EMD Signal De-noising via IMF Statistical Distribution Testing

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Solution Overview

Problem

Empirical Mode Decomposition (EMD) based signal de-noising techniques face challenges in selectively extracting information-carrying Intrinsic Mode Functions (IMFs) due to its non-linear filtering nature, where cut-off frequencies of IMFs are dependent on signal type, noise power, and sampling rate, lacking a theoretical basis for IMF selection.

Innovation Solution

The use of statistical characteristics of IMFs, specifically generalized Gaussian distribution (GGD), to identify noise-carrying and information-carrying IMFs through null hypothesis testing, allowing for partial reconstruction of the signal by discarding noise-carrying IMFs and retaining information-carrying ones.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If EMD is used for signal de-noising, then the method can handle non-stationary and non-linear signals, but the cut-off frequencies of IMFs become dependent on signal type, noise power, and sampling rate without a theoretical basis for selection

Engineering Contradiction:

Improveability to handle non-stationary and non-linear signalsVSAvoidprecision of IMF selection

Core Design Contradiction:

Adaptability or versatilityVSMeasurement precision

Solution Approach 1:

The patent applies parameter changes by transforming the statistical properties of IMFs from empirical observations to theoretical distributions. Specifically, it establishes that noise-carrying IMFs follow a generalized Gaussian distribution (GGD) while information-carrying IMFs follow a different distribution pattern. This parameter transformation enables precise identification of noise-carrying IMFs through null hypothesis testing, resolving the contradiction between adaptability to various signal types and precision of IMF selection.

Inventive Principle:

Principle #35Parameter changes

2Ease of operation

If EMD decomposes a signal into IMFs, then the signal can be analyzed in the time-domain, but it becomes difficult to selectively extract information-carrying IMFs due to the non-linear filtering nature

Engineering Contradiction:

Improvetime-domain decomposition capabilityVSAvoiddifficulty of identifying information-carrying IMFs

Core Design Contradiction:

Ease of operationVSDifficulty of detecting and measuring

Solution Approach 1:

The patent replaces the mechanical/algorithmic EMD decomposition process with a statistical identification system. Instead of relying on the non-linear filtering properties of EMD to separate noise and signal, the patent uses statistical characteristics (distribution patterns and null hypothesis testing) to identify information-carrying IMFs. This substitution transforms the difficulty of detecting information-carrying IMFs into a statistically testable problem, making the identification process more reliable and less dependent on signal-specific parameters.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

3Ease of manufacture

If EMD is used for de-noising, then the method is data-driven and requires no a priori knowledge, but it lacks a theoretical basis for distinguishing noise from signal components

Engineering Contradiction:

Improvedata-driven approach without a priori knowledgeVSAvoidreliability of noise-signal distinction

Core Design Contradiction:

Ease of manufactureVSReliability

Solution Approach 1:

The patent introduces statistical distribution patterns as an intermediary between the data-driven EMD decomposition and the reliability requirement for noise-signal distinction. Specifically, it establishes that noise-carrying IMFs follow a generalized Gaussian distribution (GGD) while information-carrying IMFs follow a different distribution. This statistical intermediary provides a theoretical basis for reliable distinction, bridging the gap between the data-driven nature of EMD and the need for reliable noise-signal separation.

Inventive Principle:

Principle #24Intermediary (Mediator)

Solution Approach 2:

The patent implements feedback through null hypothesis testing, where the statistical properties of IMFs are continuously evaluated to identify information-carrying components. The test results feed back into the de-noising process, allowing iterative refinement of the separation between noise and signal. This feedback mechanism enhances reliability by continuously verifying the statistical assumptions and adjusting the identification process accordingly.

Inventive Principle:

Principle #23Feedback

Data Source

PatentUS11257509B2Techniques for empirical mode decomposition (EMD)-based signal de-noising using statistical properties of intrinsic mode functions (IMFs)

Publication Date: 2022.02.22 UNIVERSITY OF NEW HAMPSHIRE

AI summary

Techniques for EMD-based signal de-noising are disclosed that use statistical characteristics of IMFs to identify information-carrying IMFs for the purposes of partially reconstructing the identified relevant IMFs into a de-noised signal. The present disclosure has identified that the statistical characteristics of IMFs with noise tend to follow a generalized Gaussian distribution (GGD) versus only a Gaussian or Laplace distribution. Accordingly, a framework for relevant IMF selection is disclosed that includes, in part, performing a null hypothesis test against a distribution of each IMF derived from the use of a generalized probability density function (PDF). IMFs that contribute more noise than signal may thus be identified through the null hypothesis test. Conversely, the aspects and embodiments disclosed herein enable the determination of which IMFs have a contribution of more signal than noise. Thus, a signal may be partially reconstructed based on the predominately information-carrying IMFs to result in de-noised output signal.