Gürültülü Verilerle Doğrusal Olmayan Sönümlü Sarkacın PINN Tabanlı Modellenmesi ve Lineer Kararlılık Analizi

Abstract

Doğrusal olmayan dinamik sistemlerin kararlılık analizi, kontrol teorisi ve mühendislik uygulamalarında önemli bir araştırma konusudur. Bu çalışmada, sönümlü sarkaç sisteminin kararlılık analizi Fizik Bilgili Yapay Sinir Ağları (PINN) kullanılarak gerçekleştirilmiştir. Model performansı, %5 ve %10 Gauss gürültüsü içeren 200 veri noktası ile iki senaryo altında değerlendirilmiştir. Sistem dinamiği her iki veri seti için öğrenildikten sonra lineer kararlılık analizi uygulanmış ve denge noktalarındaki Jacobian matrislerinin özdeğerleri hesaplanmıştır. Sonuçlar, modelin %5 gürültü seviyesinde kararlı denge noktasını yüksek doğrulukla tahmin ettiğini göstermiştir. %10 gürültü seviyesinde model doğruluğu azalsa da, kararsız denge noktası için kararlılık durumunu ve sistemin genel faz portresi dinamiğini her iki senaryoda da doğru belirlemiştir. Faz portresi analizleri, modelin gürültü varlığında sistem dinamiğini başarıyla öğrendiğini doğrulamaktadır. Bulgular, bu yaklaşımın gürültülü deneysel verilerle çalışan doğrusal olmayan sistemlerin modellenmesi ve kararlılık analizinde etkili bir araç olduğunu ortaya koymaktadır.

Keywords

• • Fizik bilgili sinir ağları (PINN)
• • Doğrusal olmayan sistemler
• • Kararlılık analizi
• • Sönümlü sarkaç
• • Gürültülü veri

PINN-Based Modeling of Nonlinear Damped Pendulum with Noisy Data and Linear Stability Analysis

Abstract

Nonlinear dynamic system stability analysis represents a critical research domain in control theory and engineering applications. This study employs Physics-Informed Neural Networks (PINNs) for the stability analysis of a damped pendulum system. Model performance was evaluated under two distinct scenarios utilizing 200 data points contaminated with 5% and 10% Gaussian noise, respectively. After learning the system dynamics from both datasets, linear stability analysis was performed, and the eigenvalues of the Jacobian matrices at equilibrium points were computed. The results demonstrate that the stable equilibrium point was accurately predicted at the 5% noise level. Although model accuracy decreases at the 10% noise level, the stability characteristics of the unstable equilibrium point and the overall phase portrait dynamics were correctly identified in both scenarios. Phase portrait analyses confirm the successful learning of system dynamics under noisy conditions. The findings indicate that this approach provides an effective framework for modelling and stability analysis of nonlinear systems operating with experimental noisy data.

Keywords

• • Physics-informed neural networks (PINN)
• • Nonlinear systems
• • Stability analysis
• • Damped pendulum
• • Noisy data

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