# Methods of Analysis

There are currently three different methods of alignment analysis in Novapoint Rehab. Two of these where developed for earlier program versions (Rehab v.1.0 and Sporop v.1.0). Each of the methods has its advantages and disadvantages and has different requirements for the route and measured data.

## NovaTrack v 3.0

### Horizontal Alignment

The method is based on analyzing the measured data in a curvature diagram, instead of trying to dissolve the elements (straights, curves, and transition curves) directly from the coordinates of the measured data. In the diagram, the method groups the points into groups of seven and transforms the coordinates, from X-Y to Chainage – Curvature. In a curvature diagram, all elements that are straight lines or curves are represented as straight lines (constant curvature), and the transition curves are linear increasing or decreasing functions. The elements are dissolved from a regression analysis to find best-fit lines. When the elements are identified, they are transformed back to X-Y coordinates and the result can be calculated.

### Vertical Alignment

The straight lines are found by assuming a "corridor" around the straight-line, and then see how far the straight-line can be extended without passing the corridor. The vertical angular points are inserted in the intersection between straight lines. The radii are then calculated as having a tangent length of 20.0m.

### Demands on Track Data/Measured Data

The method is somewhat sensitive to the standard of the track and measured data, but compared to the other methods, a more powerful algorithm for line calculation (NADB). With high quality on both track and measured data, the program analysis will be capable of working with relatively complicated geometry.

## Rehab v 1.0

This is the first method developed for use on roads in Novapoint Rehab. Use can configure the Rehab method.

### Horizontal Geometry

The analysis uses the least square method to find the straight lines in the alignment from the measured data coordinates and with a user-given tolerance. User can change minimum straight-line length. Between the straight lines, the "best" radius is calculated from the measured data. If a radius cannot be calculated, or is calculated to more than 25,000.0m, the radius is set to 10.0m or 25000.0m.

### Vertical Geometry

For the vertical geometry, the least square method is also used for establishing straight lines from the measured points, with the user give tolerance. User can give minimum straight-line length. Between the straight lines, "best" radius is calculated from the measured data. Where radius cannot be calculated, or calculated to more than 50000.0m, the radius is set to 50000.0m.

### Demands on Track Data/Measured Data

The disadvantage with the Rehab analysis is that it has problems detecting S-curves, especially where the minimum straight-line length is set too long. The straight-line in between is in those cases not detected.

The calculation of transition curve parameter is also a relatively simple procedure, and is done after the calculation of radii smaller than the radius given by the user. The analysis starts with the parameter A set to A = R/3, the length is reduced where there is not room for transition curves.

The Rehab analysis has lower demands on the quality of the measured data, compared to the other analyzes, and will in most cases as a minimum, be able to find the straight lines. It is then up to the user to edit the geometry until a satisfying result is reached. The analysis will on the other hand have trouble with more complicated geometry, such as S-curves and combination curves.

It is therefore not likely the Rehab analysis will generate a "perfect" geometry, but since it is a more "rugged" analysis, it will in most cases give the user a first line calculation that can be used in the continued optimization of the geometry.

## Sporop v 1.0

This is the first analysis developed for railway tracks.

### Horizontal Geometry

The analysis tries to find out when a curve starts by using a form of trend analysis. 3 and 3 points are analyzed, and the direction of the curvature (K) is calculated, +1 for right and –1 for left. As the analysis proceeds along the measured points, the curvature is accumulated. In a situation where every second point has a curvature either to the right or to the left, the accumulated curvature is set to 0. A factor is then calculated as the accumulated curvature divided by the number of points. On a stretch where all points curves in the same direction, this factor is either –1 or +1.

If the factor > 0.5, it is assumed that a curve has started.

If the factor < 0.3, it is assumed that the curve has ended.

Between 0.3 and 0.5, further analysis is done by looking at the adjacent points. If a corresponding trend is found, it is assumed that a curve has started.

User cannot change the following factors:

When the approximate chainage for the start of curves are found, 2 calculations are done:

Straight lines are calculated using the least square method.

The combination L-R-L is calculated using the iteration routine AMOEBA from the Institute of Mathematics of the Norwegian University of Technology. This routine can calculate the "best" line through a series of points, with as many unknown as you like, but the number of points must be a least 1 more than the number of unknown. In this situation there are 3 unknown, hence a minimum of 4 points are used. The application is asked by the routine to calculate an offset for each point. These results are then used to calculate a new, better alternative. The routine finishes when the result is better than the tolerance given by the application.

After these basic calculations are done, the line calculation program NADB is ran 3 times to adjust line data, because the tangent points move after each calculation.

Adjustments of line data are either of the following:

New regression analysis of straight lines

Calculation of corrected radius

Adjustment of transition curve parameter for eliminating overlapping elements

### Vertical Geometry

The analysis of the vertical geometry is done in the same way as the analysis of the horizontal geometry, but without the calculation of transition curve parameters.

### Demands on Track Data/Measured Data

In some situations, the starting point is wrongly assumed or the calculation fails to calculate the line. These are the main problems with this analysis method, it will sometimes not be able to fulfill the alignment calculation or give a result that is incorrect.

The Sporop-analysis has lower demands on measured data and alignment, but as the Rehab-analysis, more complicated geometry as S-curves or combination curves may cause the analysis to fail.

Sporop v 1.0 cannot be configured.