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A Deep Learning-Based Generic Modelling Framework for Vibration-Impacted Signals Considering Uncertainty
: An Application in Cutting Force Prediction

  • Hui Xie

Student thesis: Doctoral Thesis

Abstract

The advancement of automation and precision in Computer Numerical Control (CNC) machining has driven the progress of modern manufacturing. However, vibrations induced by inherent cutting load fluctuations and external disturbances during machining lead to uncertainties in vibration-impacted signals such as cutting force and spindle vibration. These uncertainties severely restrict machining stability and workpiece quality, creating challenges to high-precision signal prediction. Traditional filtering and modelling methods have limitations: they ignore high-frequency information by treating it as noise, exhibit poor adaptability to static parameters and suffer high computational costs. While single deep learning structures can capture nonlinear relationships, they are affected by data uncertainties, resulting in insufficient prediction accuracy and generalization capability. To address these issues, this thesis proposed a deep learning-based generic framework considering uncertainty for modelling vibration-impacted signals, with cutting force as a validation case, aiming to improve signal prediction accuracy and uncertainty management capability. The core work of this thesis includes: (1) Building a generic modelling framework for vibration-impacted signals, including five modules: comparative analysis of problem-domain models, signal complexity analysis and feature extraction, uncertainty modelling, adaptive hybrid deep learning and cross-condition validation. The module can be adapted to multiple types of vibration-impacted signals through parameter adjustment.(2) Designing five modules conforming to cutting force modelling based on the generic architecture for cutting force prediction application. Firstly, comparative analysis of Finite Element Method, Analytical Model and Deep Learning Model showed that Deep Learning outperformed traditional methods in capturing high-frequency harmonics and temporal dependencies and initial signal complexity analysis was introduced as a data preprocessing step, which is of great help for improving the accuracy of cutting force prediction. Secondly, a signal complexity analysis module was developed in detail. It determined the signal analysis boundary, quantified the contribution of different signal components and decomposed cutting force signals into deterministic harmonics, Gaussian noise and uncertainty fluctuations, enabling targeted feature extraction. These decomposed sub-signals were used as candidate data for subsequent modelling. Thirdly, for uncertainty quantification, two modelling methods were employed: one is a statistical method, which is Kernel Density Estimation (KDE) combined with Bootstrap resampling, enabling the generation of KDE functions. The other is a dual-branch Convolutional Neural Network (CNN) integrated with Bootstrap resampling. This dual-branch CNN fused cutting parameters and signal features to predict KDE curves and its performance is characterized by both strengths and limitations: 83.3% of trials achieve R² > 0.90, producing satisfactory results for uncertainty probability distributions of the three axes, with a 95% confidence interval representing the uncertainty fluctuation band. However, the model also produced extremely poor results, with the lowest R² dropping to 0.6985. In addition, its performance in cross-condition validation is not consistently stable, as it struggles to generalize across different RPM settings. For instance, when cross-validating from 3000 RPM to 5000 RPM, R² falls to the range of 0.55–0.77.Finally, a Hybrid Multi-Neural Network (HMNN) integrating CNN, LSTM and ResNet was developed, which fused time-series signals, cutting parameters and uncertainty features. In terms of performance, it achieves R² > 0.98 for Fx and Fy under Full Engagement and R² > 0.95 under Partial Engagement, though Fz predictions are more challenging (R² > 0.95 in Full Engagement and R² > 0.92 in Partial Engagement). Moreover, cross-condition validation of the model confirms its strong generalization capability. Taking Full Engagement as an example, the R² in cross-validation all exceed 0.90. In addition, a multi-group training strategy, integrating data from heterogeneous cutting conditions, further improves model robustness to unseen machining scenarios, with R² mostly exceeding 0.95. This approach enables better interpolation across intermediate cutting parameters and mitigates distribution shifts associated with single-group training. Moreover, the model maintains high prediction accuracy in an additional milling experiment on different workpiece materials, tools, and machine setups, demonstrating strong transferability without retraining. Notably, uncertainty input does not always improve prediction accuracy; instead, it verifies the non-deterministic nature of uncertainty. Thus, a 3-σ uncertainty boundary was designed to help engineer better control uncertainty. Cross-validation confirms that all its coverage rates exceed 95%, validating its effectiveness for uncertainty control. The model also achieves efficient computation, with training and prediction times compatible with practical production scenarios, supporting its potential for real-time or near-real-time applications. The proposed generic framework breaks through the limitation of single-signal modelling. Its methodologies of signal decomposition, uncertainty quantification and hybrid network design provide theoretical support for high-precision prediction and uncertainty management of vibration-impacted signals such as cutting force and spindle vibration and can promote the practical application of intelligent machining and digital twin systems.
Date of Award26 Feb 2026
Original languageEnglish
SupervisorWencheng Pan (Main Supervisor) & Andrew Longstaff (Co-Supervisor)

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