2.3.2. Random Sample Consensus (RANSAC) Algorithm

The RANSAC algorithm based on the iterative method was proposed by Fischler [22] to solve the problem of inaccurate solutions when using the least squares model on sample data with a large proportion of outliers. Song used the improved RANSAC algorithm to eliminate errors caused by high-temperature heat wave disturbances in DIC measurement [23]. This algorithm is able to classify data points as outliers or inliers and fit the mathematical model through inliers while ignoring outliers. The basic algorithm is summarized as follows:


The number of iterations *K* should be large enough to ensure that the probability *p* of at least one set of random samples not including outliers is greater than 0.99. Assuming that the probability that the data is selected as an inlier is *a*, then *b* = 1 − *a* is the probability of observing an outlier. The required number of iterations of the minimum number of points, denoted *k*, is calculated using the following function: −

$$1 - p = (1 - a^k)^K \tag{6}$$

$$K = \frac{\log(1 - p)}{\log(1 - \left(1 - b\right)^k)}\tag{7}$$

Figure 6 shows that the RANSAC algorithm classifies the thickness strain data into inlier points and outlier points. The blue point set represent the inlier points, and the red circles represent the outlier point set. Using this method, the outlier points, or noisy data, can be ignored during fitting. The result of the RANSAC algorithm fitting is shown in Figure 7. It can be seen that the red fitting curve is fitted with inlier points as the data set. Compared with the least squares algorithm, it is hardly affected by noise in the data. This indicates that the RANSAC algorithm is effective and has important significance for the subsequent R-value calculation.

**Figure 6.** Thickness strain data is classified inlier and outlier.

**Figure 7.** Fitting curve by RANSAC algorithm.

#### **3. DP980 R-Value Determination**

In this section, the R-value calculation method is reviewed first, followed by a discussion of the experimental setup and process. The composite material DP980 was used as the experimental sample. Finally, the experimental results are analyzed and discussed.
