# WORK Crack P Code Matlab 22

There have been several attempts for automation of the eggshell crack detection process with the aid of computer vision systems, but these are very costly, and their reliability is questionable. Nevertheless, the pressure of the industry has led to creative solutions, such as the one described in a patent [4], which is able to detect microcracks but also requires a pressurized chamber of alternating pressures and, therefore, is expensive and difficult to implement. This shows the difficulties faced when high precision is a factor to consider. Classification of cracked eggs with computer vision systems has proven to be difficult: Wu et al. [5] managed to achieve only 93% validated correct classification using soft-margin support vector machine (SVM) classification.

## crack p code matlab 22

In case inequality is a valid assumption, the difference between the spectra of the intact and cracked eggs should be captured in the principal components from principal component analysis (PCA). This can be easily verified by plotting the diagonal (containing the column variances) of the covariance matrix corresponding to the coefficients of the components with the highest variance explanation power (component number one) against the original variables for the two groups. Different covariance matrices manifest in different loading (coefficient) patterns, as shown in Figure 1 (for laid down position only).

The classification method proposed in this paper, based on acoustic excitation and FFT analysis of the eggs, was purposely tested against cracks that are very difficult and, in some cases, impossible to detect by candling. The 2.1% total misclassification and 0.87% false positive error rate achieved by our method, compared to many published in this field, are validated and are among the best-validated results found in the literature, showing promise for industrial application.

For classification, a range of techniques were tested, including linear and nonlinear prediction methods: KNN, SVM, decision trees, LDA and QDA. Among the metrics for performance were the total number of misclassifications, the number of false positives for cracked eggs (as the most important aspect in the industry) and the speed of classification for new independent samples, which obviously depends greatly on the computer used for estimation but is a good basis for comparison between different methods.

Structural health monitoring (SHM) techniques often require a large number of sensors to evaluate and monitor the structural health. In this paper, we propose a deep neural network (DNN)-based SHM method for accurate crack detection and localization in real time using a small number of strain gauge sensors and confirm its feasibility based on experimental data. The proposed method combines a DNN model with principal component analysis (PCA) to predict the strain field based on the local strains measured by strain gauge sensors located rather sparsely. We demonstrate the potential of the proposed technique via a cyclic 4-point bending test performed on a composite material specimen without cracks and seven specimens with different lengths of cracks. A dataset containing local strains measured with 12 strain gauge sensors and strain field measured with a digital image correlation (DIC) device was prepared. The strain field dataset from DIC is converted to a smaller dimension latent space with a few eigen basis via PCA, and a DNN model is trained to predict principal component values of each image with 12 strain gauge sensor measurements as input. The proposed method turns out to accurately predict the strain field for all specimens considered in the study.

Strain is a direct indicator of stress associated with damage. Hence, strain-based SHM, as realized through strain measurements using strain gauge sensors or fiber optic sensors, has gained increasing popularity as a reliable method for real-time strain measurements. In addition, because cracks are an important feature for determining the damage condition of structures, strain-based crack monitoring techniques for crack detection provide a qualitative indication of the presence of cracks and enable their localization. These techniques are already in use for SHM approaches in the aerospace industry and have been extensively researched in the last 2 decades. Ramdane et al. theoretically and experimentally investigated the identification of crack positions, inclinations, and lengths, as well as the magnitudes of external loading based on data from 8 to 12 strain gauges distributed along the edges of a rectangular plate by using the concept of distributed dislocations in conjunction with a genetic algorithm (GA)18,19. Haim et al. investigated the detection of straight cracks, circular holes, and holes with arbitrary shapes based on strain measurement sensors by using the extended finite element method and genetic algorithms (GA)20,21. Liang et al. investigated the identification of holes and cracks in composite plates for multiple static loading modes by using strain gauge sensors and a nonlinear optimization program that applied the boundary element method and genetic algorithm22. Yong et al. proposed a crack detection and localization method for elastic structures that combined a rectangular strain rosette structure with three fiber Bragg gratings (FBGs), body force method, and an improved particle swarm optimization (PSO) algorithm23.

Thus, previous strain-based SHM studies applied optimization algorithms such as GA and PSO, using a small number of strain gauge sensors or FBG sensors to identify the crack detection and localization of structures. In this case, the crack damage cannot be monitored in real time because the optimization algorithm requires a large number of iterations to converge to the actual crack location and length. If the crack damage is not discovered and repaired in time, the service life of the structure will be reduced and the maintenance cost will increase. Therefore, real-time detection and localization of crack damage is an important requirement.

In this paper, we propose a machine learning-based method for accurately detecting and localizing cracks in real time using a small number of strain gauge sensors. The feasibility of the approach was verified based on experimental data. Because stress concentration occurs at the crack tip, it is possible to detect the cracks, determine their position and length, and monitor their growth through real-time strain field analysis. For specimens without damage and specimens with various types of damage, a dataset of local strains measured with 12 strain gauge sensors and their corresponding strain field maps over a wide domain measured with digital image correlation (DIC) devices were used to train and evaluate the DNN model performance. The high dimensional strain field map (14 \(\times\) 12 pixel image) is compressed into a smaller dimension latent space via PCA to reduce the output dimension for the DNN . The trained DNN takes the 12 strain gauge measurements as input and accurately predict the strain field map over a wide domain. The feasibility of the proposed method is demonstrated for real-time SHM for cyclic 4-point bending test.

Figure 1 shows the real-time crack-damage monitoring system, which predicts the strain field through a machine learning model with a small number of strain gauge sensors. The target monitoring structure is an aircraft.When the aircraft is on the ground, resting on its landing gear, the force of gravity attempts to bend the wing downward. An aircraft in flight experiences a bending force on its wing as an aerodynamic lift attempts to raise the wing24. Therefore, the aircraft wing is subjected to cyclic bending moment. We prepared a dataset consisting of local strains measured with 12 strain gauges and strain field measured with the DIC device for one specimen without damage (Healthy) and seven specimens with various lengths of edge cracks (Damaged) under a cyclic bending moment. The specimen was made of a composite material laminated carbon fiber-reinforced plastic (CFRP) generally used in aircraft25. To preprocess the strain field, we represented all the strain field map from DIC in 168 dimensions (14 \(\times\) 12 pixel image) and reduced them to eight dimensions (referred to as eight principal component values, hereafter) by employing PCA26,27. The dimensionality reduction process is important for reducing the computational time and enhancing the training accuracy of DNN. Finally, the DNN model used the local strains measured with the 12 strain gauge sensors as input and predicted the eight principal component values. The DNN model prediction was transformed back into a regular strain field. By analyzing the predicted strain field, the feasibility of real-time monitoring of crack detection and localization was verified.

In Fig. 3a, the usage of singular values up to \(\sigma _1\), \(\sigma _2\), and \(\sigma _8\) (n = 1, 2, and 8) have cumulative explained variances of 93%, 95%, and 97%, respectively. Figure 3b shows the strain measured at subsets 73, 79, and 84 in the specimen with an edge crack length of 15 mm for the three singular values. Although the difference in the cumulative explained variance ratio was not large among them, significant error in strain estimation occurs at the pixels closer the closer the crack. Figure 3c shows the actual strain field from DIC and approximated strain field in the specimen with a crack length of 15 mm when the displacement load was 20 mm, which clearly shows that the improvement of strain field estimation with more singular values. Because stress concentration occurred at the crack tip, the position of maximum strain occurrence was considered as the crack tip. For precise crack localization, the position of maximum strain in the approximated strain field should correspond to the actual point of maximum strain. Figure 3d shows a comparison of the actual points of maximum strain for five specimens with a crack length of 15 mm and the approximated point of maximum strain for n = 2 and n = 8. The singular value was selected as 8 because the position of occurrence of maximum strain and strain distribution in the approximated strain field were close to the actual values. Thus, we converted the 168-dimensional strain field image from the DIC into 8-principal component values which allows us to more efficient train a DNN model.