Source-linked AI summary
Real-Time Decision-Making for Digital Twin in Additive Manufacturing with Model Predictive Control using Time-Series Deep Neural Networks
Yi-Ping Chen, Vispi Karkaria, Ying-Kuan Tsai, Faith Rolark, Daniel Quispe, Robert X. Gao, Jian Cao, Wei Chen
TL;DR
Real-time Digital Twin control requires accurate, efficient prediction and optimization for nonlinear manufacturing systems. This paper combines TiDE with simultaneous multi-step MPC for DED, using one-shot future-state prediction to regulate laser power and enforce melt pool depth constraints. The framework demonstrates accurate forecasting, temperature tracking, and constraint satisfaction, while author-reported limitations include solver-delay assumptions and constrained-control fluctuations.
Problem
Real-time Digital Twin decision-making requires efficient optimization driven by accurate predictions of highly nonlinear manufacturing systems.
Method
The paper uses a multivariate TiDE surrogate within simultaneous multi-step MPC to regulate DED laser power while tracking melt pool temperature and constraining melt pool depth.
Results
The framework accurately forecasts melt pool states, achieves temperature tracking, and handles melt pool depth constraints for proactive defect mitigation in DED.
Takeaways & Limitations
The results position TiDE-based multi-step MPC as a real-time decision-making approach for DED and similar manufacturing processes such as welding.
Takeaways & Limitations
The study assumes MPC and TiDE computation time is negligible and reports increased laser-power fluctuations under constrained control, including during unsuccessful solver iterations.
Abstract
from arXiv · showhide
Digital Twin -- a virtual replica of a physical system enabling real-time monitoring, model updating, prediction, and decision-making -- combined with recent advances in machine learning, offers new opportunities for proactive control strategies in autonomous manufacturing. However, achieving real-time decision-making with Digital Twins requires efficient optimization driven by accurate predictions of highly nonlinear manufacturing systems. This paper presents a simultaneous multi-step Model Predictive Control (MPC) framework for real-time decision-making, using a multivariate deep neural network, named Time-Series Dense Encoder (TiDE), as the surrogate model. Unlike conventional MPC models which only provide one-step ahead prediction, TiDE is capable of predicting future states within the prediction horizon in one shot (multi-step), significantly accelerating the MPC. Using Directed Energy Deposition (DED) additive manufacturing as a case study, we demonstrate the effectiveness of the proposed MPC in achieving melt pool temperature tracking to ensure part quality, while reducing porosity defects by regulating laser power to maintain melt pool depth constraints. In this work, we first show that TiDE is capable of accurately predicting melt pool temperature and depth. Second, we demonstrate that the proposed MPC achieves precise temperature tracking while satisfying melt pool depth constraints within a targeted dilution range (10\%-30\%), reducing potential porosity defects. Compared to PID controller, the MPC results in smoother and less fluctuating laser power profiles with competitive or superior melt pool temperature control performance. This demonstrates the MPC's proactive control capabilities, leveraging time-series prediction and real-time optimization, positioning it as a powerful tool for future Digital Twin applications and real-time process optimization in manufacturing.
1. Introduction
Real-time Digital Twin control in additive manufacturing is difficult because AM is nonlinear, multivariate, stochastic, and computationally demanding. The paper proposes a TiDE-based multi-step MPC framework for DED that predicts future states and handles melt pool constraints for proactive control.
- Real-time AM decision-making is challenging because complex process dynamics require computationally efficient optimization and compatible physics-based models.
- PID controllers are fast and reactive but typically regulate one process parameter against one objective, overlooking multivariable interactions and changing AM conditions.
- MPC predicts future behavior, optimizes multi-input multi-output control actions, and handles constraints such as temperature tracking and melt pool depth limits.
- Existing AM MPC studies leave gaps in nonlinear surrogate modeling, effective quality-related constraint handling, and MPC solving speed.
- The proposed framework uses TiDE to forecast future states across the prediction horizon in one shot, accelerating real-time optimization.
- The framework directly handles DED state constraints to provide proactive defect mitigation while controlling melt pool behavior.
2. Technical background
The technical background presents receding-horizon MPC and motivates TiDE as an efficient multivariate forecasting surrogate. TiDE supports future covariates and one-shot prediction, making it suitable for repeated MPC evaluations.
- 2.1. Model predictive control: MPC repeatedly solves a finite-horizon optimal control problem, applies the first action, and updates the solution as new observations arrive.
- 2.1. Model predictive control: The MPC formulation predicts system dynamics with a surrogate model while imposing state and control-action constraints.
- 2.2. Time series model: Time Series Dense Encoder (TiDE): TiDE is selected for forecasting because its residual architecture captures long-term dependencies, filters disturbances, and operates in linear time complexity.
- 2.2. Time series model: Time Series Dense Encoder (TiDE): TiDE conditions one-shot future-state forecasts on past states, future control inputs, and geometry variables as dynamic covariates.
- 2.2. Time series model: Time Series Dense Encoder (TiDE): TiDE’s dense encoder-decoder embeddings reduce dimensionality, encode interactions, and act as noise filters for prediction.
3. Thermal simulation model
The thermal simulation uses the GAMMA code to model transient part-scale heat transfer in DED with temperature-dependent material properties and GPU acceleration. The model neglects Marangoni flow, so melt pool temperatures are calibrated by scaling simulated values.
- GAMMA performs part-scale transient heat-transfer simulations for DED using temperature-dependent material properties and GPU acceleration.
- The thermal model represents heat conduction with laser, convective, and radiative heat-flux boundary conditions.
- The substrate bottom surface is fixed with a homogeneous Dirichlet condition and maintained at 300 K.
- Material deposition is modeled by activating mesh elements when the laser center approaches within the beam diameter of each element’s geometric center.
- Because GAMMA neglects Marangoni flow, it overestimates melt pool temperatures, particularly above the material liquidus point.
- The study compensates for this overestimation by multiplying extracted melt pool temperatures by 0.5, with refinement planned for 316L.
4. Data and model preparation
The study prepares DED simulation data and trains TiDE to forecast melt pool temperature and depth from temporal states and covariates. Feature extraction, moving-window segmentation, and horizon selection support multi-step prediction for MPC.
- 4.1. Target geometry and material: The target geometry is a single-track square made of 316L on a thick AISI 1018 substrate, simulated with GAMMA for feature extraction and model training.
- 4.2. Feature extraction: Melt pool temperature is extracted from nodes near the laser using radial-basis-function interpolation, while depth is estimated from a three-dimensional temperature field.
- 4.2. Feature extraction: The extracted depth can become negative in early layers or at a new layer start, and raw values are retained to reflect the GAMMA simulation.
- 4.3. Data collection: Laser-power profiles are generated across the design space, simulated in GAMMA, and converted into time series containing melt pool temperature and depth.
- 4.4. Model training: TiDE uses past targets together with past and future covariates, including geometry variables and laser power, to predict future temperature and depth.
- 4.4. Model training: Quantile loss is selected for robustness to outliers and skewed data, with the predicted median used as the response prediction.
- 4.4. Model training: The training data contain 640,277 segments of length 100, using a window size of 50 and prediction horizon of 50, split 9:1 for training and validation.
5. Model predictive control
The MPC embeds TiDE as a multi-step prediction model to track melt pool temperature while constraining melt pool depth. It uses gradient-based optimization and compares temperature tracking against a PID benchmark.
- 5.1. Multi-step MPC formulation for DED with constraints: The MPC minimizes future melt pool temperature tracking error and control effort while enforcing lower and upper melt pool depth bounds.
- 5.1. Multi-step MPC formulation for DED with constraints: The controller targets a 10%-30% dilution range to mitigate interlayer and intralayer porosity associated with low or high melt pool depth.
- 5.1. Multi-step MPC formulation for DED with constraints: Depth constraints are enforced only after the fourth layer and are omitted near corners because early-layer boundary conditions and heat accumulation violate the intended assumptions.
- 5.2. Optimization: TiDE generates the full prediction horizon in one forward pass, while automatic differentiation and L-BFGS support computationally efficient optimization.
- 5.3. MPC implementation: The GAMMA pipeline begins with open-loop simulation, then switches to closed-loop MPC, updating the first optimal control input every five simulation timesteps.
- 5.3. MPC implementation: A ten-step moving average filters periodic fluctuations in extracted melt pool temperature and depth before they enter the MPC.
- 5.4. Bench marking: PID controller: The PID benchmark evaluates temperature tracking only because it is primarily SISO and lacks intrinsic explicit constraint handling.
6. Results
TiDE accurately predicts melt pool temperature and depth, enabling simultaneous multi-step MPC for temperature tracking and depth-constraint enforcement. In simulation, the MPC produces smoother control than PID, maintains depth more effectively, and exposes computational and implementation boundaries.
- 6.1. Model evaluation: 5–15 K temperature discrepancy at corners shows TiDE captures challenging temperature and depth dynamics with smoother predictions than fluctuating ground truth.Corner turning changes laser speed and direction, causing heat accumulation.
- 6.2. Melt pool temperature control using the MPC: R2 values of 0.9907 for MPC and 0.9827 for PID show competitive temperature tracking, while MPC reduces overshoots and smooths laser-power inputs.The MPC avoids the peak laser power observed at the beginning of each PID-controlled layer by anticipating temperature rise.
- 6.3. Melt pool temperature control with melt pool depth as constraints: The constrained MPC bounds melt pool depth with only minor violations, whereas unconstrained MPC depth exceeds 30% dilution after the fifth layer.Constraint enforcement can cause temperature deviation from the reference while preserving the depth constraint.
- 6.3. Melt pool temperature control with melt pool depth as constraints: Constraint handling increases laser-power fluctuations because the MPC continuously balances depth-constraint satisfaction against temperature reference tracking.Unsuccessful solutions may reuse the previous solution or restart from the default initial guess, especially when penalties rise from infeasible starting regions.
- 6.4. Computational time: 0.2575 s mean and 0.5437 s maximum solving times occur for unconstrained MPC, compared with 0.2775 s average for constrained MPC on a 32-core CPU.The constrained timing includes warm starts and a backup initial guess when necessary.
7. Closure
The paper presents a simultaneous multi-step MPC framework using TiDE for Digital Twin decision-making in autonomous manufacturing. Validated on DED, the framework predicts melt pool features, handles depth constraints, and motivates future robust and more general Digital Twin capabilities.
- 7. Closure: The framework combines TiDE time-series prediction with simultaneous multi-step MPC for real-time decision-making in autonomous manufacturing.TiDE predicts future states for MPC, while the framework uses gradient-based optimization.
- 7. Closure: Validation on a single-track, multi-layer square demonstrates TiDE's accuracy and reliability for predicting melt pool features.
- 7. Closure: The proposed MPC handles melt pool depth constraints while delivering competitive temperature-control performance relative to PID controllers.
- 7. Closure: Future work targets uncertainty-aware robust MPC, geometry-agnostic representations, and efficient model updating for broader Digital Twin deployment.The stated goals include improved constraint-satisfaction guarantees, generality, knowledge transfer, and real-time updates.
CRediT authorship contribution statement
The CRediT statement assigns conceptualization, methodology, analysis, validation, writing, and related responsibilities across the listed contributors.
- CRediT authorship contribution statement: Yi-Ping Chen is credited with conceptualization, data curation, formal analysis, methodology, project administration, validation, visualization, and writing.
- CRediT authorship contribution statement: Vispi Karkaria is credited with conceptualization, formal analysis, methodology, validation, and writing–review and editing.
- CRediT authorship contribution statement: Ying-Kuan Tsai is credited with conceptualization, formal analysis, methodology, and writing–review and editing.
- CRediT authorship contribution statement: Faith Rolark is credited with data curation, formal analysis, software, validation, and writing responsibilities.