This review covers the group of data-analysis techniques collectively referred to as symbolization or symbolic time-series analysis. Symbolization involves transformation of raw time-series measurements (i.e., experimental signals) into a series of discretized symbols that are processed to extract information about the generating process. In many cases, the degree of discretization can be quite severe, even to the point of converting the original data to single-bit values. Current approaches for constructing symbols and detecting the information they contain are summarized. Novel approaches for characterizing and recognizing temporal patterns can be important for many types of experimental systems, but this is especially true for processes that are nonlinear and possibly chaotic. Recent experience indicates that symbolization can increase the efficiency of finding and quantifying information from such systems, reduce sensitivity to measurement noise, and discriminate both specific and general classes of proposed models. Examples of the successful application of symbolization to experimental data are included. Key theoretical issues and limitations of the method are also discussed.

We propose a low-dimensional, physically motivated, nonlinear map as a model for cyclic combustion variation in spark-ignited internal combustion engines. A key feature is the interaction between stochastic, small-scale fluctuations in engine parameters and nonlinear deterministic coupling between successive engine cycles. Residual cylinder gas from each cycle alters the in-cylinder fuel-air ratio and thus the combustion efficiency in succeeding cycles. The model's simplicity allows rapid simulation of thousands of engine cycles, permitting statistical studies of cyclic-variation patterns and providing physical insight into this technologically important phenomenon. Using symbol statistics to characterize the noisy dynamics, we find good quantitative matches between our model and experimental time-series measurements. ͓S1063-651X͑98͒08903-X͔ PACS number͑s͒: 05.45.ϩb

We propose a simple, physically oriented model that explains important characteristics of cyclic combustion variations in spark-ignited engines. A key model feature is the interaction between stochastic, small-scale fluctuations in engine parameters and nonlinear deterministic coupling between successive engine cycles. Prior-cycle effects are produced by residual cylinder gas which alters volume-average in-cylinder equivalence ratio and subsequent combustion efficiency. The model's simplicity allows rapid simulation of thousands of engine cycles, permitting in-depth statistical studies of cyclic variation patterns. Additional mechanisms for stochastic and prior-cycle effects can be added to evaluate their impact on overall engine performance. We find good agreement with our experimental data.

We describe a symbolic approach for measuring temporal "irreversibility" in time-series measurements. Temporal irreversibility is important because it excludes Gaussian linear dynamics and static transformations of such dynamics from the set of possible generating processes. A symbolic method for measuring temporal irreversibility is attractive because it is computationally efficient, robust to noise, and simplifies statistical analysis of confidence limits. We propose a specific algorithm, called "false flipped symbols," for establishing the presence of temporal irreversibility without the need for generating surrogate data. Besides characterizing experimental data, our results are relevant to the question of selecting alternative models. We illustrate our points with numerical model output and experimental measurements.

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We review developments in the understanding of cycle-to-cycle variability in internal combustion engines, with a focus on spark-ignited and premixed combustion conditions. Much of the research on cyclic variability has focused on stochastic aspects, that is, features that can be modeled as inherently random with no short-term predictability. In some cases, models of this type appear to work very well at describing experimental observations, but the lack of predictability limits control options. Also, even when the statistical properties of the stochastic variations are known, it can be very difficult to discern their underlying physical causes and thus mitigate them. Some recent studies have demonstrated that under some conditions, cyclic combustion variations can have a relatively high degree of low-dimensional deterministic structure, which implies some degree of predictability and potential for real-time control. These deterministic effects are typically more pronounced near critical stability limits (e.g. near tipping points associated with ignition or flame propagation) such during highly dilute fueling or near the onset of homogeneous charge compression ignition. We review recent progress in experimental and analytical characterization of cyclic variability where low-dimensional, deterministic effects have been observed. We describe some theories about the sources of these dynamical features and discuss prospects for interactive control and improved engine designs. Taken as a whole, the research summarized here implies that the deterministic component of cyclic variability will become a pivotal issue (and potential opportunity) as engine manufacturers strive to meet aggressive emissions and fuel economy regulations in the coming decades.

We describe a method for detecting and quantifying time irreversibility in experimental engine data. We apply this method to experimental heat-release measurements from four sparkignited engines under leaning fueling conditions. We demonstrate that the observed behavior is inconsistent with a linear Gaussian random process and is more appropriately described as a noisy nonlinear dynamical process.

We present techniques of symbolic time-series analysis which are useful for analyzing temporal patterns in dynamic measurements of engine combustion variables. We focus primarily on techniques that characterize predictability and the occurrence of repeating temporal patterns. These methods can be applied to standard, cycle-resolved engine combustion measurements, such as IMEP and heat release. The techniques are especially useful in cases with high levels of measurement and/or dynamic noise. We illustrate their application to experimental data from a production V8 engine and a laboratory single-cylinder engine. MOTIVATION Recent studies have demonstrated that cyclic combustion variations in spark-ignition engines under lean fueling exhibit patterns that can be explained as the result of noisy nonlinear combustion instabilities [1, 2, 3, 4]. These instabilities are dominated by the effects of residual cylinder gas (prior-cycle effects) and noisy perturbations of engine parameters. Because this dynamical noise obscures the underlying deterministic patterns, it is difficult to observe changes in these patterns as nominal engine parameter values are changed. This difficulty is often increased by inaccuracies in measurement of characteristic combustion parameters such as IMEP and heat release.