How do we combine the COVs of two independent, uncorrelated variables of different probability distributions?
Question
Problem Statement:
Weather-related loadings on electrical transmission lines involves incidence of wind on an iced conductor, separately and combined. Current US codes require transmission wires and structures be checked for the following load cases:
L1 Extreme Wind (high wind loads on bare conductors, upto 150 mph or 230 kmph)
L2 Extreme Ice (accumulated radial freezing ice, sometimes upto 2” to 4” in thickness)
L3 Combined Ice and Wind (¼” to ½” ice with variable winds, usually 20 mph to 40 mph)
Wind speeds are often considered to follow a Weibull or Extreme Value type distributions) while ice is generally known to be a Normal distribution. Some known COVs (coefficients of variation) are:
C1 Ice: 0.09
C2 Wind: 0.18 to 0.20
If one considers the load case L3, as shown in the sketch below, the Resultant of the ice load (V) and wind load (T) – both in force units per unit length of cable – can be expressed as:
Force Resultant R = √(V2 + T2)
Can this vectorial approach be valid for a resultant COV? Say COVR = √(C12+ C22)?
Note: Ice and Wind are totally independent variables and possess no statistical correlation whatsoever.
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Equations to calculate ice and wind loads are available in standard textbooks. Wind pressure p (psf) is generally approximated as p = 0.00256*S2 where S is the wind speed in miles per hour.
I would run Monte Carlo simulations to characterize the competition between the conditions that cause failure.
There is nothing like "failure" as such. The case involves action of wind on an iced conductor. That's all. I tried deriving equations by separating the effects and COV's of ice and wind but the results were disappointing.
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