss, representing real-world measurement experience, and the physical residuals of the transmission line telegraph equations, which characterize objective natural laws. This effectively overcomes the technical bottlenecks of traditional pure data-driven neural networks, which suffer from overfitting and frequency domain generalization collapse due to distorted high-frequency mapping relationships when dealing with complex microscopic and rough substrates. Embedding the differential residual terms of the telegraph equations into the network's objective function is equivalent to forcibly injecting the physical principles of microwave spatial attenuation propagation into the black-box-like artificial intelligence model. This forces the network, throughout its entire lifecycle of iteratively updating massive connection weights, to not only numerically approximate finite discrete test samples but also rigorously adhere to the physical laws governing the evolution of alternating electromagnetic fields within the real medium system in terms of topological deduction logic. This hybrid dual-drive architecture significantly reduces the dependence on extremely expensive high-frequency testing equipment and massive test benchmark samples, ensuring that the transmission loss assessment data ultimately generated by the network maintains a very high level of theoretical confidence and consistency with physical predictions even in extreme high-frequency bands where it was not trained.

[0111] As an example, the step of calculating the data prediction loss value based on the predicted scattering parameters and the training parameter set includes: obtaining the predicted real part sequence and the predicted imaginary part sequence in the predicted scattering parameters, and the true real part sequence and the true imaginary part sequence in the training parameter set; calculating the mean square error between the predicted real part sequence and the true real part sequence to obtain the real part error value; calculating the mean square error between the predicted imaginary part sequence and the true imaginary sequence to obtain the imaginary part error value; and performing a weighted summation of the real part error value and the imaginary part error value to obtain the data prediction loss value.

[0112] It should be noted that the predicted real part sequence refers to the set of projected values ​​of the complex scattering parameters output by the neural network onto the real axis of the complex plane, typically characterizing physical characteristics such as amplitude attenuation in high-frequency signal transmission. The predicted imaginary part sequence refers to the set of projected values ​​of the complex scattering parameters output by the neural network onto the imaginary axis of the complex plane, typically characterizing physical characteristics such as phase shift in high-frequency signal transmission. The true real part sequence refers to the set of reference values ​​of the complex broadband scattering parameters along the real axis obtained by actual measurement using microwave measuring instruments. The true imaginary part sequence refers to the set of reference values ​​of the complex broadband scattering parameters along the imaginary axis obtained by actual physical testing. The real part error value can be a statistical scalar used to quantify the overall difference between the combination of real part values ​​predicted by the network and the combination of real part values ​​measured by actual physical testing. The imaginary part error value can be a scalar data used to quantify the overall deviation distance between the network's predicted output result and the benchmark test result along the imaginary axis of the complex plane. In this example, the data prediction loss value refers to a comprehensive empirical bias evaluation index used to dominate the gradient descent direction during the neural network training phase after fusing the independent calculation biases of the real and imaginary parts with specific weights.

[0113] Understandably, the process begins by extracting the complex-form predicted scattering parameter matrix generated by the neural network's forward inference, along with a predefined training parameter set. Then, using a complex separation algorithm, the predicted scattering parameter matrix and the training parameter set are component-separated to obtain the predicted real part sequence, the predicted imaginary part sequence, and the true real part sequence and the true imaginary part sequence, all strictly aligned in the frequency dimension. This establishes model inference parameters and objective benchmark parameters for subsequent comparisons in two independent orthogonal dimensions of the complex plane.

[0114] Secondly, within a preset wideband range, the mean square error between the predicted real part sequence and the true real part sequence is calculated to obtain the real part error value, and the mean square error between the predicted imaginary part sequence and the true imaginary part sequence is calculated to obtain the imaginary part error value. The real part error value measures the deviation of the model in amplitude feature fitting, while the imaginary part error value quantifies the degree of divergence of the phase feature from the experimentally measured phase. The preset wideband range refers to the physical verification frequency band defined during neural network forward inference and loss function evaluation, and its range is consistent with the test frequency band of the broadband scattering parameter matrix (e.g., 1 GHz to 110 GHz) to ensure that the error evaluation covers the full resonant nodes transitioning from pure electric field energy storage dominance to skin magnetic field energy storage dominance.

[0115] Finally, based on the different sensitivities of high-frequency transmission loss to amplitude attenuation and phase deflection, corresponding adjustment weight coefficients are assigned to the real part error value and the imaginary part error value respectively; the real part error value and the imaginary part error value are weighted and summed with their paired weight coefficients to establish an overall numerical closeness evaluation system covering both amplitude and phase response characteristics, and finally obtain the data prediction loss value that can be used to guide the reverse iterative optimization of the bottom connection weights of the neural network.

[0116] This example establishes a comprehensive error assessment mechanism that takes into account both signal energy transmission attenuation and electromagnetic phase deflection distortion by decoupling the parameters of a high-frequency electromagnetic complex network into orthogonal real and imaginary parts and performing rigorous mean square error statistics on each. The computational architecture employing component decomposition, independent measurement, and weighted fusion effectively avoids the technical defect of directly using complex modulus values ​​to calculate loss, which easily masks phase characteristic deviations. This allows the neural network to simultaneously capture the subtle nonlinear effects of the microstructure of the high-frequency substrate surface on amplitude-frequency and phase-frequency characteristics during the backpropagation evolution stage. This provides a clearly directional and physically complete data-driven guidance for the full-band transmission loss evolution model, improving the fit between the final output and actual physical measurements.

[0117] This embodiment provides a method for evaluating signal transmission loss of high-frequency substrate materials. First, it acquires the interface three-dimensional point cloud data and broadband scattering parameter matrix of the sample high-frequency substrate material, collecting microscopic spatial coordinate information and macroscopic broadband electromagnetic response data of the material surface to provide basic real data support for subsequent feature mining and model construction. Second, it performs multi-scale feature extraction on the interface three-dimensional point cloud data to obtain a multi-scale fractal dimension feature set, thereby enabling a deep and quantitative characterization of the complex undulating geometric state of the surface micromorphology. Next, it extracts the test frequency sequence corresponding to the broadband scattering parameter matrix and constructs a model based on the multi-scale fractal dimension feature set, preset microscopic polarization parameters, and the test frequency sequence. A fractal interface impedance feature sequence is constructed, effectively mapping purely geometric morphological features into frequency-domain equivalent electromagnetic features with physical computational significance. Subsequently, based on the fractal interface impedance feature sequence and the broadband scattering parameter matrix, a physical information neural network is trained to obtain a full-band transmission loss evolution model. This process combines impedance features with broadband data, ensuring that the trained prediction model not only conforms to measured patterns but also possesses rigorous physical evolution rationality. Finally, the transmission loss of the target high-frequency substrate material to be evaluated is predicted using the full-band transmission loss evolution model, yielding signal transmission loss evaluation results. This makes the performance extrapolation process for unknown target materials more efficient and reliable. This embodiment can accurately evaluate the broadband signal transmission loss of high-frequency substrate materials caused by surface micromorphology.

[0118] Based on the first embodiment of this application, in the second embodiment of this application, the content that is the same as or similar to that in Embodiment 1 above can be referred to the above description, and will not be repeated hereafter. Based on this, please refer to... Figure 4 , Figure 4 This is a flowchart illustrating the second embodiment of the signal transmission loss assessment method for high-frequency substrate materials according to this application. Step S50 of the signal transmission loss assessment method for high-frequency substrate materials includes steps S51 to S55: Step S51: Obtain the three-dimensional point cloud data of the interface of the target high-frequency substrate material to be evaluated and the target evaluation frequency sequence, and convert the target evaluation frequency sequence into the angular frequency sequence to be evaluated; Step S52: Construct the impedance characteristic sequence of the fractal interface to be tested based on the angular frequency sequence to be tested and the three-dimensional point cloud data of the interface to be tested. Step S53: Input the impedance characteristic sequence of the fractal interface to be tested into the full-band transmission loss evolution model for inference calculation to obtain the predicted scattering parameters of the multi-band to be tested. Step S54: Perform amplitude conversion on the multi-band predicted scattering parameters to be measured to obtain broadband insertion loss curve and broadband return loss curve; Step S55: Generate signal transmission loss evaluation results based on the broadband insertion loss curve and the broadband return loss curve.

[0119] It should be noted that the 3D point cloud data of the interface under test refers to the set of 3D spatial coordinates reflecting the microscopic morphological features of the surface of the target high-frequency substrate to be evaluated. The target evaluation frequency sequence refers to the set of discrete working frequency points arranged in ascending order according to engineering requirements for analyzing signal transmission characteristics. The angular frequency sequence to be tested refers to the combination of frequency characteristics in radians per second obtained by multiplying the target evaluation frequency by twice the constant pi. The fractal interface impedance characteristic sequence to be tested refers to the complex impedance characteristic data stream that dynamically evolves with frequency, combining the fractal features of the target substrate morphology with its electromagnetic physical properties. The multi-band predicted scattering parameters to be tested refer to the complex array of numbers generated by the full-band transmission loss evolution model, characterizing the electromagnetic wave reflection and transmission capabilities of the target substrate in the corresponding frequency band. The broadband insertion loss curve refers to the mathematical trajectory reflecting the degree of energy attenuation as the signal passes through the substrate transmission line as a function of frequency. The broadband return loss curve refers to the mathematical trajectory reflecting the degree of energy reflection at the input end of the substrate transmission line due to impedance mismatch as a function of frequency.

[0120] Understandably, the process begins with a non-contact optical scan of the target high-frequency substrate material surface using a white-light interferometer. This scan captures the microscopic undulations at the interface between the copper foil and the dielectric. After trigonometric interpolation, a 3D point cloud of the interface is established, containing a wealth of 3D spatial location information. Based on the specific application frequency band requirements, a frequency range is defined, from a starting frequency of 10 GHz to an ending frequency of 100 GHz. Multiple test points are extracted with a step size of 1 GHz to form the target evaluation frequency sequence. The computational unit then uses the constant pi to multiply the value of each frequency point in the target evaluation frequency sequence by twice the value of pi, completing the physical mapping from Hertz units to radians per second units. This yields the required angular frequency sequence to meet the complex impedance calculation requirements.

[0121] Secondly, box counting is performed on the 3D point cloud data of the interface under test to extract the fundamental fractal dimension characterizing the complexity of the target substrate's microscopic surface. This fundamental fractal dimension is then combined with the measured angular frequency sequence and a preset material microscopic polarization constant, and substituted into the complex impedance equivalent circuit model to simulate the contribution of the microscopic rugged surface to the increase in inductive reactance and the change in polarization capacitive reactance under the high-frequency skin effect. By performing point-to-point physical mapping calculations for each target frequency point, the microscopic geometric morphology information is transformed into a frequency-dependent electromagnetic feature vector, ultimately constructing a measured fractal interface impedance feature sequence that reflects the impedance evolution state of the target substrate in the continuous frequency domain.

[0122] Next, a full-band transmission loss evolution model that has been trained and whose weight parameters have been fixed is loaded. The generated sequence of impedance features of the fractal interface to be tested is used as the input tensor and loaded into the input layer of the multi-layer fully connected perceptron architecture of the model, driving the internal neurons of the model to perform nonlinear feature extraction and matrix mapping based on learning experience. According to the constraint logic of the electromagnetic wave transmission line theory encapsulated internally, the model performs high-speed inference calculation on the input impedance data, and maps and generates a set of complex matrices containing amplitude and phase information in the output layer, thereby obtaining the predicted scattering parameters of the multi-band to be tested that characterize the reflection and transmission capabilities of the target substrate in the broadband range.

[0123] Then, the transmission coefficient and reflection coefficient components are extracted from the predicted scattering parameters of the multi-band test, and common logarithmic calculation functions are called in the calculation module. For the transmission coefficient, its magnitude is squared, the logarithm to base 10 is taken, and multiplied by a factor of -20 to calculate the insertion loss in decibels at each frequency point. These values ​​are then connected in frequency order to form a broadband insertion loss curve. Similarly, the magnitude is extracted and logarithmically transformed on the reflection coefficient to quantify the degree of energy reflection at the input end, resulting in a broadband return loss curve that reflects the impedance matching status, thus realizing the transformation from complex electromagnetic characteristics to an intuitive energy loss index.

[0124] Finally, the morphological characteristics of the broadband insertion loss curve and broadband return loss curve within the target frequency band are integrated and analyzed to extract key physical indicators such as resonant point location, loss slope, and maximum attenuation. These indicators are then benchmarked against preset high-frequency circuit design criteria to quantitatively score or grade the transmission performance of the target high-frequency substrate material. Finally, the loss curve graph data, core performance indicators, and material selection recommendations are summarized and packaged to generate a signal transmission loss evaluation result with data charts and conclusions, providing objective data-driven decision-making references for material selection and circuit optimization design of high-frequency electronic devices. The preset high-frequency circuit design criteria include physical attenuation extreme value boundaries set for specific application frequency bands. For example, for 77GHz automotive millimeter-wave radar applications, the criteria stipulate that the broadband insertion loss threshold per unit length must not exceed -3.0dB / inch, and the broadband return loss must be less than -15.0dB across the entire frequency band. The system performs quantitative scoring and performance compliance determination of the substrate material based on the comparison between the derived loss curve and the values ​​of these criteria.

[0125] This example combines measured microscopic morphology data with a deep learning model trained under the constraints of physical laws to achieve non-destructive, cross-frequency band rapid performance evaluation of unknown target substrate materials. This process effectively avoids the technical shortcomings of traditional experimental testing methods when verifying a large number of new substrate materials, such as long production cycles, high testing costs, and difficulty in covering the continuous evolution of the entire frequency band. Through the collaborative work of fractal geometric feature extraction and physical information neural network inference, this example significantly improves the computational efficiency and prediction accuracy of signal loss assessment while ensuring the logical consistency of the physical mechanism, providing reliable technical support for agile R&D of high-frequency materials and refined optimization of RF design.

[0126] As an example, the full-band transmission loss evolution model includes an impedance feature input layer, a multi-dimensional fully connected hidden layer, a scattering parameter output layer, and an electromagnetic wave transmission line theory constraint layer. The step of inputting the impedance feature sequence of the fractal interface to be tested into the full-band transmission loss evolution model for inference calculation to obtain the predicted scattering parameters of the multi-band to be tested includes: inputting the impedance feature sequence of the fractal interface to be tested into the impedance feature input layer for feature encoding processing to obtain an initial impedance mapping matrix; inputting the initial impedance mapping matrix into the multi-dimensional fully connected hidden layer for nonlinear feature extraction to obtain a high-dimensional impedance latent feature vector; inputting the high-dimensional impedance latent feature vector into the scattering parameter output end for mapping dimensionality reduction calculation to obtain initial frequency domain scattering parameters; and performing physical consistency correction processing on the initial frequency domain scattering parameters through the electromagnetic wave transmission line theory constraint layer to obtain the predicted scattering parameters of the multi-band to be tested.

[0127] It should be noted that feature encoding processing refers to the operation of converting the input one-dimensional or two-dimensional physical impedance data sequence into a standard tensor format suitable for weighted calculations at the bottom nodes of a neural network. The initial impedance mapping matrix can be a two-dimensional array structure containing the arrangement of basic frequency domain features, output after the impedance feature sequence has undergone preliminary multiplication by the connection weights of the input layer neurons. Nonlinear feature extraction refers to the computational process of using activation nodes containing nonlinear mathematical functions in the hidden layers of a neural network to distort and map the input data space to capture the potential correlations in complex data. The high-dimensional impedance latent feature vector refers to a set of dimensionless feature values ​​representing the potential mapping relationship between impedance and electromagnetic response in an abstract high-dimensional mathematical space after the data has been processed through multiple deep hidden layers. Mapping dimensionality reduction calculation refers to the data processing stage that uses the terminal nodes of the neural network to compress and restore the data in the high-dimensional abstract feature space to a lower-dimensional electromagnetic parameter space with clear physical meaning. The initial frequency domain scattering parameters refer to the preliminary electromagnetic wave transmission and reflection feature array directly generated at the output of the neural network, which has not yet undergone rigorous examination and correction by microwave physics rules. Physical consistency correction refers to the feedback adjustment process that uses a computational module encapsulated with objective physical law equations to perform boundary constraints and compliance smoothing corrections on purely empirical prediction data generated by neural networks.

[0128] Understandably, firstly, in the operating environment of the full-band transmission loss evolution model, the previously constructed impedance feature sequence of the fractal interface under test is loaded into the receiving port of the impedance feature input layer of the model. The impedance feature input layer uses the built-in tensor transformation mechanism to perform feature encoding processing on the impedance feature sequence of the fractal interface under test, mapping and allocating the originally discrete serial complex impedance values ​​and corresponding frequency point coordinates to the bottom layer neuron node matrix with fixed row and column dimensions. After the initial linear multiplication and addition operation of the first layer node weights, the original physical sequence structure is reconstructed into a tensor data form suitable for subsequent deep network calculations, thereby outputting the initial impedance mapping matrix carrying the basic frequency domain arrangement information.

[0129] Secondly, the acquired initial impedance mapping matrix is ​​used as the data flow driver and fed into the multidimensional fully connected hidden layer for hierarchical propagation calculation. Multiple cascaded neuron arrays are deployed within the multidimensional fully connected hidden layer. Each array utilizes the Rectified Linear Activation Function (ReLU) to perform nonlinear feature extraction calculations on the matrix node data passed to that layer. As the data penetrates layer by layer in the deep network architecture, the impedance features originally existing in the two-dimensional plane are continuously decomposed, combined, and projected into a higher-dimensional abstract mathematical space with a larger number of parameters. The nonlinear electromagnetic evolution laws hidden behind the microscopic morphology are effectively extracted, ultimately converging to generate a set of high-dimensional impedance latent feature vectors representing deep mapping relationships.

[0130] Next, the high-dimensional impedance latent feature vector, after deep mining, is extracted and imported into the scattering parameter output layer, which consists of linear output nodes. The scattering parameter output layer uses the weight matrix of the last set of neurons to perform cross-space mapping and dimensionality reduction calculations on the high-dimensional and highly abstract latent feature vector, converging and compressing the feature values ​​scattered across thousands of abstract dimensions back into a low-dimensional physical space characterizing macroscopic electromagnetic properties. Through this dimensionality reduction mapping operation, the neural network restores purely mathematical abstract parameters to a complex matrix form with clear electrophysical meaning, correspondingly generating initial frequency domain scattering parameters containing broadband reflection amplitude and transmission phase information.

[0131] Finally, the initial frequency-domain scattering parameters empirically output by the neural network are directed to the electromagnetic wave transmission line theoretical constraint layer module at the top of the model. This constraint layer module encapsulates microwave network cascade calculation rules for describing electromagnetic wave attenuation. These physical rules are used to perform physical consistency correction processing on the input initial frequency-domain scattering parameters at each frequency point. The system checks whether the slope of the loss abrupt change between adjacent frequency points exceeds the theoretical physical limit of energy dissipation in real transmission lines, and uses a moving average filtering algorithm to smooth out distortion points that deviate from the energy conservation law of microwave networks. This ensures that the final output broadband electromagnetic parameters strictly follow the objective natural laws of high-frequency signal evolution, thus outputting the predicted scattering parameters for the multi-band test that have passed physical compliance verification.

[0132] This example constructs a complete inference and prediction closed-loop link that balances in-depth data mining and physical law reduction by deploying an impedance feature input layer, a multi-dimensional fully connected hidden layer, a scattering parameter output layer, and an electromagnetic wave transmission line theory constraint layer in series. In this architecture, the equivalent impedance features of the microstructure are first nonlinearly activated and projected into a high-dimensional space by a deep neural network, fully releasing and extracting the complex frequency-dependent response laws hidden within the material. Subsequently, a pure physical constraint layer is used to perform compliance trimming and filtering correction on the black-box empirical parameters output by the neural network, effectively eliminating the numerical divergence and physical violations that are easily caused by a single data-driven model when inferring in unknown frequency bands. This forward inference process not only ensures the curve smoothness and physical realism of the predicted data across the entire frequency band but also significantly reduces the enormous computational cost and waiting time required for micro-mesh calculations using traditional full-wave 3D electromagnetic simulation software.

[0133] This embodiment first acquires the three-dimensional point cloud data of the interface to be evaluated and the target evaluation frequency sequence of the target high-frequency substrate material, and converts the frequencies into a sequence of angular frequencies to be evaluated, thus establishing the basic geometric and physical input conditions for subsequent complex impedance analysis. Second, based on the angular frequency sequence and the three-dimensional point cloud data of the interface to be evaluated, a fractal interface impedance characteristic sequence is constructed, effectively transforming the complex microscopic three-dimensional morphology into equivalent physical features usable for electromagnetic inference. Next, this fractal interface impedance characteristic sequence is input into a full-band transmission loss evolution model for inference calculation, obtaining the predicted scattering parameters for the multi-band test, achieving efficient and non-destructive prediction of the broadband electromagnetic response of the unknown target material. Then, the predicted scattering parameters for the multi-band test are amplitude-converted to obtain broadband insertion loss curves and broadband return loss curves, mapping the abstract complex evolution matrix into engineering curves that intuitively characterize energy attenuation and reflection properties. Finally, based on these two broadband loss curves, a signal transmission loss evaluation result is generated, providing an intuitive and quantitative performance evaluation basis for the practical application and selection of high-frequency substrate materials.

[0134] This application also provides a device for evaluating signal transmission loss of high-frequency substrate materials. Please refer to [link / reference]. Figure 5 The high-frequency substrate material signal transmission loss evaluation device includes: Data acquisition module 10 is used to acquire the interface three-dimensional point cloud data and broadband scattering parameter matrix of the sample high-frequency substrate material; Feature extraction module 20 is used to perform multi-scale feature extraction on the interface three-dimensional point cloud data to obtain a multi-scale fractal dimension feature set; Impedance construction module 30 is used to extract the test frequency sequence corresponding to the broadband scattering parameter matrix, and construct a fractal interface impedance feature sequence based on the multi-scale fractal dimension feature set, the preset micro-polarization parameters and the test frequency sequence. The model training module 40 is used to train the physical information neural network based on the fractal interface impedance characteristic sequence and the broadband scattering parameter matrix to obtain a full-band transmission loss evolution model. The evaluation and prediction module 50 is used to predict the transmission loss of the target high-frequency substrate material to be evaluated through the full-band transmission loss evolution model, and obtain the signal transmission loss evaluation result.

[0135] The high-frequency substrate material signal transmission loss assessment device provided in this application, employing the high-frequency substrate material signal transmission loss assessment method described in the above embodiments, can solve the technical problem of how to accurately assess the broadband signal transmission loss caused by the surface microstructure of high-frequency substrate materials. Compared with the prior art, the beneficial effects of the high-frequency substrate material signal transmission loss assessment device provided in this application are the same as those of the high-frequency substrate material signal transmission loss assessment method provided in the above embodiments, and other technical features in the high-frequency substrate material signal transmission loss assessment device are the same as those disclosed in the methods of the above embodiments, and will not be repeated here.

[0136] This application provides a signal transmission loss assessment device for high-frequency substrate materials. The high-frequency substrate material signal transmission loss assessment device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the high-frequency substrate material signal transmission loss assessment method in the above embodiment 1.

[0137] The following is for reference. Figure 6 This document illustrates a structural schematic diagram suitable for implementing a high-frequency substrate material signal transmission loss evaluation device according to embodiments of this application. The high-frequency substrate material signal transmission loss evaluation device in embodiments of this application may include, but is not limited to, mobile terminals such as mobile phones, laptops, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Android Devices), PMPs (Portable Media Players), and in-vehicle terminals (e.g., in-vehicle navigation terminals), as well as fixed terminals such as digital TVs and desktop computers. Figure 6 The high-frequency substrate material signal transmission loss evaluation device shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0138] like Figure 6As shown, the high-frequency substrate material signal transmission loss assessment device may include a processing unit 1001 (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in ROM 1002 (Read Only Memory) or a program loaded from storage device 1003 into RAM 1004 (Random Access Memory). RAM 1004 also stores various programs and data required for the operation of the high-frequency substrate material signal transmission loss assessment device. The processing unit 1001, ROM 1002, and RAM 1004 are interconnected via bus 1005. I / O interface 1006 is also connected to the bus. Typically, the following systems can be connected to I / O interface 1006: input devices 1007 including, for example, touch screens, touchpads, keyboards, mice, image sensors, microphones, accelerometers, gyroscopes, etc.; output devices 1008 including, for example, LCDs (Liquid Crystal Displays), speakers, vibrators, etc.; storage devices 1003 including, for example, magnetic tapes, hard disks, etc.; and communication devices 1009. The communication device 1009 allows the high-frequency substrate material signal transmission loss assessment device to communicate wirelessly or wiredly with other devices to exchange data. Although the figure shows a high-frequency substrate material signal transmission loss assessment device with various systems, it should be understood that implementation or possession of all the systems shown is not required. More or fewer systems may be implemented alternatively.

[0139] Specifically, according to the embodiments disclosed in this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments disclosed in this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from storage device 1003, or installed from ROM 1002. When the computer program is executed by processing device 1001, it performs the functions defined in the methods of the embodiments disclosed in this application.

[0140] The high-frequency substrate material signal transmission loss assessment device provided in this application, employing the high-frequency substrate material signal transmission loss assessment method described in the above embodiments, can solve the technical problem of how to accurately assess the broadband signal transmission loss caused by the surface microstructure of high-frequency substrate materials. Compared with the prior art, the beneficial effects of the high-frequency substrate material signal transmission loss assessment device provided in this application are the same as those of the high-frequency substrate material signal transmission loss assessment method provided in the above embodiments, and other technical features of this high-frequency substrate material signal transmission loss assessment device are the same as those disclosed in the previous embodiment method, and will not be repeated here.

[0141] It should be understood that the various parts disclosed in this application can be implemented using hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0142] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included 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.

[0143] This application provides a computer-readable storage medium having computer-readable program instructions (i.e., a computer program) stored thereon, which are used to execute the high-frequency substrate material signal transmission loss evaluation method in the above embodiments.

[0144] The computer-readable storage medium provided in this application may be, for example, a USB flash drive, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, RAM (Random Access Memory), ROM (Read Only Memory), EPROM (Erasable Programmable Read Only Memory or Flash Memory), optical fibers, CD-ROM (CD-Read Only Memory), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, system, or device. The program code contained on the computer-readable storage medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination thereof.

[0145] The aforementioned computer-readable storage medium carries one or more programs. When these programs are executed by the high-frequency substrate material signal transmission loss assessment device, the device performs the following actions: acquires three-dimensional point cloud data of the interface of the sample high-frequency substrate material and a broadband scattering parameter matrix; performs multi-scale feature extraction on the interface three-dimensional point cloud data to obtain a multi-scale fractal dimension feature set; extracts the test frequency sequence corresponding to the broadband scattering parameter matrix, and constructs a fractal interface impedance feature sequence based on the multi-scale fractal dimension feature set, preset micro-polarization parameters, and the test frequency sequence; trains a physical information neural network based on the fractal interface impedance feature sequence and the broadband scattering parameter matrix to obtain a full-band transmission loss evolution model; and predicts the transmission loss of the target high-frequency substrate material to be assessed using the full-band transmission loss evolution model to obtain a signal transmission loss assessment result.

[0146] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including LAN (Local Area Network) or WAN (Wide Area Network)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0147] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0148] The readable storage medium provided in this application is a computer-readable storage medium that stores computer-readable program instructions (i.e., a computer program) for executing the above-described method for evaluating the signal transmission loss of high-frequency substrate materials. This solves the technical problem of how to accurately evaluate the broadband signal transmission loss of high-frequency substrate materials caused by their surface microstructure. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as those of the high-frequency substrate material signal transmission loss evaluation method provided in the above embodiments, and will not be repeated here.

[0149] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the high-frequency substrate material signal transmission loss evaluation method described above.

[0150] The computer program product provided in this application can solve the technical problem of how to accurately evaluate the broadband signal transmission loss caused by the surface microstructure of high-frequency substrate materials. Compared with the prior art, the beneficial effects of the computer program product provided in this application are the same as those of the high-frequency substrate material signal transmission loss evaluation method provided in the above embodiments, and will not be repeated here.

[0151] The above description is only a part of the embodiments of this application and does not limit the patent scope of this application. All equivalent structural transformations made under the technical concept of this application and using the contents of the specification and drawings of this application, or direct / indirect applications in other related technical fields, are included in the patent protection scope of this application.

Claims

1. A method for evaluating signal transmission loss of high-frequency substrate materials, characterized in that, The method includes: Acquire the three-dimensional point cloud data of the interface and broadband scattering parameter matrix of the sample high-frequency substrate material; Multi-scale feature extraction is performed on the three-dimensional point cloud data of the interface to obtain a multi-scale fractal dimension feature set; Extract the test frequency sequence corresponding to the broadband scattering parameter matrix, and construct a fractal interface impedance feature sequence based on the multi-scale fractal dimension feature set, the preset micro-polarization parameters, and the test frequency sequence; Based on the fractal interface impedance characteristic sequence and the broadband scattering parameter matrix, the physical information neural network is trained to obtain a full-band transmission loss evolution model. The transmission loss is predicted using the full-band transmission loss evolution model for the target high-frequency substrate material to be evaluated, and the signal transmission loss evaluation result is obtained.

2. The method as described in claim 1, characterized in that, The step of predicting the transmission loss of the target high-frequency substrate material to be evaluated using the full-band transmission loss evolution model to obtain the signal transmission loss evaluation result includes: Acquire the three-dimensional point cloud data of the interface of the target high-frequency substrate material to be evaluated and the target evaluation frequency sequence, and convert the target evaluation frequency sequence into the angular frequency sequence to be evaluated; Construct a fractal interface impedance characteristic sequence based on the measured angular frequency sequence and the three-dimensional point cloud data of the interface to be measured. The impedance characteristic sequence of the fractal interface to be tested is input into the full-band transmission loss evolution model for inference calculation to obtain the predicted scattering parameters of the multi-band to be tested. The amplitude conversion of the multi-band predicted scattering parameters to be measured is performed to obtain the broadband insertion loss curve and the broadband return loss curve. The signal transmission loss assessment results are generated based on the broadband insertion loss curve and the broadband return loss curve.

3. The method as described in claim 2, characterized in that, The full-band transmission loss evolution model includes an impedance characteristic input layer, a multi-dimensional fully connected hidden layer, a scattering parameter output layer, and an electromagnetic wave transmission line theory constraint layer. The step of inputting the measured fractal interface impedance characteristic sequence into the full-band transmission loss evolution model for inference calculation to obtain the measured multi-band predicted scattering parameters includes: The impedance feature sequence of the fractal interface to be tested is input into the impedance feature input layer for feature encoding processing to obtain the initial impedance mapping matrix. The impedance initial mapping matrix is ​​input into the multidimensional fully connected hidden layer for nonlinear feature extraction to obtain a high-dimensional impedance hidden feature vector. The high-dimensional impedance latent feature vector is input into the scattering parameter output terminal for mapping and dimension reduction calculation to obtain the initial frequency domain scattering parameters. The initial frequency domain scattering parameters are physically consistent with the electromagnetic wave transmission line theory constraint layer to obtain the predicted scattering parameters for the multi-frequency bands to be measured.

4. The method as described in claim 1, characterized in that, The construction steps of the physical information neural network include: Construct a basic network structure for a multilayer perceptron that includes an impedance feature input layer, a multidimensional fully connected hidden layer, and a scattering parameter output layer; An electromagnetic wave transmission line theory constraint layer is added to the output end of the scattering parameter output layer. Construct a composite loss function that includes data-driven error and physical law residuals; Embed the frequency domain wave equation residual of Maxwell's equations into the physical law residual term in the composite loss function; A physical information neural network is constructed based on the multilayer perceptron basic network structure, the electromagnetic wave transmission line theory constraint layer, and the composite loss function.

5. The method as described in claim 1, characterized in that, The step of extracting multi-scale features from the interface 3D point cloud data to obtain a multi-scale fractal dimension feature set includes: The three-dimensional point cloud data of the interface is transformed into a spatial coordinate system to obtain a horizontal projection height matrix; The horizontal projection height matrix is ​​divided into blocks by a preset sliding window to obtain multiple local height matrices; Calculate the surface area of ​​the multiple local height matrices at different preset scale steps; Based on the preset scale step size and the surface area, a double logarithmic coordinate system mapping is performed to obtain a multi-scale logarithmic scatter set; The multi-scale fractal dimension feature set is obtained by performing regression fitting calculation on the multi-scale logarithmic scatter point set using the least squares method.

6. The method as described in claim 1, characterized in that, The steps of extracting the test frequency sequence corresponding to the broadband scattering parameter matrix and constructing a fractal interface impedance feature sequence based on the multi-scale fractal dimension feature set, the preset micro-polarization parameters, and the test frequency sequence include: The basic fractal dimension is obtained by weighted averaging of the fractal dimensions at multiple different scales in the multi-scale fractal dimension feature set. Extract the test frequency sequence corresponding to the broadband scattering parameter matrix, and convert the test frequency sequence into a multi-frequency angular frequency sequence; Calculate the fractal equivalent capacitance sequence based on the basic fractal dimension, the multi-frequency point angular frequency sequence, and the preset micro-polarization parameters; The fractal equivalent inductance value is calculated based on the basic fractal dimension and the preset skin equivalent inductance value; The fractal equivalent inductance value is combined with each element in the fractal equivalent capacitance sequence to obtain the fractal interface impedance characteristic sequence. The calculation formula for impedance combination is as follows: In the formula, This represents the fractal interface impedance value in the fractal interface impedance characteristic sequence. This represents the fractal equivalent inductance value. This represents the fractal equivalent capacitance sequence. This represents the angular frequency values ​​in the multi-frequency point angular frequency sequence. It represents the imaginary unit.

7. The method according to any one of claims 1 to 6, characterized in that, The step of training the physical information neural network based on the fractal interface impedance characteristic sequence and the broadband scattering parameter matrix to obtain a full-band transmission loss evolution model includes: The fractal interface impedance feature sequence is divided into a training impedance set and a verification impedance set, and the broadband scattering parameter matrix is ​​divided into a training parameter set and a verification parameter set; The training impedance set is used as input features, and the training parameter set is used as label data. These are then input into a physical information neural network for forward propagation prediction to obtain the predicted scattering parameters. Calculate the data prediction loss value based on the predicted scattering parameters and the training parameter set; The predicted scattering parameters are input into the preset microwave transmission line telegraph equation to calculate the physical constraint residual, and the physical residual loss value is obtained. Calculate the total loss value based on the predicted loss value and the physical residual loss value; Based on the total loss value, the network weights of the physical information neural network are updated using the backpropagation algorithm until the preset convergence condition is met, thus obtaining the full-band transmission loss evolution model.

8. A device for evaluating signal transmission loss of high-frequency substrate materials, characterized in that, The apparatus employs the signal transmission loss assessment method for high-frequency substrate materials as described in any one of claims 1 to 7, and the apparatus comprises: The data acquisition module is used to acquire the interface three-dimensional point cloud data and broadband scattering parameter matrix of the sample high-frequency substrate material; The feature extraction module is used to perform multi-scale feature extraction on the interface 3D point cloud data to obtain a multi-scale fractal dimension feature set; The impedance construction module is used to extract the test frequency sequence corresponding to the broadband scattering parameter matrix, and construct the fractal interface impedance feature sequence based on the multi-scale fractal dimension feature set, the preset micro-polarization parameters and the test frequency sequence. The model training module is used to train the physical information neural network based on the fractal interface impedance characteristic sequence and the broadband scattering parameter matrix to obtain a full-band transmission loss evolution model. The evaluation and prediction module is used to predict the transmission loss of the target high-frequency substrate material to be evaluated using the full-band transmission loss evolution model, and obtain the signal transmission loss evaluation result.

9. A device for evaluating signal transmission loss of high-frequency substrate materials, characterized in that, The device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the method for evaluating signal transmission loss of high-frequency substrate materials as claimed in any one of claims 1 to 7.

10. A storage medium, characterized in that, The storage medium is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by a processor, it implements the steps of the method for evaluating signal transmission loss of high-frequency substrate materials as described in any one of claims 1 to 7.

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