سنجش نرم افزار از سیستم یاتاقانهای مغناطیسی در رگرسیون بردار پشتیبانی و بر اساس فیلتر کالمن توسعه یافته

The rotor displacement measurement plays an important role in an active bearing system, however, in practice this measurement might be quite noisy, so that the control performance might be seriously degraded. In this paper, a soft sensing method for magnetic bearing-rotor system based on Support Vector Regression (SVR) and Extended Kalman Filter (EKF) is proposed. In the proposed method, SVR technique is applied to model the acceleration of the rotor, which is regarded as a nonlinear function of rotor displacement, rotor velocity and bearing currents; then this SVR model is used to construct an EKF estimator of rotor displacement. In the proposed method the bearing current is incorporated to the estimation of displacement, so that displacement can be precisely estimated even if very large observation noise is present. A series of experiments are performed and the results verify the validity of the proposed displacement soft sensing method.

Compared with conventional bearings, active magnetic bearings (AMBs) [1] and [2] possess several attractive advantages, such as no friction, no need of lubrication, and the ability of long-term high speed running. An AMB system includes the following parts: a rotor, bearings, sensors, a power amplifier and a controller. The sensors measure the rotor displacement real-timely, based on this measurement, the controller computes the control signal, the power amplifier transforms this signal to control current and feeds the current to the bearings, and the bearing generate magnetic force to hold the rotor in the suspension position. In an AMB system, the lateral displacement of the rotor can be measured by the displacement sensors, this measurement plays an important role in the control loop and significantly affects the control performance. Nevertheless, in practice the displacement signal may be quite noisy, especially when high power motors or invertors are nearby. The noisy signal may result in poor suspension stability and terrible acoustic noise. The main idea of this paper is that the noise in measurement can be eliminated based on a precise rotor-bearing model, in other words, this paper offers a model-based soft sensing method of rotor displacement in an AMB system. More precisely, we notice that if a precise model of rotor displacement-bearing current is available, the displacement measurement can be significantly improved in that the bearing current is involved into measurement and this additional information will help to eliminate the noise of the displacement measurement. Soft sensing [3], [4] and [5] is an approach to estimate hard-to-measure variables of a dynamic system from easy-to-measure variables. The soft sensing technique can also be applied to improve the measurement quality of some variables by incorporating information from various sources. However, to our best knowledge no achievement of soft sensing of magnetic bearing systems is reported. The model of plant is the most important part of a soft sensing method. The characteristics of an AMB system can be modeled theoretically and it is usually approximated by linearized models, however, they are inherently nonlinear. The most important source of nonlinearity is the force-current relationship of the bearing [6] and [7], due to magnetic hysteresis, machining error, eddy effect and the inaccurate and inconsistent magnetic property of iron core, in practice the theoretical model and the linearized model of bearings are sometimes not precise enough. The rotor model, namely the force-displacement relationship, is normally regarded as linear as well and can be calculated by finite element method and other numerical methods [8], but a practical rotor is usually quite complex, it may compose of many different parts, these parts may join together by screw thread, shrink-fitting and other connections, all these will lead to nonlinearity and inaccuracy of the rotor model. Moreover, the magnetic bearings introduce the so-called “negative stiffness”, namely the current-displacement relationship of the bearing-rotor system is open-loop unstable. Thus a linear-model-based soft sensing method for AMB system highly relies on the observations and will be negatively affected by the observation noise. Some researches on the nonlinear modeling of magnetic bearing systems are reported [7], [9], [10] and [11], all these works are based on parametrical regression technique, namely some mechanism and/or empirical models are utilized in modeling. Unlike these methods, in this paper a nonparametric modeling method is applied to establish a static model, and this static model is utilized to make dynamical estimation of the rotor-displacement. On the other hand, many achievements of soft sensing based on Neural Network (NN) are published [12], [13], [14], [15] and [16], however, in this paper we apply Support Vector Regression (SVR) technique [17] and [18] as a modeling method, since according to the statistical learning theory [19] it outperforms NN in generalization performance. For a rotating rotor, suppose an impulse tachometer is mounted and signals can be divided into periods according to the tachometer pulses. Then the proposed method includes the following steps: (1) The velocity and acceleration of the rotor is estimated from the displacements in the recent periods. Considering the response is periodic, this estimation can be precise enough even if the displacement data is very noisy. (2) The rotor acceleration-bearing current relationship is established by SVR. (3) The Extended Kalman Filter (EKF) [20] method is applied to make rotor displacement estimation by incorporating the displacement measurement and the estimated acceleration together. These steps can be performed online to realize real-time displacement sensing. An experimental system with a five degrees-of-freedom (DOF) suspended rotor (about 3.5 m long and 630 kg heavy) is utilized to perform a series of experiments and validate the proposed method. The experimental results show the validity of the proposed method. In this paper, the motion of the rotor in a radial plane is considered. Two displacement sensors are utilized to measure the rotor’s lateral displacements. The lateral displacements are denoted by x1x1 and x2x2, respectively. The velocities of the rotor (i.e. the derivative of x1x1 and x2x2) will be denoted as View the MathML sourceẋ1 and View the MathML sourceẋ2 and the accelerations of the rotor as View the MathML sourcex¨1 and View the MathML sourcex¨2. The notations ix1+ix1+ and ix1-ix1- stand for the currents in the plus and minus coils of the magnetic bearing x1x1. All involved signals are sampled at discrete time instants κ=1,2,…κ=1,2,… . A signal (say x1x1) at sampling instant κκ is denoted by x1(κ)x1κ. The rotational speed of the rotor is measured by an impulse tachometer in which each revolution of the rotor generates an electric pulse. Suppose the tachometer pulses occur at time instants p1,p2,…p1,p2,… . We define that the k th rotational period is started at time instant (pk-1+1)pk-1+1 and ended at pkpk.

In this paper, a soft sensing method of magnetic bearing-rotor system based on SVR and EKF is proposed. In the proposed method, firstly an SVR model is obtained. In this model, the acceleration of the rotor is modeled as a nonlinear function of the rotor displacement, the rotor velocity and the bearing currents, and the model parameters are determined based on training samples. Then this SVR model is used to construct an EKF sensing of rotor displacement. The transfer matrix and its derivative are calculated and the standard nonlinear EKF is applied. In the proposed sensing method the bearing current is incorporate to the estimation of displacement, so that displacement can be precisely estimated even if very large observation noise is present. The proposed method is prior-model independent, that is, no mechanism, computational or empirical model is necessary. This characteristic is especially meaningful for complex bearing-rotor system, where no precise model is available. A series experiments are performed on an experimental system with a rotor suspended in five DoF. The experiment results show the validity of the proposed method. The future works of this paper include: 1. Online implement of the proposed method. 2. Based on the proposed method, fault diagnosis method might be developed by comparing the estimated displacement and the measurement. Furthermore, if more information is involved, e.g. rotor displacements measured by redundant sensors, rotor velocity, bearing flux, the proposed method might offer a fault-tolerant sensing system. 3. In the proposed method, mechanism, computational and empirical models are not necessary. However, in most cases some rough models are available and contain important information about the actual model; on the other hand, many prior-knowledge based modeling methods [25] and [26] can be utilized to incorporate these models into the sample based modeling method. This incorporation can improve the modeling performance. 4. Nonlinearity can degrade the stability, robustness and dynamic performance of the bearing-rotor system. The proposed nonlinear modeling method can be utilized to improve the analyzing and designing procedure of the control method. 5. The experimental system shown in Fig. 2 is not designed for nonlinear identification experiments, so that the nonlinearity is not so obvious as shown in [10] and [11]. In the future we plan to design and construct new special system for nonlinear experiments and perform more identification experiments.