Experimental Results

This chapter presents the data collected from the Vermahide pressure and piezoelectric sensors and output from filtering and processing performed by the project's software using the DBN models introduced in Chapter 8.

Experimental methodology

Initially, `normal walking' was processed using the simpler DBN models designed to recognise the current gait cycle support phase (left, right, double or none) in order to test their response and perform any fine-tuning. Once these networks were recognising support states, they were integrated into models designed to perform higher-level abstract reasoning (detection of stumbles and falls). These were subsequently tested with recordings including normal walking, stumble events, missing data and jogging.

Presentation of Results

Results are presented in graphs of two main formats; raw signals (see Figure 9.1 for example) and evidence/belief graphs (Figure 9.2).

Raw signals are graphed as a time-series of voltage levels which have been converted directly from the datalogger's recordings. These signals usually lie in the range 0 to 50mV for Vermahide pressure sensors and -250mV to 250mV for piezoelectrics. A number of signals from different channels/sensors are usually presented together in one graph so they may be compared.

The single points displayed at the bottom of evidence/below belief graphs are used to show when and what evidence is entered into the network as a result of feature extraction. The network's belief in the system's various states are shown above the evidence as connected points. Graph keys show beliefs in the form: Bel(Node[N]=state), where N specifies which slice the belief came from, as an offset from the current. For example, Bel(Support[+1]=double is the key for the graph showing belief in the double state of the Support node from the one slice ahead of the current slice. Values in the belief graph approaching zero signify the network's low confidence in a particular state, while values approaching 1.0 signify high confidence. In most cases, evidence results in the network being expanded and updated, so evidence and belief data points appear at the same time. An exception to this is when the network is being expanded more than once per evidence entry, as used by the support-1c network to handle missing data (Section 9.5.3).

Normal walking

Figure 9.1 shows the Vermahide pressure transducer signals from a normal walking trial, consisting of 10 steps, a stop, turn, and another 10 steps. Low signals (less than or equal to 10mV) signify low pressure resulting from a foot being `in-air', while larger signals result from a foot being in support (see Figure 6.7). A foot's progression through its foot-strike to unloading gait functions (Section 2.1.1) can be seen in the signals as a strong peak in heel signals, closely followed by a peak in the toe signals. The period of double support can be seen as the overlap in one foot's heel peak with the opposite foot's toe signal peak.

  

Figure 9.1: Normal walking pressure sensor signals

Figure 9.1 shows that heel signals were in the range of 20mV to 35mV when both feet were sharing the load (double support, as shown in first 3 to 5 seconds), and peaks above 35mV when body weight was supported by one foot (single support). Differences in signal amplitudes - such as those visible between the left and right toe - can be attributed to factors such as different physical properties of the sensors, sensor placement and the toe-signal compensation built into the datalogger (Section 6.3.2). These discrepancies are not of any great concern however, as the feature extraction system uses 10mV signal crossings to trigger heel/toe up/down events (Section 8.1.3). The results of feature extraction are shown at the bottom of Figure 9.2.

The stop-and-turn phase of the recording can be seen in Figure 9.1 around the 15 second mark. Notice the drop in right foot heel/toe pressure and sustained peak in left heel pressure as the subject pivots on their left heel in order to turn around.

   
Support-1a DBN

Figure 9.2 shows the evidence extraction and DBN belief output of the support-1a model (Section 8.1), when applied to the normal walking recordings shown in Figure 9.1. Note that Figure 9.2 shows results over the time interval 0 to 16 seconds (as opposed to the full 25 seconds of recording shown in Figure 9.1) to provide a clearer view of results.

  

Figure 9.2: Beliefs from Support-1a applied to normal walking

The evidence points at the bottom Figure 9.2 clearly show successive left-up/left-down and right-up/right-down events produced by feature extraction (Section 8.1.3). It can be seen that a foot-down event is closely followed by the opposite foot-up, implying an intervening `double' support state, as expected for the walking gait cycle.

After walking starts around the 6 second mark, the belief graphs in Figure 9.2 show the sequence of left, double, right, double...supports expected for walking. An example of the DBN updating its belief to reflect new evidence is shown before walking starts, around the 2 second mark: the effect of a single right footstep on the network's support node belief distribution is seen as a change from strong belief in double support (resulting of earlier evidence), to left support (on right-up), and back to double support (following right-down).

   
Support-1b DBN

The results from the support-1b network, when applied to the data shown in Figure 9.1 are very similar to that of support-1a. The main visible differences between Figures 9.2 and 9.3 are slightly lower left and right beliefs, resulting from the `softened' conditional probability distributions.

  

Figure 9.3: Beliefs from Support-1b applied to normal walking

   
Support-2 DBN

As Figure 9.4 shows, when the support-2 network (Section 8.4) was applied to the normal walking data, it produced output very similar to that of support-1b. The only point worth mentioning with respect to this result is that the reversal of the support-action causal link did not adversely effect the network's recognition of support.

  

Figure 9.4: Beliefs from Support-2 applied to normal walking

   
Support-3 DBN

Applying the Support-3 network to normal walking produced very high beliefs (above 0.998) in the expected support states during normal ambulation. As shown in Figure 9.5, the addition of the `PrevSupport' forwarding node resulted in the network taking a few steps to stabilise due to its stronger connection to previous slices. Once it had stabilised however, support state beliefs remained very high until the gait cycle was broken.

The right foot up event around the 2 second mark did produce a lower than expected left-support belief, and higher than expected belief in no support. This was quickly corrected when the right foot came down again and the network (correctly) resumed a strong belief in double support.

  

Figure 9.5: Support node beliefs from Support-3 network applied to normal walking data

   
Stumble-1 DBN

Figure 9.6 shows belief from the Stumble-1 network (Section 8.6) status node for the newest history slice, current and first two prediction slices. As expected for stable walking, the stumble state belief remains fairly small, especially for the three slices centred around the current slice. The stumble belief for the second prediction raised noticeably to a value around 0.2. This phenomenon was investigated by reviewing some sample slices from the network in the Netica application, as shown in Figure 9.7. It was discovered that the effects of growing uncertainty in the support and interval nodes in prediction slices resulted in the status belief also becoming less certain, tending towards an even distribution. Observation of this effect led to the development of the Stumble-2 network (Section 8.7).

  

Figure 9.6: Status beliefs from Stumble-1 network, applied to normal walking

  

Figure 9.7: Slices 12 to 16 (the current slice is 14) of the Stumble-1 network during processing of normal walking data, showing uncertainty in interval and support effecting stumble belief

   
Stumble-2 DBN

The result of redesigning the stumble-1 network into stumble-2 (Section 8.7) is shown in figure 9.8, showing a noticeable drop in the stumble belief from two slices ahead, implying a better prediction of stability.

  

Figure 9.8: Status beliefs from Stumble-2 network, applied to normal walking

Stumble-3 DBN

When applied to normal walking, the output of the stumble-3 DBN (Figure 9.9) shows clear recognition (through high beliefs) during walking phases and the intermediate stop. The right foot event around the 2 second mark no longer adversely effected the `stop' belief before walking started as in previous networks. After walking started, the network maintained a high certainty in the `walk' state (around 0.98).

  

Figure 9.9: Ambulation mode beliefs from stumble-3 DBN when applied to normal walking.

Tripping/stumbling

Figure 9.10 shows the signals from a `trip' recording, consisting of 10 steps containing a stumble, stop turn and another 10 steps containing another stumble. A stumble was simulated by leaning forward while walking and performing a correctional step (Section 2.3.2). The stumble events occurred in recordings around the 6 and 14 second marks.

  

Figure 9.10: Trip test pressure and accelerometer signals

   
Support-1b DBN

The results of support-1b in Figure 9.11 show high beliefs in Support=none around the trip events, as a result of stepping strategy involving toe instead of heel strikes. It was noticed that the network also became confused by multiple foot-down without any foot-up events around the 10 second mark.

  

Figure 9.11: Beliefs from Support-1b applied to tripping data

   
Stumble-1 DBN

As seen in Figure 9.12, the stumble-1 network manages to recognise the two trip events, signified by large peaks in the stumble state belief. As in previous stumble-1 results, the network still suffers from uncertainty in the newer prediction slices.

9.12 Obvious peaks around stumble events

  

Figure 9.12: Status beliefs from Stumble-1 network, applied to tripping data

Stumble-2 DBN

Figure 9.13 produced obvious peaks in stumble beliefs for the trip events, not only in the current slices, but well into the prediction slices. Again this highlights the success of the network's forwarding node and Interval node link (Section 8.7).

 

  

Figure 9.13: Status beliefs from Stumble-2 network, applied to tripping data

Stumble-3 DBN

As shown in Figure 9.14, the stumble-3 network successfully recognised the difference between walking, trip events, and stopping with high certainty. Although suffering from some early confusion due to initial evidence, this was not as pronounced as in previous network's results. Notice that the trip events cause the network to momentarily raise its belief in running, which is soon replaced with a high `stumble' belief.

  

Figure 9.14: Ambulation mode beliefs from stumble-3 network when applied to trip data

   
Missing data

This trial was used to test the DBN models' handling of missing and incorrect data. The data presented in Figure 9.15 was taken from recordings where pressure sensors produced lower than expected signals, resulting in feature extraction `missing' important ambulation (usually `foot-up') events. The right-toe signal was especially low, suggesting incorrect placement.

  

Figure 9.15: Normal walking pressure and accelerometer raw signals resulting in missing evidence

Support-1a DBN

The effect of `100%' certainty CPTs in shown in the support-1a network's results (Figure 9.16 - note that for clarity only the interval between 10 to 25 seconds is shown). When multiple left and right foot down events occur after the 16 second mark, the network becomes confused and cannot recover, resulting in high `none' and low `double' support beliefs for the next eight or so steps. These results prompted the changes implemented in the support-1b network (Section 8.2).

  

Figure 9.16: Support belief for support-1a network on data with missing evidence

Support-1b DBN

As shown in Figure 9.17, the small uncertainty introduced into the support-1b's CPTs (Section 8.2) produced a substantial improvement in results. After foot-up evidence begins to return around the 18 second mark, the network quickly recovers and returns to recognising the normal walking support cycle.

  

Figure 9.17: Support belief for support-1b network on data producing missing evidence

   
Support-1c DBN

Figure 9.18 shows the results from applying the support-1c network (Section 8.3) to the missing data while expanding the network twice for each evidence entry. As in for the support-1b network, this network easily recovered from the missing data. However, these results seem to show an unusually high belief in the `none' support which did not occur in previous networks. This suggested the introduction of the `none' state and application of double network expansion had some negative side-effects.

  

Figure 9.18: Support-1c beliefs for normal walking with incorrect or missing data, expanding DBN two slices per observation.

   
Jogging/running

Figure 9.19 shows the pressure transducer signals from a slow-jogging recording^9.1. The effect of this ambulation mode can be seen as smaller intervals between heel and toe pressure peaks, and the lack of overlap in left/right foot supports.

  

Figure 9.19: Pressure transducer (top) and piezoelectric (bottom) signals from jogging recording

Support-3 DBN

The support-3 DBN was applied to the jogging data to investigate its detection of the running/jogging gait cycle. As shown in Figure 9.20, it does detect alternating ``left, none, right, none...'' support sequence expected.

  

Figure 9.20: Beliefs from Support-3 support node when applied to jogging

Stumble-3 DBN

The stumble-3 DBN was applied to the jogging data to see if it could detect the mode of ambulation. As shown in Figure 9.21, it does achieve a high belief in the `running' state with a value around 0.6. Due to the network's assumption that running is less stable than walking, and that running produces small timer intervals, the `stumble' state belief was increased to around 0.4. When the signal was lost around the 10 second mark, the network momentarily believes the subject has `stopped' and then resumes its belief in running when the signal returns.

Very early evidence resulted in momentary uncertainty, and the right-foot event at the 2 second mark also resulted in a small peak in the `fall' belief. Despite the initial noise, the network produced what was considered very successful high-level recognition of the ambulation state, even moving through the `walk' state (around 4.5 second mark) before establishing a consistent belief in the `running' mode when jogging started up.

  

Figure 9.21: Mode beliefs from stumble-3 network when applied to jogging data