Phương pháp giải bài toán ngược không xác suất với sự xem xét mối liên hệ cho việc xác định tham số cấu trúc

Structural and Multidisciplinary Optimization - Tập 64 - Trang 1327-1342 - 2021
Heng Ouyang1,2, Jie Liu1, Xu Han2, Bingyu Ni1, Guirong Liu3, Yixin Lin3
1State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha, People’s Republic of China
2State Key Laboratory of Reliability and Intelligence of Electrical Equipment, School of Mechanical Engineering, Hebei University of Technology, Tianjin, People’s Republic of China
3Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, USA

Tóm tắt

Bài báo này trình bày một chiến lược hiệu quả về khoảng thời gian và mối tương quan ngược cho bài toán ngược không chắc chắn, nhằm xác định đồng thời các bất định và mối tương quan không xác suất của các tham số cấu trúc. Đầu tiên, một mô hình lồi elip được áp dụng để định lượng biên độ bất định của các phản hồi đo được với các mẫu hạn chế. Sau đó, bài toán ngược không chắc chắn dựa trên mô hình lồi elip được phân tách thành bài toán ngược khoảng và bài toán ngược mối tương quan. Đối với bài toán ngược khoảng, một phương pháp phân tích phân đoạn con bị hạn chế bởi mô hình lồi elip được phát triển để đánh giá các khoảng của các phản hồi cấu trúc với chi phí tính toán thấp. Đối với bài toán ngược mối tương quan, các phương trình lan truyền mối tương quan được đưa ra để tính toán ma trận hệ số tương quan không xác suất của các phản hồi cấu trúc. Sau đó, bằng cách sử dụng các thuật toán tối ưu hóa để tuần hoàn giảm thiểu sai số của các khoảng và các hệ số tương quan giữa các phản hồi đo được và các phản hồi cấu trúc đã tính toán, các khoảng và ma trận hệ số tương quan không xác suất của các tham số cấu trúc được xác định hiệu quả, và một mô hình lồi elip của các tham số cấu trúc có thể được thiết lập cuối cùng. Hai ví dụ số và một ví dụ thực nghiệm được nghiên cứu để xác minh tính hiệu quả và độ chính xác của chiến lược ngược khoảng và mối tương quan theo chuỗi được đề xuất.

Từ khóa


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