C.S. Daw

A REVIEW OF SYMBOLIC ANALYSIS OF EXPERIMENTAL DATA

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-seriesmeasurements (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.

A simple model for cyclic variations in a spark-ignition engine

We propose a simple 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 mean 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. Additional mechanisms for stochastic and prior-cycle effects can be added to evaluate their impact on overall engine performance. We find good agreement with experimental data.

Symbolic Time-Series Analysis of Engine Combustion Measurements

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.

A proposed methodology for estimating transient engine-out temperature and emissions from steady-state maps

Abstract Many vehicle systems simulations utilize engine maps constructed from steady-state dynamometer measurements to estimate exhaust temperature and emissions as functions of engine speed and load. Unfortunately, steady-state engine behaviour is often significantly different from actual behaviour under transient driving conditions. This is particularly true for vehicles that undergo repeated engine shutdown and restart (e.g. electric hybrids). The authors propose a methodology for estimating transient engine exhaust properties and fuel economy based on corrections to steady-state maps. The suggested methodology has been implemented in the Powertrain Systems Analysis Toolkit (PSAT) and this implementation is used to demonstrate good agreement with experimental measurements for both a light-duty diesel and a flex-fuel gasoline/ethanol engine. Specific procedures are also recommended for setting key parameters required by the proposed methodology and possible directions for further improvements are suggested.

Characterization of lean combustion instability in premixed charge spark ignition engines

Abstract The focus of this study was to identify and characterize the development of lean combustion instability in spark ignition engines. Statistical techniques from non-linear dynamics were used to process experimental combustion observations to reveal previously unrecognized patterns in cycle-to-cycle combustion variations. The presence of non-linear deterministic structure was confirmed in lean combustion variations from a single cylinder research engine and a four-cylinder production engine. The transition to non-linear deterministic behaviour appeared to occur via a period-doubling bifurcation sequence. Over the bifurcation region, engine dynamics appeared to pass through distinct dynamic stages including stochastic, periodic and possibly chaotic behaviour. The level of dynamic complexity and corresponding cycle-to-cycle communication were found to be a strong function of the residual gas fraction. Experimental observations were also compared with patterns predicted by a recently proposed low-order engine model. Further analysis of the time-series results indicated that the engine frequently exhibited complicated repeating combustion patterns 15 to 20 cycles in length under certain lean operating conditions. Similar dynamics were seen for the two very different engine designs. The work suggests that the underlying cyclic dynamics may not be dependent upon the details of such processes as mixing and combustion but are characteristic of all lean premixed spark ignition engines.

Time Irreversibility and Comparison of Cyclic-Variability Models

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.

Multi-dimensional simulations of cold-start transients in a catalytic converter under steady inflow conditions

A multi-channel model is used to study the impact of flow non-uniformity during cold-start transient operations of a catalytic converter. It is seen that inlet zone recirculation can lead to significant non-uniformity of the flow in the monolith, and this non-uniformity can lead to significant differences in ignition characteristics among the channels. These ignition differences are especially pronounced at lower exhaust temperatures, where the axial location of ignition can vary from one channel to another. It is suggested that this strong effect of temperature on ignition may explain some of the apparently contradictory conclusions about the impact of flow non-uniformities in the literature. The simulations here show that the index of non-uniformity, as defined in many past studies, is an inadequate measure of the full impact on ignition characteristics. For the same index of non-uniformity, the non-uniformity effects on ignition become less significant with increasing exhaust flow rate. This implies that more detailed simulations of flow and temperatures non-uniformities caused by the recirculation zones, heat losses at the boundaries and insufficient mixing upstream of the monolith can be relevant to practical applications.

Controlling chaos in a model of thermal pulse combustion

We describe methods for automating the control and tracking of states within or near a chaotic attractor. The methods are applied in a simulation using a recently developed model of thermal pulse combustion as the dynamical system. The controlled state is automatically tracked while a parameter is slowly changed well beyond the usual flame‐out point where the chaotic attractor ceases to exist because of boundary crisis. A learning strategy based on simple neural networks is applied to map‐based proportional feedback control algorithms both with and without a recursive term. Adaptive recursive proportional feedback is found to track farther beyond the crisis (flame‐out) boundary than does the adaptive non‐recursive map‐based control. We also found that a continuous‐time feedback proportional to the derivative of a system variable will stabilize and track an unstable fixed point near the chaotic attractor. The positive results suggest that a pulse combustor, and other nonlinear systems, may be suitably cont...

Spatio-temporal dynamics in a train of rising bubbles

Abstract It has been suggested that rising bubbles in dense fluids resemble an inverted dripping faucet and that they undergo analogues period-doubling bifurcations to chaos. We present experimental results that demonstrate that this analogy is weak because the dominant source of instability in the bubble train is inherently different — mutual interactions between spatially separated bubbles as opposed to nozzle dynamics. Unlike the dripping faucet, the initial instability in a bubble train develops at a location far from the injection nozzle and progresses toward the nozzle with increasing gas flow. From qualitative and rigorous quantitative observations, we conclude that rising-bubble dynamics are best described as ‘small-box spatio-temporal chaos’ with a flow instability. Such dynamics can superficially appear to be simple temporal chaos when considering spatially localized measurements. We show similarity between our experimental results and a bubble-interaction model that accounts for drag and coalescence effects without considering any nozzle dynamics.

Controlling cyclic combustion variations in lean-fueled spark-ignition engines

This paper describes the reduction of cyclic combustion variations in spark-ignited engines, especially under idle conditions in which the air-fuel mixture is lean of stoichiometry. Under such conditions, the combination of residual cylinder gas and parametric variations (such as variations in fuel preparation) gives rise to significant combustion instabilities that may lead to customerperceived engine roughness and transient emissions spikes. Such combustion instabilities may preclude operation at air-fuel ratios that would otherwise be advantageous for fuel economy and emissions. This approach exploits the recognition that a component of the observed combustion instability results from a noisedriven, nonlinear deterministic mechanism that can be actively stabilized by small feedback control actions which result in little if any additional use of fuel. Application of this approach on a test vehicle using crankshaft acceleration as a measure of torque and fuel pulse width modification as a control shows as much as 30% reduction in rms variation near the lean limit.