Một kỹ thuật bề mặt phản ứng hiệu quả để tính độ nhạy trong phân tích độ tin cậy kết cấu=An efficient response surface technique for sensitivity estimation in structural reliability analysis

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Tác giả: Minh Quang Châu

Ngôn ngữ: vie

Ký hiệu phân loại:

Thông tin xuất bản: Khoa học và Công nghệ (ĐH Công nghiệp TP. HCM), 2024

Mô tả vật lý: tr.69-80

Bộ sưu tập: Metadata

ID: 245026

Thêm vào giỏ

Phương pháp RSM là một phương pháp có độ tin cậy về kết cấu mạnh mẽ sử dụng các giá trị của hàm tại các điểm cụ thể gần đúng với hàm trạng thái giới hạn bằng biểu thức đa thức. Hàm phân tích thay thế hàm trạng thái giới hạn chính xác mà thời gian tính toán cần thiết để đánh giá độ tin cậy của hệ kết cấu có thể giảm đáng kể. Tuy nhiên, vị trí của các điểm mẫu đã được một số tác giả nghiên cứu và hiệu quả của phương pháp bề mặt đáp ứng vẫn đang được thảo luận. Vì vậy, nghiên cứu này đề xuất một phương pháp bề mặt đáp ứng mới để tính độ nhạy của các tham số trong phân tích độ tin cậy kết cấu. Đa thức thứ nhất không có số hạng chéo được sử dụng để tính gần đúng hàm trạng thái giới hạn và có thể thu được vectơ độ nhạy của hàm trạng thái giới hạn. Thiết kế thực nghiệm với 4n+1 điểm lấy mẫu bao gồm 2n+1 điểm lấy mẫu được chọn dọc theo các trục tọa độ trong không gian U của các biến ngẫu nhiên chuẩn, như trong mô hình RSM cổ điển và 2n điểm lấy mẫu được quay theo vectơ độ nhạy của hàm trạng thái giới hạn được xây dựng. Một đa thức bậc hai được sử dụng để tính gần đúng hàm trạng thái giới hạn và có thể thu được điểm có xác suất lớn nhất (MPP) bằng cách tiến hành thuật toán HL-RF dựa trên RS đã tạo. Để cải thiện hơn nữa độ chính xác của phân tích độ tin cậy, Mô phỏng Monte Carlo (MCS) được tiến hành trên đa thức đã thiết lập để tính xác suất thất bại. Các mô hình số được xét để chứng minh những ưu điểm của phương pháp được đề xuất.The response surface method (RSM) is a powerful structural reliability method using the values of the function at specific points that approximates the limit state function with a polynomial expression. The analytical function replaces the exact limit state function which the computational time required for the assessment of the reliability of structural systems can be reduced significantly. However, the location of the sample points has been investigated by several authors and the performance of the response surface method is still under discussion. Therefore, this study proposes a new response surface method for sensitivity estimation of parameters in structural reliability analysis. A first oder polynomial without cross terms is adopted to approximate the limit-state function, and the sensitivity vector of the limit state function can be obtained. A experimental design with 4n+1 sampling points includes 2n+1 sampling points are chosen along the coordinate axes of the U-space of standard normal random variables, as in the classic RSM and 2n sampling points is rotated according to the sensitivity vector of the limit state function is built. A quadratic polynomial is adopted to approximate the limit-state function, and the most probable point (MPP) can be obtained by conducting the Hasofer-Lind-Rackwitz-Fiessler (HL-RF) algorithm based on the created response surface (RS). To further improve the precision of reliability analysis, Monte Carlo Simulation (MCS) is conducted on the established polynomial to compute the probability of failure. Three numerical examples are considered to demonstrate the advantages of the proposed method.

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