# US 2013/0158840 A1 · Asymmetric wavelet kernel in support vector learning

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- Number: US 2013/0158840 A1
- Document ID: US20130158840A1
- Status: Published application
- Kind: A1
- Application number: 13/327,925
- Filed: 2011-12-16
- Published: 2013-06-20
- Earliest claimed: 2011-12-16
- Assignees: Toyota Motor Engineering & Manufacturing North America, Inc.
- Inventors: Zhao Lu; Jing Sun; Kenneth R. Butts
- Web page: https://patentgrep.com/patent/US20130158840A1

## CPC

- G06N 20/10: using kernel methods, e.g. support vector machines [SVM]
- F02D 41/00: Electrical control of supply of combustible mixture or its constituents (F02D43/00 takes precedence {; control of engine starters F02N11/08, electrical control of engine ignition timing F02P5/145})
- F02D 41/2425: {Particular ways of programming the data}
- F02D 41/2432: {Methods of calibration}
- F02D 41/26: using computer, e.g. microprocessor
- G06F 18/2411: based on the proximity to a decision surface, e.g. support vector machines
- G06F 30/15: Vehicle, aircraft or watercraft design
- G06N 20/00: Machine learning
- F02D 41/2438: {Active learning methods}
- F02D 2041/1433: {using a model or simulation of the system}
- G06F 2218/00: Aspects of pattern recognition specially adapted for signal processing
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- F02D: CONTROLLING COMBUSTION ENGINES (vehicle fittings, acting on a single sub-unit only, for automatically controlling vehicle speed B60K31/00; conjoint control of vehicle sub-units of different type or different function, road vehicle drive control systems for purposes other than the control of a single sub-unit B60W)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

Example methods of modeling a nonlinear dynamical system such as a vehicle engine include providing a model using linear programming support vector regression (LP-SVR) having an asymmetric wavelet kernel, such as derived from a raised-cosine wavelet function. The model may be trained to determine parallel model parameters while in a series-parallel configuration, and operated in the parallel configuration allowing improved and more flexible model performance. An improved engine control unit may use an LP-SVR with an asymmetric wavelet kernel.

## Claims

### Claim 1

A method of modeling a system, the system being a nonlinear dynamical system, the method comprising:
providing a model, the model being a linear programming support vector regression (LP-SVR) having an asymmetric wavelet kernel, the asymmetric wavelet kernel being derived from a raised-cosine wavelet function;
training the model to determine model parameters, the model being trained in a series-parallel configuration; and
modeling the system, using the model in a parallel configuration and the model parameters determined in the series-parallel configuration.

### Claim 2 (depends on 1)

The method of claim 1, the wavelet kernel is derived from a scaling function φ(x), the scaling function being a raised-cosine scaling function
ϕ

(
x
)
=
sin


π

(
1
-
b
)

x
+
sin


π

(
1
+
b
)

x
2


π


x

(
1
+
2


bx
)
,
where b is a parameter.

### Claim 3 (depends on 1)

The method of claim 1, the wavelet kernel using a type-II raised-cosine wavelet function ψ(x), where
ψ

(
x
+
1
2
)
=
1
2


π


x

[
1
+
4


bx
]

[
sin


2


π

(
1
-
b
)

x
+
sin


2


π

(
1
+
b
)

x
]
-
1
2


π


x

[
1
-
2


bx
]

[
sin


π

(
1
-
b
)

x
+
sin


π

(
1
+
b
)

x
]
where b is a parameter.

### Claim 4 (depends on 3)

The method of claim 3, the kernel using a multi-dimensional type-II raised cosine wavelet basis defined by the tensor product
Ψ
j

(
[
x
1
⋮
x
n
]
)
=
∏
k
=
1
n


ψ

(
x
k
-
m
jk
d
j
)
where mj=[mj1, mj2, . . . , mjn]T is a translation vector and dj is a dilation factor.

### Claim 5 (depends on 1)

The method of claim 1, the model using a composite kernel including the asymmetric wavelet kernel and a second kernel.

### Claim 6 (depends on 5)

The method of claim 5, the second kernel representing the system input state,
the asymmetric wavelet kernel representing a system output state when the model is in the series-parallel configuration,
the asymmetric wavelet kernel representing a model output state when the model is in the parallel configuration.

### Claim 7 (depends on 1)

The method of claim 1, wherein the system is a vehicle engine, the model being a model of engine performance.

### Claim 8 (depends on 4)

The method of claim 4, wherein the training data and optimized model parameters are determined during an engine test process.

### Claim 9

A method of modeling a system, the system being a vehicle engine, the method comprising:
providing a model, the model including linear programming support vector regression (LP-SVR) having a wavelet kernel,
the model being implemented as software on an engine control unit,
the wavelet kernel being an asymmetric wavelet kernel derived from a raised-cosine wavelet function;
training the model to determine model parameters, the model being trained in a series-parallel configuration; and
modeling the system, using the model in a parallel configuration, using the model parameters determined in the series-parallel configuration.

### Claim 10 (depends on 9)

The method of claim 9, the wavelet kernel is derived from a scaling function φ(x), the scaling function being a raised-cosine scaling function having the form
ϕ

(
x
)
=
sin


π

(
1
-
b
)

x
+
sin


π

(
1
+
b
)

x
2


π


x

(
1
+
2


bx
)
where b is a parameter.

### Claim 11 (depends on 9)

The method of claim 9, further including retraining the model in the series-parallel configuration during operation of the vehicle,
retraining including reprogramming of the electronic control unit.

### Claim 12

An apparatus, the apparatus being an electronic control unit for a vehicle engine, the apparatus comprising:
engine data inputs configured to receive engine data, the engine data including engine operation data and operator input data;
engine control outputs, operable to control engine parameters, the engine parameters including fuel injection quantity; and
an electronic control circuit, the electronic control circuit comprising at least a memory and a processor, the electronic circuit using a linear programming support vector regression (LP-SVR) having a wavelet kernel as a model of the vehicle engine, the model being used to determine required engine model from the engine data,
the wavelet kernel being an asymmetric wavelet kernel derived from a raised-cosine wavelet function.

### Claim 13 (depends on 12)

The apparatus of claim 12, the engine control unit having a training mode and an operating mode,
the model having a series-parallel configuration when the engine control unit is in the training mode,
the model having a parallel configuration when the engine control unit is in the operating mode.

### Claim 14 (depends on 12)

The apparatus of claim 12, wherein the engine data comprises one or more engine parameters selected from the group of engine parameters consisting of coolant temperature, throttle position, fuel injection quantity, and valve timing.