Civil Engineering Reference
In-Depth Information
FIGURE 4-7
Weibull probability distribution function with scale parameter c=10 and shape parameters k =
1, 2 and 3.
of days have low wind. The curve in the middle with k = 2 is a typical wind
distribution found at most sites. In this distribution, more days have lower
than the mean speed, while few days have high wind. The value of k
determines the shape of the curve, hence is called the 'shape parameter'.
The Weibull distribution with k = 1 is called the exponential distribution
which is generally used in the reliability studies. For k>3, it approaches the
normal distribution, often called the Gaussian or the bell-shape distribution.
Figure 4-8
shows the distribution curves corresponding to k = 2 with dif-
ferent values of c ranging from 8 to 16 mph (1 mph = 0.446 m/s). For greater
values of c, the curves shift right to the higher wind speeds. That is, the higher
the c, the more number of days have high winds. Since this shifts the distri-
bution of hours at a higher speed scale, the c is called the scale parameter.
At most sites the wind speed has the Weibull distribution with k = 2, which
is specifically known as the Rayleigh distribution. The actual measurement
data taken at most sites compare well with the Rayleigh distribution, as seen
in
Figure 4-9
.
The Rayleigh distribution is then a simple and accurate enough
representation of the wind speed with just one parameter, the scale param-
eter “c”.
Summarizing the characteristics of the Weibull probability distribution
function:
