Narrow-band random process

Fatigue Damage Under Narrow-Band Random Processes... 

Fig. 8.37 General procedure for life analysis of narrow-band random process...

An objective criterion has been developed to distinguish nonstatlonarlty from statlonarlty when a single finite realization of a stochastic process Is given. The criterion consists of several transformations leading to a set of standard normal distributed random variables as an equivalent notion of statlonarlty. Statlonarlty can therefore be tested by a statistical test. Correlations between estimates, important for investigating narrow banded processes, can be taken into account. 

Bell Syst Tech J 23 282-332 Rychlik I (1993) On the narrow-band approximation for expected fatigue damage. Probab Eng Mech 8 1-4 Shinozuka M, Jan CM (1972) Digital simulation of random processes and its applications. J Sound Vib 25 111-128... 

There is a noticeable fine structure on the reflection spectrum of the sample with an 87 nm spacing. This fine structure is reproducible. Such structured reflectivity is expected to arise in a layered sample with a random distribution of layer thickness. (23) The fine structure will be discussed in more detail in a later publication. Figure 6 demonstrates that the broad-band reflectivity that is essential for optical limiter applications can be achieved. In fact, the reflectivity of the 87 nm layer sample is somewhat broader than is optimum for a practical limiter. It is possible to adjust the fabrication process to produce a narrower distribution of layer thickness. 

Although a narrow proportional band, like the one determined in the example, may be sufficient, for control loop stability, random fluctuations of only a few percent will drive the control valve to its limits. This may be unobjectionable in some cases, but too severe in others. Often the liquid level in a tank is used to control flow into another part of the process. It is certain that wide fluctuations in feed rate are not tolerated in most operations. To provide steady flow in these instances, the proportional band is widened and reset is relied upon to maintain control. 

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