| name | digital-twin |
| description | Digital twin framework — physics models, data assimilation, Kalman filter, uncertainty quantification, model updating, predictive maintenance, ISO 23247, aerospace/industrial applications. |
| metadata | {"priority":7,"promptSignals":{"phrases":["digital twin","digital model","physics-informed model","model updating","predictive maintenance digital","virtual sensor"],"minScore":3}} |
Digital Twin — Complete Skill
Definition Hierarchy (ISO 23247)
Digital model: physics/geometry representation; no live data connection
Digital shadow: one-way data flow from asset to model; model updated from sensor data
Digital twin (DT): bidirectional; physical asset and virtual model are synchronized; model affects asset operation
Architecture Components
- Physics model: FEA, CFD, multibody dynamics, thermodynamic cycle, mechanism model
- Data pipeline: sensor data (IoT), SCADA, historian, PLM → preprocessing
- State estimation: Kalman filter, particle filter, machine learning fusion
- Model updating: Bayesian model calibration, parameter identification
- Prediction engine: remaining useful life (RUL), fatigue accumulation, thermal budget
- Decision layer: alerts, prognostics, maintenance scheduling, what-if simulation
Physics Models (High-Fidelity)
Structural DT: FEA model (ANSYS/Abaqus) updated with strain gauge readings
Modal updating: measured natural frequencies → adjust E, ρ, boundary conditions
Virtual sensing: estimate unmeasured stress from sensor data + FE model
Thermodynamic DT (gas turbine):
Component maps (compressor, turbine) + performance model
State estimation: actual efficiency from measured T and P → identify degradation
Health index: compressor fouling factor, turbine tip clearance, combustor spread
Rotating machinery DT:
Bearing force model + vibration measurement → estimate bearing load, unbalance
Orbit plot analysis from X-Y probes → identify rub, misalignment, fluid film instability
Kalman Filter for State Estimation
Linear system: x_{k+1} = F x_k + B u_k + w_k (process)
z_k = H x_k + v_k (measurement)
w_k ~ N(0, Q); v_k ~ N(0, R) (process and measurement noise)
Kalman gain:
K_k = P_{k|k-1} H^T (H P_{k|k-1} H^T + R)^{-1}
Update:
x_{k|k} = x_{k|k-1} + K_k (z_k - H x_{k|k-1})
P_{k|k} = (I - K_k H) P_{k|k-1}
Extended Kalman Filter (EKF): nonlinear models; linearize at current estimate
Unscented Kalman Filter (UKF): sigma-point propagation; more accurate for strongly nonlinear
Particle filter: arbitrary distribution; Monte Carlo; computationally expensive
Bayesian Model Updating
Prior: p(θ) = prior distribution on uncertain parameters θ
Likelihood: p(y|θ) = probability of observed data given parameters
Posterior: p(θ|y) ∝ p(y|θ) × p(θ)
Markov Chain Monte Carlo (MCMC): sample posterior → characterize parameter uncertainty
Variational Bayes: approximate posterior as tractable distribution → faster than MCMC
Application: update FE model parameters (E, damping, BC stiffness) from measured response
Remaining Useful Life (RUL) Prediction
Paris-law based (fatigue crack growth):
da/dN = C (ΔK)^m; ΔK = Δσ √(π a) F
Integrate from current crack size a_0 to critical a_c → cycles to failure
Digital twin provides: current Δσ from load monitoring, current a from NDE/model
Data-driven RUL:
LSTM / GRU neural network trained on run-to-failure data
Health Index (HI) = function of sensor features → degradation trajectory → RUL
Physics-ML hybrid: physics model provides structure; ML corrects model error
PINN (Physics-Informed Neural Networks): loss = data loss + physics residual loss
Uncertainty Quantification (UQ)
Sources of uncertainty:
- Aleatory (irreducible): randomness in loads, material variability
- Epistemic (reducible): model error, parameter uncertainty, missing physics
Sensitivity analysis:
Sobol indices: S_i = Var(E[Y|X_i]) / Var(Y) → fraction of output variance from input X_i
Morris screening: elementary effects; identify most influential parameters
Propagation:
Monte Carlo: expensive but flexible; N = 10,000–100,000 evaluations
PCE (Polynomial Chaos Expansion): metamodel; 10× faster after training
Predictive Maintenance Integration
Condition indicators:
Vibration RMS, kurtosis, crest factor, spectral lines at gear/bearing frequencies
Temperature: bearing outer race, winding temperature, exhaust gas spread
Threshold vs. model-based:
Simple threshold: alert when value exceeds limit (no prognostics)
DT-based: predict time to failure → schedule maintenance just-in-time
Standards:
ISO 55000: asset management
ISO 13374: machine condition monitoring data formats
ISO 23247: digital twin manufacturing framework
Implementation Stack
Software: ANSYS Twin Builder, Siemens MindSphere + Simcenter, PTC ThingWorx + Creo, MATLAB/Simulink + AWS/Azure IoT
Data protocol: OPC-UA (industrial); MQTT (lightweight IoT); REST/GraphQL (cloud)
Computing: edge (real-time; low latency) + cloud (heavy computation; storage)
Output
Provide: DT architecture (model type, sensors, update frequency), Kalman filter formulation (state vector, F, H matrices), model uncertainty (parameter distributions), RUL estimate with confidence interval, predictive maintenance trigger threshold, sensor placement recommendation.
