## 4 Results and Discussion
### Average and Weighted Average Entropy  
Rather than measuring and summing the individual disorders from each AE signal with _instantaneous entropy, the average entropy_ and _weighted average entropy_ estimate the true AE voltage distribution by continuously updating the distribution as new AE signals are received. Average entropy weighs all AE signal distributions evenly, while weighted average entropy weighs voltage distributions based on signal arrival time. Because these two methods of deriving entropy are found from a continuously updated distribution that utilizes all currently received AE signals, it is not logical to view these entropies in cumulative forms. Instead, they should be plotted in their singular forms where the value at fracture is not expected to be consistent between experiments. Average and weighted average entropy are meant to estimate the current distribution of possible AE voltage values. If significant and unique microstructural damage occurs within the structure, then it is expected that AE signals with large voltage amplitudes will be received, and therefore the probability distribution will become wider. In contrast, when small microstructural damages occur and emit small amplitude AE signals, the estimated voltage distribution will become thinner and concentrate at 0 volts. The trend of average and weighted average entropy can be predicted based on this logic. First, signals received prior to and during crack initiation are assumed to be infrequent due to dislocation pile up [25] and have high disorder from the sudden release of energy when dislocations break away [18]. AE signals are received from numerous locations around the notch, because a crack has not yet initiated and the exact location of crack initiation is uncertain. Therefore, it is hypothesized that the entropies prior to crack initiation will be relatively high-valued and sporadic due to the high energy and inconsistent AE sources. High energy signals are even evident in the first few fatigue cycles as the pristine specimens are stressed for the first time. After a crack begins to initiate, previous work suggests sudden bursts of low amplitude AE signals due to micro-cleavage [25] or due to wave reflections at the extended crack boundary [14] will then be received. It is believed that these frequent and low-disordered AE waveforms are emitted from the particular microcrack leading to macrocrack initiation, rather than from multiple potential crack initiation sources. Thus, the entropy trends are believed to decrease as a crack initiates and begins to grow. Finally, high amplitude AE signals are expected once the crack propagates to a critical length and causes fracture. In turn, entropies will then increase near fracture. Only slight differences between average and weighted average entropy are expected where weighted average entropy would have a more irregular trend than average entropy. The purpose of proposing both average and weighted average entropy is to introduce two possible methods of estimating entropy from an AE signal while considering AE signals received prior to the current signal. Results validate the hypothesized entropy trends. The average and weighted average entropies for over the first 500 fatigue cycles are plotted against cycles in Figures 11a and 12a, respectively. The entropies vary for the first few signals because the voltage distribution is not yet inertial and  
Figure 10: Deviation factor for AE counts, energy, and instantaneous entropy for all experiments. heavily dependent on these first initial signal distributions. To more clearly see the variation in average and weighted average entropies at the beginning of cyclic fatigue, Figures 11b and 12b show the entropies for the AE signals versus hit count. The average and weighted average entropies are then plotted against cycles until both a measured 1-mm crack and fracture occur in Figures 13 and 14.