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1.
Autogressive moving-average (ARMA) models and their uniformly modulated forms are considered appropriate for seismic records of earthquakes by a large number of investigators. This article presents a reason for this and offers some explanation. It uses a model for wave propagation in a layered media and compares the derived transfer function for transmitted and reflected waves with those for ARMA processes. It demonstrates that the ARMA behavior of records is due to the transmission path with source acting as a modulating function (envelope function). 相似文献
2.
A. Ian McLeod K. W. Hipel 《Stochastic Environmental Research and Risk Assessment (SERRA)》1995,9(3):171-205
Current methods of estimation of the univariate spectral density are reviewed and some improvements are made. It is suggested that spectral analysis may perhaps be best thought of as another exploratory data analysis (EDA) tool which complements, rather than competes with, the popular ARMA model building approach. A new diagnostic check for ARMA model adequacy based on the nonparametric spectral density is introduced. Additionally, two new algorithms for fast computation of the autoregressive spectral density function are presented. For improving interpretation of results, a new style of plotting the spectral density function is suggested. Exploratory spectral analyses of a number of hydrological time series are performed and some interesting periodicities are suggested for further investigation. The application of spectral analysis to determine the possible existence of long memory in natural time series is discussed with respect to long riverflow, treering and mud varve series. Moreover, a comparison of the estimated spectral densities suggests the ARMA models fitted previously to these datasets adequately describe the low frequency component. Finally, the software and data used in this paper are available by anonymous ftp from fisher.stats.uwo.ca. 相似文献
3.
《水文科学杂志》2013,58(2):353-366
Abstract Statistical analyses of hydrological time series play a vital role in water resources studies. Twenty-nine statistical tests for detecting time series characteristics were evaluated by applying them to analyse 46 years of annual rainfall, 47 years of 1-day maximum rainfall and consecutive 2-, 3-, 4-, 5- and 6-day maximum rainfalls at Kharagpur, West Bengal, India. The performance of all the tests was evaluated. No severe outliers were found, and both the annual and maximum rainfall series were found to be normally distributed. Based on the known physical parameters affecting the homogeneity, the cumulative deviations and the Bayesian tests were found to be superior to the classical von Neumann test. Similarly, the Tukey test proved excellent among all the multiple comparison tests. These tests indicated that all the seven rainfall series are homogeneous. Two parametric t tests and the non-parametric Mann-Whitney test indicated stationarity in all the rainfall series. Of 12 trend detection tests, nine tests indicated no trends in the rainfall series. The Kendall's Rank Correlation test and the Mann-Kendall test were found equally powerful. Moreover, the Fourier series analysis revealed no apparent periodicities in all the seven rainfall series. The annual rainfall series was found persistent with a time lag of nine years. All the rainfall series were subjected to stochastic analysis by fitting 35 autoregressive moving-average (ARMA) models of different orders. The best-fit models for the original annual rainfall and 1-, 2- and 3-day maximum rainfall series were found to be ARMA(0,4), ARMA(0,2), ARMA(0,2) and ARMA(3,0), respectively. The best-fit model for the logarithmically transformed 4-day maximum rainfall was found to be ARMA(0,2). However, for the inversely transformed 4-, 5- and 6-day maximum rainfall series, ARMA(0,1) was obtained as the best-fit model. It is concluded that proper selection of time series tests and use of several tests is indispensable for making useful and reliable decisions. 相似文献
4.
This paper deals with the use of ARMA models in earthquake engineering. Tools and methods applied to strong ground motion are discussed emphasizing simulation of probabilistic earthquake response spectra. The ARMA models are applied to Icelandic earthquake data and a tentative model for Icelandic earthquakes is presented. This model, which is derived using 54 accelerograms, is based on a low-order, time-invariant ARMA process excited by Gaussian white noise and amplitude modulated using a simple envelope function to account for the non-stationary characteristics. This simple model gives a reasonable fit to the observed ground motion. Further, this model produces accurate earthquake response spectra, which, combined with accompanying attenuation and duration formulae, might be useful in earthquake hazard and risk assessment. 相似文献
5.
Verification of ARMA identification for modelling temporal correlations of GNSS observations using the ARMASA toolbox 总被引：1，自引：0，他引：1
The classical least-squares (LS) algorithm is widely applied in practice of processing observations from Global Satellite Navigation Systems (GNSS). However, this approach provides reliable estimates of unknown parameters and realistic accuracy measures only if both the functional and stochastic models are appropriately specified. One essential deficiency of the stochastic model implemented in many available GNSS software products consists in neglecting temporal correlations of GNSS observations. Analysing time series of observation residuals resulting from the LS evaluation, the temporal correlation behaviour of GNSS measurements can be efficiently described by means of socalled autoregressive moving average (ARMA) processes. For a given noise realisation, a well-fitting ARMA model can be automatically estimated and identified using the ARMASA toolbox available free of charge in MATLAB® Central.In the preliminary stage of applying the ARMASA toolbox to residual-based modelling of temporal correlations of GNSS observations, this paper presents an empirical performance analysis of the automatic ARMA estimation tool using a large amount of simulated noise time series with representative temporal correlation properties comparable to the GNSS residuals. The results show that the rate of unbiased model estimates increases with data length and decreases with model complexity. For large samples, more than 80% of the identified ARMA models are unbiased. Additionally, the model error representing the deviation between the true data-generating process and the model estimate converges rapidly to the associated asymptotical value for a sufficiently large sample size with respect to the correlation length. 相似文献
6.
7.
A. R. Rao A. Durgunoglu 《Stochastic Environmental Research and Risk Assessment (SERRA)》1988,2(1):35-50
Autoregressive (AR) and Autoregressive-moving average (ARMA) methods of spectral analysis have been developed and are being increasingly used as alternatives to traditional methods of spectral analysis. Two of these methods developed by Marple and Friedlander are tested in this study by using generated data from models with known spectra. The Blackman-Tukey spectral estimates are also compared to the Marple and Friedlander estimates. The variability of the Marple and Friedlander estimates with sample sizes is investigated. Although both Marple's and Friedlander's methods are satisfactory, Friedlander's method is preferred because of its ability to handle a wider class of models. 相似文献
8.
Two types of modelling approaches for simulating ground motion in Iceland are studied and compared. The first type of models, named discrete‐time series models (ARMA), are based solely on measured acceleration in earthquakes occurring in Iceland. The second type of models are based on a theoretical seismic source model called the extended Brune model. Based on measured acceleration in Iceland during the period 1986–1996, the parameters for the extended Brune models have been estimated. The seismic source models are presented here as ARMA models, which simplifies the simulation process. A single‐layer soil amplification model is used in conjunction with the extended Brune model to estimate local site amplification. Emphasis is put on the ground motion models representing the variability in the measured earthquakes, with respect to energy, duration and frequency content. Demonstration is made using these models for constructing linear and non‐linear probabilistic response spectra using a discretised version of the Bouc–Wen model for the hysteresis of the second‐order system. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
9.
Modelling long-term groundwater fluctuations by extreme learning machine using hydro-climatic data 总被引：1，自引：1，他引：0
The ability of the extreme learning machine (ELM) is investigated in modelling groundwater level (GWL) fluctuations using hydro-climatic data obtained for Hormozgan Province, southern Iran. Monthly precipitation, evaporation and previous GWL data were used as model inputs. Developed ELM models were compared with the artificial neural networks (ANN) and radial basis function (RBF) models. The models were also compared with the autoregressive moving average (ARMA), and evaluated using mean square errors, mean absolute error, Nash-Sutcliffe efficiency and determination coefficient statistics. All the data-driven models had better accuracy than the ARMA, and the ELM model’s performance was superior to that of the ANN and RBF models in modelling 1-, 2- and 3-month-ahead GWL. The RMSE accuracy of the ANN model was increased by 37, 34 and 52% using ELM for the 1-, 2- and 3-month-ahead forecasts, respectively. The accuracy of the ELM models was found to be less sensitive to increasing lead time. 相似文献
10.
新型随机地震动模型 总被引：2，自引：0，他引：2
在研究结构的随机地震反应时，要用大量的符合场地条件的地震记录作为输入数据。但强震历史记录却不是每个地区都有的，因此根据符合场地条件的现有地震记录建立随机地震动模型具有重要意义。本文利用中国抗震规范2001版修正选取的样本波作为目标波，考虑了幅值和频率的双重非平稳性，建立了新型随机地震动模型——改进的时变ARMA模型随机地震动模型。通过使用残差的卡方检验法，对多种非平稳ARMA模型生成的模拟波进行检验；同时又比较丁模拟波与目标波的功率谱密度图和反应谱图。结果证明：此法能够更精确地反映不同场地条件地震动的频谱和幅值的真实内容，从而建立符合目标场地条件的更为有效的模拟地震动，为相关研究与工程设计架起一座桥梁。 相似文献
11.
ARIMA forecasting of ambient air pollutants (O3, NO, NO2 and CO) 总被引：1，自引：0，他引：1
Ujjwal Kumar V. K. Jain 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(5):751-760
In the present study, a stationary stochastic ARMA/ARIMA [Autoregressive Moving (Integrated) Average] modelling approach has
been adapted to forecast daily mean ambient air pollutants (O3, CO, NO and NO2) concentration at an urban traffic site (ITO) of Delhi, India. Suitable variance stabilizing transformation has been applied
to each time series in order to make them covariance stationary in a consistent way. A combination of different information-criterions,
namely, AIC (Akaike Information Criterion), HIC (Hannon–Quinn Information Criterion), BIC (Bayesian Information criterion),
and FPE (Final Prediction Error) in addition to ACF (autocorrelation function) and PACF (partial autocorrelation function)
inspection, has been tried out to obtain suitable orders of autoregressive (p) and moving average (q) parameters for the ARMA(p,q)/ARIMA(p,d,q)
models. Forecasting performance of the selected ARMA(p,q)/ARIMA(p,d,q) models has been evaluated on the basis of MAPE (mean
absolute percentage error), MAE (mean absolute error) and RMSE (root mean square error) indicators. For 20 out of sample forecasts,
one step (i.e., one day) ahead MAPE for CO, NO2, NO and O3, have been found to be 13.6, 12.1, 21.8 and 24.1%, respectively. Given the stochastic nature of air pollutants data and in
the light of earlier reported studies regarding air pollutants forecasts, the forecasting performance of the present approach
is satisfactory and the suggested forecasting procedure can be effectively utilized for short term air quality forewarning
purposes. 相似文献
12.
大跨度桥梁风场模拟方法对比研究 总被引：18，自引：4，他引：14
本文将基于线性滤波器的ARMA模型应用于大跨度桥梁的风场模拟,推导出自回归(AR)阶数P和滑动回归(MA)阶数q不等情况下,ARMA模型用于模拟多变量稳态随机过程的公式,将ARMA风场模拟方法与目前广泛应用于大跨度桥梁风场模拟的谐波合成法应用于一座实际大跨度斜拉桥的风场模拟,通过对比研究得出一些有意义的结论,并证实了ARMA法能够在保证模拟精度的前提下,大大提高风场模拟的效率。 相似文献
13.
The potential of applying shifting level (SL) models to hydrologic processes is discussed in light of observed statistical characteristics of hydrologic data. An SL model and an ARMA (1, 1) model are fitted to an actual hydrologic series. Computer simulation experiments with these models are carried out to compare maximum accumulated deficit and run properties. Results obtained indicate that the mean maximum accumulated deficit, mean longest negative run length, and mean largest negative run sum for both models are similar while there are differences in their corresponding variances. 相似文献
14.
An efficient Auto-Regressive Moving–Average (ARMA) approximation method is presented for simulating stationary random processes with specified (target) power spectra in conjunction with structural dynamics applications. It involves an iterative algorithm developed for minimizing a physically motivated ‘energy’ measure, in the frequency domain, of the ARMA approximation of an AR representation of the target spectrum. The iterative algorithm can be used to adjust, for better spectral matching, the parameters of an arbitrary ARMA approximation of the random process determined by any other method; this is accomplished without increasing the requisite order of the ARMA approximation. The efficiency of the proposed method is demonstrated by considering spectra which are commonly used in earthquake engineering and ocean engineering. 相似文献
15.
Abstract The natural variability of precipitation in agricultural regions both in time and space is modelled using extensions of Box & Jenkins (1976) methodology based on the ARMA procedure. This broad class of aggregate regional models belongs to the general family of Space-Time Autoregressive Moving Average (STARMA) processes. The paper develops a three-stage iterative procedure for building a ST ARMA model of multiple precipitation series. The identified model is STMA (13). The emphasis is placed on the three stages of the model building procedure, namely identification, parameter estimation and diagnostic checking. In the parameter estimation stage the polytope (or simplex) method and three further classical nonlinear optimization algorithms are used, namely two conjugate gradient methods and a quasi-Newton method. The polytope method has been adopted and the developed model performed well in describing the spatio-temporal characteristics of the multiple precipitation series. Application has been attempted in a rural watershed in southern Canada. 相似文献
16.
The methods behind the predefined impulse response function in continuous time (PIRFICT) time series model are extended to cover more complex situations where multiple stresses influence ground water head fluctuations simultaneously. In comparison to autoregressive moving average (ARMA) time series models, the PIRFICT model is optimized for use on hydrologic problems. The objective of the paper is twofold. First, an approach is presented for handling multiple stresses in the model. Each stress has a specific parametric impulse response function. Appropriate impulse response functions for other stresses than precipitation are derived from analytical solutions of elementary hydrogeological problems. Furthermore, different stresses do not need to be connected in parallel in the model, as is the standard procedure in ARMA models. Second, general procedures are presented for modeling and interpretation of the results. The multiple-input PIRFICT model is applied to two real cases. In the first one, it is shown that this model can effectively decompose series of ground water head fluctuations into partial series, each representing the influence of an individual stress. The second application handles multiple observation wells. It is shown that elementary physical knowledge and the spatial coherence in the results of multiple wells in an area may be used to interpret and check the plausibility of the results. The methods presented can be used regardless of the hydrogeological setting. They are implemented in a computer package named Menyanthes (www.menyanthes.nl). 相似文献
17.
《Journal of Hydrology》1999,214(1-4):74-90
Four time series were taken from three catchments in the North and South of England. The sites chosen included two in predominantly agricultural catchments, one at the tidal limit and one downstream of a sewage treatment works. A time series model was constructed for each of these series as a means of decomposing the elements controlling river water nitrate concentrations and to assess whether this approach could provide a simple management tool for protecting water abstractions. Autoregressive (AR) modelling of the detrended and deseasoned time series showed a “memory effect”. This memory effect expressed itself as an increase in the winter–summer difference in nitrate levels that was dependent upon the nitrate concentration 12 or 6 months previously. Autoregressive moving average (ARMA) modelling showed that one of the series contained seasonal, non-stationary elements that appeared as an increasing trend in the winter–summer difference. The ARMA model was used to predict nitrate levels and predictions were tested against data held back from the model construction process – predictions gave average percentage errors of less than 10%. Empirical modelling can therefore provide a simple, efficient method for constructing management models for downstream water abstraction. 相似文献
18.
Adaptive neural-based fuzzy inference system (ANFIS) approach for modelling hydrological time series
《水文科学杂志》2013,58(4):588-598
Abstract The main aim of this study is to develop a flow prediction method, based on the adaptive neural-based fuzzy inference system (ANFIS) coupled with stochastic hydrological models. An ANFIS methodology is applied to river flow prediction in Dim Stream in the southern part of Turkey. Application is given for hydrological time series modelling. Synthetic series, generated through autoregressinve moving-average (ARMA) models, are then used for training data sets of the ANFIS. It is seen that the extension of input and output data sets in the training stage improves the accuracy of forecasting by using ANFIS. 相似文献
19.
The non‐stationary Functional Series time‐dependent autoregressive moving average (TARMA) modelling and simulation of earthquake ground motion is considered. Full Functional Series TARMA models, capable of modelling both resonances and antiresonances, are examined for the first time via a novel mixed parametric/non‐parametric estimation scheme, and critical comparisons with pure TAR and recursive ARMA (RARMA)‐recursive maximum likelihood (RML) adaptive filtering type modelling are made. The study is based upon two California ground motion signals: a 1979 El Centro accelerogram and a 1994 Pacoima Dam accelerogram. A systematic analysis, employing various functional subspaces and model orders, leads to two Haar function based models: a TARMA(2,4)8 model for the El Centro case and a TARMA(6,2)10 model for the Pacoima Dam case. Both models are formally validated and their simulation (synthesis) capabilities are demonstrated via Monte Carlo experiments focusing on important time domain signal characteristics. The Functional Series TAR/TARMA models are shown to achieve parsimony, as well as superior accuracy and simulation capabilities, over their RARMA counterparts. Copyright © 2001 John Wiley & Sons Ltd. 相似文献
20.
现有的多数综合模型，大多忽略了各种异常在震前所显示不同的持续时间，本文针对各前兆在时间轴上的不均匀，由可容纳不同异常持续时间的动态系统模型，依据知于不可逆过程的ＡＲＭＡ参量预测模型，以华北北部区域为例，探讨了进行未来强震危险性的预测的途径，最后，对影响预测精度的因素进行了分析和讨论。 相似文献