Noncontact Distance and Amplitude-Independent ... - Semantic Scholar

3 downloads 50987 Views 2MB Size Report
where fc and ϕ(t) denote the carrier frequency and the phase noise of the .... The audio speaker is driven by a standard signal generator, i.e., an Agilent function ...
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 1, JANUARY 2014

145

Noncontact Distance and Amplitude-Independent Vibration Measurement Based on an Extended DACM Algorithm Jingyu Wang, Xiang Wang, Lei Chen, Jiangtao Huangfu, Changzhi Li, Member, IEEE, and Lixin Ran

Abstract— Utilizing microwave continuous-wave Doppler radars to wirelessly detect mechanical vibrations have been attracting more and more interests in recent years. In this paper, aiming to solve the null point and nonlinear issues in small-angle approximation-based Doppler radar sensors and eliminate the codomain restriction in the arctangent demodulation approach, we propose and investigate an extended differentiate and crossmultiply (DACM) algorithm. With an additional accumulator, the noise performance of the original DACM algorithm is improved. Moreover, the amplitude information of the vibration can be directly retrieved from accumulation without involving any distance-dependent issue. Experimental validations show that the proposed algorithm can fully recover the vibration patterns with the measured noncalibrated amplitude agreeing well with the known precalibrated data. Application examples of mechanical fault detection and human vital sign detection are demonstrated, showing a wide range of potential applications of this algorithm. Index Terms— Arctangent demodulation, differentiate and cross multiply (DACM), noncontact vibration measurement, nonlinear phase modulation, radar sensor.

I. I NTRODUCTION

M

ICROWAVE Doppler radars have been used to sense mechanical vibration for decades. Applications include cardiopulmonary monitoring [1], through-the-wall life detection [2], rotational movement sensing [3], victims search and rescue [4], displacement sensing, and low velocity measurement [5]. With a shorter optical wavelength, a laser vibrometer can theoretically obtain higher measurement precision than microwave vibrometer [6]. However, it can only be used when vibrations under test can be directly “seen.” For a

Manuscript received January 16, 2013; revised March 13, 2013; accepted April 2, 2013. Date of publication August 21, 2013; date of current version December 5, 2013. This work was supported in part by the NSFC under Grant 61071063 and Grant 61131002, in part by the NSF under Grant ECCS1254838, and in part by the Cancer Prevention Research Institute of Texas under Grant RP120053. The Associate Editor coordinating the review process was Dr. Sergey Kharkovsky. J. Wang, J. Huangfu, and L. Ran are with the Laboratory of Applied Research on Electromagnetics, Zhejiang University, Hangzhou 310027, China (e-mail: [email protected]; [email protected]; [email protected]). X. Wang is with Zhejiang University School of Medicine, Hangzhou 310003, China (e-mail: [email protected]). L. Chen is with the China Aerospace Science and Industry Academy of Information Technology, Beijing 100070, China (e-mail: radiumchen@ 126.com). C. Li is with the Department of Electrical and Computer Engineering, Texas Tech University, TX 79409 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2013.2277530

microwave vibrometer, instead, it can perform through-theobstacle measurements. This unique property is very important in practical applications. A continuous wave (CW) Doppler radar detects the vibration of a target by measuring the phase modulated to the wave reflected off the moving target. Traditionally, to detect a “weak” vibration whose amplitude is much smaller than the wavelength of the CW carrier, a small-angle approximation approach is used to demodulate the phase shifts caused by the movement of the object [8]–[12]. Because the output of CW Doppler radar receivers is modulated by the target motion through a sinusoidal function, it suffers from two problems associated with the detection distance and the vibration amplitude. First, the small-angle approximation-based measurement is distance-dependent: when the distance between the target and the radar sensor changes, the detection sensitivity of the receiver will also change, resulting in alternately appearing “optimum” and “null” points where the receiver exhibits the best and the worst noise performance [7]–[9]. To solve this problem, multiple solutions have been proposed and investigated. In [7], quadrature demodulation was introduced in the receiver, such that at least one channel that is not working at the null point can be chosen to obtain an acceptable demodulation. In [8], a frequency tuning and a double-sideband transmission were used. By choosing a proper frequency separation, the severe null point problem was relieved. In [9], a voltage-controlled RF phase shifter was employed to tune the transmission delay, which is equivalent to the adjustment of the detection distance. However, to maintain the sensor always working at the optimum point without involving distance dependency, extra costs of system complexity and adaptive feedback loop have to be paid. Second, the small-angle approximation is not valid in cases when vibration amplitudes are comparable to the carrier wavelength. In this case, strong nonlinear harmonics and intermodulation products that do not reflect the real movement of the target will be generated, even when the measurement is performed at the optimum point [11]. Besides, in the small-angle approximation approach, the amplitude information of the vibration under test is not directly retrieved from the measured data. One validated method is to calculate the harmonic ratios of the baseband signal with the help of Bessel function expansion [11]. However, this approach is currently only available when a limited number of vibration tones exist. In addition, there is a strict

0018-9456 © 2013 IEEE

146

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 1, JANUARY 2014

requirement that the harmonic ratios need to be measured accurately. To solve the above problems, an arctangent demodulation approach has been proposed [5], [13]. It has been demonstrated that this approach is able to obtain satisfactory measurements compared with the small-angle approximation approach. However, a direct arctangent function mathematically has a native codomain range (−π/2, π/2). Once the demodulation exceeds this range, a discontinuity will occur. Theoretically, such discontinuity can be eliminated by phase unwrapping algorithms that shift the discontinuous point by an integer multiple of π. However, it is practically nontrivial for a hardware (or software) to make a judicious choice on which point needs a shift, especially when the vibration amplitude is large. On the other hand, even when the vibration amplitude is small, automatic calibration may still be difficult when noise exists. As indicated in [14], this kind of phase unwrapping is not always effective due to the presence of noise in practice. Recently, an alternative phase demodulation algorithm without the codomain restriction, called differentiate and crossmultiply (DACM), has been proposed in optical signal processing [15]. As an efficient phase demodulation algorithm in optical systems, DACM can effectively avoid the major disadvantages of the small-angle approximation and the direct arctangent demodulations. Thus, it could be a good candidate in the CW Doppler sensors. In this paper, to meet the specific distance- and amplitude-independent requirements of noncontact vibration measurement, an extended DACM algorithm is proposed and investigated. With an additional accumulator added to the original digital domain DACM, the noise performance can be significantly improved. Both small and large amplitude information of a mechanical vibration can be directly retrieved from the accumulation process, without involving any distance and amplitude dependency and codomain restriction issues. Experimental validations show that the proposed algorithm can fully recover the vibration patterns. This paper is organized as follows. In Section II, theoretical analysis of the extended DACM algorithm is presented. Measurement results and analysis are presented in Section III. To illustrate the effectiveness of the proposed approach, two application examples are raised in Section IV. Finally, a conclusion is summarized in Section V. II. T HEORY Fig. 1 illustrates the traditional architecture of a Doppler radar sensor that is commonly used to detect mechanical vibration. Neglecting the amplitude variation and normalizing the signal amplitude to 1, the radar typically transmits the following CW carrier to the vibrating target: T (t) = cos [2π f c t + ϕ (t)]

(1)

where f c and ϕ(t) denote the carrier frequency and the phase noise of the transmitter, respectively. After being reflected by the target at a nominal detection distance d0 with a time-varying displacement x(t), the received signal is quadrature demodulated, and the baseband in-phase (I ) and

Fig. 1. Common configuration of traditional Doppler radar to sense mechanical vibration.

quadrature-phase (Q) outputs are I (t) = A I cos [ (t)] Q (t) = A Q sin [ (t)]

(2) (3)

where

4π x (t) + ϕ (t) . (4) λ In the above equations, A I and A Q denote the amplitude of the two quadrature outputs, ϕ(t) is the residual phase noise, θ is a constant phase shift, and λ is the wavelength. Note that θ = 4πd 0 /λ + θ 0 is determined by the nominal detection distance d0 and the phase shift θ 0 at the reflection surface. According to the range correlation theory, when coherent demodulation is applied and the detection distance is not too long, ϕ(t) can be neglected [7]. Therefore, when processing the baseband signal using small-angle approximation, the amplitude of θ will determine the system performance. Taking I (t) as an example: when the vibration amplitude is small enough and θ is an odd multiple of π/2   4π x (t) + ϕ (t) . I (t) ≈ A I (5) λ  (t) = θ +

Under such conditions, the system is at an optimal point and outputs signals with the best signal-to-noise ratio (SNR). On the other hand, if θ is an integer multiple of π, I (t) is at a null point and takes a form of   1 2 (6) I (t) ≈ A I 1 − · [4π x (t) /λ + ϕ (t)] . 2 Its spectrum consists of DC component and the even order harmonics of x(t) [7]. It is obvious that near the null point, recovering x(t) from I (t) becomes difficult. Furthermore, when the amplitude of vibration is comparable to λ, the odd order harmonics of x(t) would appear at the optimum point, and it is possible that the fundamental component of the output can be even smaller than its harmonics [11]. By applying an accurate phase demodulation, such as the arctangent demodulation [5], [13], (t) can be recovered from the I /Q signals regardless of the target position. However, due to its native multiple-valued characteristic, the arctangent function only returns its principal value Atan(t) = arctan

Q (t) I (t)

(7)

which is restricted to its codomain range (−π/2, π/2). Once there are some points of the demodulation result exceeding this

WANG et al.: NONCONTACT DISTANCE AND AMPLITUDE-INDEPENDENT VIBRATION MEASUREMENT

Case I

Case II

Case III

Q[n]

Φ(t) (rad)

π/2 (a)

0

147

1-Z

t

-1

Accumulator ω[n] Φ[n]

(b)

Atan (t) (rad)

-π/2

1-Z

π/2 0

t

-π/2

Fig. 2. (a) Desired phase demodulation results and (b) the corresponding arctangent demodulation results. Case I: the vibration amplitude is small and the DC component of the desired result is far from the boundary of (−π /2, π /2). Case II: the vibration amplitude is small and the DC component of the desired result is close to π /2. Case III: the vibration amplitude is larger than λ/8.

range, discontinuity may occur. And the system performance will be degenerated. Fig. 2 illustrates the desired phase demodulation results and the corresponding arctangent results with codomain limitation for three different cases. It is seen from cases I and II that when the vibration amplitude A is small enough, the discontinuous points only occur if the DC component of (t) (i.e., θ ) is near the boundary of (−π/2, π/2). These discontinuous points can be easily calibrated after shifting them by π (or −π) in the amplitude axis. However, the problem becomes more severe in case III when A is larger than λ/8. Under the circumstance of 4πA/λ > π/2, the discontinuities cannot be avoided, regardless of θ . All the points that are larger than π/2 and smaller than −π/2 will appear with undesired patterns. To calibrate the discontinuity, some signal segments need to be shifted by π, while others need to be shifted by −π. As A gets even larger, the calibration gets more and more complicated. It is difficult to implement such an automatic discontinuity calibration in a real adaptive system, especially when noise is inevitable. Different from the direct arctangent process, the DACM algorithm computes a derivative to the arctangent function instead   I (t) Q˙ (t) − I˙ (t) Q (t) Q (t) d = (8) arctan ω (t) = dt I (t) I (t)2 + Q (t)2 where Q˙ (t) and I˙ (t) denote the time derivative of Q(t) and I (t), respectively. Detailed derivation of (8) is provided in Appendix. Because (t) has something to do with the displacement function x(t) of the vibration under test, ω(t) is related to the velocity function of the same vibration. Be aware that the calculated ω(t) is a single-valued function, such that there is no codomain restriction involved. However, the need for differentiators in the traditional DACM algorithm makes the calculation of ω(t) very sensitive to noise, especially the high frequency noise [15]. To suppress the noise brought by the differentiator, we further add an integration procedure to retrieve (t). By doing so, all noises with zero means can be effectively suppressed. The addition of the integration would also benefit the retrieval of both the frequency and the amplitude information

-1

Z

-1

I [n]

Fig. 3.

Block diagram of the extended DACM algorithm.

of the vibration under test. For small-angle approximation, the demodulated result is the displacement function x(t) times A I . Because A I would depend on the path loss and the loop gain, it is impossible to precisely retrieve the vibration amplitude without calibration. However, according to (4), once (t) is obtained, x(t) is directly obtained, given that all the vibration information are contained in the phase of demodulated signals, which has nothing to do with either the path loss or the system loop gain. Only the interference to the phase, such as the residual phase noise, will potentially influence the retrieved result. In digital domain, the proposed extended DACM algorithm can be rewritten in a discrete form n  I [k] {Q[k]− Q[k − 1]}−{I [k]− I [k −1]} Q[k] [n] = I [k]2 + Q[k]2 k=2

(9) where the differentiation is approximated by a forward difference, and the integration is replaced with an accumulation. The block diagram is illustrated in Fig. 3, in which some procedures are represented in z-transformation, where the transfer function Z −1 denotes a unit delay, and 1 − Z −1 represents a forward difference operation. It is seen that this algorithm is simple and straightforward, without using any complicate mathematical functions. Its traditional counterparts, such as coordinate rotation digital computer (CORDIC), are generally sequential in nature [16], making them rather slow in a system without hardware multiplier. On the contrary, the block diagram of the extended DACM indicates its native parallel computable characteristic. The four multiplications can be carried out simultaneously with hardware, which could significantly reduce the processing time by a factor of 75%, making it quite suitable for real-time applications. III. E XPERIMENTS AND D ISCUSSION A. Experimental Setup To validate the proposed algorithm, measurements have been conducted with the experimental setup shown in Fig. 4. In order to obtain a precisely controlled vibration surface to reflect the incident carriers, a light copper plate driven by an audio speaker is chosen to generate monotone vibrations. The audio speaker is driven by a standard signal generator, i.e., an Agilent function generator 33210A. By tuning the output of the 33210A, the frequency and the amplitude of the copper surface can be easily controlled. The speaker-plate assembly

148

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 1, JANUARY 2014

Fig. 4. Experimental setup for monotone vibration measurements. (a) Block diagram. (b) Photographs of the experimental setup.

Agilent spectrum analyzor E4407B 10 MHz Reference

IF

Agilent vector signal analyzor 89600s I [n]

Q[n]

Agilent signal generator E8267C

Fig. 5.

Block diagram of the instruments-based radar sensor.

is placed on a 1-D translation stage, which is driven by a step motor (HS200 of Danaher Motion GmbH) with a horizontal step-by-step movement resolution higher than 0.1 mm. In this way, the detection distance (i.e., d0 ) can be precisely controlled. The audio speaker is a moving-coil speaker (PA8 from Swans Speaker Systems Inc.). According to the speaker operating theory [17], under normal operating conditions, a moving coil speaker can be modeled as a linear system that converts an electric signal into a mechanical vibration. Although the frequency response of a speaker is not flat in the whole frequency band, the reproducibility is guaranteed when the speaker is driven by an input signal with a constant power and a single sinusoidal frequency. A radar sensor with a digital intermediate frequency (digital-IF) architecture is implemented with standard microwave instruments. This instrument-based radar system has been reported in [18]. Compared with the zero-IF architecture widely used in CW Doppler radar sensors [4], [5], and [7], it is free of DC-offset, I /Q mismatch and flicker noise issues. Fig. 5 illustrates the block diagram of the radar sensor. It mainly consists of three instruments, i.e., an Agilent

vector signal generator E8267C, an Agilent spectrum analyzer E4407B, and an Agilent vector signal analyzer 89600s. The signal generator E8267C serves as the transmitter to generate microwave carriers with stable phase and amplitude in a wide frequency range from 250 kHz to 20 GHz. The receiver consists of the E4407B that acts as the down-convertor and the 89600s that acts as the IF processor. The E4407B down converts the reflected wave to a 70 MHz IF. Then the IF signal is sampled and quadrature demodulated by the 89600s, and the I /Q signals described in (2) and (3) can be obtained, which are further analyzed with the extended DACM algorithm on PC. The antennas we used are two standard K -band horn antennas HD-140HAX manufactured by Hengda Microwave Inc. When operating at 20 GHz, each of them has a gain of 22 dBi. The far-field range is calculated as 0.94 m based on the Fraunhofer distance. Since the targets have smooth metallic surface, and the cross-polarization of the standard horn antenna is very small (