Over the past decade, diesel engine aftertreatment systems have been developed rapidly to comply with strict diesel emission standards—which have also changed rapidly during this period. Today’s diesel aftertreatment systems are highly complex components, and designing and optimizing aftertreatment systems is an essential part of the engine development process.

A well-calibrated aftertreatment system keeps emissions at regulation levels while enabling the engine to target its most efficient operating points for fuel economy. To meet this goal, engineers need to perform simultaneous optimization of multiple subsystems, including the engine, the controls, the vehicle, and the aftertreatment system.

This article describes a workflow for simulating and optimizing the ammonia oxidation catalyst (AOC) component of a diesel engine aftertreatment system. In this workflow MATLAB^{®} and Simulink^{®} are used to optimize a model built and simulated in GT-SUITE.

## Tightening Regulations and Other Challenges

Regulated emissions include carbon monoxide (CO), unburned hydrocarbons, particulate matter or soot, and nitrous oxides (NOx). An exhaust aftertreatment system reduces these emissions by means of the catalytic reactors and filters that make up the exhaust system between the engine and the tailpipe. Because some of these reactors require precious metals, such as platinum and palladium, they represent a significant cost for manufacturers.

In the on-road and off-road vehicle industries, regulation of harmful emissions continues to tighten. EPA Tier 4 regulations for nonroad diesel engines call for a further 90% reduction in exhaust emissions and require in-use diesel fuel to reduce sulfur levels by more than 99%.

Greenhouse gas emissions, most notably carbon dioxide (CO2), are now coming under closer scrutiny. European regulatory bodies have been regulating CO2 emissions for some time. Meanwhile, the EPA is tightening restrictions on heavy-duty CO2 emissions, and developing nations such as China and India are rolling out their own targets. The solution to reducing CO2 emissions is to increase vehicle fuel economy.

Reducing emissions and increasing fuel economy are difficult objectives to achieve simultaneously. To meet these competing requirements, the aftertreatment system and the engine must be designed at the same time since each system affects the performance of the other. For example, adding a filter or a catalyst to the exhaust system creates higher back-pressure for the engine, reducing engine efficiency and fuel economy. Similarly, engine design decisions regarding exhaust gas recirculation, fuel injection parameters, air-fuel ratio, and warm-up strategies affect aftertreatment system performance and, therefore, vehicle emissions.

## Performing Parameter Estimation with MATLAB

We begin by setting up an aftertreatment model in GT-SUITE. System components are linked together in sequence. For a diesel engine these components can include a diesel oxidation catalyst (DOC), a diesel particulate filter (DPF), a selective catalytic reduction (SCR) subsystem, and an ammonia oxidation catalyst (AOC) (Figure 1).

Gases coming from the engine cylinders pass through the DOC and DPF where CO, unburned hydrocarbons, and soot are eliminated. They then flow to the SCR subsystem, which removes NOx by using upstream injection of aqueous urea solution, or diesel exhaust fluid (DEF). This fluid breaks down to produce ammonia, which reduces or removes NOx in the SCR. A final catalyst, the AOC, oxidizes excess ammonia before it leaves the tailpipe.

Having good parameter values for exhaust aftertreatment models is necessary to ensure that we get meaningful results from the model. However, few of these parameters can be directly measured. The steps outlined below describe how to use parameter estimation to calibrate the AOC component in the GT-SUITE model using experimental data. These same steps can be applied to each component in the aftertreatment system.

The behavior of the AOC can be modeled in GT-SUITE using six global reactions, with the temperature dependence of each reaction rate represented as an Arrhenius equation with two rate constants (Figure 2).

There are 14 independent variables (parameters) to be estimated: the two rate constants for each of the six reactions, and two global inhibition constants for the AOC.

We want to find values for these 14 parameters so that the results of the GT-SUITE simulation match the experimental (measured) data (Figure 3). The optimization problem is to minimize the difference between the simulated data and the measured data by finding optimal values for the 14 reaction parameters.

The controller will be implemented in Simulink. Simulink also provides a conduit for the optimizer to access GT-SUITE model parameters. We begin by adding a Simulink harness block to the GT-SUITE model (Figure 4). This block is used to communicate with a Simulink model. The Simulink model uses a corresponding GT-SUITE model block to pass values for the 14 reaction parameters to GT-SUITE.

We run hundreds of cosimulations with Simulink and GT-SUITE using different parameter values. To find a set of values that minimizes the differences between the simulated and the measured results, we write a simple MATLAB script that calls the `MultiStart`

solver, an optimization solver in Global Optimization Toolbox that searches for the global minimum of a constrained nonlinear multivariable function.

Because each simulation takes several seconds to run, it can take about an hour for the optimization to find a good fit (Figure 5). This process can be accelerated by using Parallel Computing Toolbox™ to execute the simulations in parallel on multiple computing cores. Note that MultiStart uses a gradient-based optimization solver, and it works best when the objective function is smooth. If the objective function is nonsmooth, or has discontinuities, MATLAB has several other global optimization solvers that can be used.

The optimization gives us a set of parameter values that enable the model to produce results that closely match the results measured in the lab. By updating the GT-SUITE model of the AOC with these values and repeating this process for other aftertreatment system components, we ensure that our system-level simulations will produce accurate and meaningful results.

## Performing System-Level Optimization

Now that we have a well-calibrated aftertreatment system model, we can perform a variety of system-level studies such as analyzing interactions between emissions, engine back-pressure, and fuel economy, or exploring controller strategies for diesel exhaust fluid injection. We can also identify optimal sizes for aftertreatment system components, including the AOC. Because the AOC uses platinum as its catalytic material, if it is too big, it will be too expensive. If it is too small, however, it will not meet emissions requirements.

To analyze the tradeoff between NOx emissions and AOC cost, we need to solve a multiobjective optimization problem in which the variables are the SCR length, the AOC length, and the AOC catalytic material loading.

To set up this optimization problem, we build a vehicle model that includes engine, aftertreatment system, driver control (which takes the vehicle through the New European Driving Cycle (NEDC)), and vehicle. As with the parameter estimation problem, we build a Simulink model with an interface to the GT-SUITE model (Figure 6). A controller in the Simulink model manages the urea dosage in the GT-SUITE model based on the measured NOx, temperature, and ammonia slip (the ammonia passing through the SCR). This setup supports closed-loop cosimulation using the GT-SUITE model as the plant.

We write a MATLAB script that uses a multiobjective genetic algorithm solver (`gamultiobj`

) to tune parameters in the GT-SUITE model. The solver runs thousands of simulations with different combinations of SCR length, AOC length, and AOC loading, and evaluates their cost and NOx emissions on the NEDC.

In a multiobjective optimization problem like this one, no single solution simultaneously optimizes each objective. There are many optimal solutions along the Pareto front (Figure 7).

The blue circles in Figure 7 represent optimal solutions along the Pareto front, making it easy to see the tradeoff between NOx emissions and AOC cost. These solutions minimize cost for a given NOx emissions limit—or, from another perspective, minimize emissions for a given set cost. Since our goal is to keep emissions below a specific limit, we select the solution along the Pareto front that is below that limit and has the lowest cost. For example, if the emissions target is 0.18 g/km, then the minimal AOC cost will be under $20.

Simulating an entire drive cycle thousands of times can be a lengthy process—to run all the necessary simulations for one optimization took approximately five days on a single processor. Fortunately, genetic algorithms are well-suited to acceleration using parallel computing techniques. We used Parallel Computing Toolbox and MATLAB Parallel Server™ to run the simulations on a 64-core computing cluster. Because we had 64 cores available, we selected a population size of 64 for the genetic algorithm, making it possible for the algorithm to simultaneously evaluate 64 points in each iteration or generation. On the computing cluster, our optimization took about four hours.

## Extending this Approach

The approach described in this article can be applied to the tuning of additional parameters, or it can be used to support additional objectives such as minimizing vehicle weight. For example, it can be used to trade off control strategies and optimize controller parameters to minimize diesel exhaust fluid consumption—and as a result, reduce the ownership cost of the vehicle. By using the vast numbers of computational resources available today, engineers can quickly investigate design changes and optimize several parameters at a system level.