Iterative inversion for topology mapping of branched networks using time domain reflectometry

Branched wiring networks are interconnections of wires that provide for the connection of dc and RF (Radio Frequency) components in an aircraft or other type of apparatus or structure. If by age or by mechanical means the wiring network develops a wiring fault such as bare wire, it can cause fire or other types of emergencies which may cause the loss of life and or property. A Steepest Descent Method is applied to the determination of the topology of a network of branched wires from the Time Domain Reflectometry (TDR) response of the network. Inversion theory is used to derive the equations necessary for the Steepest Descent Method. Functional Spaces are explained, and the properties of the Hilbert Space are used in the minimization of the Misfit Functional. A computer algorithm is written taking into account all a priori information so as to speed the process of finding the wire topology map. The method works reasonably well if the data are perfect (no noise). With the addition of noise the algorithm needs to be modified. Noise causes the impedance values to spread, making the determination of characteristic impedance more problematic.