Automated Process Control Using Doubly Stochastic Count Forecasting
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Automated systems face challenges in effectively controlling processes using time series data, particularly when the data lacks meaningful structure and is intermittent, as classical methods assume continuous and normally distributed data.
Innovation Solution
The system employs a doubly stochastic model to analyze time series data by estimating a driver that underlies the observed data, using algorithms such as Expectation/Maximization (EM) and Markov Chain Monte Carlo (MCMC) to determine a probability model and generate realistic future scenarios for controlling automated processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If classical time series methods are used, then the analysis is simple and straightforward, but the methods fail when data is intermittent and lacks meaningful structure
Solution Approach 1:
The patent transforms the time series analysis problem by changing the parameterization approach. Instead of using classical methods that assume continuous normal distribution, the invention uses a doubly stochastic model where the intensity parameter itself is a stochastic process. This allows the model to adapt to intermittent data by letting the intensity parameter vary randomly over time, thus resolving the contradiction between maintaining analytical simplicity and achieving reliability for non-standard data patterns.
Solution Approach 2:
The patent introduces an intermediary intensity process that mediates between the observed count data and the underlying stochastic driver. This intensity process acts as a bridge, transforming the intermittent count observations into a continuous stochastic framework that can be analyzed using standard methods while still capturing the intermittent nature of the original data. The intermediary allows classical analytical tools to work effectively on transformed data that preserves the essential characteristics of the original intermittent process.
2Reliability
If a doubly stochastic model is used to accurately characterize intermittent data, then the analysis becomes more complex, but the results become more reliable
Solution Approach 1:
The patent segments the complex estimation problem into distinct computational phases. The doubly stochastic model estimation is divided into: (1) specifying the stochastic driver process, (2) defining the intensity process that links the driver to observed counts, (3) implementing the EM algorithm for parameter estimation, and (4) generating forecasts. This segmentation allows each component to be handled with appropriate computational techniques, reducing the overall complexity while maintaining accuracy.
Solution Approach 2:
The patent employs feedback mechanisms in the estimation algorithm, specifically using the Expectation-Maximization (EM) algorithm where parameter estimates are iteratively refined. The EM algorithm uses feedback from the likelihood function to update parameter estimates, which in turn improve the intensity process estimation, which then improves the driver process estimation, creating a feedback loop that converges to accurate results. This iterative feedback approach manages complexity by breaking down the estimation into manageable iterations rather than requiring a single complex calculation.
3Measurement precision
If iterative algorithms like EM and MCMC are used to estimate model parameters, then the precision of parameter estimation improves, but the computational time increases
Solution Approach 1:
The patent applies preliminary action by using the EM algorithm to obtain initial parameter estimates before applying MCMC methods. The EM algorithm provides a fast, preliminary estimation that converges quickly to reasonable parameter values. These preliminary estimates then serve as starting points for the more computationally intensive MCMC analysis, which only needs to refine rather than discover the parameters from scratch. This preliminary action significantly reduces the total computational time while maintaining the precision benefits of iterative methods.
Solution Approach 2:
The patent implements a two-stage estimation approach where the EM algorithm provides a partial estimation that is sufficient for many practical purposes, and the MCMC method provides an excessive (more thorough) estimation when higher precision is needed. This partial-or-excessive action strategy allows users to stop at the EM stage for quick results or continue to MCMC for maximum precision, thus managing the time-precision tradeoff flexibly based on specific application needs rather than always requiring the full computational burden of MCMC.
Data Source
AI summary
A system and method for controlling an automated process based on a time series of count data. The approach includes characterizing an observed time series of counts by modeling the underlying dynamics that give rise to the observed data, including evaluating the time series with a driver estimation process, wherein the driver estimation process identifies a model by an iterative process that includes: providing a probability model; and utilizing a combined MCMC and EM algorithm to determine a set of model parameters for the time series; outputting an estimated sequence of driver values based on the identified model; outputting a series of statistically plausible future counts, and controlling the automated process based on the estimated sequence of driver values.