# Development of Digital Training Twins in the Aircraft Maintenance Ecosystem
## 2 Materials and Methods
### Algorithmic Orchestration Workflow
After training with resource \(r\), the updated competence is computed as follows:  
\[\mathbf{C}_{t+1}=\mathbf{C}_{t}+\alpha_{i}\cdot E_{r}\cdot\mathbf{G}_{r}\]  
where \(\alpha_{i}\in(0,1)\) is the learner's responsiveness coefficient, \(E_{r}\in(0,1]\) is the effectiveness of resource \(r\), \(\mathbf{G}_{t}\in\mathbb{R}^{n}\) is the skill gain vector of the resource. To select the best resource, the system minimizes a cost function:  
\[J(r)=w_{1}\cdot D(\mathbf{C}_{t},\mathbf{T}_{r})+w_{2}\cdot\phi_{r}+w_{3}\cdot \beta_{r}+w_{4}\cdot\tau_{r}\]  
where \(\mathbf{T}_{r}\in\mathbb{R}^{n}\) is the target skill vector associated with resource \(r\), \(D(\mathbf{C}_{t},\mathbf{T}_{r})=\|\mathbf{T}_{r}-\mathbf{C}_{t}\|_{2}^{2}\) is the squared Euclidean distance measuring the skill mismatch, \(\phi_{r}\in\{0,1,2\}\) is the fidelity cost (e.g., 0 = low, 1 = medium, 2 = high), \(\beta_{r}\in[0,1]\) is the normalized Bloom cognitive complexity score (scaled from levels 1 to 6), \(\tau_{r}\) is the session duration, and \(w_{1},w_{2},w_{3},w_{4}\) are configurable weights. The optimal training resource \(r^{*}\) is then as follows:  
\[r^{*}=\operatorname*{argmin}_{r\in\mathcal{R}}\mathrm{J}(r)\]  
This ensures that resource selection is competence-driven, cost-aware, and pedagogically efficient. The target competence vector \(\mathbf{T}_{r}\in\mathbb{R}^{n}\) represents the ideal skill profile that a given training resource aims to reinforce. These vectors are defined during the system configuration phase by instructional designers in consultation with subject matter experts. Each dimension corresponds to a specific competence (e.g., diagnosing electrical faults, performing torque checks), and its value indicates the desired mastery level on a normalized \([0,1]\) scale. This allows the model to account for different depths of knowledge, including basic recognition, procedural application, and problem-solving capabilities. To reflect hierarchical cognitive depth, each training resource is also assigned a Bloom-level complexity score \(\beta_{r}\) normalized to the interval \([0,1]\), where lower values correspond to simple recall tasks (e.g., knowledge) and higher values represent synthesis or evaluation (e.g., diagnosis, troubleshooting). These values are assigned based on existing instructional taxonomies and learning outcome frameworks commonly used in aviation maintenance training requirements such as those defined by EASA Part-66 [32]. The orchestration engine uses \(\mathbf{T}_{r}\) to calculate competence misalignment and \(\beta_{r}\) to penalize inappropriate cognitive overload for lower-skilled learners. This dual consideration enables adaptive training paths that match both the domain-specific competence gaps and the cognitive maturity of each learner. This orchestration process operates as a closed-loop control system: after each competence update, new gaps are re-evaluated, and subsequent training resources are re-optimized accordingly. The system iterates until all gaps are sufficiently minimized below an acceptable tolerance, thus ensuring complete regulatory compliance while optimizing the learning trajectory for each individual learner. Figure 2 presents the conceptual training flow diagram, which illustrates the core sequence of operations in the orchestration logic. Each training cycle begins with the initialization or update of the learner's digital profile. This profile is represented as a competence vector containing normalized values across multiple skill domains (e.g., aircraft hydraulic systems, sensor diagnostics, failure recovery procedures). These values are derived from xAPI logs and prior simulation results. The system determines whether additional training is required by comparing the learner's current profile against predefined regulatory or operational target vectors. If the learner's performance already meets or exceeds the expected thresholds across all competencies, no further training is assigned.