I. Core Breakthrough: Addressing Two Long-standing Pain Points in the Industry

Pain point 1 : The design geometry is decoupled from the actual manufactured preform, causing the simulation results to deviate entirely from engineering reality.

Existing ADFP All simulations employ an ideal, uniform tow model, neglecting the width variations, local thinning, and random gaps caused by roller compaction during layup, robot motion, and the viscoelastic behavior of the material. Moreover, most stochastic models treat tow width and thickness as independent variables, which violates the physical principle of constant tow cross-sectional area, rendering the resulting virtual geometries physically infeasible and leading to substantial errors in permeability and mechanical property predictions. Breakthrough: A successful attempt was made to incorporate online laser‑measured data. +  Physical volume conservation constraints are embedded in stochastic modeling, ensuring that as the width of a tow increases, its thickness decreases accordingly, thereby replicating the extrusion‑induced deformation observed in real‑world layup and generating high‑precision virtual preforms that conform to physical laws in their “manufactured state.”

Pain point 2 : There is no quantitative method for predicting the effect of manufacturing defects on resin flow performance; one must rely on conservative margins and physical testing.

LCM During forming, the permeability of the preform directly determines the mold-filling time and the occurrence of dry spots. /  Pore‑defect risks, interstitial “runway effects,” and localized compaction bottlenecks can significantly alter the resin flow front. Conventional studies have only provided qualitative descriptions of defect impacts, failing to quantify the performance degradation caused by process variability. Aerospace composite certification relies on a “building‑block test pyramid,” which entails extremely high testing costs. Breakthrough: Establishing a comprehensive quantitative workflow—from laser‑based online measurement and stochastic geometry generation to rapid permeability prediction—enabling the quantification of process variations. -  The penetration‑rate reduction curve directly provides performance‑degradation coefficients for equipment and materials, replacing some physical testing and accelerating the implementation of virtual certification.

II. Technological Innovation: Four Original Technology Systems

Innovation 1 : A bivariate Gaussian process for robot placement paths ( BGP ) Stochastic Geometric Modeling

• Linear Co-kriging Model LMC : Synchronous modeling of tow width W , thickness T Two-dimensional random field, obtained through field measurements. - 0.51 Its negative correlation coefficient precisely characterizes the compaction‑extrusion effect, rigorously ensures fiber volume conservation, and eliminates the total fiber‑mass distortion inherent in conventional independent‑variable models.
• Matern 3/2 Kernel space‑related constraints: Unlike the infinitely smooth Gaussian kernel and the sawtooth exponential kernel, this approach employs a once‑differentiable … Matern Nuclear, matching the smooth filament waviness induced by continuous contact with the robot’s roller, restores the spatial correlation of real‑world geometric fluctuations;
• Logarithmic domain transformation: prevents non-physical negative values in width and thickness, ensuring that all generated geometries are fully engineering‑feasible.
• Path-based modeling: directly constructs a random field along the robot’s laying trajectory, adapting to… ADFP Compared with full‑field grid Gaussian random field computation, the sequential‑path deposition process achieves a substantial boost in computational efficiency and can be directly calibrated using single‑pass tow laser data, eliminating the need for three‑dimensional reconstruction of the entire field.

Innovation 2 : Multi-stage Signal Processing Pipeline for Laser-Based Online Profile Measurement

Equipped with a line laser scanner (lateral resolution 12.9 mu m ) Integrated into the placement head, it synchronizes the robot’s six-axis motion data via… Savitzky-Golay Filtering, sub-pixel edge detection, IQR Abnormality filtering, multi-step hierarchical verification, removal of equipment noise, and extraction of continuous residual signals for tow width and thickness, in order to… BGP Provides a reliable manufacturing statistics baseline, enabling a data closed-loop where “layup equals measurement, and measurement equals modeling.”

Innovation 3 : Multi-scale permeability coupling solution + High-Speed Hydraulic Network Proxy Model

• Multiscale analysis theory: microscale approach Gebart The model computes the permeability within the tow, employs a Poiseuille-series solution for mesoscale rectangular channels to characterize flow in the interfilament voids, and uses a hydraulic circuit approximation to simplify the flow in parallel channels at the hierarchical level.
• Million‑scale Monte Carlo high‑speed solving: abandoning the hours‑long computation for a single scenario. CFD Simulation and analytical surrogate models achieve sub-millisecond computation times per run, supporting… 1000  Batch statistics of randomly preformed assemblies;
• OpenFOAM CFD Benchmark validation: Three typical geometric configurations—narrow gap, standard gap, and wide gap—are selected for comparative verification; the analytical model’s error is at most only 7.11% , meeting the engineering statistical accuracy requirements.

Innovation 4 : Process - Performance Quantitative Mapping Curve ( Process Design Curve )

• By traversing the standard deviation σ of the tow width _W , plot the permeability reduction factor F_KD Nonlinear correspondence curve for process variability:
• High-precision placement (σ _W ≤ 0.10mm ): Retain penetration rate 97% The above;
• The calibration operating condition of this test (σ _W=0.151mm ): Reduction factor 0.955 , penetration rate declines 4.4% ；
• Large-fluctuation placement (σ _W=0.40mm ): The penetration rate is retained only 77% The curve can be calibrated with a single click for different equipment and materials, enabling direct application to process window design and the selection of structural strength safety factors.

III. Application Scenarios

• Virtual Certification of Aerospace Composite Structures (Core Scenario)

Military aircraft /  Dry fiber placement for the fuselage, wings, and tail assembly preforms of a passenger aircraft. LCM Molding simulation. The framework can generate digital twin parts that incorporate realistic manufacturing defects, accurately predict mold-filling times and porosity risks, reduce the scale of physical testing, and minimize structural weight increases caused by conservative safety factors, thereby supporting the industry’s transition toward “virtual testing replacing physical trials.”

• Optimization of Automated Lay-up Process for Large-Scale Wind Turbine Blades

100-meter-class wind turbine blade ADFP Dry fiber tow placement: Prior simulation of tow waviness under varying compaction pressures, heating temperatures, and laying speeds enables the selection of an optimal process window, balancing production efficiency with uniform resin impregnation and reducing the incidence of dry‑spot defects within the blade.

• Process Calibration for Mass Production of Lightweight Composite Automotive Components

Mass-production line for integrated composite preforms of new-energy vehicle chassis and battery packs, with laser-based online acquisition of real-time process‑variability data for rapid calibration. BGP The model predicts the range of permeability fluctuations under mass production, optimizes the resin‑injection runner design and injection pressure parameters, and enhances production‑line consistency.

• Digital Quality Control for Advanced Composite Material Production Lines

ADFP Factory‑level calibration and on‑line, closed-loop quality control on the production line: laser sensors capture geometric variations in real time, feeding this data into the framework to generate real-time predictions of resin‑transfer‑rate degradation; when process fluctuations exceed allowable limits, an early warning is issued, along with recommended layup pressures. /  Speed correction scheme, enabling manufacturing. -  Integrated online quality control for performance.

• Pre‑geometry input for multiphysics simulation

Beyond permeability‑based flow simulations, the generated manufacturing‑state laminate model—accounting for gaps and thickness variations—can be directly imported into structural finite element and thermal cure simulations to predict stiffness degradation, non‑uniform curing temperatures, and other issues, enabling a single geometric model to support multidisciplinary digital simulations.

IV. Summary of the Article

Theoretical Level: A Successful Attempt Establish online measured data +  of physical conservation constraints ADFP A stochastic preform modeling paradigm addresses the core limitations of conventional stochastic geometric models, which neglect the coupling between tow width and thickness and rely on data that deviates from actual manufacturing conditions. It demonstrates that the compaction‑induced squeezing effect of tows systematically reduces preform permeability, and that manufacturing‑related geometric variability is not random noise but rather a quantifiable, predictable source of performance degradation.

Engineering Value: Building a low-cost, high-efficiency “laser online inspection” system. -  Random Geometric Generation -  A full‑process tool for rapid penetration‑rate prediction, accompanied by ready‑to‑implement process design curves that quantify the impact of manufacturing deviations on… LCM By influencing forming performance, it significantly reduces the number of physical tests required for composite‑material structural certification, leading to weight reduction and cost savings.

Extensibility: The modeling framework is process-agnostic and is applicable not only to dry fibers. ADFP , and can also be extended to prepregs. AFP Lay-up and various automated fiber placement processes; the resulting stochastic geometric models can serve as universal input for multiphysics simulations involving mechanics, thermodynamics, and fluid dynamics, providing a common underlying technical foundation for end-to-end digital twins of composite materials and virtual certification in intelligent manufacturing.

Industry Insights: In the future, composite material design cannot rely solely on ideals. CAD To strike a balance between lightweight design and stable mass production, the model must embed manufacturing features such as layup and compaction into the digital simulation and leverage measured manufacturing data to drive performance prediction.

Image and Text Guide

Figure 1. ADFP Schematic diagram of the deposition process.

Figure 2.  Graphical summary of the virtual reconstruction model: (a) Define the geometric relationships of the clearance; (b) Statistical relationship between trailing width and gap-width variability.

Figure 3.  Flowchart of the multi-stage feature extraction algorithm. The process comprises initial signal preprocessing, context labeling based on channel numbers, and a final validation stage, ensuring that the detected drag points and gap coordinates are robust.

Figure 4. ADFP The physical implementation structure on the head.

Figure 5.  Top-down two-dimensional reconstruction of a manufactured laminated structure based on online measurement data.

Table 1 Geometric and statistical parameters obtained through online metrology (N = 489)

Figure 6.  Detrended drag‑width residuals (point data) and the fitted theoretical curve Matern 3/2 The relevant model (solid line) and BGP Comparison of measured empirical autocorrelation values with the average autocorrelation function (dashed line) of the drag simulation results. The results demonstrate that the calibrated random generator accurately reproduces the spatial correlation structure that governs the variability in drag width.

Figure 7.  Scatter plot of thickness residuals versus width residuals. Negative regression slope ( rho ≈− 0.51 ) This confirms the physical property of mass conservation, thereby demonstrating that it is reasonable to use a bivariate Gaussian process to link these two dimensions.

Table 2 : Network model and OpenFOAM Validation and Comparison of Computational Fluid Dynamics Results ( K The value range is 10 ⁻¹¹ m ²). The numerical values represent each operating condition. N=15 The mean of a random geometric instance.

Figure 8.  Gap-width distributions extracted from virtual preforms generated via a bivariate Gaussian process. The solid red line represents the theoretical probability density function derived from online measurement data. (For an explanation of the color coding in the figure legend, please refer to the online version of this article.)

Table 3 presents a summary of the Monte Carlo simulation scenarios defined to separate geometric variability from physical coupling effects.

Figure 9.  Baseline model (design model), uncoupled model (independent-variable model), and coupled model ( BGP Comparison of penetration rate distribution for the model.

Table 4  Comparison of macroscopic permeability results under three physical scenarios ( N = 1000 )

Figure 10.  Permeability reduction design curve. This chart quantifies the decline in flow performance ( F _KD ) Process variation degree ( Ϭ width ) of the relationship. The marked points correspond to the calibrated experimental process states ( Ϭ _omega = 0.151 mm ，  F _KD = 0.955 ).

Table 5  Effective permeability to the wide-thick coupling coefficient ( rho ) sensitivity