Following layer classification, the Rouard model was applied to globally fit each layer’s thickness. This model, coupled with the genetic algorithm for parameter optimization, enabled accurate thickness determination even when the number of layers was initially unknown. The genetic algorithm iteratively adjusted the model parameters to minimize the difference between the measured and calculated THz signals. The feasibility and effectiveness of the proposed method were validated through experiments on curved multi-layer samples using a robotic arm-driven THz-TDS system.

The THz-TDS system employed in experiments was shown to be capable of high-resolution measurements, covering a broad spectral range. The robotic-arm integration allowed for precise positioning and orientation of the THz probe, ensured accurate data collection from curved surfaces. This setup mimicked real-world industrial applications in which components often had complex geometries.

The THz reflection data clearly depict the distinct characteristics of different layer structures. The layer thickness measurements using the Rouard model are highly accurate, with the first, second, and third layers of paint averaging (47.93±5.81) μm, (98.86±0.57) μm, and (57.20±0.79) μm, respectively. These measurements are consistent with the actual thickness values obtained using an eddy current thickness gauge.

The KPCA-ISSA-SVM model also demonstrates robustness and efficiency in classifying the number of layers, which is crucial for subsequent thickness measurements. The improved classification and measurement accuracy underscore the potential of the proposed method in industrial applications in which precise and non-contact thickness measurements are required.

The optimization of SVM parameters using advanced algorithms such as ISSA and WOA significantly improves the model’s ability to classify the number of layers accurately. The inclusion of KPCA for feature extraction from the THz spectral data enhances the model’s performance by reducing dimensionality and focusing on the most informative features. This combination of techniques results in a highly accurate and efficient classification model that can be applied to various industrial scenarios requiring precise layer thickness measurements.

The experiment demonstrates the method’s capability in handling complex multi-layer structures on curved surfaces, which is a common challenge in practical applications. The robotic arm-driven THz-TDS system provides a versatile platform for accurate and repeatable measurements, further validating the method’s practicality and effectiveness. The system’s ability to adapt to different surface geometries and layer configurations highlights its potential for widespread industrial adoption.

The study explores the effects of different optimization algorithms on the classification accuracy of the SVM model. The ISSA algorithm, with its adaptive parameter adjustment and dynamic population update strategies, shows superior performance in terms of convergence speed and accuracy. The WOA algorithm also demonstrates competitive results, although it is slightly less efficient than ISSA. Despite its accuracy, the traditional GS method is time-consuming and less practical for real-time applications.

Future work will explore the integration of additional features and further improvements in algorithmic efficiency to enhance real-time capabilities. The potential for applying this methodology to other non-destructive testing scenarios, such as the evaluation of composite materials and detection of defects in layered structures, will also be investigated.

Terahertz (THz) thickness measurement technology is widely recognized for its high precision and non-contact nature, making it a novel method for measuring the thicknesses of multi-layer structures. However, because the number of layers in some applications is often unknown, the accuracy and applicability of THz measurements are affected, and this poses a challenge to the technology’s further development. In many industrial scenarios, accurately determining the layer thickness is critical for quality control and material characterization. This study attempts to address this issue by optimizing a support vector machine (SVM) model to determine the number of layers and comparing the performances of different improved classification algorithms. The ultimate goal is to enhance the precision and applicability of THz thickness measurements in multi-layer structures with unknown layers, thereby improving the reliability of measurements in various industrial applications.

The proposed method used THz time-domain spectroscopy (THz-TDS) for thickness measurements. The kernel principal component analysis (KPCA) technique was first employed to extract THz spectral features. KPCA helped to reduce the dimensionality of the data while preserving the most informative features, thereby enhancing the performance of the classification model. Various advanced algorithms were then utilized to optimize the SVM for layer classification, including the grid search (GS), sparrow search algorithm (SSA), improved sparrow search algorithm (ISSA), and whale optimization algorithm (WOA). The optimal parameters for the SVM, including the penalty factor (C) and radial basis function (RBF) kernel parameter (g), were determined using these optimization techniques. The performances of these algorithms were then evaluated using five-fold cross-validation to ensure robustness and reliability.

Experimental results demonstrate the effectiveness of the proposed method. The optimized KPCA-ISSA-SVM model achieves the highest classification accuracy, reaching 98.33% on the test set. This method significantly outperforms other optimization techniques in terms of convergence speed and prediction accuracy. The detailed experimental setup involves scanning single-, double-, and triple-layer paint samples on a curved surface, with the THz-TDS system capturing time-domain spectral data.

This study presents a novel approach that uses an optimized SVM model to determine the number of layers in multi-layer structures. By integrating KPCA for feature extraction and employing advanced optimization algorithms for SVM parameter tuning, the proposed method significantly improves classification accuracy and efficiency. Subsequent application of the Rouard model for thickness measurement further enhances the precision of THz thickness measurement technology. The experimental validation on curved multi-layer samples demonstrates the feasibility and effectiveness of this approach, providing a robust solution for real-time high-precision thickness measurements in industrial settings.