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1、GPS数据的处理方法在结构变形监测的应用摘要：全球定位系统(GPS)现在正积极应用静态和动态位移法在有风的情况下对大型土木工程结构进行监测。然而,多路径效应和低采样频率的精度影响GPS位移测量。另一方面,加速度计静态和低频不能有效的措施结构反应,但可以精确测量高频结构的反应。因此,本文仅探讨GPS与测量结合的可能性，信号提高对测量准确度的(静态加上动态)一个结构的位移响应。集成数据处理技巧,利用两个经验模式分解(EMD)和自适应滤波的方法。一系列的运动模拟台试验，然后根据站点使用三个GPS接收器,一个加速度、“桌子”和一个运动仿真可以模拟各种类型的运动定义为输入，在波时间历程一个预先定义的静态

2、的位置。该数据处理技术应用：记录的GPS和加速度计数据，发现两者都有静态和动态位移。这些结果通过实测位移运动产生运动仿真的“桌子”。比较结果表明,该技术能显著提高测量准确度。关键词：GPS变形监测、结构、加速度计；综合数据处理、静态和动态位移法、EDM的经典分解模式；自适应滤波器。1、介绍：结构位移是评估一个大型土木工程结构的完整和安全关键参数。如高楼大厦或一个长桥在风力影响下的情况。风影响这样一个大型结构主要是由加速度计监测,然后采用动态位移响应表达式，用双重整合的测量加速度响应。一个加速度计是可以做到提取加速度响应，自然频率达1000赫兹,因为它具有极高的取样频率。(罗伯茨丁晓萍.2004

3、)然而,加速度计不敏感加速度的变化。速度和位移集成加速度随着时间的推移,信号将漂移，由于未知集成常量,以及一个高通滤波器，用于处理中引入低频漂移一体化进程。因此,认识到一个加速度计是无法测量静态和低频动态位移。全球定位系统(GPS)正积极地应用静态和动态位移测量。反应大土木工程结构在全球风力范围和连续工作的气象条件下的变形。然而,GPS位移测量的准确性取决于许多因素,包括卫星覆盖,大气的影响,多路径,GPS数据处理方法。奈奎斯特频率的现代化GPS接收器20赫兹的双采样率10赫兹,这是足以侦测自然频率民用工程结构。然而,关于结构动力位移监测、量化的准确性结构的动力位移是很重要的。这就要求采样率大

4、大高于感兴趣的频率成分的连续构造变形的信号。例如,当考虑一个10赫兹正弦波的存在每秒20样品取样时,只有两个样品为每一个获得正弦波周期,这是肯定的没有足够的重建这个正弦波。为了评估表现最好的GPS (莱卡GX1230 GPS接收器)。在动态位移测量、校准试验用的是一个运动仿真表进行开放地区采访。结果表明,GPS可以测量动态位移正确1赫兹。如果测站略被改变了，这个结果可能改变。显然,GPS测量性能与加速度计互补。本文从而进一步GPS-measured结合的可能性accelerometer-measured的信号提高，测量准确度(静态优先动态)位移响应的大型土木工程结构。集信号的概念GPS和加速度

5、计结构变形监测。提出融合算法的罗伯茨丁晓萍。(2004)从一个加速度计测量信号被过滤，由传统的滤波器来去除高频噪声,微小的GPS信号被过滤，自适应滤波降低了多路径。单一集成加速度信号然后从加速度计进行找到速度信号。由GPS数据，速度、加速度计信号，利用速度不断被重新计算。这些校准速度信号获得位移信号集成,位移信号,与全球定位系统。最后重置获得际的位移协调的结构。他们的研究结果显示,用该集成计划,millimeter-accurate定位可以保持在几十秒钟。这位移方法所获得的实际上是早些时候动力位移而已。李丁晓萍。(2005) 在大风影响下，进一步孤立的静态和静态位移组件由GPS数据和增加了他们

6、的动力学特性得到总变形位移。大型土木工程结构通常是非常好,因此他们的低频反应,是很难精确测量加速度计。此外,除了风致动力位移、风致静力位移、GPS测量结构中可能的污染还要很多路径。因此,很难适用现有的集成方案预测总位移与大型土木工程结构的反应。在这方面,提出了不同的综合GPS ，加速度计数据处理技术,为基础的在经验模态分解(EMD)和一个自适应滤波算法,提高了测量精度(静态加上动态)的位移响应大型土木工程结构。这是一个数据处理工具,能分解任何复杂的数据集少量的固有模态函数(IMF)和一个最后residualIn。该方法已成功应用，从提取时变平均风速。自适应滤波技术是信息信号提取的兴趣从污染信号

7、采用互相关系参考和主要的时间序列之间(Ge丁晓萍。2000年,罗伯特丁晓萍2002)。在认识到,多路径在每一天是可以重复的恒星 。评估的有效性集成数据处理技术,一系列的运动仿真，根据表测试站点使用三个GPS接收器,一个加速度计,和一个运动仿真桌子上。静力试验,用GPS天线安装在运动模拟表,在固定的条件,首先表现在测试网站的估计多径的数量。运动模拟桌子上,然后用产生不同类型的动态在一个预先定义的静态位移响应位置。GPS和加速度计测量数据记录在同一时期为静态的测试第二恒星的一天。该数据处理技术然后被用于记录GPS和加速度计静态数据找出动态位移。有效的最后通过评估综合方法进行比较综合结果与原运动模拟

8、运动产生的桌子。2、经验模式分解和自适应滤波器的这个EDM被用于这项研究，是为了分解GPS测量结构位移与星历表，使他成为一系列IMF组件和筛选残留过程。x(t) =cj(t) + r(t)Ne这里Ne是大量IMF的组件；(t)Ne是最后的残余。这最后的残余的结构位移与响应时间的历史,用GPS的一个单调函数,可以定义为位移的结构的意思。作为这个分解的概念是基于直接提取法、能源消耗的不同内在时间尺度的时间历史本身,模式的混合筛选过程中是不可能的。一个标准,虽然被检查,因此黄丁晓萍建议分离不同的波浪时间模式基础上成不同时期长度。在这项研究中,还是有止回阀和截止频率c是用来处理加速度时程来衡量一加速度

9、计以获得高频动态响应频率成分比截止频率。提出了一种自适应滤波器,作为一个信号,运作从两个测量的信息输入具有相同的长度：(1)主要测量p(k)期望信号包含的利息(k)的污染噪音n(k), (2)参考测量r(k)的噪音信号n(k)。为了提取满意信号s(k)从污染的主要测量p(k)利用自适应滤波技术,两个条件满足了:(1)所要求的信号s(k)和噪声n(k)primarymeasurement彼此之间不存在;噪音n(2)(k)测量振荡器的参考所需的信号s(k),但相关与噪声成分n(k)的初选信号。当多径测量由运动接收机类似于被测静止接收器，在我们之间试验基地的恒星天。自适应滤波技术可以应用tomiti

10、gate多径。位移测量和GPS一个移动的天线作为主要的测量p(k),其中包括预期的结构位移s(k)和多路径效应n(k)。测量信号的GPS天线与固定在同一时间期间动态测量,但在未来或以前的恒星天,作为参考的测量r(k)= n(k)。只有假设理想的结构位移是与多径而振荡器的参考测量和结构位移之间,但在某种程度上与相关的多径效果,因此应用自适应滤波研究。除了多径缓解,该研究也采用自适应滤波技术来提取低频动态从GPS-measured位移响应数据运用高频动力位移响应作为一个参考的加速度计测量。11An integrated GPSaccelerometer data processing techni

11、quefor structural deformation monitoringW. S. Chan Y. L. Xu X. L. Ding W. J. DaiReceived: 9 November 2005 / Accepted: 11 August 2006 / Published online: 7 September 2006 Springer-Verlag 2006Abstract Global Positioning System (GPS) is being actively applied tomeasure static and dynamic displacement r

12、esponses of large civil engineering structures under winds. However, multipath effects and low sampling frequencies affect the accuracy of GPS for displacement measurement.On the other hand, accelerometers cannot reliably measure static and low-frequency structural responses, but can accurately meas

13、ure highfrequency structural responses. Therefore, this paper explores the possibility of integrating GPS-measured signals with accelerometer-measured signals to enhance the measurement accuracy of total (static plus dynamic) displacement response of a structure. Integrated data processing technique

14、s using both empirical mode decomposition (EMD) and an adaptive filter are presented. A series of motion simulation table tests are then performed at a site using three GPS receivers, one accelerometer, and one motion simulation table that can simulate various types of motion defined by input wave t

15、ime histories around a pre-defined static position.The proposed data processing techniques are applied to the recorded GPS and accelerometer data to find both static and dynamic displacements. These results are compared with the actual displacement motions generated by the motion simulation table. T

16、he comparative results demonstrate that the proposed technique can significantly enhance the measurement accuracy of the total displacement of a structure.Keywords：GPS structural deformation monitoring Accelerometer Integrated data processing Static and dynamic displacements Empirical mode decomposi

17、tion (EMD) Adaptive filter1 IntroductionStructural displacement is a key parameter to assess the integrity and safety of a large civil engineering structure,such as a tall building or a long cable-supported bridge, under winds. Wind-induced responses of such a large structure are mainly monitored by

18、 accelerometers,and dynamic displacement responses are then obtained often through a double integration of the measured acceleration responses. An accelerometer is able to extract acceleration responses of a structurewith natural frequency up to 1,000 Hz because of the high sampling frequency (Rober

19、ts et al. 2004).However, an accelerometer is insensitive to lowfrequency acceleration changes. The velocity and displacement integrated from the uncompensated acceleration signals will drift over time due to unknown integration constants, and a high-pass filter should be used to cope with low-freque

20、ncy drift introduced during the integration process. It is therefore recognized that an accelerometer is incapable of measuring static and low-frequency dynamic displacement responses of a structure.Global Positioning System (GPS) is now actively applied to measure static and dynamic displacement re

21、sponses of a large civil engineering structure under winds due to its global coverage and continuous operation under all meteorological conditions. However, the accuracy of GPS for displacement measurement depends on many factors such as satellite coverage,atmospheric effects, multipath, and the GPS

22、 data processing method. The Nyquist frequency of a modern dual-frequency GPS receiver of 20 Hz sampling rate is 10 Hz, which is good enough to detect natural frequencies of a civil engineering structure.However, when concerning structural dynamic displacement monitoring, the accuracy of quantizatio

23、n of the structural dynamic displacement is important. This requires the sampling rate to be much higher than the frequency components of interest in the continuous signal of structural deformation. For instance, when considering a 10 cycles per second sinusoidal wave being sampled at 20 samples per

24、 second, only 2 samples can be obtained for each sine wave cycle, which is definitelynot enough to reconstruct this sine wave.In order to assess the best performance of GPS (Leica GX1230 GPS receiver) in dynamic displacement measurements, calibration tests using a motion simulation table were carrie

25、d out in an open area in Hong Kong (Chan et al. 2005). The results showed that the GPS could measure dynamic displacements properly if themotion frequencywas1Hz. This result may change slightly if the measurement site is changed.Clearly, the measurement performance of GPS is complementary to that of

26、 an accelerometer. This paper thus explores the possibility of integrating GPS-measured signals with accelerometer-measured signals to enhance the measurement accuracy of total (static plus dynamic) displacement response of large civil engineering structures. The concept of integrating signals from

27、GPS and accelerometer for structural deformation monitoring was presented by Roberts et al. (2004). and Liet al. (2005).In the integration algorithms proposed by Roberts et al. (2004), the measurement signals from an accelerometer were filtered by a conventional filter to remove high-frequency noise

28、, and themeasurement signals from a GPS were filtered using an adaptive filter to reduce multipath. The single integration of acceleration signals from the accelerometer was then performed to find velocity signals. The velocity signals from the accelerometer were reset using the velocity constant ca

29、lculated from the GPS data. These calibrated velocity signals were integrated to obtain displacement signals, and the displacement signals were finally reset with the GPS coordinates to obtain the actual displacement of a structure. Their results revealed that, with the proposed integration scheme,

30、millimeter-accurate positioning could be maintained within several tens of seconds. The displacement obtained by the earlier method was actually dynamic displacement only. Li et al. (2005) further isolated the static and quasi-static displacement components from the GPS data and added them to the dy

31、namic displacement to obtain the total displacement of a structure under winds.Large civil engineering structures are typically very slender and accordingly their low-frequency responses to winds are very difficult to accurately measure with accelerometers. Furthermore, besides wind-induced dynamic

32、displacement, wind-induced static displacement of a structure measured by GPS is likely to be contaminated by multipath. Hence, it is difficult to apply the existing integration scheme to the total displacement response of large civil engineering structures.In this regard, this paper presents differ

33、ent integrated GPS/accelerometer data processing techniques, based on the empirical mode decomposition (EMD) and an adaptive filter, to enhance the measurement accuracy of total (static plus dynamic) displacement response of a large civil engineering structure under winds. The EMD developed by Huang

34、 et al. (1998) is a data-processing tool that can decompose any complicated data set into a small number of intrinsic mode functions (IMF) and afinal residual.The EMD method has been successfully used to extract time-varying mean wind speed from typhooninduced non-stationary wind records for long ca

35、blesupported bridges (Xu and Chen 2004) and tall buildings (Chen and Xu 2004). The adaptive filter is a signal decomposer that extracts information of interest from the contaminated signal using the cross-correlation between reference and primary time series (Ge et al. 2000, Roberts et al. 2002). In

36、 recognition that the multipath is repeatable on every sidereal day, Ge et al. (2000) successfully applied adaptive filtering to GPS data to reduce the multipath.To assess the effectiveness of the proposed integrated data processing techniques, a series of motion simulation table tests are performed

37、 at a site using three GPS receivers, one accelerometer, and one motion simulation table. Static tests, with the GPS antenna installed on the motion simulation table that is in stationary condition, are first performed at the test site to estimate the amount of multipath. The motion simulation table

38、 is then used to generate various types of dynamic displacement response around a pre-defined static position.TheGPS and accelerometer measurement data are recorded within the same time period as the static tests but on the next sidereal day. The proposed data processing techniques are then applied

39、to the recorded GPS and accelerometer data to find both static and dynamic displacements. The effectiveness of the integrated methods is finally assessed through the comparison of the integrated results with the original motions generated by the motion simulation table.2 Empirical Mode Decomposition

40、 and Adaptive FilterThe EMD used in this study is to decompose GPSmeasured structural displacement response time history x(t) into a number of IMF components and a final residual through a sifting process (Huang et al. 1998):x(t) =cj(t) + r(t)NewhereNe is the number of IMF components; and r(t)Ne is

41、the final residual. This final residual of the structural displacement response time history, measured by GPS, is a monotonic function that can be defined as the mean displacement of the structure. As the concept of this decomposition is based on the direct extraction of the energy associated with v

42、arious intrinsic time scales of the time history itself, mode mixing during the sifting process would be possible. A criterion, termed the intermittency check, was thus suggested by Huang et al. (1999) to separate the waves of different periods into different modes based on the period length. In thi

43、s study, the EMD with an intermittency check and a cutoff frequency _c are used to process acceleration time history measured by an accelerometer so as to obtain a high-frequency dynamic response of frequency components greater than the cutoff frequency.An adaptive filter, used as a signal decompose

44、r, operates on the information from two measurement inputs with the same length: (1) a primary measurement p(k) that contains the desired signal of interest s(k) contaminated by noise n(k), and (2) the reference measurement r(k) of noise signal n_(k). In order to extract the desired signal s(k) from

45、 the polluted primary measurement p(k) by using the adaptive filter, two conditions have to be satisfied: (1) the desired signal s(k) and noise n(k) in theprimarymeasurement are uncorrelated with each other; (2) the noise n_(k) in the reference measurement is uncorrelated with the desired signal s(k

46、) but correlated in some way with the noise component n(k) of the primary signal. As the multipath measured by the moving receiver is similar to that measured by the stationary receiver between sidereal days at our test site (Chan et al. 2005), the adaptive filter can actually be applied tomitigate

47、the multipath. The displacement measured by the GPS with a moving antenna is taken as the primary measurement p(k), which includes the desired structural displacement s(k) and the multipath effect n(k). The signal measured by GPS with a stationary antenna during the same timeperiod as the dynamic me

48、asurement, but on the next or previous sidereal day, is taken as the reference measurement r(k) = n_(k).By assuming that the desired structural displacement is uncorrelated with the multipath while the reference measurement is uncorrelated with the structural displacement, but correlated in some way

49、 with the multipath effect, the adaptive filter can thus be applied in this study. Apart from the multipath mitigation, this study also uses the adaptive filter to extract low-frequency dynamic displacement response from the GPS-measured data by using high-frequency dynamic displacement response from the accelerometer as a reference measurement.