# Simulation of Real Defect Geometry and Its Detection Using Passive Magnetic Inspection (PMI) Method
## 5 Conclusions  
Being able to detect defects in steel infrastructure would substantially improve risk management and condition evaluation over time. To this end, mathematical simulations were carried out on a pre-flawed specimen that was laser-scanned to generate a point cloud surface map. This map was then used as a basis to develop a model. The intent was to establish detectability limits for very small flaws in order to reduce Type I and Type II errors in anomaly detection. The magnetic behavior of the ferromagnetic rebar specimen was simulated with a finite element-based software considering the background magnetic field. Different components of magnetic flux densities on the surface showed consistent harmonic trends because of the corrugated shape of the rebar. However, there were specific irregularities in the direction and values for the different components of magnetic flux densities at the location of Hole 2. Simulated patterns could be correlated with the experimental data at the holes' locations, so the top hole (Hole 2) was easily located, but Hole 1 was not, because of its orientation in the magnetic field and because the point cloud model did not replicate its true depth. The gamma probability distribution was chosen to statistically assess the magnetic flux density behavior of the rebar. Two main outcomes were extracted: 0.76% of the scanned section of the rebar was considered defective, and if the rebar specimen were longer, the Z-component magnetic flux density values indicating flawless rebar would be predicted to lie between 76-100 uT with 98% confidence. The values of the different components of magnetic flux densities at different distances from the rebar were reviewed. Increasing the vertical distance of the data recording line led to a logarithmic reduction of magnetic flux density values. As this distance was increased, the magnetic flux density values became approximately constant and close to the background magnetic field. In conclusion:  
* The pattern of the simulation results at defect locations were similar to the outputs of previous physical experiments;
* The background magnetic field had a significant effect on the trend and values of different components of the magnetic flux density;
* All of the magnetic flux density components displayed correctly located anomalies corresponding to the defect on the top surface of the rebar;
* Increasing the distance from the rebar changed the trend and values of the magnetic flux densities such that at some distance, the anomaly became undetectable;
* To detect various shapes and sizes of defects at different places along a rebar specimen, additional magnetic parameters should be considered. For instance, the Z-component of the magnetic flux density was totally constant on the sides of the rebar, and could not detect the anomaly arising from Hole 1;
* The stray magnetic field around the rebar decreased relatively symmetrically by increasing the distance from the rebar; and
* The choice of the gamma distribution to model the Z-component magnetic flux density values of the numerical simulation resulted in valuable interpretations. Conceptualization, M.M., S.M. and M.B.D. ; Data curation, M.M. and S.M. ; Formal analysis, M.M. ; Funding acquisition, M.B.D. ; Investigation, M.M. ; Methodology, S.M. ; Supervision, M.B.D. ; Writing--original draft, M.M. ; Writing--review & editing, M.M., S.M., and M.B.D. This research received no direct funding. The authors would like to thank Inspecterra Inc. for providing access to the PMI device used in this study. We would like to acknowledge CMC Microsystems for the provision of products and services that facilitated this research, including the providing of a COMSOLR software license. In addition, we express our thanks to Professor [PERSON] and Professor [PERSON] for permitting us to use their laboratory (Infrastructure and sensing analysis laboratory) during our studies. we also extend our thanks to their lab member Mr. [PERSON] due to his support for scanning the rebar by the 3D-laser scanner.