Fault Prediction With Regression Models

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By:    Elliott D. Reitz

Date: 1/10/91

Submitted in partial fulfillment for the requirements for the degree of Master of Science in Electrical Engineering in the Graduate School of the State University of New York at Binghamton.


A computer based fault prediction system has been developed to increase aircraft safety and reduce maintenance cost. The approach developed uses a Recursive Least Squares Minimization (RLSM) parameter estimation routine to estimate parameters of a control-plant model equation, followed by a Box-Jenkins filter to predict future values of the parameter based on past estimates. Confidence intervals are investigated to determine the certainty of predictions. The prediction routine was proven to be practical for parameters experiencing slow linear drift.


Chapter 1. Introduction

1.1 Predictive Diagnostics Design Goal

1.2 Maintenance Costs

1.3 System Safety

1.4 Application of Predictive Diagnostics

1.5 Related Research

Chapter 2. Methods and models of failure prediction

2.1 Failure Detection Isolation Prediction (FDIP)

2.2 Methods of trend analysis and prediction

2.3 Problem Definition

2.3.1 General System Architecture

2.3.2 Typical Control-Plant System

2.3.3 Second Order Tendency

2.3.4 Simulation of Failure Development

Chapter 3. On-Line Parameter Estimation

3.1 Application of parameter estimation procedures

3.2 The Recursive Least Squares Method (RLSM)

3.3 Simulation of on-line parameter estimation

Chapter 4. Trend Analysis and Failure Prediction

4.1 Development of predictive models.

4.1.1 Model Selection The AR(n) Model The AR(n) Model

4.2 Confidence Analysis of Model Based Predictions.

4.3 Simulation of a Failure Prediction System

Chapter 5. Discussion

5.1 Discussion of Results

5.2 Suggestions for further Study



Matlab Routines

1. Input Constant Generator

2. RLSM Parameter estimation Routine

3. Parameter Prediction Routine with an AR(p/skip)

4. Parameter Prediction Routine with an ARMA(1,1)

5. Motor servo comparison of step response

6. Motor fault simulation routine

7. Plot routines


Figure 1, Fault Prediction System

Figure 2, General System Architecture

Figure 3, Typical Control-Plant System

Figure 4, 3rd Order vs 2nd Order Step Responses

Figure 5, Dominant Pole vs Torque Constant Kt

Figure 6, Dominant Pole vs Friction Constant F

Figure 7, Dominant Pole vs Armature Resistance, Ra

Figure 8, Dominant Pole vs LSM Estimate

Figure 9, RLSM System Configuration

Figure 10, Configuration of Prediction Filter

Figure 11, Configuration of Prediction Filter

Figure 12, Prediction of p1 with AR(200/20)

Figure 13, Prediction of p1 with AR(200/40)

Figure 14, Prediction of Sine Wave with AR(200/20)

Figure 15, Prediction of Sine Wave with AR(200/40)

Figure 16, Prediction of Parabolic Wave with AR(200/20)

Figure 17, Prediction of Parabolic Wave with AR(200/40)

Figure 18, Prediction of p1 with ARMA(1,1)/20

Figure 19, Prediction of p1 with ARMA(1,1)/40


Chapter 1 - Introduction

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