Machine learning enables roughness-driven inverse design of milling processes

Technical Summary: Machine Learning-Driven Inverse Design for Milling Processes

Problem Statement
The paper addresses the challenge of inverse design in milling processes, specifically the task of determining optimal machining and tool parameters to achieve a target surface roughness. While forward predictive models (mapping parameters to roughness) are well-established, inverse design is complicated by the "many-to-one" mapping inherent in machining data. Multiple distinct combinations of input parameters (e.g., cutting speed, feed rate, tool geometry) can yield identical or nearly identical surface roughness outcomes due to complex, nonlinear interactions and compensatory effects. Directly training machine learning (ML) models by swapping inputs and outputs often leads to "averaged" predictions that fail to represent physically feasible or optimal parameter sets. Furthermore, the scarcity of high-quality experimental datasets for training robust ML models poses a significant barrier.

Methodology
The authors propose a framework that couples forward-trained ML models with Bayesian Optimization (BO) to solve the inverse design problem without relying on direct inverse model training. The methodology proceeds through the following stages:

1. Synthetic Dataset Generation:

   • A high-fidelity computational framework based on a Forward Solution Method (FSM) is employed to generate a dataset of 10,000 samples.
   • The FSM discretizes the cutting edge, workpiece, and time to simulate surface topography. It accounts for kinematic equations involving six input parameters: cutting speed ($v_c$), feed rate ($f_z$), number of inserts ($z$), insert radius ($r_i$), radial run-out ($\varepsilon_r$), and axial run-out ($\varepsilon_a$).
   • The outputs are the average surface roughness ($S_a$) and maximum surface height ($S_z$).
   • The computational model is validated against experimental data from face milling of HT300 grey cast iron, showing an average relative error of approximately 7%.

2. Multiplicity Analysis:

   • An exploratory analysis using Density-Based Spatial Clustering of Applications with Noise (DBSCAN) confirms the existence of many-to-one relationships. Distinct input configurations are shown to produce similar surface characteristics, validating the need to avoid direct inverse regression.

3. Forward Model Training:

   • Two ML models are trained on the synthetic dataset to learn the forward mapping (parameters $\to$ roughness):
     • Deep Neural Network (DNN): A fully connected network with a funnel-shaped architecture (three hidden layers: 512, 256, 128 nodes) using ReLU activation, batch normalization, and dropout.
     • Random Forest (RF): An ensemble of decision trees.
   • Both models are optimized using Optuna for hyperparameter tuning (e.g., learning rate, depth, number of trees) for both single-output ($S_a$) and multi-output ($S_a, S_z$) scenarios. The RF model generally demonstrated lower validation Mean Squared Error (MSE) than the DNN.

4. Inverse Design via Bayesian Optimization:

   • The trained ML models serve as differentiable, fast proxies within a Bayesian Optimization loop.
   • The objective is to minimize the deviation between the predicted roughness and a user-specified target.
   • To address the tendency of BO to converge to local optima and the discrete nature of tool parameters, the framework explicitly enumerates discrete variables (number of inserts and radius) and runs separate optimizations for each combination. A diversity penalty is also incorporated to encourage broader exploration of the continuous parameter space.

Key Results
The framework was evaluated through two case studies targeting different regions of the roughness distribution:

• Case 1 (Low Roughness): Target $S_a = 2$, $S_z = 10$. The framework successfully identified diverse feasible solutions. The RF model achieved an average relative error of 2.12% for $S_a$ and 1.93% for $S_z$ against the computational reference, outperforming the DNN (4.96% and 3.74%, respectively).
• Case 2 (High Roughness): Target $S_a = 6$, $S_z = 33$. Despite the sparser data distribution in this region, the framework identified valid parameter sets. The RF model maintained high accuracy with average relative errors of 1.1% for $S_a$ and 2.7% for $S_z$.

Across both scenarios, the top-performing design candidates achieved average relative errors below 5% when compared to the reference computational results. The study demonstrates that the RF model generally provides superior predictive accuracy and robustness compared to the DNN in this specific context.

Significance and Claims
The paper claims to present a robust methodology for the inverse design of milling processes that overcomes the limitations of many-to-one mappings and data scarcity. By integrating forward ML models with Bayesian Optimization, the approach avoids the pitfalls of averaged predictions inherent in direct inverse regression. The framework successfully identifies diverse, optimal combinations of machining and tool parameters to meet specific surface quality targets.

The authors emphasize that the proposed method is particularly valuable for reducing trial-and-error in manufacturing design. They note that while the current study relies on synthetic data generated from a geometric model, the framework is flexible enough to incorporate additional constraints (e.g., specific tool selections or neglecting run-out errors) and could be extended to include physical phenomena like cutting forces or vibrations in future work. The work concludes that this ML-driven inverse design pipeline offers a reliable pathway for determining process parameters with acceptable prediction errors, facilitating more efficient and intelligent manufacturing planning.