Characterizing dilute combustion instabilities in a multi-cylinder spark-ignited engine using symbolic analysis

Abstract

Spark-ignited internal combustion engines have evolved considerably in recent years in response to increasingly stringent regulations for emissions and fuel economy. One new advanced engine strategy ustilizes high levels of exhaust gas recirculation (EGR) to reduce combustion temperatures, thereby increasing thermodynamic efficiency and reducing nitrogen oxide emissions. While this strategy can be highly effective, it also poses major control and design challenges due to the large combustion oscillations that develop at sufficiently high EGR levels. Previous research has documented that combustion instabilities can propagate between successive engine cycles in individual cylinders via self-generated feedback of reactive species and thermal energy in the retained residual exhaust gases. In this work, we use symbolic analysis to characterize multi-cylinder combustion oscillations in an experimental engine operating with external EGR. At low levels of EGR, intra-cylinder oscillations are clearly visible and appear to be associated with brief, intermittent coupling among cylinders. As EGR is increased further, a point is reached where all four cylinders lock almost completely in phase and alternate simultaneously between two distinct bi-stable combustion states. From a practical perspective, it is important to understand the causes of this phenomenon and develop diagnostics that might be applied to ameliorate its effects. We demonstrate here that two approaches for symbolizing the engine combustion measurements can provide useful probes for characterizing these instabilities.

Invited Review: A review of deterministic effects in cyclic variability of internal combustion engines

“…The different partitioning schemes can reveal different patterns in the data; for instance, rare events such as misfires are often highlighted more with equispatial than equiprobable partitioning. 47 Symbolization is an efficient technique to find patterns within complicated signals and can form the basis for effective characterization and control. 40,42,45,48…”

“…Examples of SSH structure differences are seen in Figure 1, with panels (a) and (b) representing roughly unstructured data and panels (c) and (d) exhibiting increasing levels of structure, which is also seen in their corresponding time series and return maps. On the SSH plots, the symbolization is n = 8 and L = 2, and the equiprobable level of 1/64 = 0.015625 is bounded on either side by 95% empirical confidence intervals; 45,47 symbolic patterns outside of these bounds represent a degree of determinism, either in greater or lesser than expected frequency. The onset of deterministic instabilities becomes pronounced starting with the 21% EGR case, with the emergence of sequence 7, which represents a partial burn or misfire (symbol 0) followed by a largest-level combustion event (symbol 7), labeled as 0-7 in the figure.…”

“…When words are formed using simultaneous measurements from several signal sources, for instance from multiple engine cylinders, the resulting symbol synchrogram can highlight episodes of synchronized behavior among multiple cylinders. 46,47 Figure 4 shows two such synchrograms, one without persistent intercylinder correlation and the other with persistent intercylinder correlation in which the cylinders are synchronized. Some incidental correlation can occur by chance, but some causes of persistent intercylinder coupling include manifold dynamics, both with acoustic oscillations in intake and exhaust, and with fueling feedback in external EGR loops.…”

Enhancing dynamical signatures of complex systems through symbolic computation

“…The contributions can be roughly divided into theoretically oriented studies, where the methodology is the focus and archetypal examples of applications are provided for illustrations, and problem-driven investigations, where the emphasis is on the application, whereas mathematical details are discussed without a systematic approach. It is worth stressing that the majority of contributions provide a comprehensive extension to the multivariate case [20][21][22][23][24][25][26][27], thus providing tools fully helpful in contexts where multiple traces are acquired.…”

“…Among the application-driven contributions, Cysarz et al [28] apply several symbolization strategies to spontaneous beat-to-beat changes of fetal heart period and test their performances in following the development of the fetus during gestation; Valencia et al [29] show that symbolic indexes derived from the beat-to-beat series of heart period and ventricular repolarization duration separate ischaemic-dilated cardiomyopathy patients and healthy age-matched controls better than more traditional linear time and frequency domain markers; Schlemmer et al [30] propose a method based on symbolization to study sleep stage transitions and their modifications in relation to ageing and sleep disorders; Daw et al [23] provide an industry-driven application of symbolic analysis to control dilute combustion instabilities in a multi-cylinder spark-ignited engine; Baumert et al [24] review applications exploiting joint symbolic analysis to identify the pathophysiological changes of specific cardiovascular control mechanisms such as cardiac baroreflex and cardiopulmonary reflexes; Schulz et al [25] present an application of a high-resolution joint symbolic analysis to separate patients suffering from paranoid schizophrenia from their healthy first-degree relatives and age-matched controls; Porta et al [26] propose a conditional joint symbolic technique to assess the nonlinear interferences of respiration over cardiac and sympathetic 'baroreflexes' and apply it to an experimental protocol designed to evoke postural syncope; and Lee et al [27] review the basic principles of the neurobiology of consciousness, the problem of 'covert consciousness' (i.e. the presence of conscious experience coupled with the absence of responsiveness) and the recent advances in assessing levels of consciousness and cortical connectivity using symbolic dynamics and symbolic transfer entropy.…”