2.1.2. Structural Dynamics

Estimating dynamic system properties is associated with uncertainties [44]. The uncertainties stem from environmental and operational variability, non-stationary sea states (fluctuating mean sea water level), time-variant structural conditions (corrosion, scour), output noise, and the formulation of the structural model, including modeling of highly uncertain parameters such as soil stiffness, joint stiffness and damping. We note that the output noise relates to the noise in the acceleration and/or strain signals, which is propagated through system identification procedures and results in uncertainty of the updated structural model parameters [44]. The structural dynamics uncertainty is included in (1) through the stochastic variable *Xd*.

#### 2.1.3. Loading

Depending on the location of the wind turbine, the loading may include the following exogenous sources and their inherent uncertainties:


If loading uncertainty is quantified based on information from digital twins, the main part of the uncertainty is related to obtaining the structural response due to external loading. This response is typically estimated based on virtual sensing methods, which are associated with uncertainties [34,45]. The loading uncertainty is included in (1) through the stochastic variable *Xl*.

#### 2.1.4. Stress Concentration

Stress ranges in specific locations can be estimated based on simplified parametric equations, for example, Efthymiou [46] or detailed finite element (FE) models. The stress concentration uncertainty is included in (1) through the stochastic variable *Xs*. The stress concentration uncertainty can be quantified if a detailed FE model is used to establish hot spot stresses [47] or if hot spot stresses are measured directly.

#### 2.1.5. SN Curve

The uncertainty in parameter estimation from the SN curve approach [48] is included in (1) through the stochastic variable *K* and the deterministic parameter *m*. If a bi-linear SN curve is used, then stochastic variables are used to model the two branches of the SN curve. The SN curve uncertainty can be quantified if fatigue testing is performed [48].

#### 2.1.6. Fatigue Damage

Uncertainties related to the accumulated fatigue damage model (Miner's rule [49]) and the crack propagation method (Paris–Erdogan [50] or fracture mechanics) is included in (1) by modeling the resistance, Δ, as a stochastic variable.

#### *2.2. Current State-of-Practice for Reliability Updating*

Design standards define a specific level of reliability that offshore wind substructures must fulfill, for example, a target annual reliability index of Δ*β* = 3.3 in IEC 61400-1 [31,40]. Reliability levels indicated in standards assume a generic level of uncertainty representative for all types of substructures and locations. Because the uncertainty is assumed to cover a wide range of structures and locations, the resulting design is, in many cases, conservative. The level of conservatism can be quantified when new information specific to a particular structure becomes available. One way of obtaining such information is by means of digital twins, which can be used to quantify the uncertainty and subsequently update the structural reliability.

#### **3. Structural Reliability Updating Framework**

In this paper, we propose a probabilistic framework in which digital twin information is used to update the uncertainties associated with the fatigue damage accumulation, which are then used to update the structural reliability. In particular, we use the updated parameters from the established digital twins to quantify the model uncertainties of the structural dynamics, *Xd*, and load modeling, *Xl*. The updated uncertainties are quantified based on a forward propagation method, which allows quantifying separate uncertainty sources stemming from specific model parameters. Having updated the relevant uncertainty contributions from the updated model parameters, the reliability is updated based on the linear probabilistic limit state Equation (1). Finally, the updated reliability serves as a decision basis for a decision model update. A schematic illustration of the framework is seen in Figure 2, and steps one to six are described in Sections 3.1–3.6.

**Figure 2.** Structural reliability updating framework based on information from a digital twin. Updated parameters from the digital twin are used to quantify uncertainty in fatigue damage accumulation. Subsequently, the structural reliability is updated.

#### *3.1. Model Updating*

It is assumed that an updated structural model (step one) is available, which can be obtained based on well-established model formulation and updating procedures [51].
