Denizcilik Matematiği için Entegre Bir Dijital İkiz Çerçevesi: Seyrüsefer, Mühendislik, Lojistik ve Risk Değerlendirmesi

Öz

Matematik, navigasyonun ilk kullanımlarından hesaplamalı akışkanlar dinamiğine, stokastik optimizasyon ve güvenilirlik modellerindeki çağdaş uygulamalara kadar, tarihsel olarak denizciliğin ayrılmaz bir parçası olmuştur. Bu çalışma, geleneksel olarak küresel trigonometri ve logaritmik tablolarla kolaylaştırılan navigasyonla başlar. Şu anda, navigasyon GPS ve AIS teknolojileri içinde doğrusal olmayan cebirsel sistemlere ve Kalman filtrelemesine dayanmaktadır. Deniz mühendisliğinde, hidrodinamik, gövde optimizasyonu ve dalga yüklemesi altında yapısal güvenilirlik, diferansiyel denklemler, özdeğer kararlılık analizi ve sonlu elemanlar yöntemleriyle desteklenmektedir. Liman verimliliği için kuyruk modelleri, filo tahsisi için doğrusal programlama ve rotalama için çizge teorisi dahil olmak üzere optimizasyon metodolojileri, deniz lojistiğinde giderek daha hayati hale gelmektedir. Güvenlik ve sürdürülebilirlik alanındaki uygulamalar, yakıt verimliliği ve emisyon azaltımı için konveks optimizasyonu, dalga modellemesi için aşırı değer teorisi, Bayes risk değerlendirmesi ve olasılık teorisini kullanmaktadır. Çalışmanın birincil katkısı, risk, mühendislik, navigasyon ve lojistikten elde edilen matematiksel modelleri birleştirerek birleşik bir öngörücü ve uyarlanabilir mimaride birleştiren entegre bir dijital ikiz çerçevesidir. Çerçeve, deterministik ve stokastik modellerden oluşan matematiksel bir temel ile gerçek zamanlı fiziksel verileri (sensörler, GPS, AIS ve çevresel izleme) entegre ederek öngörücü simülasyonu, gerçek zamanlı optimizasyonu ve risk odaklı karar almayı kolaylaştırır. Önerilen DT, matematiksel uygulamaları alanlara göre bölümlere ayıran geleneksel yöntemlerin aksine, alanlar arası entegrasyonu kolaylaştırır, otonom karar verme sistemlerini destekler ve sürdürülebilir denizcilik operasyonlarına geçişi hızlandırır. Matematiksel titizliğin dijital ikiz mimarisiyle entegrasyonu, matematiği sadece tanımlayıcı bir araç olmaktan ziyade, yeni nesil denizcilik inovasyonu için dönüştürücü bir katalizör olarak konumlandırır.

Anahtar Kelimeler

• Denizcilik matematiği
• dijital ikiz çerçevesi
• optimizasyon ve lojistik
• risk ve güvenilirlik analizi
• otonom deniz sistemleri

An Integrated Digital Twin Framework for Maritime Mathematics: Navigation, Engineering, Logistics, and Risk Assessment

Öz

Mathematics has historically been integral to shipping, from its early use in celestial navigation to contemporary applications in computational fluid dynamics, stochastic optimization, and reliability models. It enhances the sustainability, durability, and efficiency of shipping. This review commences with navigation, which has traditionally been facilitated by spherical trigonometry and logarithmic tables. Currently, navigation relies on nonlinear algebraic systems and Kalman filtering within GPS and AIS technologies. In marine engineering, hydrodynamics, hull optimization, and structural reliability under wave loading are underpinned by differential equations, eigenvalue stability analysis, and finite element methods. Optimization methodologies, including queueing models for port efficiency, linear programming for fleet allocation, and graph theory for routing, are increasingly vital in maritime logistics. Applications in safety and sustainability utilize convex optimization for fuel efficiency and emission mitigation, extreme value theory for wave modeling, Bayesian risk assessment, and probability theory. The primary contribution of the study is an integrated digital twin framework that consolidates mathematical models from risk, engineering, navigation, and logistics into a unified predictive and adaptive architecture. The framework facilitates predictive simulation, real-time optimization, and risk-informed decision-making by integrating real-time physical data (sensors, GPS, AIS, and environmental monitoring) with a mathematical foundation comprising deterministic and stochastic models. The proposed DT facilitates cross-domain integration, endorses autonomous decision-making systems, and propels the transition to sustainable maritime operations, unlike traditional methods that compartmentalize mathematical applications by domain. The integration of mathematical rigor with digital twin architecture positions mathematics as a transformative catalyst for next-generation maritime innovation, rather than merely a descriptive instrument.

Anahtar Kelimeler

• Maritime mathematics
• digital twin framework
• optimization and logistics
• risk and reliability analysis
• autonomous maritime systems

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