Tính chất của hình ảnh môi trường xốp tổng hợp thông qua phân tích phân mảnh và đa phân mảnh

Springer Science and Business Media LLC - Tập 14 - Trang 1-29 - 2023
Pablo Pavón-Domínguez1,2, Marina Díaz-Jiménez1
1Department of Mechanical Engineering and Industrial Design, University of Cádiz, Cádiz, Spain
2Graphical Methods, Optimization and Learning (GOAL) TIC-259 Research Group, Cádiz, Spain

Tóm tắt

Phân tích phân mảnh và đa phân mảnh của các hình ảnh môi trường xốp cho phép mô tả các môi trường xốp thông qua một sự hiểu biết không phụ thuộc vào tỷ lệ. Đã có nhiều công trình nghiên cứu sử dụng những kỹ thuật phân tích này để mô tả một sự đa dạng lớn của các môi trường xốp thực tế. Tuy nhiên, những nghiên cứu này thường mang tính so sánh, khiến việc phân biệt vai trò của kích thước lỗ và phân bố lỗ trong kết quả của phân tích phân mảnh và đa phân mảnh trở nên khó khăn. Công trình này phát triển một nghiên cứu sâu sắc về các môi trường xốp tổng hợp khác nhau từ một góc độ phân mảnh và đa phân mảnh, trong đó cả kích thước lỗ và sự phân bố của nó trong môi trường đều được tham số hóa. Do đó, một tập hợp các hình ảnh nhị phân tổng hợp đã được tạo ra, thu được những cấu trúc xác định và ngẫu nhiên với các kích thước lỗ cố định khác nhau, cũng như với các tỷ lệ kích thước lỗ khác nhau. Lacunarity cũng được tính toán để hoàn thiện phân tích đã đề cập. Kết quả cho thấy rằng chiều phân mảnh tăng lên theo kích thước lỗ và cao hơn khi sự phân bố lỗ tuân theo phân bố ngẫu nhiên so với phân bố xác định. Tuy nhiên, khi kích thước lỗ rất lớn, chiều phân mảnh tương tự nhau bất kể sự phân bố lỗ. Từ góc độ đa phân mảnh, kích thước lỗ có mối tương quan âm với mức độ đa phân mảnh. Trên thực tế, trong các hình ảnh có sự pha trộn của các kích thước lỗ khác nhau, cũng tìm thấy rằng tỷ lệ của các lỗ nhỏ càng lớn thì mức độ đa phân mảnh càng cao. Ngược lại, khi tỷ lệ của các lỗ lớn có độ quan trọng, mức độ đa phân mảnh cũng tăng lên do sự hợp nhất của các macro-lỗ.

Từ khóa

#phân tích fractal #phân tích multifractal #môi trường xốp #cấu trúc xốp #lacunarity #kích thước lỗ #phân bố lỗ

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