By Seifedine Kadry
Industrial Prognostics predicts an business system's lifespan utilizing likelihood measurements to figure out the way in which a laptop operates. Prognostics are crucial in deciding on having the ability to are expecting and forestall disasters sooner than they take place. for that reason the advance of responsible prognostic tactics for engineering structures is necessary to extend the system's functionality and reliability.
Diagnostics and Prognostics of Engineering platforms: equipment and Techniques presents common insurance and discussions at the tools and methods of analysis and analysis structures. together with functional examples to show the method's effectiveness in real-world purposes in addition to the most recent traits and examine, this reference resource goals to introduce primary thought and perform for method prognosis and prognosis.
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Extra info for Diagnostics and Prognostics of Engineering Systems: Methods and Techniques
With model (7), Equation (2) can be written as a nonlinear function of x (k ) as follows: γ(y, u(k ), F (k )) = R(y )Ex (k ) + rn (y )h(Ex (k )) + ω(y, u(k ), F (k )) (9) Different from the models considered in (Guo and Wang, 2005), the proposed discrete-time square root RBFNN model is more practical and better suited to digital control. Γ1 Γ2 ∆(k ) In order to detect the fault based on the changes of PDFs, the following nonlinear observer is considered: xˆ(k + 1) = Axˆ(k ) + Bu(k ) + Gg(xˆ(k )) + Lε(k ) ε(t ) = ∫ b a µ(y )( γ(y, u(k, F )) − γˆ(y, u(k )))dy γˆ(y, u(k )) = R(y )Exˆ(k ) + h(Exˆ(k ))rn (y ) 6 (10) a b n a b (12) a It can be seen that ε(k ) = Γ1e(k ) + Γ2 [h(Ex (k )) − h(Exˆ(k ))] + ∆(k ) (13) From ω(y, u(k ), F ) ≤ δ , it can be verified that ∆(k ) = 4.
2006, Guo and Wang, 2005). Subsequently, an improved design approach has been applied for the general stochastic system by using a square root B-spline model and nonlinear filter design (Guo and Wang, 2005). Due to the high demand for reliability and safe operation, many FTC methods were developed in the past four decades, which have the capability of detecting the occurrence of faults and maintaining the performance of the system in the presence of faults at a prescribed level (Iserman, 2006).
1. , 2006), consider uk (i ) ∈ Rr is the input of a discrete-time dynamic stochastic system at the i th time instant within the k th batch and y ∈ [a, b ] is the output. At sample time k, y can be described by its PDF, γk (y, uk (i )). Assuming that [a, b ] is known and the probability density function is continuous and bounded within each iteration, then the well-known RBF neural networks can be used to approximate the square root of the output PDF as n ( ) γ(y, uk (i )) = ∑νl ,k uk (i ) rl ,k (y ) l =1 (42) where γ(y, uk (i )) is the output PDF measured at the i th time instant within the k th batch.
Diagnostics and Prognostics of Engineering Systems: Methods and Techniques by Seifedine Kadry