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High-resolution positioning for maglev trains is implemented by detecting the tooth-slot structure of the long stator installed along the rail, but there are large joint gaps between long stator sections. When a positioning sensor is below a large joint gap, its positioning signal is invalidated, thus double-modular redundant positioning sensors are introduced into the system. This paper studies switching algorithms for these redundant positioning sensors. At first, adaptive prediction is applied to the sensor signals. The prediction errors are used to trigger sensor switching. In order to enhance the reliability of the switching algorithm, wavelet analysis is introduced to suppress measuring disturbances without weakening the signal characteristics reflecting the stator joint gap based on the correlation between the wavelet coefficients of adjacent scales. The time delay characteristics of the method are analyzed to guide the algorithm simplification. Finally, the effectiveness of the simplified switching algorithm is verified through experiments.

The suspension function of high speed maglev trains is carried out by the electromagnetic attractive force between the electromagnets and the rail, and the train is driven by a linear synchronous motor [

Because of the non-contact between the train and the rail, the technical requirements for the position and speed measurements of a maglev train are different from those for wheel-track systems [

Detecting coils fixed on one side of the positioning sensor facing the long stator are driven by high frequency signal sources. Taking one of the coils for example, when the coil moves along the stator at a certain suspension gap, its inductance varies periodically. As a result, the amplitude of the coil signal varies accordingly forming an amplitude modulation signal. Then, a square signal corresponding to the tooth-slot structure can be obtained by comparing the amplitude demodulation signal to a certain threshold.

By counting the jumping edges of the square signal, the number of tooth-slot periods passed by the train can be determined and the positioning with higher resolution in a tooth-slot period can be achieved by looking up the mapping table between the sampled values of the amplitude demodulated signals and the relative position.

A magnetic pole period of the 3-phased windings contains six tooth-slot periods as shown in

In practice, due to installation requirements, there are some large joint gaps between long stator sections. The length of a gap is about 2 tooth-slot periods as shown in

In order to identify the invalidated positioning signal in time, fault diagnosis technologies can be adopted. Generally speaking, fault diagnosis technologies can be classified into three categories: methods based on system models, methods based on signal processing and methods based on knowledge. Because model parameters such as carriage mass, tractive force, electrical brush friction and slop grade of the rail are unknown to the positioning sensor, methods based on model are not feasible. Besides, methods based on knowledge usually require complicated inference procedures and knowledge bases, so it's hard for these methods to satisfy the time limit in this situation. Therefore, the methods based on signal processing are considered to implement the switching of the positioning sensors in real time.

In [

In order to enhance the reliability of the switching algorithm, wavelet analysis is adopted to suppress measuring disturbances without weakening the signal characteristics caused by the stator joint gaps based on the correlation between the wavelet coefficients of adjacent scales in this paper. The time delay characteristics of the method are analyzed to guide the algorithm simplification. Finally, the effectiveness of the simplified algorithm is proven through simulations and experiments.

As

The jumping edges of the sawtooth phase wave containing lots of high frequency harmonic components will complicate the signal prediction and characteristics extraction. Therefore, firstly the phase signal needs to be converted to a certain form to eliminate the influence of the jumping edges. Let _{h}

Because of the slight time differences between the jumping edges of the phase signal and those of the tooth-slot number signal, there are spike pulses in signal _{ha}

The converted phase signal near a large joint gap is shown in

The converted phase signal is not a stationary random process. Its statistical properties vary continually. In this case, the least-mean-square-error adaptive linear prediction is applicable to predict the phase signal based on the evaluation of the short time statistics of the signal.

The basic idea of the switching algorithm is to predict _{ha}_{ha}_{ha}_{ha}_{ha}_{ha}_{ha}_{ha}

Let _{ha}

Reference [_{max} denotes the maximal eigenvalue of the matrix _{ha}_{ha}^{T}.

In

However, as

Low Pass Filters (LPF) can be used to smooth the converted signal and suppress noise, but they will also weaken the signal characteristics reflecting the stator joint gaps at the same time, whereas, the method based on the correlation between the wavelet coefficients of adjacent scales [

Generally, for a signal, the Lipschitz index is larger than zero at continuous sections and equal to zero at step type discontinuous points, whereas, the Lipschitz index of a noise signal is less than zero. Accordingly, the wavelet coefficients of the three cases have different propagation characteristics on each transformation scales. For the former two cases, the wavelet coefficients of adjacent scales have a relatively strong correlation, but for noise signal, the correlation is not obvious. Hence, by multiplying each wavelet coefficient of a scale by the corresponding coefficient of an adjacent scale respectively, the noise can be suppressed, and at the same time, the valid signal characteristics are enhanced [

For a discrete parameter wavelet transformation, the numbers of the wavelet coefficients of different scales are not the same because of binary down sampling, so it's not feasible to do the one-to-one multiplication for the coefficients of adjacent scales straightforwardly. In order to solve this problem, stationary wavelet transform algorithm (a'trous algorithm) is adopted to make the number of the wavelet coefficients of each scale equal to the length of the original data when finite length problem is not considered.

Consider an orthogonal discrete parameter wavelet with a limited support interval. Let ^{j}^{j}^{j}

Let _{ha}^{j}^{j}_{ha}^{j}_{ha}^{j}

According to ^{j}_{ha}_{ha}_{ha}^{j}^{+1}^{j}^{+1}(_{ha}_{ha}_{ha}^{j}^{+2}^{j}^{j}^{j+1}^{j}^{j}^{j}^{+1}(^{j}^{j}^{+1}(

For different wavelets,

The analytical results of the converted signal _{ha}

Considering the time limit and calculation load requirement of the sensor's practical operating condition, the “db1” wavelet (“haar” wavelet) is selected, which has the shortest filter length with

^{j}^{j}

Choose a threshold ^{j}^{j}^{j}^{j}

Compared to the original signal _{ha}

At first, we consider the switching method based on adaptive linear prediction without the noise suppression process. Because the prediction error _{ha}

When the discrete wavelet transformation is introduced into the process, the finite length problem (boundary effect) needs to be considered except for the “db1” wavelet. The data affected by the boundary effect are always the latest sampled values of the phase signal. Considering the algorithm based on

One way to solve the boundary problem is to add certain data behind the latest sampled datum to extend the original signal artificially until the serial number of the latest transformation coefficient is equal to that of the latest sampled value. However, the added data are different from the real data sampled later, so the corresponding coefficients can't reflect the signal characteristics exactly.

References [

Furthermore, the signal reconstruction will also introduce a delay. Let _{ha}_{ha}_{ha}_{ha}^{j}_{j}_{ha}^{j}_{j}_{j}

Furthermore, we denote the serial number of the latest reconstructed datum on the 0^{th} scale obtained based on _{j}_{0}. k_{0}

The analysis above indicates that the switching algorithm combining the adaptive linear prediction and the stationary wavelet transformation has a time delay of about 2^{j}^{+1}

In engineering practice, the positioning sensor is only enabled when the train is running at a speed below 20 km/h. When the running speed of the train exceeds 20 km/h, the position and phase information can be obtained by detecting the back electromotive force of the primary windings. In a time span of 2 ms, the train can run a distance of about 11 mm with a speed of 20 km/h. Considering that the length of a tooth-slot period is about 86 mm, this algorithm can avoid the tooth-slot period number counting loss in time.

In order to further reduce the time delay and computation needs, the algorithm discussed in Section 4 needs to be simplified. Actually, after the noise suppression pretreatment, the signal characteristics due to the stator joint gap has already been distinguished from the noise obviously according

According to _{j}

That is to say, if _{ha}^{j}^{+1}^{j}^{+1}

The experiments are carried out on the 1.5 km high speed maglev train test line in Shanghai, China. Large joint gaps shown in

The sensors are connected with an upper computer via communication cables, and upload the phase signal via RS485 interface in real time. The upper computer identifies the signal characteristics due to the joint gaps based on the correlation between the wavelet coefficients of adjacent scales and then implement the sensor switching. The flow chart of the switching algorithm of the upper computer is shown in

The switching experiment results are shown in

From

This paper studies the two-modular switching algorithms for the positioning sensors to solve the problem caused by the stator joint gaps. At first, adaptive filtering is applied to predict the phase signal of the sensor, and the switching is triggered based on the prediction error. In order to enhance the reliability and effectiveness of the switching algorithm, wavelet analysis is introduced in to suppress measuring disturbance without weakening the signal characteristics affected by the stator joint gaps based on the correlation between the wavelet coefficients of adjacent scales. To improve the response speed of the algorithm, a simplified algorithm is proposed, and its time delay characteristic is analyzed. The analytical and the experimental results show that when the train is running at a speed below 20 km/h, the designed algorithm can switch the positioning sensors in good time and can effectively eliminate the accumulated phase errors due to the tooth-slot period number counting losses.

This work was performed at the Engineering Research Center of Maglev Technology at National University of Defense Technology with funding from National Natural Science Foundation of China under grant No. 60974128.

(

The relationship between the electrical phase angle and the tooth-slot structure.

The phase requirement at a large joint gap.

(

The converted phase signal.

(

(

The product of the wavelet coefficients of the 1st and 2nd scales.

The reconstituted signal and predicted signal.

The prediction error.

The flow chart of the switching algorithm.

The experimental results of the two-modular switching.