Neural Distribution Function Selection for Stationary and Changing Time Series
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Solution Overview
Problem
Existing methods for determining distribution functions in time series of measurement data require high computing capacity and are inefficient in handling temporally non-stationary and stationary distributions.
Innovation Solution
A method using neural networks to determine a statistical distribution function and its parameters, involving a first neural network to classify data as temporally stationary or non-stationary and a second neural network to evaluate distribution functions, reducing computing requirements by employing kernel density estimation and maximum likelihood estimation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If parameters of all known distribution functions are estimated using maximum likelihood estimators, then the accuracy of distribution function selection is improved, but the computing capacity required increases significantly
Solution Approach 1:
The patent applies preliminary action by using a neural network to pre-classify the time series data as either temporally stationary or non-stationary before proceeding with distribution function estimation. This preliminary classification eliminates the need to estimate parameters for all possible distribution functions, thereby reducing computing capacity while maintaining accurate distribution function selection.
Solution Approach 2:
The patent segments the distribution function selection process into distinct pathways based on temporal stationarity. One pathway handles temporally stationary distribution functions while another handles non-stationary cases, allowing the system to apply appropriate estimation methods only to relevant distribution functions rather than all known distributions.
2Reliability
If the temporal course of parameters is monitored by further estimators for each distribution function, then the reliability of capability determination is improved, but the complexity of the system increases
Solution Approach 1:
The neural network performs preliminary classification of temporal stationarity before distribution function estimation, which simplifies subsequent parameter monitoring. By knowing in advance whether the distribution is stationary or non-stationary, the system only needs to apply appropriate monitoring methods for that specific case, reducing overall system complexity while maintaining reliability.
Solution Approach 2:
The patent applies different parameter monitoring strategies based on the local characteristic of temporal stationarity. Temporally stationary distributions receive one type of monitoring while non-stationary distributions receive another, allowing the system to optimize reliability for each case without uniformly increasing complexity across all distribution functions.
Data Source
AI summary
Teaching herein include methods for determining a statistical distribution function and for determining parameters for the distribution function, with which a time series of measurement data can be displayed. An example includes: determining a first probability for a predetermined quantity of statistical distribution functions for each function that the measurement data has a distribution corresponding to this distribution function; determining a second probability that the measurement data originates from a temporally stationary source; determining, for the predetermined quantity of distribution functions for each distribution function, an evaluation variable for the respective distribution function from the assigned first probability, a temporal changeability of the distribution function, and the second probability; using the evaluation variable to select a distribution function from the quantity of distribution functions as a suitable distribution function for the measurement data; and determining parameters for the display of the measurement data for the selected distribution function.