Comportamiento óptimo de sistema eléctrico

Cycle counting of random signals is a two part process. It is necessary to first identify the events to count, and then to determine how to extract these events from the continuous signal. The significant events in a stress history are,

- the stress reaches a maximum or minimum value - the stress varies over a certain range

- the stress crosses a certain level, either increasing or decreasing

There are several methods for extracting these events from a continuous record, and the assessment of fatigue damage depends on the method used. The techniques most relevant to fatigue stress histories are discussed in the following paragraphs.

(i) Simple range counting

This is the simplest and most popular method of cycle extraction, and counts each transition from a local maximum to a local minimum and vice versa, as a half cycle. If the mean of each pair of reversals is also recorded, then the technique is referred to as simple range-mean counting, and the results can be presented as a range-mean matrix. The main disadvantage of the method is that for wide band or noisy signals it produces a very large number of small cycles and virtually no large ones. This situation is not representative in fatigue terms, since the crack growth rate is more likely to depend on the larger fluctuations in stress intensity factor associated with a somewhat longer term time window.

(ii) Peak counting

Peak counting counts all the local extrema in the signal as cycles, i.e. positive-going peaks above the mean level and negative-going peaks below it. Troughs, which are negative peaks above the mean level and positive peaks below it, are not counted directly. The signal may be reconstituted by pairing positive peaks with negative peaks of the same magnitude. Again, this method can produce a very large count of small cycles for wide band signals. The method does have the advantage that probability distributions for peaks can be obtained in closed form for narrow band processes; however, to use these it must be assumed that the peak-trough amplitudes are exactly twice the peak amplitudes, which is not always the case.

(ill) Zero-crossing counting

Counting of zero-crossings has some relevance to Offshore service stress histories, since it is the method used to identify significant wave heights. The

the largest maximum between a zero up-crossing and the next down-crossing of the zero level is counted; the largest minimum value between successive zero-crossings is obtained in an analagous way. In contrast to the two methods described above, this technique produces a very small count for wide band signals, comprised mostly of large cycles. Practically, the method has the disadvantage that it requires prior knowledge of the signal average, which may be difficult to ascertain in situations where significant signal drift occurs.

(iv) Rainflow counting

A method which is gaining popularity in fatigue assessment uses so-called rainflow algorithms [3.15]. One reason for this is that in fatigue of plain specimens, these identify cycles as closed stress-strain hysteresis loops, and thus represent the most accurate method for a local strain-type analysis. In effect, these algorithms replace some of the cycles obtained by counting all transitions with some of those obtained from the zero-crossing count. However, they tend to produce more very small cycles than simple range counting and also some cycles larger than obtained using either the simple range or zero-crossing methods. A disadvantage of most rainflow algorithms is that the peaks and troughs must be shuffled before counting so that the entire sequence needs to be known in advance; certain algorithms have been developed to overcome this limitation (e.g. [3.16]).

(v) Discussion of cycle counting

The various cycle counting techniques are illustrated schematically in Figure 3.5. The difference counts produced by each method are primarily dependent upon the bandwidth of the signal, and the degree of stationaiity of the signal with respect to the time window used for counting. Zero-crossing utilises a time window defined by the zero-crossings, and for signals of low bandwidth such as WASH sequences this time window is almost as short as that defined by range counting. In this case, the zero-crossing count is comparable to the range count with a "gate" applied to remove the very small cycles. In the case of rainflow counting however, the sample period is generally much larger and stationaiity becomes more significant. One problem with rainflow counting is that the SRPD obtained from counting an entire history is not always exactly the sum of the

SRPDs for the two halves counted separately. If the signal is stationary within the sample period, then this problem does not arise. An indication of the stationaiity of WASH sequences can be obtained by determining how long it takes for an equivalent stress range calculated from increasingly large samples of a seastate to stabilise. For WASHW seastates, the equivalent stress range (based on a range count) stabilises to within 1% after approximately 1 0 , 0 0 0 seconds

(2,500 cycles), and it may be assumed that a rainflow count will stabilise in a similar manner.

The most suitable choice of counting method for use in fracture mechanics predictions is influenced by the size of the sample window in relation to the anticipated crack growth rate. For instance, if using rainflow counting there is little point in pairing a positive peak with a subsequent negative peak when these two are separated by a large increment of crack growth. If the crack growth rate is likely to be very high, then range counting might provide a better estimate of the effective stress intensity factor during that period. In the context of the tubular joint fatigue tests described in the next Chapter, the cyclic growth rates are such that either range or rainflow counts may be used to make crack growth predictions at intervals of 2,500 or more cycles, which is comparable to the cyclic intervals used for crack measurement.

A final point about counting methods concerns the use of an equivalent stress range in presenting variable amplitude fatigue life results for comparison with similar constant amplitude data. As discussed above, the rainflow counting method is frequently used in fracture mechanics predictions, and one reason for this is that it produces the largest estimate of Miner’s damage (see 3.4.2) for a given sequence. Conversely, using an equivalent stress based on a rainflow count to plot fatigue life data on SN curves gives the most optimistic presentation of the data. The same argument also applies to gating of variable amplitude sequences to remove non-damaging cycles. It is therefore desirable to plot variable amplitude data in a variety of ways so as to assess the effect of different data presentation techniques.