Nonlinear Process Identification Using Orthonormal Bases

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Solution Overview

Problem

Conventional process control systems rely heavily on linear models, which are inadequate for capturing nonlinear dynamics in industrial processes, requiring highly skilled resources and being time-consuming, limiting their widespread acceptance in industries like manufacturing and chemical refining.

Innovation Solution

The use of orthonormal bases and ordinal splines in a process control system for nonlinear process identification, enabling the creation of empirical-based nonlinear models that can accommodate complex dynamics and be directly used for control, allowing for flexible model structures and online calculations.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If linear models are used in process control systems, then the control implementation is simple and widely accepted, but the models are inadequate for capturing nonlinear dynamics in industrial processes

Engineering Contradiction:

Improvecapability to capture nonlinear dynamicsVSAvoidmodel complexity

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent transforms the nonlinear modeling problem by changing the parameter representation from traditional complex nonlinear functions to a linear combination of orthonormal basis functions. This allows the model to capture nonlinear dynamics through parameter estimation rather than complex structural relationships, resolving the contradiction between adaptability and complexity.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent substitutes traditional iterative system identification methods with a direct linear algebraic solution approach. By using orthonormal bases, the complex iterative identification process is replaced with a straightforward computational method, reducing model complexity while maintaining nonlinear capture capability.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Reliability

If first principle models are used for nonlinear control, then the models can capture system behavior, but the process is time-consuming and requires highly-skilled resources

Engineering Contradiction:

Improvemodel accuracyVSAvoidmodel development time

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The patent enables the system to automatically identify nonlinear models from process data without requiring highly-skilled personnel to manually derive first principle models. The orthonormal basis approach allows the system to self-identify models through data-driven methods, maintaining reliability while eliminating the need for expert intervention and reducing time consumption.

Inventive Principle:

Principle #25Self-service

Solution Approach 2:

The patent performs preliminary transformation of the modeling problem into a linear framework using orthonormal bases before identification. This preliminary action simplifies the subsequent identification process, allowing accurate nonlinear models to be obtained quickly without time-consuming iterative derivation by skilled personnel.

Inventive Principle:

Principle #10Preliminary action

3Reliability

If first principle models are used for nonlinear control, then the models can capture system behavior, but continuous model updating is required

Engineering Contradiction:

Improvemodel accuracyVSAvoidoperational efficiency

Core Design Contradiction:

ReliabilityVSProductivity

Solution Approach 1:

The patent replaces the continuous iterative updating process with a direct linear algebraic solution method. The orthonormal basis transformation allows model parameters to be updated efficiently through straightforward computation rather than continuous iterative solving, maintaining model accuracy while improving operational efficiency and reducing the burden of continuous updates.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

4Adaptability or versatility

If nonlinear programming is used to solve differential algebraic equations, then nonlinear control can be achieved, but the process is very time-consuming and requires highly-skilled resources

Engineering Contradiction:

Improvenonlinear control capabilityVSAvoidease of implementation

Core Design Contradiction:

Adaptability or versatilityVSEase of operation

Solution Approach 1:

The patent substitutes complex nonlinear programming and differential algebraic equation solving with a linear algebraic approach using orthonormal bases. This substitution maintains full nonlinear control capability while dramatically simplifying the implementation process, making it easier to operate and not requiring highly-skilled resources for model identification and updating.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Data Source

PatentUS9199860B2Apparatus and method for nonlinear process identification using orthonormal bases and ordinal splines in a process control system

Publication Date: 2015.12.01 HONEYWELL INTERNATIONAL INC

AI summary

A method includes receiving data associated with operation of an industrial process system. The method also includes identifying a model defining a behavior of the industrial process system using the data, an orthonormal bases function, and an ordinal spline bases function. The orthonormal bases function can be generated using estimated poles of the industrial process system. The ordinal spline bases function can be generated using a specified set of cubic splines. The ordinal spline bases function can also be generated using a distribution of knots and multiple ordinal spline functions associated with the knots. More knots can be associated with a more nonlinear portion of the industrial process system, and fewer knots can be associated with a less nonlinear portion or a linear portion of the industrial process system.