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Optimization Problems You Can Solve with CAGE

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Point Optimization Problems Sum Optimization Problems

Point Optimization Problems

CAGE provides a flexible optimization environment in which many automotive optimization problems can be solved. These problems can be divided into two main groups, point and sum problems. This section describes point problems.

In a point problem, a single optimization run can determine optimal control parameter values at a single operating point. To optimize control parameters over a set of operating points, an optimization can be run for each point.

Examples of point problems that CAGE can be used to solve are described below:

• Find the optimal spark timing (SPK), intake valve timing (INTCAM) and exhaust valve timing (EXHCAM) at each point of a lookup table whose axes are engine speed (N) and relative load (L).

  Optimized values of the control parameters are determined by running the following optimization at each point of the lookup table:

  Objective: Maximize engine torque, TQ = TQ(N, L, SPK, EXHCAM, INTCAM)

  Constraints:

  • Residual fraction <= 17% at each (N, L) operating point

  • Exhaust temperature <= 1290°C at each (N, L) operating point

  • Engine to be operated inside the operating envelope of the engine

• Find the optimal mass of fuel injected (F), rail pressure (P), pilot timing (PT) and main timing (MT) at each point of a lookup table whose axes are engine speed (N) and engine torque (TQ).

  Optimized values of the control parameters are determined by running the following optimization at each point of the lookup table:

  Objective: Minimize brake specific fuel consumption, BSFC = BSFC(N, TQ)

  Constraints:

  • Engine out NOx <= 0.001 kg/s at each (N, TQ) operating point

  • Engine out Soot emissions <= 0.0001 kg/s at each (N, TQ) operating point

• Find the optimum spark timing (SPK) and exhaust gas recirculation (EGR) at each point of a set of operating points defined by engine speed (N), engine load (L) pairs. Optimized values of SPK and EGR are determined by running the following optimization at each point:

  Objective: Maximize engine torque, TQ = TQ(N, L, SPK, EGR)

  Constraints: Engine out NOx <= 400 g/hr at each (N, L) operating point

• For a new engine, find out the optimal torque versus NOx emissions curve for this engine over the operating range of the engine. This is a multi-objective optimization, and CAGE Optimization contains an algorithm (NBI) to solve these problems.

  For this example, the optimal torque-NOx curve is determined by solving the following optimization problem for optimal settings of spark timing (SPK) and exhaust gas recirculation (EGR):

  Objectives:

  • Maximize engine torque, TQ = TQ(N, L, SPK, EGR)

  • Minimize engine out NOx = NOx(N, L, SPK, EGR)

  To find out more about solving multiobjective optimization problems in CAGE, see Setting Up Multiobjective Optimizations.

To find out more about solving point optimization types of problems in CAGE, see Creating an Optimization.

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Sum Optimization Problems

In a sum optimization, a single optimization run can determine the optimal value of control parameters at several operating points simultaneously. All the control parameters for the operating points are optimized by calling the algorithm once (there's only one call to foptcon per run for a sum optimization). This approach contrasts with a point optimization, which has to make a call to the algorithm for every point to find the optimal settings of the control parameters.

• Find the optimal spark timing (SPK), intake valve timing (INTCAM) and exhaust valve timing (EXHCAM) at each point of a look-up table whose axes are engine speed (N) and relative load (L).

  Optimized values of the control parameters are determined by running the following optimization once:

  Objective: Maximize weighted sum of engine torque, TQ = TQ(N, L, SPK, EXHCAM, INTCAM) over the (N, L) points of a look-up table.

  Constraints:

  • Difference in INTCAM between adjacent cells is no greater than 5°.

  • Difference in EXHCAM between adjacent cells is no greater than 10°.

  • At each table cell, residual fraction <= 17%

  • At each table cell, exhaust temperature <= 1290°C

• Find the optimal start of injection (SOI), basefuelmass (BFM), fuel pressure (P), turbo position (TP) and lift of the EGR valve (EGR) at a set of mode points defined by engine speed (N), engine torque (TQ) pairs.

  Optimized values of the control parameters are determined by running the following optimization once:

  Objective: Maximize weighted sum of brake specific fuel consumption, BSFC = BSFC(SOI, BFM, P, TP, EGR, N, TQ) over the (N, TQ) mode points.

  Constraints:

  • Weighted sum of brake specific NOx must be less than a legislated maximum

  • At each mode point, air fuel ratio must be greater than a specified minimum

  • At each mode point, turbo speed must not exceed a specified maximum

To find out more about solving these types of problems in CAGE, see Setting Up Sum Optimizations.

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Using Optimization in CAGE

Creating an Optimization

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