Design of multi sensor measuring device based on data fusion

Scientific Journal of Information Engineering June 2014, Volume 4, Issue 3, PP.99-103

Design of Multi-Sensor Measuring Device Based on Data Fusion Xin Li School of Information Engineering, Chongqing Institute of Engineering, Chongqing 400037, China Email: 94266636@qq.com

Abstract A new method of multi-sensor measurement in sections based on Kalman filter and correlation analysis is proposed, aiming at the problems of poor measurement precision, poor reliability, without estimating the status between measurement points for single sensor. It absorbs well the advantages both the data fusion based on Kalman recursive filter and correlation analysis, with which the precision and reliability are enhanced and the status between the points can be estimated also. It avoids the limitation of Kalman filter on math model and noise statistics characteristic at the same time. A character parameters measurement device of a dynamic load track was developed in succession. The data process results of the device demonstrated that the method is effective and the effect is significant.

Keywords: Sectional Measurement; Multi-Sensor; Kalman Filter; Correlation Analysis

1 INTRODUCTION The measurement limitations did not meet some needs for single sensor, e.g. accuracy, reliability, information preservation, sensor fault in large measuring range and judgment of anomalies information between measured points.

Multi-sensor measurement is used in sections for the same measured physical quantity, and using data fusion method to estimate measured state, the measurement are more precise and reliable than single sensor. Kalman filter is a linear minimum variance unbiased estimation, which has greatly estimating ability for non-stationary signal. Therefore, the method is proposed to seek measured parameters of mean square estimation error minimum value based on Kalman recursive filter multi-sensor data fusion, which can acquire more precise and reliable measure parameters. Correlation function can analyse fused data, e.g. self-correlation information of measured point and cross-correlation information of between adjacent measured points.

2 MULTI-SENSOR MEASUREMENT IN SECTIONS BASED ON KALMAN FILTER AND CORRELATION ANALYSIS fused data

‌

sensors

1

signal pre-process n module

adjacent measure data devices fusion based on auto-correlation Kalman correlation cross-correlation filter analysis fused data module wireless transmitreceive module

FIG.1:DATA PROCESSING AND TRANSMISSION OF MEASURED POINTS

The structure of Multi-sensor measurement in sections based on Kalman filter and correlation analysis is shown in Fig.1. It is composed of signal pre-process module, data fusion module based on Kalman filter, correlation analysis module and wireless transmit-receive module. Measure devices are preset on measured subsection areas, and a number of sensors have been placed on the measured points. Sensors signals are fused based on Kalman recursive filter after pre-process. Using self-correlation information of measured points and cross-correlation information of - 99 http://www.sjie.org

adjacent measurements that are transmitted wirelessly, it can analyze the information of measured points and unscanned areas, and estimate relative position of anomalies for unscanned areas.

3 MULTI-SENSOR DATA FUSION AND CORRELATION ANALYSIS 3.1 Multi-Sensor Data Fusion Based on Kalman Filter The data are decentralized treatment firstly, and proceeded global fusion to seek measure parameters of mean square estimation error minimum value based on Kalman recursive filter multi-sensor data fusion. Local filter information isolates well sensor fault, and acquires local optimal estimation which is synthesized by fusion algorithm in the main filter, and acquires global estimation finally [1-3].

State equations and observation equation of n sensors dynamic system is assumed: x(t+1)=Φx(t)+Γw(t), (1) y (t)=Hx(t)+υ (t), in the equations, characteristics of state vector x (t) are observed by n sensors during sampling time t, x (t)∈Rn, state observation value y (t)∈Rn, system noise w (t)∈Rm, observation noise υ (t) ∈Rn; observing matrix H, state transition matrix Φ and system matrix Γ are respectively known n×n, n×n and n×m matrices.

Zero-mean-value matrix w (t) and covariance matrix υ (t) are set as non-correlation Gaussian sequence of Q and R. Satisfiable equations : E[w(t)]=0, E[w(t)wT(t)]=Q(t); E[υ(t)]=0, E[υ(t)υT(t)]=R(t);

(2) (3)

in the equations, E is expectation.

Initial state x (0) is set as non-correlation random variable with w (t) and υ (t). Satisfiable equations: E[x(0)]= μ0, E[(x(0)-μ0) (x(0)-μ0)T]=P0.

(4) State x (t) can be acquired via using Kalman recursive filter based on global information optimization fused estimation xˆ  t  and estimating error covariance matrix P (t). K (t) is set as gain matrix of Kalman filter. Kalman recursive filter is xˆ (t  1 t  1)  K (t  1) y(t  1)  xˆ (t t )[Φ  K (t  1) H ] , 1

K  t  1  P (t t ) H T  HP (t  1 t ) H T  R(t )  ,

P  t  1 t   ΦP  t t  ΦT  ΓQ  t  Γ T ,

(5)

P (t  1 t  1)  [ I n  K (t  1) H ]P (t  1 t ) , xˆ (0 0)  0 , P (0 0)  P0 .

Performance index of weighting fusion estimation [4] is min J  E[( x  xˆ 0 )( x  xˆ 0 )T ] ,

(6)

according to minimizing diagonal matrix. L x∈R unbiased estimation is xˆ i , and homologous covariance matrix is n

Pij  E [(x  xˆ i )(x  xˆ j )T ] , i, j=1,…L,

(7)

and so fusion estimation xˆ 0 of x is:  a j1  xˆ 0    j 1    0 L

a j2

0   xˆ  j  a jn 

in the equation, optimum weighted coefficient row vector element e  1 1 T

 P11ii  1 , P ii     PL1ii  

(8)

a ji 

eT  P ii 

1

eT  P ii  e 1

, i  1 n, j  1 L ,

P1Lii    there into, P (ii) is P (i, i) diagonal element. Here components of kj kj   ii   PLL  - 100 http://www.sjie.org

minimum square sum of fusion error are 1

1 tr P0   eT  P ii  e , i  1 , n .  i 1  n

(9)

3.2 Correlation Analysis Consequence of Multi-sensor data fusion is analyzed the similarity degree after elapsed time τ according to correlation function, and the information of measured points and adjacent measured points are acquired. With two signals of measured sensors xi (t) and xk (t+τ), cross-correlation function Rxi,xk (τ) is defined:

1 T xi  t xk  t    dt T  T 0

Rxi,xk    lim

 xi， xk 



 



1 T xi t    xi  xk t      xk dt T 0

lim

 

(10)

 xi xk

lim

1 T xi  t   xk  t    dt  xi xk T 0

 xi xk

Rxi,xk     xi  xk

 xi xk in the formula, μxi and μxk are mathematical expectation of xi (t) and xk (t), σxi and σxk are standard deviation of xi (t) and xk (t). ρxi, xk signifies linear correlation extent of two signals,  xi,xk ≤1. If ρxi, xk=±1, explain that two variables xi and xk ideal linear correlation. ρxi, xk =0 expresses xi and xk is non-correlation.

In the formula (10), xk (t+τ) is replaced to get self-correlation function Rxi (τ) by xi (t+τ). Similarly, self-correlation coefficient ρxi can be got. xi (t) makes a self-correlation analysis with standard function xi0 (t) of xi (t) in practical application.

When the self-correlation coefficient of one measured signal is smaller than threshold value, it shows that this measured point has fault. When the cross-correlation coefficient of two measured signals is smaller than threshold value according to time difference τ, it could inference relative position of fault point of non-measured range.

4 REALIZATION OF MULTI-SENSOR MEASUREMENT IN SECTIONS The design of the dynamic load measure system, has mainly focused on multi-sensor data fusion and correlation analysis, and has manufactured a dynamic load measure board which can send wireless data, to verify the accuracy and validity of this measure method.

Characteristic of Track Analysis

measuring device for characteristic parameter of dynamic loading sensors and signal pre-process module

ADXL202 acceleration sensors

filtering and amplifying circuit

DS18B20 temperature sensors

data collection, fusion and correlation analysis STM32F103RB

nRF24E1 wireless transmit-receive module wireless transmitreceive module

wireless transmitreceive module

host computer

constantan wire strain sensors

Central Processor Module

FIG.2 CHARACTERISTIC PARAMETERS OF THE DYNAMIC LOAD TRACK MEASURE DEVICE - 101 http://www.sjie.org

Track is widely used in manufacturing, transportation, and other industries. The basic characteristics measurement of the dynamic load track could provide important referenced parameters for the safety estimation. Measure board is composed of sensors and signal pre-process module, central processor module and wireless transmit-receive module, as shown in Fig.2. The main hardware design is using STM32F103RB [5-6] chip which is based on the Cortex-M3 core as the core microprocessor which collect and pre-process parameters, and then use the wireless transmission module nRF24E1 to send pre-processed and original data to the PC. Software design is mainly the naturalization of the ÎźC/OS-II real-time operating system [7] on STM32F103RB, which contains data collection and process, wireless transceiver module.

In the experiment, simply-supported beam JZ-81A is adopted to simulate the track, loading capacity 4 kg. A loaded car is mounted on the simply-supported beam and runs regularly, which is installed a micro-motor with eccentric block to supply vibration signals. Because they are important measured points on the 1/4, 1/2 and 3/4 of the track, the measure devices are preseted there to measure subsection region. Every measured point is placed 4 strain sensors, 4 acceleration sensors and 4 temperature sensors for multi-sensor measurement fusion.

Comparing the received data and the theoretical value, the results showed that the dynamic load measure system works well and its acquired data is quite approaching to the theoretical value, as shown in Fig.3-a, b, c, d, e, f. They are different among per group measure data according to the Fig.3-a, c, f shown, using data fusion method, which acquire the fusion value to reflect measured point strain. In the Fig.3-b, d, e shown, fusion and theoretical value are very approximate, maximum error <3.7%.

(a) MEASURE OF STRAIN ON 1/4 OF THE TRACK

(b) FUSION OF STRAIN ON 1/4 OF THE TRACK

(c) MEASURE OF STRAIN ON 1/2 OF THE TRACK

(d) FUSION OF STRAIN ON 1/2 OF THE TRACK

(e) MEASURE OF STRAIN ON 3/4 OF THE TRACK (f) FUSION OF STRAIN ON 3/4 OF THE TRACK FIG..3 MEASURE VALUE AND FUSION VALUE OF STRAIN ON 1/4, 1/2 AND 3/4 OF THE TRACK - 102 http://www.sjie.org

5 CONCLUSIONS In this paper, multi-point measurement of subsection parameters for dynamic load system is used, which is, a number of sensors have been placed on the measured points, and using Kalman filter recursive data fusion method to search for the minimum mean square estimation error of the measured parameters. According to the track parameters after the fusion, use the self-correlation and cross-correlation to analysis the change of the parameter and the anomalies of the track’s unscanned areas. It absorbs well the advantages both the data fusion based on kalman recursive filter and correlation analysis, with which the precision and reliability are enhanced and the status between the points can be estimated also. It avoids the limitation of kalman filter on math model and noise statistics characteristic at the same time. The experiment has proved that the dynamic load measure system can track those parameters, and effectively wireless transmits them to the host computer.

ACKNOWLEDGMENT We are deeply indebted to Professor C. Haiguan for his painstaking and thorough criticisms of this paper. He invested greater efforts into his criticisms than I had put into my original thoughts. Specially, we sincerely appreciate the Chongqing Computer Federation for giving us such an opening international conference to present our research results.

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AUTHORS 1

Xin LI (1981- ), male, Han Chinese, master, instructor, devote exclusively to intelligent control and embedded

systems development and applications.

Email: 94266636@qq.com.

- 103 http://www.sjie.org