CLC number: TG502.15

On-line Access: 2014-08-19

Received: 2014-03-04

Revision Accepted: 2014-08-01

Crosschecked: 2014-09-29

Cited: 1

Clicked: 6701

Chen-hui Xia, Jian-zhong Fu, Yue-tong Xu, Zi-chen Chen. A novel method for fast identification of a machine tool selected point temperature rise based on an adaptive unscented Kalman filter[J]. Journal of Zhejiang University Science A, 2014, 15(10): 761-773.

@article{title="A novel method for fast identification of a machine tool selected point temperature rise based on an adaptive unscented Kalman filter",

author=" Chen-hui Xia, Jian-zhong Fu, Yue-tong Xu, Zi-chen Chen",

journal="Journal of Zhejiang University Science A",

volume="15",

number="10",

pages="761-773",

year="2014",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.A1400074"

}

%0 Journal Article

%T A novel method for fast identification of a machine tool selected point temperature rise based on an adaptive unscented Kalman filter

%A Chen-hui Xia

%A Jian-zhong Fu

%A Yue-tong Xu

%A Zi-chen Chen

%J Journal of Zhejiang University SCIENCE A

%V 15

%N 10

%P 761-773

%@ 1673-565X

%D 2014

%I Zhejiang University Press & Springer

%DOI 10.1631/jzus.A1400074

TY - JOUR

T1 - A novel method for fast identification of a machine tool selected point temperature rise based on an adaptive unscented Kalman filter

A1 - Chen-hui Xia

A1 - Jian-zhong Fu

A1 - Yue-tong Xu

A1 - Zi-chen Chen

J0 - Journal of Zhejiang University Science A

VL - 15

IS - 10

SP - 761

EP - 773

%@ 1673-565X

Y1 - 2014

PB - Zhejiang University Press & Springer

ER -

DOI - 10.1631/jzus.A1400074

**Abstract: **A novel method is presented for fast identification of a machine tool selected point temperature rise, based on an adaptive unscented Kalman filter. The major advantage of the method is its ability to predict the selected point temperature rise in a short period of measuring time, like 30 min, instead of 3 to 6 h in conventional temperature rise tests. A fast identification algorithm is proposed to predict the selected point temperature rise and the steady-state temperature. An adaptive law is applied to adjust parameters dynamically by the actual measured temperature, which can effectively avoid the failure of prediction. A vertical machining center was used to validate the effectiveness of the presented method. Taking any selected point, we could identify the temperature rise at that point in 28 min. However, if the method was not used, it took 394 min to obtain the temperature rise curve from the start-up of the machine tool to the time when it reached a steady-state temperature. The root mean square error (RMSE) between the estimated and measured temperatures in the period of 394 min was 0.1291 °C, and the error between the estimated and measured steady-state temperatures was 0.097 °C. Therefore, this method can effectively and quickly identify a machine tool selected point temperature rise.

温升；快速辨识；自适应无味卡尔曼滤波；机床

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1. Introduction

Xia et al. (

The unscented Kalman filter (UKF) was first proposed by Julier and Uhlmann (

Because the UKF has an advantage in nonlinear state estimation and parameter identification, it is also used in selected point temperature rise identification. Therefore, a new method for fast identification of a machine tool selected point temperature rise based on an adaptive UKF is proposed. The purpose is to identify a selected point temperature rise in a short time using the measured temperature data of only a selected point. An adaptive law is introduced to adjust dynamically the covariances of the process and measurement noise.

2. Identification method based on an adaptive unscented Kalman filter

For the discrete nonlinear system, the normal UKF algorithm can be expressed as follows:

1. Initialize the mean

2. Construct a set of sigma points (

3. Time updating

Calculate the a priori state estimate and covariance by substituting the sigma points into the state function:

4. Measurement updating

Calculate the mean and covariance of the measurement vector by substituting the sigma points into the measurement function:

The cross covariance of the state vector and the measurement vector is calculated according to

The Kalman gain is calculated by

The a posteriori mean and covariance estimate of

Assuming it takes time

Therefore, we propose a novel adaptive UKF algorithm, in which the process noise covariance matrix

The a posteriori mean

Here, we define a variable

A positive threshold value (

As mentioned above, if

The variables

The solution of Eq. (

Then, the expression of the solution of Eq. (

Therefore, Eq. (

The temperature rise model is transformed into a discrete state-space model form. Assume state vector

Here, the measuring time

Assume first that temperature is measured during a sampling time

When the sampling period is increased to

For each of the four sampling times, the RMSE is minimal with the same identifying time,

For a certain identifying time with a certain sampling period, the temperature rise of the selected point can be predicted according to the novel adaptive UKF algorithm within the identifying time, and according to the normal UKF algorithm after the identifying time. Furthermore, the RMSE between the estimated temperature and the measured temperature in the sampling period can be calculated. Then, RMSEs for different identifying times and sampling periods can also be obtained and the minimal time for identification can be searched according to the above process. When the minimal time for identification is found, the measurement test can be stopped and the selected point temperature rise can be predicted accurately. The minimal time for identification is always short, around 30 min. In practice, it takes 3–6 h or even longer to obtain a selected point temperature rise from the start-up of a machine tool until a steady-state temperature is reached. Therefore, the presented method for selected point temperature rise identification based on a novel adaptive UKF can be applied to greatly decrease the time taken to obtain the temperature rise curve. The method has good prospects for industrial application.

3. Tests on a vertical machining center

The room temperature was about 17.9 °C. When the vertical machining center started and the spindle was running at a speed of 5000 r/min, the temperature rise test began. The sampling interval Δ

First, some parameters needed to be initialized. The initial state vector of the temperature rise model was chosen as

According to the above method, Figs.

In the identifying time of 28 min, the adaptive UKF algorithm was adopted to identify the selected point temperature rise. The parameters

For the state vector

Then, we can calculate the RMSEs between the predicted and measured temperatures with different identifying times in the period of time from the start-up of the machine tool to the time a steady-state temperature is reached (394 min). Fig.

Using the fast identification method based on UKF without the adaptive algorithm, the changes in RMSE with different identifying times in different sampling periods can be calculated. Figs.

Fig.

4. Conclusions

* Project supported by the National Nature Science Foundation of China (No. 51175461), the Science Fund for Creative Research Groups of National Natural Science Foundation of China (No. 51221004), and the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20120101110055), China

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