digital-twin

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

1. Physics model: FEA, CFD, multibody dynamics, thermodynamic cycle, mechanism model
2. Data pipeline: sensor data (IoT), SCADA, historian, PLM → preprocessing
3. State estimation: Kalman filter, particle filter, machine learning fusion
4. Model updating: Bayesian model calibration, parameter identification
5. Prediction engine: remaining useful life (RUL), fatigue accumulation, thermal budget
6. 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:

1. Aleatory (irreducible): randomness in loads, material variability
2. 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.