Algorithm 2: Simulation for CS Assignment Simulation Process

Input: Budget, $r$;

Output: Cost Expectation, $E$; Cost Variance, $V$

1: for $i\in \left[1,2,3,\dots ,1000\right]$ do: 2:   All Predicted Crack Widths 🡰 Simulation for AI-based Crack Width Detection Process 3:   Manually Inspect Bridges 🡰 Randomly Select based on r and the Prediction Results 4:   $Cos{t}_i$ 🡰 r + Misassignment Cost of CS for Rest of Bridges 5: $E$ 🡰 ${{\displaystyle \sum }}_{i=1}^{i=1000}Cos{t}_i$/1000 6: $V$ 🡰 ${{\displaystyle \sum }}_{i=1}^{i=1000}{(Cos{t}_i-E)}^2$/1000