Sequential State Estimation for Nonlinear Drilling Systems
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Solution Overview
Problem
Existing Bayesian inference methods face challenges in accurately estimating system states and parameters from uncertain measurements, particularly in nonlinear systems, due to computational complexity and the need for numerous forward model simulations, which limits real-time applications in industries like oil and gas.
Innovation Solution
A method involving a processor that builds an approximate model of the system, samples system parameter values from an approximate posterior probability distribution, and simulates the evolution of system states, using techniques like Single Component Metropolis Hastings sampling and piecewise model approximation to reduce computational burden and enhance estimation efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If particle filtering or standard Bayesian inference methods are used to determine system states from measurements, then measurement precision and reliability are improved, but device complexity and computational time increase significantly
Solution Approach 1:
The patent segments the complex Bayesian inference problem into discrete time intervals, processing measurements sequentially rather than all at once. This allows the system to handle complex nonlinear relationships while reducing computational burden by breaking the problem into manageable segments that can be processed in real-time
Solution Approach 2:
The patent transforms the continuous state estimation problem into a discrete parameter sampling problem. By representing system states as a finite set of discrete parameters with associated probabilities, the system achieves accurate estimation while enabling efficient computation through discrete sampling rather than continuous calculation
2Manufacturing precision
If numerous forward model simulations are performed to achieve accurate parameter estimation, then manufacturing precision is improved, but productivity decreases due to computational time requirements
Solution Approach 1:
The patent performs preliminary sampling of discrete parameters and pre-computes their associated probabilities before actual real-time processing. This preliminary action creates a ready-to-use probability distribution that can be quickly updated with new measurements, eliminating the need for extensive forward simulations during critical real-time operations
Solution Approach 2:
The patent creates simplified copies of the system model in the form of discrete parameter representations with probability distributions. These computational copies approximate the complex forward model behavior, enabling rapid parameter estimation without requiring numerous expensive forward simulations of the actual system
3Reliability
If standard Bayesian inference techniques are applied to nonlinear systems, then reliability of state determination is improved, but loss of time increases due to computational burden
Solution Approach 1:
The patent implements periodic updating of the discrete parameter probability distributions at defined time intervals rather than continuous computation. This periodic approach maintains reliable state estimation by regularly incorporating new measurements while avoiding unnecessary computational overhead between update cycles
Solution Approach 2:
The patent introduces discrete parameters with probability distributions as intermediary representations between the raw measurements and the final state estimation. These intermediaries simplify the computational path by providing a structured probabilistic framework that requires less computational time than direct Bayesian inference on continuous variables
Data Source
AI summary
A method of determining a parameter and state of a system from a time series of a system measurement, comprising using a processor to: a) build an approximate model of the system; b) sample a plurality of approximate system parameters for a current time interval from a posterior probability distribution; c) determine an estimate of the system parameter at the current time interval from the distribution of the plurality of approximate system parameters; d) determine an estimate of the system state at the current time interval given the estimate of the system parameter; e) repeat b) to d) for the next time interval. An apparatus for performing the method is disclosed, and application of the method to drilling and wellbores is discussed.