What Should the Twin Learn Next?

CORE PURPOSEInformation → decision

Use new information where it can change the reliability decision most.

The twin does not collect every possible measurement. While the reliability interval still crosses the target, it selects the next experiment by balancing expected uncertainty reduction against information cost.

1Acquireone new observation
2Updatethe Bayesian belief
3Evaluatethe reliability interval
4Actstop or experiment again

SEQUENTIAL INFORMATION DECISION

Decide what to learn next

Core

Current question The reliability interval crosses 0.999.

Recommended next action Run an FE simulation

RELIABILITY AFTER INFORMATION

Posterior density versus the fixed target

S₀

The current 95% reliability interval crosses 0.999, so more information is required.

No new experiment has been run. The reliability band still crosses 0.999. Choose an experiment or acquire the recommended data.

Requirement satisfied

Lower bound > 0.999

Insufficient information

Band crosses 0.999

Requirement not satisfied

Upper bound < 0.999

PHYSICAL–VIRTUAL SYNCHRONIZATION

Pipe evidence updates the virtual belief

Sync

PHYSICAL PIPE Swipe sideways to rotate · tap a defect

Defect A · axial position 44% Estimated depth d = 5.20 mm

ObservationWaiting for new evidence

Virtual statePrior belief S₀

VIRTUAL PROBABILISTIC MODEL Ready

Defect depth d5.20 mm±26% epistemic

Surrogate p̂_FE12.48 MPa±32% epistemic

Discrepancy μ_m0.980±24% epistemic

True capacity p_c12.23 MPaprobabilistic output

PROBABILISTIC DIGITAL TWIN

Watch evidence update the Bayesian network

Central

ACTIVE UPDATE PATH Waiting for experiment data

Tap a node to inspect it. The network combines physical inputs, a probabilistic FE surrogate, model discrepancy, demand and structural reliability.

PHYSICS → SURROGATE → RELIABILITY

How the PDT computes failure probability

Model

Finite-element model

Selected pipe geometry, material, defect and location inputs generate a theoretical pressure capacity.

[D,t,s,d,l,x] → p_FE

pFE = 12.48 MPa

Probabilistic surrogate

A stochastic surrogate approximates expensive FE runs and carries epistemic uncertainty between sampled input points.

p_FE → p̂_FE

12.48 ± 3.99 MPa

Structural reliability

Model discrepancy corrects capacity. Demand and capacity define the limit state and failure probability.

g = p_c − p_d → p_f → R

pf = 1.08 × 10⁻³

UNCERTAINTY SEPARATION

Separate what can be learned

Diagnosis

REDUCIBLE

Epistemic uncertainty

Choose data that reduces the most decision-relevant uncertainty per unit cost.

d Unknown true defect depth 26%

p̂_FE Unknown surrogate function 32%

μ_m Unknown mean model discrepancy 24%

PROPAGATED

Aleatory uncertainty

Natural variability in load, material and observation noise is propagated rather than eliminated by one experiment.

Important: a defect measurement is an information-gathering action, not an uncertainty type. The unknown true depth is epistemic; measurement error ε remains part of the observation model.

↻

CLOSED INFORMATION LOOP

Data → update → evaluate → decide → repeat

Loop

1Data inputWaiting for an observation
2Bayesian updateUpdate one epistemic belief
3Reliability evaluationCompare the full band with 0.999
4Sequential decisionRecommend FE simulation

INFORMATION HISTORYNo experiments yet

Acquire the recommended data or run a selected experiment to start the sequence.

MODEL SCOPETeaching reconstruction

Based on Agrell, Dahl and Hafver (2023)

The page reconstructs the paper’s corroded-pipeline example, three information actions, reliability threshold, action costs and 40-experiment stopping limit.

Interactive values explain the method. They do not reproduce the trained DQN weights, synthetic episode data, or the full DNV GL RP-F101 engineering calculation, and they are not an engineering assessment.

Open the paper DOI