Diesel Engine Drive-Cycle Optimisation with Liger

Diesel Engine Drive-Cycle Optimisation with Liger Stefanos Giagkiozis, Robert J. Lygoe, Ioannis Giagkiozis, and Peter J. Fleming Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, S1 3JD, UK [email protected],[email protected],[email protected]. uk,[email protected] http://www.sheffield.ac.uk

Abstract. In the current market, engineers are continually required to optimize their designs to realise improved performance whilst meeting ever more stringent regulations and competing for market share. This reality increases the demand for optimization. Due to these, and several other reasons, real-world optimization problems often have a large search space, are non-convex, and have expensive-to-evaluate objective functions that have many conflicting objectives. However, even if these problems are overcome, to select an acceptable solution, the decision making process itself is equally demanding. Some of these difficulties could be alleviated if a tool existed to support the analyst and decision maker throughout the entire process. The aim of this work is to illustrate and share insight gained in using Liger in such a scenario. Liger is an open source integrated optimization environment and its use is described in a case study of involving the calibration of a diesel engine using multi-models. The benefits of using Liger are demonstrated along with the procedure we followed to obtain an optimized engine calibration that complies with performance and regulatory requirements. Keywords: Diesel Engine Optimization, Liger, Integrated Optimization Environment, Multi-Objective Optimization, Drive-Cycle Optimization.

1

Introduction

Designing a modern day vehicle is a feat that requires many considerations to be taken into account. These considerations are based on constraints imposed by the industry, the customers and government regulations. We could argue that the main objective of the industry is profit from vehicle sales, which requires high appeal to customers and low production cost. Governments are introducing ever more stringent regulations pertaining to the reduction of harmful emissions to humans and the environment. Broadly speaking, although customer requirements are quite varied, they can be split into a small number of groups, such as purchase cost and vehicle safety along with fuel economy, performance, design and brand. The design process has to incorporate all these requirements simultaneously.

2

Diesel Engine Drive-Cycle Optimisation with Liger

Diesel engines by design are reliable, safe and their main advantage is fuel economy. They have a high thermal efficiency, which is a result of their high compression ratio, but this also leads to increased nitrogen oxide (NOx) emissions[21]. Modern diesel engines have been vastly improved, resulting in reduced emissions and an overall cleaner engine, while maintaining their high efficiency. More detailed analyses of the different emission control technologies currently applied on diesel engines can be found in [10] and [11]. What is of interest now is how to best utilise the hardware described above, in order to obtain optimal, or at least improved performance. The design parameters of the hardware and the calibration of the software parameters controlling that hardware can be used to alter the engine performance. Therefore, it is preferable to automate this procedure by means of an optimization algorithm (stochastic, gradient-based or some other alternative) to reduce the engineering overhead that would be introduced with empirical calibration. Furthermore, although for non-convex problems a certificate of optimality cannot be issued, as is the case for a large number of convex problems, empirical calibration often produces inferior results. The use of optimization enables the study of a number of additional issues that could not be easily addressed with empirical calibration. One issue is the fact that the number of competing objectives is usually large but is kept to a relatively small number to reduce the complexity for the decision maker (DM). Nevertheless, multi-objective optimization is becoming more and more prevalent, given that it can be applied to different kinds of real-world problems (e.g. [13], [15], [19], [20]). An issue associated with population-based algorithms, is that due to the sheer number of available algorithms it is virtually impossible, even for experts in the field, to select the best algorithm for a given problem. Even if a small subset of algorithms is shortlisted for evaluation, their implementation can be challenging and costly for the practitioner. In [7], an overview of populationbased algorithms and the considerations in choosing an appropriate algorithm are given. It is obvious from the conclusions in [7], that it is not a trivial task to make a decision on the algorithm family, implementation or the selection of the configurable parameters. Some of the problems identified above can be solved by developing tools that make the use of optimization algorithms straightforward and provide tools to assist the DM in exploring the resulting solutions. Such tools are, for example, the OpenMDAO [8], OpenOpt [2], TAO [16] and Liger [6]. Tools such as these can simplify the task of optimisation by incorporating state-of-the-art algorithms into their libraries and providing advanced visualization to assist in the design of experiments. The use of such tools can reduce engineering time while producing as good or better solutions in comparison with algorithms built by practitioners that are potentially non-experts. In this case study, we are interested in reducing fuel consumption, nitrogen oxide (NOx) emissions and particulate matter (PM) production in a diesel engine drive-cycle. The diesel engine under investigation is equipped with an exhaust gas recirculation (EGR) and turbocharging systems and a common rail injection


3

system. Optimization tasks like this one, are very commonly performed in the industry and we are interested in evaluating the effectiveness of using an integrated optimization environment in performing this task, while we obtain a set of possible settings that can be used on the real engine. Liger [6] is used, in order to complete all of the optimizations; statistical models of the engine, provided by Ford, represent an entire drive-cycle of the engine under investigation. It is not our goal to compare algorithms or other optimization frameworks, but merely demonstrate the use of one such tool, Liger, to solve a practical problem. We also do not claim that Liger is the best available alternative, but we want to stress its strengths and its weaknesses. This could potentially help other developers of similar tools improve their own software. The remainder of this paper is organised as follows. In Section 2 we describe the diesel engine model and in Section 3 we present the mathematical formulation of our optimization problem. Section 4 provides details on the experiment set up and the use of Liger to complete the experiments. Subsequently, in Section 5 we present and comment on the obtained solutions with Liger. In Section 6 we discuss shortcomings, benefits and future potential in the use of Liger for engineering design problems. Lastly, this work is summarised and concluded in Section 7.

2

Diesel Engine Drive-Cycle Model

Modern diesel engines are comprised of a large number of control variables. Many of the components that are added on the powertrain to reduce emissions, improve efficiency or vehicle performance, can be calibrated in order to improve their performance. However, optimal performance of an isolated component does not guarantee that the collection of components will perform equally well. This, in turn, increases the scope of the optimization problem and increasing its parameter space. Furthermore, the operating conditions of the engine vary in time from turn-on to turn-off. An operating period from engine turn-on to turn-off is called the drive-cycle. During a drive-cycle the engine is subjected to varying environmental and usage parameters, for example, temperature, humidity, oxygen density, load and speed requirements. The engine performance will not be the same for different points in this parameter space. Since models of the engine are not built from first principles (since such a task would be prohibitively complex and expensive), creating a single model that will describe all those variations in the engine state usually leads to inaccurate models. The alternative scenario is to create models in the neighbourhood of a set of parameter points (operating points) and then combine this set of models to obtain the estimated response of the engine throughout a drive-cycle. Such models are called multi-models. 2.1

Multi-models

Multi-models provide the engine response for different operating points. The collection of local models for all operating points comprise the global model. For

4


example, when fuel consumption is to be evaluated for the engine, the operating point at which the evaluation is required must be provided. If the operating point provided matches one of the local models in the global model for the fuel consumption response, then an output can be evaluated. If the operating point is not in the discrete set of operating points, an output cannot be evaluated, since no interpolation takes place between local models. The layers of the entire engine model, can be seen in Figure 1. Local models provide a local response, based on the local inputs. The local model is chosen by the operating point (global inputs), which in our case is a set of engine speed and brake torque.

Fig. 1. A general view of how multi-layer models are used to estimate a response, based on a predefined set of operating points.

A disadvantage of using multi-models is that a large amount of data is required; more engine physical tests (bench-tests) are required in order to estimate the parameters of the local models. Another disadvantage is that local models cannot be used to interpolate between operating points. This means that if we want to obtain data at an operating point that is not in the discrete set of operating points, we must design another experiment for that operating point and estimate the parameters for that new local model. 2.2

Obtaining the Multi-models

In order to obtain the models for each of the responses that we are interested in, discrete sets of engine speed and brake torque were first defined. These sets are discrete operating points of the engine and represent the drive-cycle profile, on which the vehicle will be tested. Each country has a different drive-cycle, for


5

which the emissions need to be limited. In total, there are 30 operating points in our models. These operating points are split into two test plans, based on the engine operating temperature, namely the hot-fast and warm operating regions. In the hot-fast regions 18 sets of engine speed and brake torque operating points are defined and in the warm region there are 12 such sets. At each set of speed and torque, experiments were performed and 29 outputs were measured. Finally, using the MATLAB model-based calibration (MBC) toolbox, a local model for all the responses was obtained, for each of the operating points. Amongst those responses are the fuel consumption, NOx emissions and PM production, which we are interested in minimising. 2.3

System Control Inputs

The inputs of the system model are also the values we are interested in calibrating. So we must identify parameters of the engine that are of interest to us, based on their effect on the whole system. As previously stated, the diesel engine we are working on is fitted with an exhaust gas recirculation (EGR) system, a common rail (CR) injection system and a turbocharger. The amount of recirculated exhaust gas is controlled with a valve, the EGR valve. Using an EGR system can lower the NOx emissions of a diesel engine, but it increases the PM production and after a certain point it can cause instabilities in the combustion process. These instabilities can cause loss of power and an increase in carbon based emissions. For a detailed study about the effects of EGR, see [21]. The common rail (CR) injection system is controlled by the engine control unit (ECU). The controlled states of the CR injection system are the pressure in the CR, the quantity of injected fuel and the timing of the injection. These variables have an effect on the NOx emissions, particulate production and the performance of the engine. The emissions can be controlled by changing the rate of the injected fuel [17]. The amount of PM produced can be controlled by changing the pressure in the common rail. The NOx emissions also depend on the timing and quantity of injected fuel by a pilot injection [14]. This pilot injection is also used to reduce the noise generated by the combustion process. The turbocharger increases the density of the air inside the cylinder, which increases the overall pressure in the cylinder and the power output. This is controlled using the turbocharger valve and is described as a percentage of actuation. More information on turbocharging and effects of the different techniques of turbocharging can be found in [11]. The controlled states of the hardware described above are the local inputs of our multi-models and can be optimized in order to obtain a better performance. The hot-fast region models have six inputs, the percentage amount that the EGR and turbocharger valves are from being fully open, the main injection phase, the CR pressure and the pilot injection phase and quantity. The warm region models have two more inputs, the quantity and timing of a second pilot injection. Both the hot-fast and the warm region models have two global inputs, the engine

6


speed and the brake torque, that are used for the switching between the local models, as described previously (Figure 1). Finally, the range of the inputs is also defined in the models and is given by the convex hull boundary. A sample convex hull boundary for three of the inputs of the system can be seen in Figure 2. All values for the inputs inside the “blue” mass, are valid. Any values outside the constraint are not allowed.

Fig. 2. A convex hull boundary example for three of the system inputs Turbocharger valve actuation (TrbCh rActB1 [%] ) on the y-axis, CR pressure (RailP pFit [hPa] ) on the x-axis and EGR valve (EGRVlv rAct [%])) actuation on the z-axis.

3

Diesel Engine Parameter Optimization

The models described in Section 2, will be used to define our objective functions, based on which we will measure the performance of the engine model for each of our decision vectors. As seen in the previous section, the calibration settings have different effects on the performance of the engine and sometimes opposing effects. For example, according to [11], the EGR can reduce NOx emissions, but has been associated with increased PM production. Based on the study in [18], the pilot injection timing and quantity, controlled by the CR injection system, can reduce PM, previously increased by the EGR system, but at the cost of increased combustion noise. It is clear that there is a trade-off relationship between a number of the objective functions. Because we are dealing with a multi-objective problem, there are many possible solutions that cannot be distinguished in terms of fitness from one another.


7

After the optimization process is performed, a set of solutions is obtained. The feasible solutions are selected from the final population. The decision maker, identifies the trade-offs between the objective functions and, in turn, will make an informed decision about the final design. 3.1

Formulation of the Optimisation Problem

Our engine calibration problem is split into two parts, each being a separate optimization problem. In the first part, the PM production response is defined as a constraint. In the second part, it is defined as an objective. Re-defining the PM as an objective, might reveal solutions that do not satisfy the initial PM production constraint posed, but result in a large benefit in another objective. It should also be noted that the NOx and PM outputs of the engine can be further reduced by the addition of exhaust after-treatment techniques. The aftertreatment requirements should also be taken into consideration by the decision maker. The first part, as stated previously, is to perform a drive-cycle optimization. In order to perform the drive-cycle optimization, the objective functions are multiplied by a time-weight and then summed for each of the set-points of engine speed and brake torque. Mathematically, the optimization problem is defined as follows, ! 30 30 X X Tk f2k (Xj ) Tk f1k (Xj ), minimize F = Xj

subject to

k=1

k=1

0