Post Training Evaluation

A set of criteria commonly used in control chart analysis is used to determine if the post- training data are out-of-control. If the data satisfies one of the five sets of criteria, then the process is deemed out-of-control, and the system is alarmed. The criterion includes (Stamatis, 2003).

1. A single point outside 3-sigma limits

2. At least seven consecutive points above (or below) the centerline 3. At least seven upward (or downward) consecutive changes

4. At least two of three consecutive points beyond two standard deviations from the centerline (where both are on the same side of the centerline)

5. At least four of five consecutive points beyond one standard deviation from the centerline (where all 4 are on the same side of the centerline)

Criteria 1 signals an immediate change in the measured parameter and further analysis and/or field inspection should be performed immediately. Criteria 2 and 3 signals a drift in the process average which may be a result from girder and/or deck deterioration. Further investigation is needed and recalculating the control limits may be required. Criteria 4 and 5 provide an early warning of a process shift. Note the probability of a false-positive detection for criteria 4 and 5 is about 2% (Stamatis, 2003).

3.7.2 The Runs Test

Another control chart technique to recognize important signals in a process is termed the Runs Test. A run is defined as a series of consecutive positive (or negative) values. The runs test checks whether the number of runs in a sample is about right for a random series. A long run in the distribution factor above or below the centerline would indicate an increase or decrease in the girder stiffness, respectively. The concept of the runs test is to base a

statistical test on the value of Z under the null hypothesis of randomness. For instance, if the absolute value of Z is greater than 1.96, then the null hypothesis of randomness is rejected at the 0.05 significance level (Stamatis, 2003).

For each truck group (i.e. average of five center truck events, ̅ ) a 1 is associated if ̅ > ̿ and 0 if ̅ < ̿. For example, a sequence of 0’s and 1’s may be 1, 0, 0, 0, 1, 1, 0, 0, and 1. A run is a consecutive sequence of 0’s or 1’s; As such, the given series has five runs. The runs test uses the following equations to determine whether five is about the right number of runs for a random series.

( )

( ) √

Where:

T = number of truck groups (total number of 0’s and 1’s) = number of truck groups above the mean (number of 1’s) = number of truck groups below the mean (number of 0’s) R = number of observed runs

If the value of Z is large and positive, then there are too many runs in the process. As a result, a zigzagging behavior would be observed in the control chart. Although the

zigzagging behavior causes a statistical concern, it likely does not indicate a stiffness change on the bridge as the parameters are neither increasing nor decreasing. If the Z value is large and negative, there are fewer runs than expected under the null hypothesis of randomness. This condition is of greater concern as fewer runs implies the average girder DF or NA is either increasing or decreasing. Therefore, girders with a large negative Z value will require further investigation.

3.7.3 Post Training Data

For demonstration, 80 center truck events (i.e.16 truck groups) of post-training data were evaluated using the control criterion and the Runs Test. The first 40 center events represent the normal behavior of the bridge and the last 40 events represent a change in the transverse stiffness of the bridge. Specifically, the transverse stiffness of the bridge was altered by removing the midspan cross bracings attached to Girder 3. The DF control chart for all 80 center truck events is illustrated in Figure 22 and the control chart criterion and runs test results are presented in Table 6. The UCLs and LCLs established during the training period are shown in red and ̿ are shown in green (Figure 22). Furthermore, zones A, B, and C represent the limits based on 1-sigma, 2-sigma, and 3-sigma, respectively. As expected, the first 40 events suggest the process is in-control, providing no indication of a change in structural integrity.

It should be noted that false-positive data points occasionally occur even when no change in the process has occurred (i.e. no change in bridge behavior). As a result, the number of false-positive data points is monitored. The limits on the process may need to be changed if false-positive data points occur more frequently when no change in the bridge behavior is assured.

Figure 22: 80 Center Truck Events during Post Training

Table 6: Post-Training Output G1 (DF) G2 (DF/NA) G3 (DF/NA) G4 (DF/NA) G5 (DF/NA) G6 (DF)

_{Runs Test Z-value -0.70 0 / -1.44 0.33 / 0.58 -2.57/1.03 -0.53/-0.76 1.0}

C

ri

ter

ia

1 N Y/N Y/N Y/N N/N N

2 N N/N Y/N Y/N N/N N

3 N N/N N/N N/N N/N N

4 N N/N Y/N Y/N N/N N

5 N N/N Y/N Y/N N/N N

The data from the last 40 events suggest an obvious shift in the process particularly in Girders 3 and 4. The data suggests the DFs for Girders 3 and 4 satisfy 4 of the 5 control chart criterion, indicating the process is out-of-control. The absolute value of the Z-value in Girders 4 is greater than 1.96; therefore, the null hypothesis of randomness is rejected at the 0.05 significance level. The Z-value of -2.57 is large and negative, implying there are fewer runs in the process than expected. An interesting observation is that the Runs Test did not result in a significant Z-value for Girder 3 when an obvious shift in the process is clearly present and nonrandom behavior exists. The error is due to a relative small number of truck groups (i.e. 16). The Runs Test assumes the distribution of the number of runs (R) is

approximately normal when the number of truck groups (T) is large. Further, it is recommend the number of sampled truck groups should be larger than 20 (Stamatis, 2003). As a result, in the future the Runs Test will only be applied to a large sample of truck groups. Finally, the NA data did not indicate an out-of-control process. This is expected as the transverse stiffness alteration should not, theoretically, change the neutral axis position.

Removing the cross bracings connected to Girder 3 had an interesting effect on the lateral load distribution. The data shows the DF in Girder 4 increases while the DF in Girder 3 decreases. However, an increase in the Girder 3 DF is expected as removing the cross bracing should reduce the lateral load distribution to the surrounding girders. On-going bridge testing is being performed to further investigate this unusual behavior. Errors in constructing the bridge or the variable properties of timber may be an explanation for the observed behavior. Although the shift in DF cannot currently be explained, the SHM system was able to observe the unusual behavior, thus leading to further investigation.