JOURNAL OF COMPUTERS, VOL. 6, NO. 2, FEBRUARY 2011 359 Weak Signal Detection Research Based on Duffing Oscillator Used for Downhole Communication Xuanchao Liu School of Electronic Engineering, Xi’an Shiyou University, Xi’an, China [email protected] Xiaolong Liu School of Electronic Engineering, Xi’an Shiyou University, Xi’an, China [email protected] Abstract—Weak signal detection is very important in the information transmission. Thus, the study of weak signal downhole acoustic telemetry system. This paper introduces detection technology is of great significance. the Duffing oscillator weak signal detection method for the Weak signal detection is an emerging technical downhole acoustic telemetry systems. First, by solving the discipline, mainly researches detection principle and Duffing equation, analyzed the dynamics characteristic of method of the weak signal buried in the noise, which is a Duffing oscillator and weak signal detection principle; and then on this basis, built Duffing oscillator circuit based on kind of comprehensive technology in the signal the Duffing equation, by circuit simulation to study the processing technology, mainly utilizes the modern Duffing circuit sensitive to different initial parameters, electronics, the information theory and the physics conducted a detailed analysis for how the different method, to analyze reason and rule the noise producting, parameters impacted the system statuses and the low-pass to study statistical nature and difference of the detecting filter with simplicity and availability was proposed for signal and the noise; uses a series of signal processing signal demodulation. The results show that the method method, achieves the goal that weak signal buried in the could effectively detect the weak changes of input signal and background noise is detected successfully. suppress strong noise; it is feasible, advanced and practical Generally, weak signal detection mostly makes used for downhole acoustic telemetry system. periodic signal as the main detecting signal. Fully makes Index Terms—weak signal detection, Duffing oscillator, use of the additivity of periodic signal and the Duffing chaos circuit simulation, downhole communication, randomness of noise to extract useful signal effectively, downhole acoustic telemetry system achieves the goal of signal detection. Because the sinusoidal signal has the simplicity and the easy determinism in the extraction of frequency characteristic I. INTRODUCTION and phase feature as well as in the signal processing aspect, specially its Single frequency characteristic makes In the oil field exploration and development process, it has unique advantage in the anti-interference which needs timely to obtain downhole information, processing aspect, makes sinusoidal signal become an downhole acoustic telemetry system (D-ATS) is an important object of study in the weak signal detection effective wireless transmission way to achieve downhole domain. information [1] [2]. It based on the theory of acoustic can The most common of several mature weak signal be transmitted along the steel medium (oil pipe or drill detection methods are mainly the following [3]: pipe) to complete information transmission. The main realization of ways including: downhole high-power and A. Periodic signal relevant detection method low-frequency sine acoustic wave signal transmitters, This method can pick-up the periodic signal drowned transmission medium and ground weak acoustic receiver. in random noise, it uses the feature of signal related in The ground weak signal detection is very important part time. The way in achieving is divided into self-correlation of it. Because of poor working conditions, high detection method and the cross-correlation detection temperature, little space and only the case of battery- method. Self-correlation detection method uses the signal powered， therefore, the signal intensity of downhole characteristics of periodic and noise characteristics of acoustic generator is subject to certain restrictions. When random, through the relevant operation to remove noise. it is transmitting, not only subjected to natural absorption Cross-correlation detection method is based on the attenuation, but a variety of random noise disturber. frequency of known signal and needed a same frequency Finally, we get a weak acoustic signal which drowned in reference signal, which through reference signal and the noise at the ground. Whether can accurately detect the detecting signal make cross-correlation to remove noise. useful signal is the key to success or failure of The detection effect of cross-correlation method is better © 2011 ACADEMY PUBLISHER doi:10.4304/jcp.6.2.359-367 360 JOURNAL OF COMPUTERS, VOL. 6, NO. 2, FEBRUARY 2011 than self-correlation method, but the detected signal Signal detection based on chaos was developed from frequency must be known. the 1990s; this method had high sensitivity and low detection threshold to weak signal, as well as B. Periodic signal sampling points integral method characteristic of strong abatement ability to noise, and This method uses the signal characteristics of periodic hopefully to reduce the cost of testing equipment, so and noise characteristics of random, divides periodic became hot spot in the weak signal detection research signal into some time intervals, and then sample signal at areas as soon as it appeared, and once had presented these time intervals, and averaged the sample values many outstanding methods [6][7]. which in the each cycle same position by analog circuits Chaos theory for the detection of weak signals derived integral or through computer with digitally processing from the discovery of chaos in nonlinear dynamic system. method. This method is aimed at enhancing useful signal The research of chaos theory indicates that certain and suppressing noise to achieve effective detection for nonlinear chaos systems have the sensitivity to small signal. signal and the immunity to noise under the controlled C. Single frequency lock detection method condition, utilizing this characteristic, takes detecting signal as the driving force of the chaos system, although This method uses the signal’s single frequency or the noise is intense, it has no influence on system mode's narrow-band cosine (or sine) characters to complete change; however once has specific signal, even if its narrow band processing, and then making use of cross- amplitude is quite small, also will make the system correlation theory for cross-correlation processing of the change. The computer recognizes system modes by the signal under test and reference signal with the same method of image recognition or envelope abstraction and frequency. At last, it can detect the useful signal buried in so on, and then judges whether signal is exist, thus noise. achieve the goal of detecting weak signal from strong With continuous development of the integrated circuits background noise. The extreme sensitivity of the chaotic and computer technology, the people still continue to dynamic system behavior for the initial parameters results explore various weak signal detection methods, for in to study it on weak signal detection. Especially, example, based on wavelet transform detection method, because of clear physical meaning and convenient based on Chaos theory detection method, based on fuzzy debugging of Duffing oscillator, it became the hotspot of mathematics detection method, based on artificial neural weak signal detection research. network detection method and so on. Duffing equation is a mathematical model which In the above methods of weak signal detection, the describes weak damping motion of Duffing oscillator traditional weak signal detection mainly uses the method (soft spring oscillator) [8][9]. It is a second order of linear filtering and signal superimposition to extract differential equation containing a cubic item. In the the signal, but it is often unable to survey signal when the external excitation, the equation behavior would oscillate background noise is very strong and the detecting signal which can be expressed as the periodic motion and is very weak, can not meet the needs of weak signal chaotic motion. The concrete expression is the following. detection requirements. In the new field of study. Although modern detection methods have obvious effect, χ '' + κχ ' − χ + χ 3 = F(t) = γ sin(t) . (1) strong adaptability, but most of them have complex structure, difficult to achieve and to promote. Therefore, γ sin(t) for period driving force, k for damping ratio, the weak signal detection technology has a new -x(t) +x3(t) for nonlinear restoring force. When k is fixed breakthrough when the chaos theory is introduced in the (such as k=0.5), the system status would present the signal detection domain successfully. The Chaos marvelous change with γ changing. detection method is different from a variety of existing measuring methods, which is a new signal processing As γ is zero, let -x(t) +x3(t)=0, we could achieved 3 method. stable points, x=0, x=-1, x=1. According to original status Particularly, the method based on Duffing oscillator of difference, it would fall on the different position, showed chaos theory received considerable attention. This as Fig1 ~Fig3. method has made a lot of research results. Study finds that this method is especially suited for downhole acoustic telemetry system with good detecting effect, simple structure, more easy achievement and other advantages. But, most studies are still at the stage of theory exploratory;