Across the two days of recordings, 9 freight train and 53 passenger train passbys were recorded. Due to the nature of the subjective test, the selection of the stimuli had to be quite strict. The subjective test took the form of a paired comparison test, which can result in extremely long tests when the number of stimuli is large, or the stimuli are of long duration. Since the nature of the research requires that some of the stimuli will be freight train passbys, which typically are of longer duration than passenger trains, it was necessary to significantly reduce the number of stimuli.
Firstly, the 9 freight passby noise recordings were inspected for contamination by wind noise or other noise sources since these passbys were of significantly longer duration and hence had a greater chance of being contaminated. Audible inspec- tion of the freight passby noise recordings revealed that 6 of the 9 recordings had some noise contamination and so were discarded. Since the nature of the research is focuses on the difference in response to freight and passenger noise and vibration, it was deemed important to include as many freight passbys as feasibly possible, so the 3 remaining freight passbys were included in the subjective test. The remain- ing signals in the test are made up of passenger passbys and the selection criteria was to include as many as possible, without the test being prohibitively long. For a complete paired comparison test, the subject is required to make judgements on N(N2−1) pairs of stimuli, where N is the number of stimuli included in the test. A selection of 10 stimuli, comprised of 7 passenger and 3 freight passbys, would therefore result in 45 pairs in the subjective test. With the duration of the sig- nals known, the duration of a test containing these 45 pairs was estimated to be approximately 25-35 minutes depending on how quickly the subjects were able to make their judgements. Adding an extra passenger signal to the stimuli set would increase the number of pairs to 55 and the estimate of the test duration to approximately 30-40 minutes. To avoid fatigue due to a higher number of paired judgements and an increased test duration, the stimuli set with 7 passenger and 3 freight passbys was chosen.
The 7 passenger signals selected for the subjective test were taken from the set of 53 recorded passbys. In order to obtain a varied stimulus set, signals were se- lected based on the results of a principle component analysis on various calculated objective properties of the vibration signals. The calculated properties included the rms acceleration and the VDV. The spectral centroid was calculated as a measure of the signal’s spectral distribution. Temporal factors of the signal were quantified by the kurtosis, the skewness, the crest factor and the duration defined by the 3 dB and 10 dB downpoints of the signal. For further details on these vi- bration descriptors, see Section 3.5.2. Further aspects of the signal envelope were quantified by the modulation depth and modulation frequency. The modulation depth is defined as the average difference between the maxima and minima of the signal envelope, and the modulation frequency is the inverse of the average period between the maxima of the signal envelope. The scree plot of the principal compo- nent analysis on these descriptors, showing the percentage of variance explained by each of the recovered principle components, is shown in Figure 5.1. A four dimensional principal component solution, accounting for approximately 94% of the explained variance in the descriptor space, was chosen for examination.
1 2 3 4 5 0 10 20 30 40 50 60 70 80 90 100 Principal Component Variance Explained (%)
Figure 5.1: Scree plot of the percentage of variation explained by each
Figures 5.2 to 5.4 show the positions of the 53 passenger vibration signals on the first four principal components, along with the weighting of each of the calculated descriptors on the components, indicated by the projections in the figures. Since the solution is of more than two dimensions, some of the projections are shorter than others, indicating that they are partially projecting into other dimensions not represented in the two-dimensional figures.
Though it can be hard to visually interpret the weightings of the descriptors on each principal component, and the interpretation is something of a subjective nature, some judgements can be made about which principal components could be related to which descriptors. For example, the first principal component could be related to the duration of the signal, the second component could be related to exposure magnitude and peaks in the signal, the third component could be related to envelope modulation and the fourth component could be related to envelope modulation and peaks in the signal. To select a varied passenger signal stimulus set, each principal component was equally divided into two portions and a signal was randomly selected from each half, resulting in a set of 8 passenger signals. One signal was then randomly removed, resulting in the desired selection of 7 passenger train signals. The noise pressure time histories and the vibration acceleration time histories of the 10 selected stimuli are presented in Figures 5.5 and 5.6 respectively. Note that the time axes are extended for the three freight train signals: stimuli 8, 9 and 10.