PSI - Issue 64

A. Di Benedetto et al. / Procedia Structural Integrity 64 (2024) 2254–2262 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

2258

5

I

r Max f

 = I

( )

 

o

q

c

1 f r I f r 2 o

( )

(2)

r Max f

 = I

( )

 

q

c

( )

where r is the distance of the i-th point to the scanner (range), computed for each point of the extracted scan line. The scan lines have been extracted using GPS time. 3.2. Unrolling algorithm The implemented process is used to "unroll" the scanned point cloud. The entire procedure is based on the following steps: 1. Each individually extracted box is roto-translated into a local reference system (x', y', z') where the x' axis parallel to the longitudinal axis of the box and the y' axis parallel to the cross-sectional axis of the box and the z' axis aligns with the h axis of the global system. The rotation is performed by calculating the direction angle of the axis of the individual box. 2. To transform from the 3-D System (x', y', z') to the plane system (x, y), it is necessary to calculate the center of the semi-circumference relative to each individual box. The generic semi-circular section of the box is created by projecting the points of the generic box onto the section plane ( ', '). 3.The interpolation of points on a circumference is conducted using the RANSAC (RANdom SAmple Consensus) method. Specifically, the function employs the M-estimator sample consensus (MSAC) algorithm, a variant of the RANSAC algorithm, to fit the data. This facilitates robust interpolation even in sections characterized by high noise, particularly with artifacts not belonging to the tunnel intrados. The outputs are the parameters of the circumference, i.e., the coordinates of the center (y' c , z' c ) in the plane ( ', ') and the radius R. 4. For each of the points contained in the plane ( ', '), a translation is performed with respect to the ' axis by a quantity ' and along the ' axis by ' so that all points belonging to the cone are concentric with respect to the origin of the interpolated circle. The quantities and are given by: ' ' (3) where y' i and z' i are the coordinates of the i-th point belonging to the plane ( ', '). Subsequently, the distance of the i-th point from the center of the circumference is calculated as: 2 2 i r Dy Dz = + (4) The plane coordinates ( i , i , i ) of the i-th point are determined by: ' 1 i i i i i x x y r  (5) ' c Dy y y Dz z z = − = − ' i c i

= =−   = −

z r R

i

i

where angle w i is calculated using the formula:

Dz Dy      

arctan2 (6) the function 2 returns the four-quadrant inverse tangent, is in the domain [- ; ] and retains the sign of the i  =