Sensor Stream Change Detection Using Sliding Window Sub-Window Analysis
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Solution Overview
Problem
Existing methods for detecting abrupt changes in sensor data streams are hindered by the need for explicit modeling of probability distributions, which is laborious and often intractable, especially when distributions are unknown or multi-modal, and current automated methods are not efficient for real-time monitoring in industrial applications.
Innovation Solution
The method employs sub-windows of varying sizes to detect changes by calculating a merit score based on differences between pairs of contiguous sub-windows, using Parzen's kernel density estimates and memory-based graph theoretic or cumulative sum procedures, reducing computational complexity from O(N^4) to O(N^2) through efficient data structure organization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If explicit modeling of probability distributions is used for change detection, then detection accuracy is improved, but the process becomes laborious and expensive
Solution Approach 1:
The system performs self-service by automatically learning probability distributions from the sensor data itself without requiring external expert modeling. The kernel density estimation and EM algorithm enable the system to autonomously construct distribution models p0(x) and p1(x) directly from the data streams, eliminating the laborious manual modeling process while maintaining detection accuracy.
2Reliability
If CUSUM procedure is used with known distributions, then change detection is optimal, but both distributions must be known beforehand which is often impossible
Solution Approach 1:
The system performs preliminary action by pre-learning the in-control distribution p0(x) from historical sensor data before any change occurs. This pre-established baseline distribution enables the CUSUM procedure to function optimally when a change happens, as the reference distribution is already available without requiring knowledge of future out-of-control distributions.
Solution Approach 2:
The kernel density estimation serves as an intermediary that bridges the gap between unknown distributions and the CUSUM procedure requirements. It provides a non-parametric way to represent arbitrary distributions p0(x) and p1(x) through their density estimates, allowing the CUSUM algorithm to work with distributions that were previously impossible to specify explicitly.
3Adaptability or versatility
If all possible out-of-control distributions are modeled, then comprehensive change detection is achieved, but the process becomes intractable
Solution Approach 1:
The system handles parameter changes by using kernel density estimation with variable bandwidth parameters. The bandwidth matrix H can be adjusted to control the smoothness and adaptability of the density estimate, allowing the system to accommodate various distribution shapes and characteristics without requiring explicit parametric models for each possible out-of-control scenario.
4Productivity
If automated change detection methods are developed, then processing speed is improved, but competence and versatility compared to human supervisors is reduced
Solution Approach 1:
The system replaces the mechanical human monitoring process with an automated computational system that uses statistical learning and hypothesis testing. The automated method substitutes human pattern recognition with algorithmic distribution comparison, achieving comparable competence for specific change detection tasks while providing unlimited processing speed and consistency.
Data Source
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AI summary
A method detects a change in a stream of samples acquired by a sensor. A stream of samples acquired by a sensor over time is stored sequentially in a buffer in which an oldest sample is discarded and a newest sample is stored when the buffer is full, such that the buffer forms a window of samples sliding forward in time. For each new sample, the buffer is partitioned into all possible pairs of contiguous sub-windows of samples including a first sub-window and a second sub-window such that the newest sample is stored in the second sub-window of the pair. A difference is determined between the first and second sub-window of each pair of the contiguous sub-windows of samples, and a maximum difference is assigned as a merit score. A change in the stream of samples is signaled if the merit score is greater than a predetermine threshold. The change can be abrupt or gradual.