Time series recording

Finally, the value of extensive time-series records extends beyond the identification of a specific problem. Long-term time-series permits verification that decisions are effective (or not) solutions are, indeed, working (or not) and the ongoing costs and benefits of the given control program are assessed accurately. With proper design of what to measure, it can also assist in understanding the why or why not. 

Atmospheric methane has a mean 5 C-value of around —47%c (Stevens 1988). Quay et al. (1999) presented global time series records between 1988 and 1995 on the carbon and hydrogen isotope composition of atmospheric methane. They measured spatial and temporal variation in and D with a slight emichment observed for the southern hemisphere (—47.2%c) relative to the northern hemisphere (—47.4%o). The mean 5D was —86 3%c with a 10%o depletion in the northern relative to the southern hemisphere. 

A key factor in modeling is parameter estimation. One usually needs to fit the established model to experimental data in order to estimate the parameters of the model both for simulation and control. However, a task so common in a classical system is quite difficult in a chaotic one. The sensitivity of the system s behavior to the initial conditions and the control parameters makes it very hard to assess the parameters using tools such as least squares fitting. However, efforts have been made to deal with this problem [38]. For nonlinear data analysis, a combination of statistical and mathematical tests on the data to discern inner relationships among the data points (determinism vs. randomness), periodicity, quasiperiodicity, and chaos are used. These tests are in fact nonparametric indices. They do not reveal functional relationships, but rather directly calculate process features from time-series records. For example, the calculation of the dimensionality of a time series, which results from the phase space reconstruction procedure, as well as the Lyapunov exponent are such nonparametric indices. Some others are also commonly used ... 

The following represents a time series recorded at 40 points in time. (The first column represents die first 10 points in time, and so on.) The aim of diis problem is to look at a few smoothing functions. 

Dymond J. and Roth S. (1988) Plume dispersed hydrothermal particles—a time-series record of settling flux from the endeavour ridge using moored sensors. Geochim. Cosmochim. Acta 52, 2525-2536. 

Fig. 15 Stress time series recorded after start-up of flow experiment at a fixed shear rate 7= 25 s for different temperatures (a) T = 31.5°C, (b) T = 28.8°C, (c) T = 27.2°C, (d) T = 26.5 °C, (e) T = 26 °C. The sample under scrutiny is made of hexadecyltrimethylammonium p-toluenesulfonate (CTAT) at 2 wt. % mixed with 100 mM NaCl in water. The time sequences are found to be (a) time-independent, (b) periodic, (c) quasi-periodic, (d) intermittent and (e) chaotic. Reprinted with permission from R. Ganapathy and A.K. Sood [207]...

Fig. 10. Time series recorded at the central point x = 1/2. (a), (b), (c) and (d) correspond respective ) to the spatio-temporal patterns shown in Figure 9.

In Fig. 1 examples of accelerometric and velocimetric time series recorded close to the source at sites located on rock and stiff soil (STS and AQA stations) and intermediate distances on soft sites (MDN and CESV) are plotted. Each time series is characterized by peculiar features, such as (i) presence of surface waves (MDN) (ii) impulsive behavior (STS) (iii) low-frequency velocity pulse (AQA) and (iv) absence of low-frequency waves (CESV). 

Accelerometric time series recorded during moderate and strong seismic events are fundamental for earthquake engineers and engineering... 

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