Spectra of modular and small-world matrices

We compute spectra of symmetric random matrices describing graphs with general modular structure and arbitrary inter- and intra-module degree distributions, subject only to the constraint of finite mean connectivities. We also evaluate spectra of a certain class of small-world matrices generated from random graphs by introducing shortcuts via additional random connectivity components. Both adjacency matrices and the associated graph Laplacians are investigated. For the Laplacians, we find Lifshitz-type singular behaviour of the spectral density in a localized region of small |?| values. In the case of modular networks, we can identify contributions of local densities of state from individual modules. For small-world networks, we find that the introduction of short cuts can lead to the creation of satellite bands outside the central band of extended states, exhibiting only localized states in the band gaps. Results for the ensemble in the thermodynamic limit are in excellent agreement with those obtained via a cavity approach for large finite single instances, and with direct diagonalization results.

In situ diagnostics and prognostics of wire bonding faults in IGBT modules for electric vehicle drives

This paper presents a diagnostic and prognostic condition monitoring method for insulated-gate bipolar transistor (IGBT) power modules for use primarily in electric vehicle applications. The wire-bond-related failure, one of the most commonly observed packaging failures, is investigated by analytical and experimental methods using the on-state voltage drop as a failure indicator. A sophisticated test bench is developed to generate and apply the required current/power pulses to the device under test. The proposed method is capable of detecting small changes in the failure indicators of the IGBTs and freewheeling diodes and its effectiveness is validated experimentally. The novelty of the work lies in the accurate online testing capacity for diagnostics and prognostics of the power module with a focus on the wire bonding faults, by injecting external currents into the power unit during the idle time. Test results show that the IGBT may sustain a loss of half the bond wires before the impending fault becomes catastrophic. The measurement circuitry can be embedded in the IGBT drive circuits and the measurements can be performed in situ when the electric vehicle stops in stop-and-go, red light traffic conditions, or during routine servicing.