Time-series analysis techniques

Stochastic identification techniques, in principle, provide a more reliable method of determining the process transfer function. Most workers have used the Box and Jenkins [59] time-series analysis techniques to develop dynamic models. An introduction to these methods is given by Davies [60]. In stochastic identification, a low amplitude sequence (usually a pseudorandom binary sequence, PRBS) is used to perturb the setting of the manipulated variable. The sequence generally has an implementation period smaller than the process response time. By evaiuating the auto- and cross-correlations of the input series and the corresponding output data, a quantitative model can be constructed. The parameters of the model can be determined by using a least squares analysis on the input and output sequences. Because this identification technique can handle many more parameters than simple first-order plus dead-time models, the process and its related noise can be modeled more accurately. 

The application of time series techniques to electrochemical data is promising. It is possible to use the ARIMA analysis to study the behavior of a single coating system. It is also possible to use time series analysis to rank coatings with respect to the properties under study. 

The precision of time series predictions far into the future may be limited. Time series analysis requires a relatively large amount of data. Precautions are necessary if the time intervals are not approximately equal (9). However, when enough data can be collected, for example, by an automated process, then time series techniques offer several distinct advantages over more traditional statistical techniques. Time series techniques are flexible, predictive, and able to accommodate historical data. Time series models converge quickly and require few assumptions about the data. 

One final note While the techniques used here were applied to control temperature In large, semi-batch polymerization reactors, they are by no means limited to such processes. The Ideas employed here --designing pilot plant control trials to be scalable, calculating transfer functions by time series analysis, and determining the stochastic control algorithm appropriate to the process -- can be applied In a variety of chemical and polymerization process applications. 

Autocorrelation and time series analysis have been successfully applied in testing spatial inhomogeneities (Ehrlich and Kluge [1989], Do-erffel et al. [1990]). This techniques are generalized in the theory of stochastic processes (Bohacek [1977a, b]) which is widely used in chemical process analysis and about them. 

A set of experiments on gas-liquid motion in a vertical column has been carried out to study its d3mamical behavior. Fluctuations volume fraction of the fluid were indirectly measured as time series. Similar techniques that previous section were used to study the system. Time-delay coordinates were used to reconstruct the underl3ung attractor. The characterization of such attractor was carried out via Lyapunov exponents, Poincare map and spectral analysis. The d3mamical behavior of gas-liquid bubbling flow was interpreted in terms of the interactions between bubbles. An important difference between this study case and former is that gas-liquid column is controlled in open-loop by manipulating the superficial velocity. The gas-liquid has been traditionally studied in the chaos (turbulence) context [24]. 

Otnes R.K., Enochson L., Applied time Series Analysis. Basic Techniques, New York (1978). 

Regression analysis in time series analysis is a very useful technique if an explanatory variable is available. Explanatory variables may be any variables with a deterministic relationship to the time series. VAN STRATEN and KOUWENHOVEN [1991] describe the dependence of dissolved oxygen on solar radiation, photosynthesis, and the respiration rate of a lake and make predictions about the oxygen concentration. STOCK [1981] uses the temperature, biological oxygen demand, and the ammonia concentration to describe the oxygen content in the river Rhine. A trend analysis of ozone data was demonstrated by TIAO et al. [1986]. 

The autoregression technique as the alternative was developed for such autocorrelated variables and errors, which are frequently available in time series analysis. 

There are numerous books on digital signal processing (DSP) and Fourier transforms. Unfortunately, many of the chemically based books are fairly technical in nature and oriented towards specific techniques such as NMR however, books written primarily by and for engineers and statisticians are often quite understandable. A recommended reference to DSP contains many of the main principles [29], but there are several similar books available. For nonlinear deconvolution, Jansson s book is well known [30]. Methods for time series analysis are described in more depth in an outstanding and much reprinted book written by Chatfield [31]. 

In some cases cyclic events occur, dependent, for example, on time of day, season of tire year or temperature fluctuations. These can be modelled using sine functions, and are tire basis of time series analysis (Section 3.4). In addition, cyclicity is also observed in Fourier spectroscopy, and Fourier transform techniques (Section 3.5) may on occasions be combined with methods for time series analysis. 

Although clustering methods have been widely used in array time series analysis, the majority of these techniques treat time as a categorical or ordinal variable and not as a continuous variable. This distinction is important because the kinetic parameters derived from ordinal variable treatments will not carry meaning except in the case where the time points are evenly spaced. 

Otnes, R. K. Enochson, L. Applied Time Series Analysis Basic Technique-, Wiley New York, 1978. 

Basically, four main areas of methods for gear fault detection have been published. Signal processing techniques. Statistical analysis (ANDRADE, ESAT, BADI, 2001 BAYDAR eta/., 2001 TUMER HUFF, 2003 HE, KONG, YAN, 2007), Time-series analysis (ZHAN JARDINE, 2005 ZHAN, MAKIS, JAR-DINE, 2006) and Artificial neural networks AYA ESAT, 1997 SAMANTA, 2004 SANZ, PERERA, HUERTA, 2007 RAFIEE et cd., 2007). 

The factor of safety (FOS) of the slope can be determined through FEM simulation coupled with automatic strength reduction technique. The rehabihty of determined FOS can be improved by time series analysis which requires periodical TLS scanning campaign. 

The ab initio molecular dynamics technique provides a powerful method in studying the properties of chemical systems under varying thermodynamic conditions without having to employ any empirical interaction potentials. In this chapter, a brief review has been made on our recent studies on water dynamics by using this method combined with a time series analysis. We have discussed the frequency-structure correlations of water molecules in both supercritical and normal water. Our calculations reveal that hydrogen bonds still persist to some extent in the supercritical state. However, the quantitative details of hydrogen bonding depend on the density. At... 

FDA is a multi-step process in which the existing data is converted to a functional form, smoothed using Fourier functions or B-spline functions, and then modelled using a functional one-way ANOVA (fANOVA). In other words, FDA uses information along curves (or functions). This technique is therefore useful to examine adaptive behaviour that clearly changes over space and time (Figure 18.3). This differs from the time-series analysis previously described, in that a FDA does not require equally spaced time intervals. 

ZUK 12] Zukowska J., Road safety analysis in Poland using time-series modelling techniques . Journal of Polish Safety and Reliability Association, Summer Safety and Reliability Seminars, vol. 3, nos. 1-2, 2012. 

II, Floud, 1973, 85-124, and II, Harnett, 1975, 439-475, offer readable introductions to time series analysis, while II, Croxton et c/., 1967, 214-342, is a vade mecum of the art. For techniques of nonlinear least-squares estimation, only highly technical texts (such as II, Bard, 1974) are available. Derek de Solla Price has discussed the implications of exponential and logistic growth for the scientific enterprise in II, Price, 1963, esp. 20-32. For a stimulating apphcation of these concepts to the description of social change in general, see II, Hamblin et al, 1913. 

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