Technical Summary: Uncertainty–Aware Functional Behavior Prediction and Material-Fatigue Assessment for Circular Factory

1. Problem Statement

The transition toward a circular economy requires manufacturing systems capable of reusing returned products across multiple life cycles. However, returned products (e.g., used power tools) enter the "Circular Factory" (CF) with heterogeneous degradation states, usage histories, and remaining capabilities. Conventional reliability assessments, which often rely on homogeneous population assumptions or fixed operating conditions, are insufficient for instance-specific redeployment decisions.

A critical gap exists in current Prognostics and Health Management (PHM) approaches:

• Functional vs. Material Separation: System-level functional prediction (will the tool work?) is rarely linked to component-level material fatigue assessment (will a critical part fail?).
• Uncertainty and History: Existing methods often struggle with variable usage histories and fail to provide uncertainty-aware predictions necessary for risk assessment under future, prescribed usage scenarios.
• Decision Support: Redeployment decisions cannot be based solely on current inspection; they must account for how functional behavior and material integrity will evolve under specific future service conditions.

This paper addresses these challenges by proposing a unified framework for the instance-specific assessment of a returned angle grinder, linking functional behavior prediction with material-fatigue assessment to support redeployment decisions.

2. Methodology

The proposed framework integrates two complementary pipelines—functional behavior prediction and material-fatigue assessment—into a single streaming reliability workflow.

2.1. System Functional Behavior Prediction

The functional branch models the future state of the tool as a conditional sequence-learning problem.

• Inputs: The model accepts a current state vector (thermal, electrical, rotational, and geometric variables like clearances) and a recent usage history (force and torque windows).
• Architecture:
  • Encoders: A 1D Convolutional Neural Network (CNN) extracts local temporal patterns (peaks, transients) from force-torque windows. A Multi-Layer Perceptron (MLP) encodes the current state vector.
  • Recurrent Backbone: The fused representations are processed by a Long Short-Term Memory (LSTM) network. The LSTM predicts increments rather than absolute values to anchor forecasts to known initial conditions.
  • Output Head: A probabilistic head outputs a Gaussian mean and variance for nine functional variables (e.g., motor current, speed, clearances).
• Training: The model is trained using a weighted Gaussian Negative Log-Likelihood (NLL) loss, enabling the estimation of both expected values and predictive uncertainty.
• Scenario Conditioning: The framework allows for "scenario-conditioned inference" by prescribing future usage windows, enabling reliability assessment under planned or hypothetical operating conditions.

2.2. Component Material-Fatigue Assessment

The material branch evaluates the remaining fatigue capability of the output shaft using the same operational load history.

• Stress Reconstruction: Finite Element Analysis (FEA) is used to map external force-torque loads to local notch stresses. An interpolation model translates measured time histories into stress-time histories at the critical notch.
• Fatigue Modeling:
  • Initiation: A Basquin-type S-N curve (fitted to rotating bending data) combined with the Palmgren-Miner rule and Haibach extension (for sub-limit cycles) estimates cumulative damage.
  • Propagation: A Paris-law crack-growth model estimates the life of a crack from an initial size ($a_0$) to a critical size ($a_c$), bounded by the case-hardened depth.
• Integration: The material model outputs cumulative damage and a material reliability estimate ($R_{mat}$).

2.3. Streaming Reliability Consolidation

A streaming replay algorithm (Algorithm 3) consolidates both branches:

• It processes data windows sequentially, updating functional reliability ($R_{func}$), material reliability ($R_{mat}$), and system reliability ($R_{sys} = \min(R_{func}, R_{mat})$).
• It handles gaps in observation by propagating damage estimates over missing cycles.
• It identifies the "governing branch" (functional vs. material) at each inspection point to determine the limiting factor for redeployment.

3. Key Contributions

1. Unified Functional-Material Space: The paper establishes a framework that combines current system state, recent usage history, and material degradation into a common representation for instance-specific redeployment.
2. Uncertainty-Aware Prediction: An LSTM architecture trained with Gaussian NLL predicts both the expected functional response and its uncertainty, facilitating threshold-based reliability assessment.
3. Scenario-Conditioned Inference: The ability to prescribe future usage windows allows for the evaluation of functional behavior and reliability under explicit, planned operating conditions.
4. Integrated Material Assessment: Component-level fatigue is integrated via stress reconstruction, S-N/Miner damage evaluation, and Paris-law crack-growth analysis, linked directly to the system-level usage history.
5. Streaming Workflow: A consolidated algorithm updates reliability trajectories in real-time, supporting dynamic decision-making for returned products.

4. Results

The framework was validated using an angle grinder case study with experimental data from a test bench (400 operating hours) and material testing of output shafts.

4.1. Functional Prediction Performance

• Accuracy: The model achieved a mean 2%-tolerance accuracy of 0.9652 across nine outputs on held-out test data.
• Variable Performance:
  • Thermal variables (gearbox and stator temperature) were predicted near-perfectly ($R^2 \approx 0.9999$).
  • Dynamic variables (drive motor current and load speed) were the most challenging but still showed high global trend capture ($R^2 = 0.9750$ and $0.9924$, respectively), though strict local tolerance accuracy was lower (0.9174 and 0.8675).
• Architecture Comparison: The conventional LSTM outperformed GRU and xLSTM in this short-history setting, likely due to the stability of the simple recurrent block when local patterns are pre-extracted by the CNN.
• Input Sensitivity: Ablation studies confirmed that including torque history significantly improved predictions for motor current and load speed, highlighting the necessity of load-history data over static inspection alone.

4.2. Reliability and Uncertainty

• Calibration: For drive motor current (the only variable with sufficient exceedance events), the predicted exceedance probabilities closely matched observed rates (e.g., predicted 0.0600 vs. observed 0.0646). The Expected Calibration Error (ECE) was low (0.0085–0.0086).
• Survival Analysis: Weibull analysis yielded a B10 life of 5.22 relative steps for motor current exceedance.

4.3. Material Fatigue and Reusability

• Nominal Conditions: Under nominal service stresses (approx. 2.88 MPa notch stress), the output shaft showed negligible Miner damage, indicating high reusability.
• Sensitivity to High-Load Events: The Paris-law analysis revealed extreme sensitivity to rare high-load events.
  • Nominal Load: ~31 potential reuse cycles.
  • 1.2x Amplification (upper 10% stress): ~20 cycles.
  • 1.6x Amplification: ~3 cycles.
  • 2.0x Amplification: ~1 cycle.
• Implication: Material reusability is governed by the upper tail of the load spectrum, not just average usage.

4.4. Integrated Replay

A sequential replay over 18 inspection files demonstrated that the functional and material branches operate coherently. In the tested scenario, both $R_{func}$ and $R_{mat}$ remained at 1.0 (safe), with the material branch identified as the governing limit only due to a tie. The drive motor current remained the primary functional risk indicator.

5. Significance and Claims

The paper claims to provide the first integrated assessment framework that links measured operational loading to both future functional fulfillment and remaining structural fatigue life within a single streaming workflow.

• Shift in Decision Paradigm: The work supports a shift from inspection-based classification to prediction-based redeployment. It argues that a returned product's suitability depends on its expected future function and component integrity, not just its current state.
• Instance-Specificity: The framework enables decisions for individual products with heterogeneous histories, moving away from population-level assumptions.
• Modest Limitations: The authors explicitly state that while the framework demonstrates consistent workflow integration, the specific case study did not exhibit strong physical coupling between functional degradation and material fatigue because the tested loads were far below the fatigue-critical regime. The results primarily prove the feasibility of the method and the workflow, rather than a strong physical degradation trajectory in this specific dataset.
• Future Needs: The paper concludes that robust application requires validation on heterogeneous, real-world returned products, more event-rich degradation data for calibration, and improved load-to-stress reconstruction methods.