2022 年 63 巻 2 号 p. 257-260
In this study, the mechanical properties of aluminum foam were classified by machine learning from their X-ray computed tomography (CT) images. It was found that aluminum foam samples with high and low compressive strengths can be classified with an accuracy rate of more than 95%. In addition, it was indicated that the accuracy rate can be further improved by increasing the amount of training data. From these results, it is expected that the quality assurance method of aluminum foam can be established by nondestructively acquiring the images of the manufactured aluminum foam product.
Fig. 4 Accuracy rate for each combination in (a) Case 1 and (b) Case 2.
Aluminum (Al) foam is a multifunctional material with both light weight and high shock absorption properties. It is known that the mechanical properties of Al foam, such as Young’s modulus and plateau stress, are greatly affected by porosity (volume fraction of pores),1,2) in addition to the pore diameter and arrangement.3–6) However, it is difficult to evaluate how each pore structure affects the mechanical properties of Al foam. In particular, the Al foam produced by the casting7,8) or precursor9,10) method undergo a foaming process in which it is slightly difficult to control the pore structures. Thus, there are some variations in the mechanical properties of the obtained Al foam. Therefore, a quality assurance method for manufactured Al foam products is required. It is desirable to evaluate whether the manufactured product meets the intended mechanical properties from the images obtained by nondestructive inspection.
Recently, machine learning has been attracting much attention as a method of evaluating the characteristics of the products using a large amount of their image data.11–13) Attempts have begun in the field of material science to evaluate the characteristics of target materials from metallurgical images. There are some studies related to the classification of microstructures by machine learning. In such studies, some specific microstructural features were extracted from microstructure images, and the extracted features were used as the input data of machine learning for classification.14–17) In another study, the mechanical properties were predicted from the extracted features of microstructures, crystallographic texture, and material genomes by machine learning.18–20) In those studies, feature quantities were first extracted from the images and then used as input data in the subsequent machine learning.
There are a few examples of applying machine learning related to foam. Some researchers predicted the compressive strength of foamed concrete by machine learning. In this prediction, input parameters, such as cement content, density, water-to-binder ratio, and sand-to-cement ratio, were used.21,22) For polystyrene foam, strain energy absorption was estimated by machine learning using input parameters, such as density and compressive loading rate.23) Also, the compression response of 3D-printed foam was predicted using an artificial neural network. In this prediction, features such as filament size, the number of layers, and filament spacing were used as input data.24)
However, little research has been carried out in estimating the characteristics using the images of foam as input data. If the characteristics can be estimated directly from the images of foam, feature extraction will be unnecessary, and a quality assurance method for nondestructively acquiring the images of the manufactured product can be established.
In this study, we investigated whether Al foam samples with high and low compressive strengths can be classified by machine learning from their X-ray computed tomography (CT) images without extracting specific features.
In this study, we used three Al foam samples with high compressive strength (Group A) and three Al foam samples with low compressive strength (Group B). There is a clear difference in strength between Al foam samples in Group A and those in Group B, as shown by the compressive stress–strain curves in Fig. 1. Note that A-I, A-II, etc. in Fig. 1 corresponds to three-dimensional X-ray CT images of Al-foam shown in Fig. 3 described below. The porosity, p, which was obtained from the measured weight and dimensions of the specimen was also shown in Fig. 1. The details such as the fabrication method and X-ray CT inspection of the Al foam samples are described in Ref. 25). Briefly, the Al foam samples were prepared by the friction stir welding route precursor method26–29) from Al–Si–Cu based Al alloy ADC12 die-casting plates. No foaming agent was used, and only the gas introduced during the die casting process was used for foaming. The compressive strength of Al foam was changed by varying the amount of foaming by adjusting the amount of gas contained. After the precursor was foamed by heat treatment, a compression test specimen of a cube with a side of 15 mm for Group A and a cube with a side of 20 mm for Group B was cut out from the foamed sample. Since the amount of foaming of Al foam in Group A was small, a large compression test specimen cannot be obtained, and the compression test specimens were smaller than those in Group B. Before performing the compression test, each Al foam sample was subjected to microfocus X-ray CT inspection to obtain the images of pore structures of the entire sample. The actual compression test was performed at a strain rate of 4.2 × 10−3 s−1 in accordance with Japanese Industrial Standards.30)
Stress–strain curves of Al foam samples used.
Figure 2 shows photographs of the surface pores of the actual compression test specimens in Group A and Group B, and the corresponding X-ray CT cross-sectional images. In the X-ray CT cross-sectional images, the white part is Al and the gray part is the pores. The input image data of Al foam samples were prepared as follows. First, the resolution of the X-ray CT images was adjusted so that the number of pixels per 1 mm was 17. The resolution of the X-ray CT cross-sectional images was different for each sample; therefore, it was adjusted to the lowest image among the samples used in this study. Next, the obtained X-ray CT cross-sectional images were laminated to reconstruct a three-dimensional image. Then, an image of a cube with a side of 13 mm and 221 pixels was extracted from the reconstructed three-dimensional image.
Photographs of Al foam compression test specimens of (a) Group A and (b) Group B. (c) and (d) X-ray CT cross-sectional images corresponding to (a) and (b), respectively.
Figure 3 shows three-dimensional images extracted into a cube shape with a side of 13 mm for all the samples used in this study. The z direction indicates the observation direction of X-ray CT cross-sectional images in Fig. 2. It can be observed that Al foam samples in Group B have more pores and a higher porosity than those in Group A. However, as shown by arrows, dense parts and coarsened pores can be observed, and slight variations in shape can be observed.
Reconstructed three-dimensional X-ray CT images of Al foam samples used.
Machine learning was carried out using Mathematica (Version 12.2). Two types of training dataset were prepared (see Table 1). One was the set of x-y cross-sectional (horizontal cross-sectional) images acquired from the three-dimensional image (Case 1). The other was that of the x-y cross-sectional images as well as y-z cross-sectional and z-x cross-sectional images acquired from the three-dimensional image (Case 2). For each cross section, 221 images were obtained from each sample. That is, for Case 1, 221 x-y cross-sectional images were used for each sample, and for Case 2, a total of 663 images were used for each sample (i.e., 221 images for each cross section). The test was performed on 221 x-y cross-sectional images for both Case 1 and 2. Two samples from Group A and two samples from Group B (a total of four samples) were used for training. The remaining one sample for each group was used for the test. This was carried out for all combinations, and the accuracy rate for each combination was calculated. For example, samples Group A-II and -III and Group B-ii and -iii were all used in training, and samples Group A-I and Group B-i were used in the test (such a combination will be referred to as Sample I-i, etc., based on the test sample number, hereinafter).
The “Classify” function of Mathematica was used for training. Logistic Regression was used for the classification, and the quasi-Newton method was used for the optimization. This is because the learning efficiency was the highest in the preliminary trial. The “Classifier Measurements” function was used for the test.
Figure 4(a) shows the accuracy rate for each combination in Case 1. The accuracy rate was the ratio of the number of images in test dataset that could be classified among a total of 442 images (221 images each for Group A and Group B used in the test dataset). That is, the ratio of (“number of the images in Group A test dataset, those classified as Group A” + “number of the images in Group B test dataset, those classified as Group B”) to (“221 images in Group A test dataset” + “221 images in Group B test dataset”). The average accuracy rate of all combinations was 95.1%, but there was a variation ranging from 83.7% to 100% for each combination. This is considered to be due to the small amount of X-ray CT image data for the training.
Accuracy rate for each combination in (a) Case 1 and (b) Case 2.
Figure 4(b) shows the accuracy rate for each combination in Case 2. The average accuracy rate of all combinations was 97.9%, which was improved compared with that in Case 1. In addition, the variation decreased to a range from 94.8% to 100%. Therefore, it was found that the accuracy rate could be further improved by increasing the amount of training data.
These results suggest that machine learning can classify Al foam samples with different mechanical properties using only images.
In this study, we investigated whether Al foam samples with high and low compressive strengths can be classified by machine learning using their X-ray computed tomography (CT) images. The following conclusions were obtained from the experimental results:
This work was financially supported partly by Light Metal Education Foundation and Gunma University Center for Mathematics and Data Science.
