### Information Entropy of Individual AE Waveforms  
The disorder of AE signals with information entropy can be estimated through several different methods. All of the methods developed in this work have one commonality: a probability distribution is formed based on voltage readings in individual AE waveforms. Again, this compares to the AE features such as counts and energy that are acquisition system outputs and which summarize AE waveforms. Because information entropy is a measure of uncertainty about a random variable's value as described by its probability distribution, the AE information entropy can directly reflect microstructural changes. This idea is exemplified in Figure 2, which depicts three independent AE signals, their waveforms, and voltage distributions. One can infer that Signal A is caused by a less significant microstructural change compared to Signal B and Signal C. As such, the voltage distribution can be formed and the information entropy of these distributions can be calculated based on Equation (1). Thus, it is evident that an AE signal believed to reflect a larger microstructural change will have a greater entropy value. It must be noticed that the shape and characteristics of the AE signals varies depending on the degradation stage of the experiment. In order to visualize the change in the shape of the acoustic  
Figure 2: Waveforms, voltage distributions, and information entropy values for three AE (acoustic emission) signals: (**a**) Signal A captured during relatively little microstructural change; (**b**) Signal B captured during a moderate microstructural change; and (**c**) Signal C captured during a relatively significant microstructural change. emission signals, six signals are demonstrated in Figure 3. Figure 3a depicts the first two signals that are measured in the test S1 (we call experiments 1-8 as S1-8). These two signals are measured during the deformation of the sample. The next two signals that are demonstrated in Figure 3b correspond to the instant of crack initiation in the test S2. It has been observed that such signals have a sharp peak comparing to the Figure 3a. The signals received in the beginning of the test and instant of crack initiation are burst type signal. However, continuous types of emissions are measured at the time of fracture of the specimen, which is depicted in Figure 3c. The last two acoustic emission signals are measured in the course of the fatigue test, S2. There are two general steps for estimating information entropy from AE signals regardless of the method. A probability distribution of the random variable describing the AE signals must first  
Figure 3: Representative AE waveforms at various instances during the S2 experiment: (**a**) two signals measured in the beginning of the S2 test; (**b**) two signals measured in the instant of crack initiation in the S2 test; and (**c**) two signals measured at instant of complete fracture of the specimen in S2 test. be formed, and then the amount of disorder exhibited by the distribution via Equation (1) must be quantified. In this case, the chosen random variable is the signal amplitude expressed in units of voltage where the AE voltage probability distribution represents the microstructural disorder, and the distribution is evolving as fatigue damage progresses. During the early part of a fatigue experiment, the \"true\" AE voltage probability distribution is completely unknown until a first AE signal is recorded. Let this AE signal be described by its 2048 voltage readings, which are 2048 samples from the current underlying voltage probability distribution. Because the true AE voltage probability distribution is unknown, an imprecise distribution is estimated from these 2048 voltage values. The disorder of this distribution is then quantified by Equation (1). When a second AE signal is received, the new set of 2048 voltage values provides new information about the voltage probability distribution and needs to be considered.