Seyrek Tanılama Yöntemi ile Doğrusal Olmayan Dinamik Sistemlerin Model İncelenmesi

Öz

Doğrusal olmayan sistemleri tanımlamak için seyrek regresyon tekniklerine dayanan doğrusal olmayan dinamiklerin seyrek tanımlanması (SINDy) son yıllarda ortaya konan veriye dayalı model tanımlama yöntemlerinden biridir. Sistem tanılamada sistemin model denklemleri verilerden çıkarılır. Mühendislik, sağlık hizmetleri ve ekonomi bilimlerinin çoğundan yeterli veri mevcut olmasına rağmen, sistem davranışını temsil eden çok az sayıda iyi tanımlanmış model vardır. Sistemin davranışı, veriye dayalı yöntemlerden de tahmin edilebilir. Bu motivasyon göz önünde bulundurularak, bu çalışma doğrusal olmayan sistemlerin matematiksel modelini oluşturmak için çevrimdışı veri odaklı tanımlama tekniklerini ele alır. Doğrusal olmayan sistemlerin veriye dayalı seyrek tanımlanması bir dizi örnekle detaylandırılır. Tanımlama işleminin performansı, gürültülü ölçümlerin varlığında bir takım nicel ölçümler üzerinden tartışılır.

Anahtar Kelimeler

• Doğrusal Olmayan Sistemler
• Seyrek Tanılama
• Seyrek Regresyon
• Model Keşfi
• Sistem Tanılama

Model Investigation of Nonlinear Dynamical Systems by Sparse Identification

Abstract

The sparse identification of nonlinear dynamics (SINDy), which is based on the sparse regression techniques to identify the nonlinear systems, is one of the recent data-driven model identification methods. The model equations of the system are extracted from the data. Although sufficient data is available from most of the engineering, healthcare, and economic sciences, there are few well-defined models to represent the system behaviour that can also be estimated from data-driven methods. With this motivation in mind, this study presents offline data-driven identification techniques to build the mathematical model of nonlinear systems. The data-based sparse identification of nonlinear systems is elaborated with a number of examples. The performance of the identification procedure is discussed in terms of quantitative metrics in the presence of noisy measurements.

Keywords

• Nonlinear System
• Sparse Identification
• Sparse Regression
• Model Discovery
• System Identification

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