Balanceo Automático de un Sistema Rotor-Cojinete: Identificador Algebraico en Línea del Desbalance Para un Sistema Rotodinámico

Recursive Filter With Exponential Kernel for Nonstationary Systems

“…The equations considered have associated gains that are related to the internal properties of the system from which the signals come. When describing these gains by means of some filtering technique, an estimation of parameters [2] is being carried out, and they are used to describe the internal dynamics of the system states [3]. One of the applications for these two areas is the Black Box (BB) system, which is a system, as represented in Figure 1, whose only measurable characteristics are the inputs and outputs, whilst the internal dynamics is unknown; thus, there is no direct strategy to model its exact behavior, but approximations through estimations and identification techniques.…”

“…Let 𝑆 be a BB system and let 𝑦 𝑘 be an observable signal. If 𝑆 is described by means of its internal states as (1) and its observable signal as (2), then there is an optimal recursive model in a sense of identification probability associated with 𝑆 given by (3).…”

“…) Evaluating the stochastic gradient with respect to the output 𝑦 𝑘 that minimizes the functional of the error 𝐽 𝑘 , there is the optimal recursive identification model as shown in (3). ∎ Considering a kernel function 𝐾𝑒𝑟(𝑣 𝑖 ) as a linear operator that relates the variables 𝑣 𝑖 , operating point to point, and maintaining the domain of the estimation and identification results, 𝐾𝑒𝑟: 𝑅 [𝑛×𝑛] → 𝑅 [𝑛×𝑛] , due to the rate of change required to follow the stochastic signals, the base selected for the kernel is of the exponential type, defined as in (13), 𝐾𝑒𝑟 (𝐴 ̃𝑘, 𝜀 𝑘 ) = 𝑠𝑖𝑔𝑛 (𝐴 ̃𝑘) 𝑒 𝑠𝑖𝑔𝑛(𝐴 ̃𝑘)𝜀 𝑘 (13) where 𝐾𝑒𝑟(•), represents the kernel function, 𝜀 𝑘 is the identification error, 𝐴 ̃𝑘 the estimated parameters, sign(•) indicates the sign function, and e [•] indicates the exponential function.…”

“…(Estimation using the kernel function). Let 𝑆 be a BB type system and let 𝑦 ̂𝑘 be the output signal identified as in (3). If 𝐴 ̃𝑘 is the unknown parameter matrix associated with 𝑆 obtained by minimizing the error functional ∇𝐽 𝑘 = 0 then there is an estimator with kernel 𝐾𝑒𝑟 (𝐴 ̃𝑘, 𝜀 𝑘 ) that corrects the estimate according to (14).…”

Optimization and Experiment of Mass Compensation Strategy for Built-In Mechanical On-Line Dynamic Balancing System

“…A multi degree of freedom rotation system based on the finite element method was developed to determine the magnitude of the rotor unbalance and its angular position on the rotor so that the magnitude and position of the compensation could be determined [9]. Kuen Tai Tsai simultaneously used the influence coefficient method and genetic algorithm to obtain the balance weight and angle plane of each balance so that the balance weight could be placed on multiple balance planes at the same time, which helped to shorten the time of field dynamic balance test and improve the dynamic balance efficiency [10].…”