Objective
The object of this work was to see if anything could be learned about the "spikes" problem from a detailed study of individual datasets. I only looked at LY and RY in the raw data and at F1 (F1 = k*(LY-RY)). The areas I looked at were:

• Can we explain the features of a typical LY and RY dataset in terms of known track features? Are the spikes in the right places and in the right sense? (It turns out that they are)
• Look again at the central bearing issue by putting the central bearing features (the "empirical" plot) on to the same plot as the inclinometry features. (No effect in the raw data, some effects at the 1/2 to 1 arcsecond level in the model difference plots.)
• What happens if we correlate the spikes in the model changes with wheel/track joints? Are there particularly bad joints or wheels? (Joints 3/4, 4/5, and 9/10 are the worst - wheels 2 and 3 see larger effects than 1 and 4.)
• Can we learn anything from comparing the two results above? Is it the case, for example, that spikes appear mostly in places where the track joints have a particularly large effect on the raw data? (Not really)
• Can we learn anything from looking at a single model change and breaking it down into its LY and RY change components? (Deferred, with other things, to a later paper)

I chose for study one raw dataset, 971214. I checked that the features in it were similar to another set, 980606. There were only small differences and so I assume that any raw data would have by and large the same gross features. For model differences I took 980222-14, 980810-15, and 981006-04 because they all had some meaty spikes in them. I added 980721-13 later for reasons explained below.

Plots of raw data vs joints and vs empirical correction

1. I plotted 1214LY and 1214RY with track joints and empirical corrections superposed. In order to make it a little easier to distinguish big spikes from small ones, I fitted a sin curve to the data (the same one for both) to take out and overall slope of the track. Interestingly, the phase angle for the sin curve was less than 1 degree - I assume this is a coincidence. The magnitude was about 4 arcseconds. See figure 1.

Plots of model differences vs joints and empirical correction

2. I also plotted the three model difference datasets, F1 only, also with the track joints and empirical corrections. I reversed the sense of the dataset 1006-04F1; the sense is arbitrary and it helps to get it the same for all three sets. See figure 2.
3. Looking at both figures, I don't see any particular correlation between the central bearing empirical correction and features in the raw data, but I do see a few instances of possible small correlations in the difference plots. See azimuths 10, 25, 75, 110 (maybe), 160, 205, 265, 290. There may be effects at other azimuths, masked by the track joint effects which in any case much larger. I am not surprised to see some effect, it is also clear that the central bearing is not a big player in the "spikes" phenomenon. It is, however, interesting to see the remarkable similarity between the August and October datasets - remember they are both differences, so they show how much things have changed.

Tabulated results - Azimuth sequence

4. Turning back to the first plot, the data 1214LY and 1214RY. I tabulated the presence of spikes, either up or down, with a rather approximate technique of looking at each wheel/joint interaction and deciding whether there was a large or a small spike either up or down in each trace. I divided the interactions into fourteen "clusters" and named the members a to d. Each corresponds to a particular wheel crossing a particular joint. Table 1 shows the clusters, their members, the joint for each wheel in each cluster, and the results of my look through the 1214 data. I used the notation, eg, 4 to refer to joint 4/5 for compactness. (Ignore the last four columns in the table for now.)

Table 1. Location sense and approximate magnitude of spikes U = upwards spike, u = small upwards spike, D = downwards spike, d = small downwards spike
cluster	member	Wheel/track joint				Spikes in raw data		Model change spikes
		1	2	3	4	L	R	0222-14F1	0810-15F1	1006-04F1	0721-13F1
1	a		9			d	D	U	u	u	Few really sharp spikes
1	b	6					U
1	c				2	u		U
1	d			13
2	a				3			U
2	b		10			d	D	U
2	c	7				?	U
2	d			14		?
3	a				4	U		U
3	b		11
3	c	8					U
3	d			1		d
4	a				5			U	U	U
4	b		12
4	c	9					U		D	D
4	d			2		D
5	a				6	U	u	U	U	U
5	b		13				d
5	c			3		D		d	D	D
5	d	10					U		D	D
6	a				7	U		U	U	U
6	b		14						d	d
6	c			4		D		d	D	D
6	d	11						d
7	a				8	U		U	U	U
7	b		1				d		d	d
7	c			5		D
7	d	12					u
8	a				9	U		U	u	u
8	b			6		D		U
8	c		2				d	U
8	d	13
9	a		3			d	D	U	u	u
9	b				10			U
9	c			7		d
9	d	14
10	a		4			d	D	U	u	u
10	b				11
10	c			8		d
10	d	1					U
11	a		5					U	u	u
11	b				12				u	u
11	c			9		D			d	d
11	d	2					U		d	d
12	a		6			d	D	U	U	U
12	b				13	u
12	c	3					U	d	D	D
12	d			10		D			D	D
13	a		7			d	D	u	U	U
13	b				14				d	d
13	c	4					U	d	D	D
13	d			11		d
14	a		8			d	D	U	U	U
14	b				1	u
14	c	5					U		d	d
14	d			12		d

The queries refer to features where it wasn't clear if there was spike or not.

Tabulated results - wheel/track joint

5. I transferred the information to a second table made in terms of wheels and track joints:

Table 2. Spikes in raw data for each wheel/track joint.
Track Joint	Affect on LY trace (left-hand A frame)					Affect on RY trace (right-hand A frame)
	Wheel					Wheel
	1	2	3	4		1	2	3	4
1			d	u		U	d
2			D	u		U	d
3		d	D			U	D
4		d	D	U		U	D
5			D			U
6		d	D	U		U	D		u
7	?	d	d	U		U	D
8		d	d	U		U	D
9		d	D	U		U	D
10		d	D			U	D
11			d
12			d			u
13				u			d
14			?

The layout of the wheels is:

Left hand side, wheel 4 at the front and 3 at the back.

Right hand side, wheel 1 at the front and 2 at the back.

 

I would therefore expect to see effects on the left-hand side from wheels 3 and 4, opposite in sense, with perhaps some small effects transferred from 2 and 1; similarly on the left. This is just what I see. The strongest cross-coupling seems to be associated with wheel 2, which affects the left hand side even though it is on the right. Track joints 11-14 seem to have smaller effects than the others.

 

6. I then did the same thing for the F1 difference plots. Although there are some differences between the two later datasets, they have the same spikes:

• The features of the raw LY and RY data can be explained in terms of the known wheel/track joint locations.
• The central bearing is having an effect on the model differences at the level of 1/2 to 1 arcsecond in a few places, but it is NOT the culprit for the large spikes that are the object of this work.
• Wheels 2 and 4, and track joints 3, 4 and 9 seem worse than others for spikes
• There is little obvious correlation between the presence of spikes in the raw data and those in the model differences, except perhaps that joints 11 to 14 seem to give fewer features in both cases.
• Further work:
• Study a few difference datasets to break them down into their LY and RY components
• Add more model difference datasets to the study to see if there are a small number of distinct "populations" of inclinometry result
• Try to generate a set of LY, RY data by using the known track profile (from radial arm inclinometry) and wheel/track locations. See if there are simple changes in the way the track profile feeds into the LY, RY results that could credibly give the results we see.
• Practical tests on the track! Measure deflections, install calibration shim, etc.