基於多目標拓樸優化與熵權法於船舶桅杆結構之優化與設計

Abstract

在船舶桅杆結構設計中，通常依賴設計者的經驗來進行設計，然而，這種方式不僅耗時，且設計出的結構未必符合實際應用之需求。為此，本文提出以多目標拓樸優化結合客觀賦權法進行船舶桅杆結構設計，以達到提升桅杆結構的剛度、降低重量並減少振動訊號的目的。 首先，對原始設計之桅杆結構進行了船舶設計負載分析、模態分析以及隨機振動分析，建立優化前後結構的比較標準。接著，根據可設計的尺寸範圍和需要安裝的設備等設計條件，建立桅杆結構之優化設計空間，並利用拓樸優化之密度法進行優化設計。 在單目標優化中，分別考慮了應變能最小化和重量最小化，並通過單目標優化的分析結果，建立了決策矩陣，利用客觀附權法之熵權法計算各單目標的權重係數，並進行多目標優化。完成多目標優化後，根據優化後的材料分佈情況重建結構，並將其與原始設計的桅杆結構進行比較，評估優化效果。

Conventional ship mast structure design heavily relies on experiential methods, often resulting in time-intensive processes and structures that may not fully align with practical requirements. This study introduces a methodology that integrates multi-objective topology optimization and an objective weighting approach to refine ship mast structure design, aiming to bolster structural rigidity, minimize weight, and attenuate vibration signals. The original mast design undergoes vessel design load analysis, modal analysis, and random vibration analysis to establish benchmarks for comparing pre- and post-optimization structures. Defining optimization design parameters considering dimensional constraints and equipment installations, the mast structure's optimization design space is determined. Utilizing density methods, topology optimization is performed. In single-objective optimization, strain energy and weight reduction are separately assessed. Analysis results from the single-objective optimization form the basis for a decision matrix. The entropy weighting method, part of the objective weighting approach, determines coefficients for each objective, facilitating multi-objective optimization. Post multi-objective optimization, the optimized material distribution reconstructs the structure for comparative evaluation against the original mast design to assess optimization effectiveness.