Convex Optimization for Multivariable Fault Diagnosis
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Solution Overview
Problem
Conventional diagnostic systems face challenges in accurately detecting and diagnosing faults in complex systems due to their univariate approach, combinatorial complexity, and inability to handle nonlinearities and discrete variables, leading to suboptimal performance and false positives/negatives.
Innovation Solution
A method for multivariable diagnostic estimation using convex optimization, which processes data from sensors to compute fault conditions and likelihood parameters, employing a formulator to set up a convex optimization program and an optimizer to solve it efficiently, allowing for real-time fault detection and improved accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If univariate diagnostic functions are used to monitor single sensors or control loops, then the diagnostic function is simple to implement, but it cannot detect faults that simultaneously impact multiple sensors
Solution Approach 1:
The patent combines multiple univariate diagnostic functions into a single multivariable framework by integrating data from multiple sensors and low-level diagnostic codes. The convex optimization program simultaneously processes these multiple inputs to produce unified fault estimates, enabling detection of faults that affect multiple sensors while maintaining computational efficiency.
Solution Approach 2:
The multivariable diagnostic framework serves multiple functions simultaneously: it monitors individual sensors, detects correlated faults across sensors, estimates fault states, and provides diagnostic recommendations. This universal approach replaces multiple specialized univariate functions with a single multi-functional system.
2Reliability
If AI reasoning methods are used to integrate multiple fault diagnostic codes, then fault detection capability is improved, but computational complexity increases due to combinatorial problems
Solution Approach 1:
The patent transforms the diagnostic problem from a combinatorial AI reasoning task into a convex optimization problem by changing the mathematical parameters and formulation. Instead of using heuristic AI methods that struggle with combinatorial complexity, the invention uses convex optimization with well-defined parameters and constraints, guaranteeing global optimality and reducing computational burden.
Solution Approach 2:
The patent replaces the mechanical AI reasoning process with a mathematical optimization approach. Rather than using iterative heuristic search methods typical of AI, the invention employs convex optimization algorithms that provide systematic, efficient, and guaranteed convergence to the optimal solution.
3Ease of operation
If linear models are used for multivariable diagnostic estimation, then computational simplicity is maintained, but the system cannot handle nonlinearities and structure changes
Solution Approach 1:
The patent implements a dynamic diagnostic system that adapts to changing system conditions. The convex optimization framework can incorporate time-varying parameters and constraints, allowing it to handle nonlinearities and structural changes in the monitored system while maintaining computational efficiency through the convex formulation.
4Use of energy by moving object
If conventional diagnostic methods are used, then computational resources are conserved, but false positives and negatives increase
Solution Approach 1:
The patent applies partial optimization by focusing computational resources on the most critical fault detection tasks while maintaining acceptable performance. The convex optimization framework allows selective refinement of diagnostic estimates for specific fault conditions, achieving high accuracy for critical faults without proportionally increasing overall computational burden.
Data Source
AI summary
Proposed is a method, implemented in software, for estimating fault state of an apparatus outfitted with sensors. At each execution period the method processes sensor data from the apparatus to obtain a set of parity parameters, which are further used for estimating fault state. The estimation method formulates a convex optimization problem for each fault hypothesis and employs a convex solver to compute fault parameter estimates and fault likelihoods for each fault hypothesis. The highest likelihoods and corresponding parameter estimates are transmitted to a display device or an automated decision and control system. The obtained accurate estimate of fault state can be used to improve safety, performance, or maintenance processes for the apparatus.