基于ARMA模型的隧道位移时间序列分析

在新奥法隧道施工中,隧道位移监测对于评价围岩稳定性和支护结构合理性起重要作用。目前大都采用AR模型对隧道位移进行时间序列分析,避开了非线性估计,致使拟合精度和模型实用性较差。为此,介绍了具有较高预测精度和较好适用条件的ARMA模型及其常用参数估计方法,基于其参数非线性估计带来的不便性,提出一种ARMA模型参数估计近似线性方法,把残差用Taylor级数一阶展开,将非线性估计线性化,用线性最小二乘法估计参数最终值。用该方法对重庆市大足县南环二路南山隧道位移监测数据进行时间序列建模分析,预测与实测值吻合较好,证明了该方法的实用性。     

隧道围岩压力的神经网络时间序列分析

围岩压力是隧道开挖后重要的反馈信息之一,受不确定性因素影响,围岩压力监测数据是一个不平稳的时间序列,包括趋势项和随机项。采用BP网络对不平稳时间序列进行数据拟合,处理趋势部分,利用ARMA模型处理随机部分。结合累进算法,对浙江某新建隧道围岩压力进行时间序列预测。结果表明该方法具有较高的预测精度,最大相对误差为3.73%,能够应用于工程实际当中。     

应用CARMA模型评价矿井疏水对泉流量的影响

受控自回归滑动平均模型是用来描述随机现象中输入与输出关系的一类线性动态模型。本文以大柳塔井田双沟泉域为例,应用该模型分别对双沟泉域在天然条件和矿井疏水条件下的泉流量进行预测,并据此评价矿井疏水对泉流量的影响。     

Stochastic modeling of gold mineralization in the Champion lode system of Kolar gold fields (India)

Stochastic modeling of gold mineralization in the Champion lode of Kolar gold fields was carried out using assay data taken from developmental headings. After dividing the lode into 71 horizontal and 18 vertical strata, autoregressive (AR), moving average (MA), and autoregressive and moving average (ARMA) models were developed and applied. The model selection with the acf and pacf for the various strata showed that in most of the cases, ARMA modeling of first-order would forecast gold headings with a reasonable degree of confidence. This was substantiated by comparing the coefficients of variation. From a parsimony point of view, AR (1) model may also be considered valid. The best overall models are: ARMA (1, 1), ; AR (1), , where a_t is N (0, _a ² ), x is in logarithms of in-dwt, and t is in block units of 100 ft. The applications of these models to a specific stratum are given. These models would also be helpful to describe the characteristics of the gold mineralization process of this lode.     

Variation in the value of mineral resources. Part I. The USA

The value of mineral resources produced in the USA during the 93 years, 1880–1972, deflated to 1967=100, totals 921 billions of dollars; this yields a value of $303,289 per mi² for the conterminous 48 states. Alaska has aggregated some 4160 millions of dollars during the same period, an average yield of some 7107 deflated dollars per mi². If we assume Alaska will achieve the average level of the “lower 48,”the potential value of its mineral resources is 178 billions of deflated 1967 dollars. Fuels account for about two-thirds of this value followed by about 20 percent for each of the aggregates, nonmetals and metals. The deflated dollar value of these four aggregate figures, fuels, nonmetals, metals, and total, during the period 1880–1972 are four time series and the economic processes which produced these series may be modelled through Box-Jenkins procedures. The value of fuels has steadily increased through the period, except for the depression years of the 1930s; this series may be represented as a multiplicative seasonal ARIMA(1,1,0)(1,0,1) model with periods at 4 and 3 yr for the autoregressive (AR) and moving average (MA) terms. Forecasts for 1973 to 1980, using the model, show the value of fuels produced to be about 20 billions of dollars per annum. The value of nonmetals also increased throughout the period except for a somewhat larger drop during the depression years of the 1930s. A multiplicative seasonal ARMA(1,0,0)(1,0,1) model with period at 7 yr for both the AR (autoregressive) and MA (moving average) terms appears to best reflect this series; the forecasts with this model fluctuate around their present annual value of some 6 billions of dollars. The value of metals behaves less consistently; it was much more strongly affected by the Great Depression and its subsequent growth is slower and less consistent than those of the fuels and nonmetals. It is appropriately represented by a multiplicative seasonal ARMA(1,0,0)(0,0,2) model with moving average (MA) periods at 6 and 11 yr respectively. Forecasts with this model show a decline in value for years beyond 1972; the large residual “error” \((\hat \sigma _e = 0.0925)\) , which is about twice as large as the equivalent errors for the value of fuels and nonmetals ( \(\hat \sigma _e = 0.0408\) and 0.0532, respectively), makes this forecast less firm. The total value of mineral resources is composed of all three series and, because fuels account for two-thirds of the total value, the two series closely resemble each other. The total value is not a simple aggregate of the three series; it is appropriately fitted by a multiplicative seasonal IMA(0,1,0)(0,0,2) model with periods at 7 and 11 yr (and error \(\hat \sigma _e = 0.0423\) ). Forecasts using this model imply that the total value of mineral resources produced will be over 30 billions of dollars per annum through 1980.     

Univariate and multivariate stochastic modeling of the chemical composition of iron ores in Northern Goa, India

Chemical components such as SiO ₂,TiO ₂,MnO, P ₂ O ₅,and especially Fe ₂ O ₃ of the iron ores of Bicholim Mine, Northern Goa, have been determined for lateral and vertical sections of the mine at equal intervals of 3 and 1 m, respectively, so as to form the spatial (time) series. Univariate stationary models of the type Autoregressive moving average—ARMA (p, q)—were established for each series on the basis of statistical analyses of their auto (acf) and partial auto (pacf) correlation functions. These models were used for forecasting assay values at different lead distances from any pivot. Principles of parsimony simplified all of the candidate ARMA (p, q) models to pure AR (p) models, and the univariate forecasts were significantly improved by multivariate stochastic forecasts.     

基于改进广义S变换二次时频谱反褶积在南海工区的应用

传统的时频域反褶积模型虽然吻合地震子波在粘弹性介质传播过程中的衰减特征,但受拟合函数和时频分析窗函数的影响,使得其算法缺乏稳定性和准确性。为了避免这一问题,推导出一种基于改进广义S变换二次时频谱反褶积方法。利用改进广义S变换的灵活性来获取非平稳地震记录时频谱,再对其傅里叶变换得到二次时频谱,从而以一种低通滤波的方式提取子波时频谱,实现二次时频谱反褶积。经理论模型论证和实际数据处理结果表明,利用二次时频谱提取子波具有较高的准确性,同时能够有效地分辨薄层,在不用考虑Q值的条件下直接恢复地震波被地层吸收所引起的衰减。     

Standard cumulative semivariograms of stationary stochastic processes and regional correlation

The standard cumulative semivariograms (SCS), obtained analytically from the currently employed stationary stochastic processes, provide a basis for the model identification and its parameter as well as regional correlation estimations. The analytical solutions for different stationary stochastic processes such as independent (IP), moving average (MA), autoregressive (AR), and autoregressive integrated moving average ARIMA (1,0,1) processes give rise to different types of SCSs which can be expressed in terms of the autocorrelation structure parameters only. The SCSs of independent and MA processes appear as linear trends whereas other type of processes have SCSs which are nonlinear for short distances but become linear at large distances. Irrespective of the stationary stochastic process type the linear portions of SCSs have unit slopes. The vertical distance between these linear portions and that of the IP cumulative semivariogram (CS), provide an indicator for measuring the regional correlation. In the case of stationary processes, the straight line portions of any CS are parallel to each other. Hence, it is possible to identify the model from the sample CS. Finally, necessary procedures are provided for the model parameters estimation. The methodology developed, herein, is applied to some hydrochemical ions in the groundwater of the Wasia aquifer in central part of Kingdom of Saudi Arabia.     

Estimation of semivariograms by the maximum entropy method

A wide variety of semivariograms may be represented in terms of a first- or second-order autoregressive (AR) process, and the nugget effect may be included by use of a moving average (MA) process. The weighting parameters for these models have a simple functional dependence on the value of the sill and the semivariance at the first and second lag. These may be estimated either graphically from the semivariogram or directly from the computed values. Improved spectral estimates of geophysical data have been obtained by the use of the maximum entropy method, and the necessary equations were adapted here for the estimation of the weighting parameters of the AR and the MA processes. Comparison among the semivariograms obtained for the ideal case, the observed case, and the estimated case for artificial series show excellent correspondence between the ideal and estimated while the observed semivariogram may show marked divergence.     

Post-stack high-resolution deconvolution using Cauchy norm regularization with FX filter weighting

High-resolution deconvolution can mathematically be viewed as a regularized inverse problem. Besides, the result of the high-resolution deconvolution is generally accepted as reflectivity series of the layered media. On the other hand, lateral continuity is frequently poorer than vertical resolution on post-stack seismic section after application of any high-resolution deconvolution. However, because of the ill-posed inherent of the deconvolution problem, the Cauchy norm regularization term, a non-quadratic prior-information is widely used to provide the stability and uniqueness of the problem. But, it does not provide adequate quality of deconvolution if the noise in the data is strong. In this study, a stable and high-resolution deconvolution of post-stack seismic data was accomplished by an iterative inversion algorithm incorporating the Cauchy norm regularization with FX filter weighting. Cauchy norm regularization was utilized to force the solution to a spikiness structure, while the effective random noise reduction was performed by using the FX filter. Applications to synthetic and real post-stack data showed that the resolution in the vertical direction and continuity in the lateral direction are better improved. Thus, we think that this process makes seismic sections obtained especially from thin layered sedimentary basins more interpretable.     

Automatic identification of fake patterns caused by short-width wavelets in seismic data

Despite the popularity of using the Haar wavelet filter in many applications, it sometimes introduces fake patterns into the multi resolution analysis (MRA) of seismic data. In this work, we compared different wavelet filters to demonstrate that these patterns are fake and not part of the original waveforms and to show that they are a result of using the Haar wavelet filter as a short-width wavelet. To achieve this, many seismic waveforms from two different sources: the Egyptian National Seismic Network (ENSN) and the High Sensitivity Seismograph Network Japan (Hi-net) are used with different wavelet filters. We propose an algorithm based on an autoregressive (AR) model to detect these patterns automatically and fully.     

Caspian Sea level prediction using satellite altimetry by artificial neural networks

The demand for accurate predictions of sea level fluctuations in coastal management and ship navigation activities is increasing. To meet such demand, accessible high-quality data and proper modeling process are critically required. This study focuses on developing and validating a neural methodology applicable to the short-term forecast of the Caspian Sea level. The input and output data sets used contain two time series obtained from Topex/Poseidon and Jason-1 satellite altimetry missions from 1993 to 2008. The forecast is performed by multilayer perceptron network, radial basis function, and generalized regression neural networks. Several tests of different artificial neural network (ANN) architectures and learning algorithms are carried out as alternative methods to the conventional models to assess their applicability for estimating Caspian Sea level anomalies. The results derived from the ANN are compared with observed sea level values and with the forecasts calculated by a routine autoregressive moving average (ARMA) model. Different ANNs satisfactorily provide reliable results for the short-term prediction of Caspian Sea level anomalies. The root mean square errors of the differences between observations and predictions from artificial intelligence approaches can be significantly reduced by about 50 % compared with ARMA techniques.     

改进的子波反褶积在天然气水合物地震资料处理中的应用

天然气水合物地震勘探的实际工作,需要在三维空间对天然气水合物矿体进行精细刻画,为此必须获得高分辨率的地震资料,而反褶积处理是提高地震资料分辨率的主要手段之一。本研究设计的改进子波反褶积算法,对地震记录的对数功率谱进行滤波,不但可有效识别BSR,同时可克服反射系数非白噪声的影响;采用谱间的互相关平均代替算术平均,可有效提高地震资料的分辨率;在提取子波的过程中,采用希尔伯特变换算法,提取子波简单、方便。通过对南海北部海域HS621测线的地震数据进行处理,证明该算法不但能稳定、清晰地追踪BSR,并且能有效地提高地震数据分辨率,满足天然气水合物地震资料精细处理的要求。     

Estimation of the transfer function by autoregressive deconvolution techniques—An application to time series analysis

The transfer function of time-dependent models is classically inferred by the ordinary least squares (OLS) techniques. This OLS technique assumes independence of the residuals with time. However, in practical cases, this hypothesis is often not justified producing inefficient estimation of the transfer function. When the residuals constitute an autoregressive process, we propose to apply the Box-Jenkins' method to model the residuals, and to modify in a simple manner the primary convolution equation. Then, a multivariate regression technique is used to infer the transfer function of the new equation producing time-independent residuals. This three-step autoregressive deconvolution technique is particularly efficient for time series analysis. The reconstitution and the forecasting of real data are improved efficiently. Theoretically, the proposed method can be extended to the convolution equations for which the residuals follow a moving average or an autoregressive-moving average process, but the mathematical formulation is no longer direct and explicit. For this general case, we propose to approximate the moving average or the autoregressive-moving average process by an autoregressive process of sufficient order, and then the transfer function. Two case studies in hydrogeology will be used to illustrate the procedure.     

Prediction of weather parameters on a very short time scale by an Auto Regressive process for aviation flight planning

Forecasting weather parameters such as temperature and pressure with a reasonable degree of accuracy three hours ahead of the scheduled departure of an aircraft helps economic and efficient planning of aircraft operations. However, these two parameters exhibit a high degree of persistency and have nonstationary mean and variance at sub-periods (i.e. at 0000, 0300, 0600,…, 2100UTC). Hence these series have been standardised (to have mean 0 and variance 1) and thereafter seasonal differenced (lag 8) to achieve almost near stationarity. An attempt has been made to fit the standardised and seasonal differenced series of Chennai (a coastal station) and Trichy (an inland station) airport into an Auto Regressive (AR) process. The model coefficients have been estimated based on adaptive filter algorithm which uses the method of convergence by the steepest descent. The models were tested with an independent data set and diagnostic checks were made on the residual error series. An independent estimation of fractal dimension has also been made in this study to conform the number parameters used in the AR processes. The models contemplated in this study are parsimonious and can be used to forecast surface temperature and pressure.     

Ground penetrating radar signal processing improves mapping accuracy of underground voids and seawater table: an application in deteriorating coastal structure, Nanfangao Port, Taiwan

Efficient restoration of deteriorating coastal structures requires an accurate picture of both above ground and underground features. Although ground penetrating radar (GPR) can map underground features, it creates reflection artifacts. Here, a model for deconvolution calibration was developed in an outdoor small-scale experiment. GPR parameters were established, then applied at a deteriorating fishing port in northeast Taiwan. The deconvolution filter removed repetitive reflection patterns under the lowest part of the void creating a more accurate map. A 3D-map was created from interpolated sketched void boundaries. Due to its high lossy nature at radar frequencies and large contrasting relative dielectric permittivity (RDP) to the upper medium, the seawater table (SWT) is easily identified. The upper boundary of reflection-free area in the deconvoluted radargram, therefore, indicates the SWT. The methods developed here are easily modified to fit a wide range of situations.     

一种可靠的强噪声三分量微地震数据初至拾取方法

精确的初至拾取是微地震数据处理中至关重要的环节。主流的长短时窗比法(STA/LTA)和基于自回归模型的赤池信息准则(AR-AIC)方法,对强噪声数据的拾取效果并不理想。为了更为精确的估计强噪声数据初至,提出了一种基于小波多尺度分析(WMA)和AIC算法的联合拾取方法。首先使用WMA对强噪声三分量(3C)微地震数据进行分解,并重构其近似数据作为实际计算数据,同时计算其绝对值的最大值点,来约束AIC计算数据段,最终选取AIC序列的全局最小值点作为其初至点。文中采用合成数据和实测数据对该改进算法进行了验证,拾取结果表明该算法能有效适用于强噪声微地震数据初至拾取,并明显提高其拾取精度(误差在0.25～0.5 ms之间)。     

基于LSSVM-ARMA模型的基坑变形时间序列预测

如何准确预测和控制基坑变形是基坑工程的一个难点,提出了一种基于小波变换、粒子群优化的最小二乘支持向量机（PSO-LSSVM）和自回归移动平均模型（ARMA）的基坑变形时间序列预测方法。首先,利用小波变换将基坑变形时间序列分解和重构为2个子序列--趋势时间序列和随机时间序列,在该基础上,采用PSO-LSSVM模型与ARMA模型分别预测趋势时间序列与随机时间序列未来值,将2个子序列的预测值求和作为最终预测结果。最后,将该方法应用于昆明某基坑工程的深层水平位移预测,不断地利用前期工况的最新实测数据建模,对后期工况未来变形量进行滚动预测,获得了令人满意的结果。     

基于SVD-TLS算法的非预测欧拉反褶积

针对地下有多个异常源时,单一预测构造指数难于表征多个异常源。采用非预测欧拉反褶积以避免可能错误确定构造指数使得欧拉解过度发散的问题;同时针对欧拉反褶积超定方程组的条件数很大,致使欧拉反褶积解集中良解占优率低等解的非唯一性和解的不稳定性等局限性,采用奇异值分解总体最小二乘法（SVD-TLS算法）,以降低由于奇异值分析不当造成计算欧拉解非唯一性和解的不稳定性的问题,并利用SVD-TLS的截断误差构造阈值函数对解集进行过滤。数值结果表明了算法的有效性和可靠性。      

基于不同小波变换与同态滤波结合的CBERS-02B卫星CCD图像的薄云去除

卫星CCD图像的去云处理对遥感信息的增强与提取有重要的意义,尤其是在云覆盖严重的低纬度地区。为去除CBERS-02B卫星CCD图像中薄云的影响,分别使用Mallat和à trous 2种小波变换对图像进行分解;利用同态滤波对2种小波分解图像的低频系数进行处理,衰减其低频信息;将处理后的小波低频系数与分解的高频系数进行小波重构,从而达到去云的目的。定量分析基于Mallat和à trous小波变换结合同态滤波法的去云结果表明,经à trous小波变换结合同态滤波法的去云影像所包含信息量大,细节信息丰富,去云效果较好。