Physics-guided machine learning for milling stability: A numerical study of model training and updating Jiang Jiang and Tony L. Schmitz Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte, Charlotte, NC, USA Introduction Physics-based model descriptions receptance coupling substructure analysis (RCSA) used to predict the tool point receptance mechanistic force model used to relate the cutting force to the commanded chip area mean force frequency domain analysis used to predict stability limit using the first two models as inputs Physics-based model uncertainty deterministic models include uncertainty for example, the actual extension length of the endmill from the holder results in uncertainty in the tool point receptance which, in turn, leads to uncertainty in the stability limit if a test is performed to determine the actual stability behavior of a spindle speed-axial depth combination, there is no straightforward mapping between this result and the model input parameters New approach use the (uncertain) physics-based stability model to train a machine learning (ML) algorithm ML model is defined in the desired test domain of spindle speed-axial depth updating can then proceed directly by collecting stability results and modifying the dataset used to re-train the ML stability model. leverage Industry 4.0, where data collected during and after machining is used to achieve process improvement each part becomes an experiment and the uncertainty in operating parameters can be reduced over time Numerical case study Physics-based models with intentionally inserted error Updating Strategy 2 – grid ‘lazy update’ that selects a grid of equally spaced points over the full domain number of points varied from 50 to 410 if the cut is unstable, then all the points with the same spindle speed but higher depth of cut are updated as unstable if the cut is stable, then all the points with the same spindle speed but lower depth of cut are updated as stable Define force model using best information available (includes errors). Modeled force data 700 N/mm2 specific cutting force 68 deg force angle True force data 800 N/mm2 specific cutting force 60 deg force angle Define tool-holder-spindle-machine using best information available (includes errors). Modeled tool 12 mm diameter 50 mm extension length from holder 4 teeth True tool 53 mm extension length from holder Tool point frequency response function for incorrect extension length Chatter Stable Chatter Stable GOAL By updating the training dataset, transform the stability limit from left (with errors) to right (true model) Updating Strategy 3 – climbing ‘efficient update’ that uses fewer tests, 101 to 183 check stability for all points at 5 mm depth for stable points, test at 7 mm depth (same spindle speeds) for stable points, test at 10 mm depth (same spindle speeds) requires less points and yields a better result captures stability limit over full spindle range Generate original dataset from incorrect stability model, generate dataset with the shape of 20 (depth of cut/m) * 101 (spindle speed/rpm) provides base for updating and online learning, features were normalized dataset was divided into training set and test set with 70:30 ratio Stage 1: Replicate the stability boundary use three machine learning algorithms to replicate the stability boundary determine accuracy from the test set (compared to the stability limit with input error) Stage 2: Update the stability boundary with test cuts Updating Strategy 1 – frequency analysis ‘smart update’ leverages physical knowledge to generate updating data points select largest stable depth-spindle speed as the first cut, use MATLAB simulation to determine the process signals determine if cut is stable or unstable, as well as the chatter frequency if it is unstable use equation to find the spindle speed of the next cut repeat Physics-based model, y = f(x) Input, x, related to output Simulated output, ys Physics-guided machine learning model, Y = f(x, ys, ym) Output, Y Measured data, ym, for input, x AdaBoost KNN SVM 97.03% 96.20% 91.09% Conclusion study provides feasibility of physics-guided machine learning for milling stability machine learning models to predict cutting stability for test dataset (with errors) updated stability limit with error-free data results were compared to the observed/true stability limit accuracy of two updating strategies with three ML algorithms evaluated climbing method for updating had highest accuracy AdaBoost provided accuracy of 92.24% (model is correct for 92.24% of the test dataset compare to the true stability limit) future research will consider other machine learning algorithms, such as neural network combination of both synthetic and measured data will be used in future study Machine learning defined by Tom Mitchell as machine learns with respect to a particular task T, performance metric P, and type of experience E, if the system reliably improves its performance P at task T, following experience E closely related to computer science, statistics, psychology and neuroscience data mining, knowledge discovery, algorithm development, and problem solving K-nearest neighbors (KNN) makes decisions by referring to the K data points closest to selected data point does not make assumptions over the distribution of the dataset does not produce a generalized rule over the dataset Support vector machine (SVM) creates a hyperplane to separate the data points into two classes chosen by maximizing distance between the hyperplane and the closest data points maps the data points to a higher dimension, if required, so that a hyperplane can still divide them AdaBoost ensemble algorithm that groups weak classifiers into a combined classifier with each round of training, the examples that were misclassified by the previous round get more weight when calculating the accuracy of the current classifier forces the algorithm to focus on mistakes base classifiers have weighted votes to generate the final results Example Test cut 1 with  = 15600 rpm, b = 20 mm use MATLAB simulation to determine process signals cut is unstable choose spindle speed for Test cut 2  = 3046.7(60)/((j + 1)4) = 15233 rpm for j = 2, keep b = 20 mm No. Spindle Speed (rpm) Depth of Cut (mm) Status 1 15600 20 2 15233 3 15 4 5 15000 6 Test AdaBoost KNN SVM Original dataset 81.19% 80.03% 84.82% Grid   n=50 81.85% 80.20% 85.48% n=110 82.01% 80.86% 86.14% n=210 82.84% 82.18% 87.13% n=410 Climbing n=101 86.96% 87.79% n=154 90.92% 89.60% 89.27% n=183 92.24% 91.25%