An Extreme Learning Machine Approach to Predicting Near Chaotic HCCI Combustion Phasing in Real-Time

Fuel efficient Homogeneous Charge Compression Ignition (HCCI) engine combustion phasing predictions must contend with non-linear chemistry, non-linear physics, period doubling bifurcation(s), turbulent mixing, combustion deposits, model parameters that can drift day-to-day, and air-fuel mixture state information that cannot typically be resolved on a cycle-to-cycle basis, especially during transients. In previous work, a generalized cycle-to-cycle mapping function coupled with e-Support Vector Regression was shown to predict experimentally observed cycle-tocycle phasing over a wide range of engine conditions, despite some of the aforementioned difficulties. The main limitation of the previous approach was that a partially acausual randomly sampled training dataset was used to train proof of concept offline predictions. The objective of this paper is to address this limitation by proposing a new online adaptive Extreme Learning Machine (ELM) extension named Weighted Ring-ELM. This extension enables fully causal phasing predictions at randomly chosen engine set points, and is shown to achieve results that are as good as or better than the previous offline method. The broader objective of this approach is to enable a new class of real-time model predictive control strategies for high variability HCCI and, ultimately, to bring HCCI’s low engine-out NOx and high fuel efficiency to production engines. Introduction HCCI is an advanced engine combustion technique that uses unthrottled low temperature autoignition of lean airfuel mixtures to achieve high fuel efficiency and low engineout NOx (a smog precursor) compared to traditional combustion techniques such as spark ignition or Diesel combustion. While the use of autoignition is the central idea behind HCCI, autoignition itself is difficult to predict and there is no direct actuator to control its timing relative to the motion of the piston (e.g. a spark). A key challenge for gasoline engine HCCI is generating a high enough air-fuel mixture temperature to ensure autoignition [1]. This is commonly achieved by carrying over ∗There are no fundamental changes in this updated version of the original October 14th, 2013 paper. This version includes algebraic simplifications, minor corrections, and improved body text. a sizable fraction (typically 20-60% [2, 3]) of residual gases from the previous burn to promote combustion on the next cycle using Negative Valve Overlap (NVO). While convenient for a number of practical reasons described in [1], the use of residual gases introduces strong cycle-to-cycle coupling on top of the already non-linear chemistry and physics that occur throughout a complete engine cycle [4]. Further compounding the issues with residual gases is that neither the airflow to the cylinder(s) nor the quantity of residual gases in the cylinder can be accurately resolved before a burn happens on a cycle-to-cycle (not mean value) basis with commonly available sensors, especially during transients. Beyond residual gas influences, there are also complex secondary influences on combustion behavior such as turbulent mixing, manifold resonance effects, combustion deposits, different varieties of fuel and even ambient temperature variations [5, 6]. While HCCI is already a significant challenge given the above complexity, the combustion mode also exhibits a period doubling bifurcation cascade to chaos [4, 7, 8], similar to what is seen in high residual spark ignition engines [9]. When nearly chaotic, HCCI is still deterministic but becomes oscillatory and very sensitive to parameter variations (e.g. residual gas fraction fluctuations [7, 8]). This oscillatory “stability limit" behavior is commonly referred to as high Cyclic Variability (CV) and it severely constrains the available load limits of HCCI. Motivation and goals A primary constraint for HCCI is the need to keep combustion phasing between the ringing and combustion stability limits [10]. At the ringing limit, excessive pressure rise rates are encountered, and at the stability limit, high CV in combustion phasing is observed [10]. Since these limits play a key role in constraining HCCI’s usable operating range, it is desirable to explore new methods to predict the behavior at and beyond these constraints. In particular, the ability to predict and correct for high CV might enable the use of late phased combustion to mitigate the excessive pressure rise rates that currently constrain HCCI’s high-load operation [11], while also potentially addressing the high CV experienced at low-load. Towards the end goal of expanding the HCCI load envelope, this paper builds on previous work [4] by describing a new online adaptive learning 1 ar X iv :1 31 0. 35 67 v2 [ cs .L G ] 2 4 Se p 20 14 method that enables fully causal cycle-to-cycle phasing predictions across randomly chosen engine set point transients that include both stable and the near chaotic bifurcation behavior described in [4, 7, 8]. Experimental Observations In the authors’ previous publication [4], engine combustion was abstracted into a generalized mapping function within the framework of a discrete dynamical system: next combustion = f unction( previous combustion, parameters) (1) This abstraction was intended to convey a conceptual understanding of the experimental cycle-to-cycle behavior seen in Fig. 1’s return maps. CA10 n [°ATDC] C A 10 n+ 1 (a) Cyl. 1 −15 0 15 30 45 −15 0 15 30 45