1. Introduction and Motivation
Engine calibration is a process consisting of a large effort to optimize a large number of parameters in order to achieve the desired engine performance. This process refers to the control of the engine’s actuators to yield optimal performance and fuel economy while fulfilling emission legislation. Static maps (look-up tables), which store the values of engine’s optimal control values, have been a common control strategy in the internal combustion engine industry. Finding these optimal maps is important but challenging for the manufacturers. Much research has been conducted over the years to solve the problem with different optimization and searching methods.
The research in [
1] proposed an optimization method using univariate search in which each input factor is varied at a time until the search does not provide any significant reduction in the objective function [
2]. It is an exhaustive and inefficient method because only one factor is varied at a time and it requires that all varied factors are independent, which might lead to finding the local minimum not the global minimum. Advanced methods such as neural networks or genetic algorithms have been applied earlier in [
3,
4,
5,
6]. These types of methods provide a good solution for the optimization problems but they are not convenient and suitable for large engine research because they need to have a large amount of data to be able to learn the system and find an optimum. Large engines always require much time and human labor to operate. It also takes time for the measurement to be stable before recording.
Furthermore, there are two efficient and similar searching methods which are the Folding, Shrinking Hyper Parallelepiped (FSHP) search (proposed in [
7]) and the Response Surface Methods (RSM). Optimization using the RSM has been presented in [
8,
9,
10]. In both methods, different level fractional factorial experiments are conducted which then allow the objective function to be represented in a hypersurface. The experiments are often designed by statistical design methods such as the Design of Experiments (DoE) method. The hypersurface should contain the entire parameter domain of interest and the evaluation of the objective function can be proceeded from point to point and covers all corners of the hypersurface. These searching methods assure that the optimum point is global because all factors are investigated at once and interactions between factors are taken into account. Moreover, they are also more efficient than the neural networks and the genetic algorithms methods as there are fewer experiments needed (the number of experiments depends on the selection of the level of fraction). Thus, this research was conducted using a similar response surface method.
Nevertheless, in the above mentioned research, the emission legislation aspect was not clearly discussed and operational profile based optimization has not been considered. In some applications such as base load power plants, engines run at constant and steady state conditions while in other fields engines have to perform in a broader speed and load range. For many marine applications, engines operate in a broad operating profile (
Figure 1 shows an example of percentual running time at various engine power loads for a diesel-electric propulsion system in a specific ferry) and a hardware set with fixed control system gives little opportunity for a good optimization. Utilizing the situation by optimizing the engines for different operating profiles can bring benefits on fuel saving and yet fulfill the emission regulations [
11]. Engine optimization considering the operational profile has been little investigated. Recently, Knafl et al. [
12] introduced an optimization algorithm for air- and fuel-path using operational profiles in medium-speed diesel engines. The work has solved very well the optimization problem and even taken the IMO emission regulations into account. However, the method was not presented clearly due to confidentiality reasons.
This research presents an operational profile based diesel engine optimization method, specifically targeting to large bore, medium-speed diesel engines used in marine transportation and in stationary power plants. The fundamental optimization algorithm is inherited from the proposed method in [
13] and then extended in this work with the presence of engine’s operational profiles. The IMO emission regulation for Nitrogen Oxide (
) is taken as nonlinear constraint for the optimization. However, a key issue to note is that the
constraint is not given in advance. It can vary as long as it fulfills the IMO constraint over the whole operation range of the engine.
The aim of this study is to prove that by using operational profile based optimization method, the fuel consumption over the whole engine’s working cycle can be effectively reduced without exceeding the IMO limits.
The remainder of this paper is structured as follows.
Section 2 presents the problem formulation and the IMO emission regulations. In
Section 3, the operational profile based optimization algorithm is presented alongside with the engine test bed configuration. The optimization results and detailed analysis results are shown in
Section 4.
Section 5 discusses possible improvements and future works. Conclusion of the paper is given in
Section 6.
2. Problem Formulation
There is a vast number of input parameters which can affect the engine’s performance, but in this paper the following three parameters are investigated: the charged air pressure , the fuel injection pressure and the start of injection . The brake specific fuel consumption (BSFC) is used as the engine’s output response and the nitrogen oxide () emissions are the optimization constraints. The output response and the constraints are chosen according to the aim of the research as to reduce the fuel consumption and to fulfill the emission regulations. The input parameters are considered as the ones which have significant effects on the fuel consumption and emission production. Moreover, these inputs are accessible and measurable in the test site.
Each of the inputs has different impacts on the fuel consumption and the emissions produced. The charged air pressure can be set to a high value to increase the efficiency of combustion and to reduce the unburned components [
14] but too high pressure can boost the
formation [
15]. High injection pressure can increase the fuel economy but increases the
emissions at the same time [
16]. Early injection timing can increase in-cylinder pressure, temperature and hence increase the
formation while a later injection timing reverses the results [
17]. However, using early injection increases the engine’s efficiency and reduces the fuel consumption. Due to the direct trade-off between the fuel consumption and the
formation, attempt to overminimize one of them will lead to failure in fuel economy (too low
, too high BSFC) or problems in fulfilling emission regulations (too low BSFC, too high
). In this study, the
emissions are considered as constraints for the BSFC minimization problem to meet the IMO regulations.
Emissions limits for international maritime engine applications are published by the International Maritime Organization (IMO) in the revised MARPOL annex VI, “Regulations for the prevention of air pollution from ships” [
18].
emissions limits for Tier II and III are shown in
Figure 2, although in this paper only Tier II is studied and its limit is defined in Equation (
1).
in which
w is the rated speed in revolution per minute (rpm). Based on the engine application, a test cycle consists of a number of stationary test points with individual weighting factors defined. Test cycle E2 (Constant-speed main propulsion application including diesel-electric drive and all controllable-pitch propeller installations) was chosen with the following test points and weighting factors in
Table 1.
The test cycle is conducted in a way that the engine is operated at the four operating test points in
Table 1 and the
production at each point is recorded. The weighted sum of
emissions level over the E-2 test cycle as calculated in Equation (
2) is then compared to the respective Tier II limit.
in which
are the
levels (g/kWh) at the test points in
Table 1, respectively. An example set of experiment values of
with corresponding loads are shown in
Figure 3.
limits for other loads which are outside of the E2 test cycle are expected to lie on the line connecting the limits from the E2 test cycle (to be called
line). Each unique set of [
] results in a different
line and hence creates a new set of
limits for the whole power range (
Figure 4).
Figure 4 shows three different example sets of
production. It indicates that with different engine settings, the
productions at each of the four points in the E2 test cycle are different but the weighted sum of
emissions of each setting still fulfills the IMO Tier II regulations.
Since the emissions are used as the constraints in the fuel consumption optimization, different sets of lines affect the optimization results differently. For example, too strict limits may cause the fuel consumption to raise up. The goal is to find an optimal limit set that can minimize the fuel consumption while fulfilling the IMO Tier II regulation.
This paper introduces an approach to determine the best limit set based on the IMO Tier II emission regulations and then use it as a constraint to solve the fuel consumption minimization problem over the whole working cycle of the engine according to the vessel operational profile.