Gasoline Case Study Overview

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Case Study Introduction Why Use Design of Experiment and Engine Modeling? Problem Definition Introduction to Two-Stage Modeling

Case Study Introduction

This case study demonstrates how to systematically develop a set of optimal steady-state engine calibration tables using the Model-Based Calibration Toolbox product. This case-study uses a 2.2L inline 4 cylinder, naturally aspirated DOHC (Dual Overhead Cams) 4 valve per cylinder spark ignition (SI) engine equipped with dual-independent variable cam-phasing (DIVCP) hardware and electronic throttle.

Optimal steady-state engine calibration tables for intake cam phase, exhaust cam phase, and spark advance are developed as part of the case study process.

This example takes you through the following steps:

1. Create a design for your experiment — see Designing the Experiment.

2. Import the resulting data (taken using the design) to examine and filter it in preparation for modeling — see Importing and Filtering Data.

3. Make statistical models based on the data.

   1. How Is a Two-Stage Model Constructed?

   2. Building the Models

   3. Selecting Local Models

   4. Creating Boundary Models

   5. Selecting Global and Two-Stage Models

   6. Using Validation Data

4. Export these models to the CAGE part of the toolbox to generate optimal calibration tables — see Exporting the Models.

5. The Model Browser section of the case study involves design of experiment, data handling, and model construction and export. In the CAGE browser section of the case study you use the models to complete the optimization of the calibration tables, see Optimized Calibration.

The following sections introduce the benefits of applying model-based calibration methods to solve this case study problem:

• Why Use Design of Experiment and Engine Modeling?

• Problem Definition

• Introduction to Two-Stage Modeling

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Why Use Design of Experiment and Engine Modeling?

These approaches can be used to ensure that you develop optimal engine calibrations for complex engines with many controllable variables (such as variable valve timing, variable valve lift, and cylinder deactivation) at minimum cost and time.

Test bed time is expensive, and Design of Experiments methodology can help you choose the most effective points to run to get the maximum information in the shortest time. You can break the exponential dependency between the complexity of the engine (number of inputs) and the cost of testing (number of tests). You can collect the most statistically useful data, and just enough of it to fit the models.

Experimental design test points can be constrained based on previous experience to avoid damaging expensive engine hardware prototypes at unrealistic operating points.

The act of statistically modeling engine data can help identify the effect of interactions between calibration settings and engine performance, which can be vital to understanding how to optimally meet emissions constraints.

Accurate statistical models of engine data can also be used to develop calibration tables that have smooth transitions between the operating range of the engine and the edge regions of calibration tables where the engine will not be operated.

Optimal calibrations can be generated from statistical engine models in a methodical, repeatable process to ensure that maximum performance is achieved subject to emissions, driveability, and material limit constraints.

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Problem Definition

The aim of this case study is to produce optimized tables for

• Intake Cam Phase

• Exhaust Cam Phase

• Spark Timing Schedules

  as a function of Load and rpm, subject to the following constraints

  • Constrain solutions to lie within the boundary constraint model (to keep the engine within its operating region)

  • Constrain cam phase solutions so they do not change by more than 10^o between table cells (that is, no more than 10^o per 500 RPM change and per 0.1 load change).

  • Constrain residual fraction <= 25% at each drive cycle point (to ensure stable combustion). Residual fraction is the percentage of burned gas mass in the cylinder at intake valve close, relative to the total mass in the cylinder at intake valve close. Constraining maximum residual fraction is a simple and reasonable way of ensuring stable combustion. Residual fraction = 100 * Burned Gas Mass from Last Cycle / (Burned Gas Mass From Last Cycle + Fresh Air Mass)

To produce these tables, you need to make accurate models of the behavior of torque, exhaust temperature, and residual fraction at different values of speed, throttle area, spark, and cam timings. You need engine data to build these models, so the first step is constructing an experimental design to collect the most useful set of points.

Before you can design an experiment you need to set up a two-stage test plan and define your model inputs and model type.

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Introduction to Two-Stage Modeling

What is a two-stage test plan? You use a test plan to set up models in the Model Browser. The two stages refer to the way that engine data is often collected. For example, in each test, spark (the local variable) is swept while the other variables (such as speed and load) are held constant — these are referred to as global variables. Each test is taken at a different point in the global variables. Building the statistical models to take into account these individual sweeps makes it possible to incorporate engineering knowledge in the process. You can see plots of torque/spark sweeps, and use variables such as MBT (maximum brake torque) in modeling, rather than solely abstract mathematical properties of curves. You can then apply previous knowledge about the expected behavior of these variables to help you select good models.

You can easily identify outliers when you can see the sweep in which they were taken. The Model Browser allows you to visualize the data in a way that can help you identify and investigate suspect sweeps, and decide what kind of models will produce the best fit to the shapes of the data. The more controllable variables there are in an engine the more useful it is to have these visual aids to investigate complex data. Constructing models to take into account the way the data is collected helps build good models that you can have more confidence in. Statistically, it is the correct thing to do as it allows you to partition the errors within sweeps and the errors between sweeps separately.

You use a two-stage test plan to build your models because this data is suited to it. Spark is varied as the other variables are held constant, so the data is collected in a hierarchical structure; your models attempt to capture this information. You come to more detail on how this two-stage model is constructed after creating a design and obtaining data.

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Gasoline Engine Calibration Case Study

Designing the Experiment

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