Métodos Iterativos de Regularização para Identificação do Coeficiente de Rigidez na Equação de Euler-Bernoulli para Vigas
DOI:
https://doi.org/10.5540/tcam.2022.023.02.00363Keywords:
identificação do coeficiente de rigidez, métodos iterativos, problemas inversos.Abstract
Nesta contribuição analisaremos o problema inverso de identificação do coeficiente de rigidez em vigas modeladas pela equação de Euler-Bernoulli, a partir de medidas da deflexão. Apresentaremos o problema na forma de uma equação de operador parâmetro-para-medidas, para o qual provaremos propriedades importantes, como compacidade e continuidade. Mostraremos ainda que o operador parâmetro-para-medidas é Fréchet diferenciável e que satisfaz a condição do cone tangente. Essas propriedades são suficientes para recuperarmos de forma estável e convergente (método de regularização) o coeficiente de rigidez através de métodos iterativos como Landweber e Steepest descent. Por fim, apresentamos os efeitos de estabilidade das soluções aproximadas com relação as medidas com diferentes níveis de ruídos através de exemplos numéricos.References
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