The colors of the wires are not standardized, so to determine which wire corresponds to which function, most of the time it is sufficient to measure the resistance between each pair of wires.
Take 2 wires and measure the resistance between them with a multimeter. Keep only one of the 2 wires, choose another wire, and measure the resistance again. The pair of wires which has the greatest resistance will be taken for the excitation of the gauge (E+ and E-), the 2 other wires (which should have the same resistance as E+ and E-) will be taken for the measurement (A+ and A-).
Explanation :
A strain gauge is a Wheatstone bridge:
An excitation voltage is applied between E+ and E- and the voltage V between A+ and A- is measured, which varies when one or more resistors change. On a strain gauge the resistances vary when the gauge is deformed under the effect of a force.
In practice most of the time the resistances are equal to each other.
So if R=R1=R2=R3=R4, we will measure only 2 possible resistances between the wires: the one between E+ and E- or A+ and A- which will be the largest and which will have the value R, and the one between E+/A+, E+/A-, A+/E- or A-/E- which will be the smallest and which will have the value 0.75xR 1/(1/R + 1/(3xR)).
So whatever the combinations of wires to measure the resistance, you will only find 2 possible resistances, the smallest having the value of 3/4 of the largest one.
Once the pairs have been found, they can be inverted because the circuit is perfectly symmetrical (E+/E- instead of A+/A-). The measurement voltage will be positive for a force applied in one direction, and negative for the other direction. Please note that the gauges generally have an arrow to indicate in which direction the force should be applied. Analog to digital converters used to measure voltage are typically used in differential mode, so polarity doesn't matter, but if it does, you can invert the measurement voltage by swapping the leads on the measured part.
