SUMMARYThe Vincent Thomas Bridge in the Los Angeles metropolitan area, is a critical artery for commercial tra c ow in and out of the Los Angeles Harbor, and is at risk in the seismically active Southern California region, particularly because it straddles the Palos Verdes fault zone. A combination of linear and non-linear system identiÿcation techniques is employed to obtain a complete reduced-order, multiinput-multi-output (MIMO) dynamic model of the Vincent Thomas Bridge based on the dynamic response of the structure to the 1987 Whittier and 1994 Northridge earthquakes.Starting with the available acceleration measurements (which consists of 15 accelerometers on the bridge structure and 10 accelerometers at various locations on its base), an e cient least-squares-based time-domain identiÿcation procedure is applied to the data set to develop a reduced-order, equivalent linear, multi-degree-of-freedom model. Although not the main focus of this study, the linear system identiÿcation method is also combined with a non-parametric identiÿcation technique, to generate a reduced-order non-linear mathematical model suitable for use in subsequent studies to predict, with good ÿdelity, the total response of the bridge under arbitrary dynamic environments.Results of this study yield measurements of the equivalent linear modal properties (frequencies, mode shapes and non-proportional damping) as well as quantitative measures of the extent and nature of nonlinear interaction forces arising from strong ground shaking. It is shown that, for the particular subset of observations used in the identiÿcation procedure, the apparent non-linearities in the system restoring forces are quite signiÿcant, and they contribute substantially to the improved ÿdelity of the model. Also shown is the potential of the identiÿcation technique under discussion to detect slight changes in the structure's in uence coe cients, which may be indicators of damage and degradation in the structure being monitored. Di culties associated with accurately estimating damping for lightly damped long-span structures from their earthquake response are discussed. The technical issues raised in this paper indicate the need for added spatial resolution in sensor instrumentation to obtain identiÿed mathematical models of structural systems with the broadest range of validity.

A significant event happened for electrical engineering in 2008, when researchers at HP Labs announced they had found "the missing memristor", a fourth basic circuit element that was postulated nearly four decades earlier by Dr. Leon Chua, who was also instrumental in developing the mathematical theories of memristive, memcapacitive and meminductive systems, resulting in an entire class of "mem-models" that are the foundation of the present work. By applying well-known mechanical-electrical analogies, the mathematics of mem-models may be transferred to the setting of engineering mechanics, creating the mechan-

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