Measurement of behavioral uncertainties in mechanical vibration systems: A symbolic dynamics approach

Maturity of engineering and scientific theories in recent decades has facilitated creation of advanced technology of human-engineered complex (e.g., electro-mechanical, transportation, and power generation) systems. A vast majority of these systems are often subjected to mechanical vibration. A possible consequence is performance degradation and structural damage that may eventually lead to widespread catastrophic failures. This chapter presents a recently reported technique of data-driven pattern recognition, called Symbolic Dynamic Filtering (SDF), for online detection of slowly evolving anomalies (i.e., deviation from the nominal characteristics) and the associated behaviorial uncertainties. The underlying concept of SDF is built upon the principles of Statistical Mechanics, Symbolic Dynamics and Information Theory, where time series data from selected sensor(s) in the fast time scale of the process dynamics are analyzed at discrete epochs in the slow time scale of anomaly evolution. Symbolic dynamic filtering includes preprocessing of time series data using the Hilbert transform. The transformed data is partitioned using the maximum entropy principle to generate the symbol sequences, such that the regions of the data space with more information are partitioned finer and those with sparse information are partitioned coarser. Subsequently, statistical patterns of evolving anomalies are identified from these symbolic sequences through construction of a (probabilistic) finite-state machine that captures the system behavior by means of information compression. The concept of SDF has been experimentally validated on a special-purpose computer-controlled multi-degree of freedom mechanical vibration apparatus that is instrumented with two accelerometers for identification of anomalous patterns due to parametric changes.