Bayesian Failure Probability Assessment for Variable Machine Loads
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Solution Overview
Problem
Existing methods for calculating failure probabilities in machine systems, such as those in factories or power generation facilities, are limited by the instability of operation states and varying loads, which reduces the accuracy of failure rate and life expectancy estimates based on historical data.
Innovation Solution
The calculation of a posterior probability distribution using Bayesian estimation, where the latest operation state is considered, with past failure data serving as a prior probability distribution, to assess failure probabilities in machine systems with limited failure records.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If statistical analysis using historical failure records is used to estimate failure rates, then failure probability can be calculated, but the accuracy is insufficient when operation states are unstable and loads vary
Solution Approach 1:
The patent transforms the static failure rate into a dynamic concept by introducing time-varying failure rates λ(t) that adapt to changing operation states. The cumulative time-varying failure rate integrates these dynamic rates over time, allowing the model to respond to unstable operation conditions and varying loads, thereby resolving the contradiction between measurement precision and adaptability.
Solution Approach 2:
The patent changes the parameter representation from a constant failure rate to a time-dependent failure rate λ(t). By modeling the failure rate as a function of time and operation states, the system can accurately capture the effects of unstable operations and varying loads, improving both estimation accuracy and adaptability simultaneously.
2Measurement precision
If simple failure rate per unit time assessment is used, then calculation is straightforward, but estimation accuracy of number of failures and life expectancy is limited
Solution Approach 1:
The patent performs preliminary action by pre-defining the functional form of the time-varying failure rate λ(t) and establishing the cumulative time-varying failure rate model before actual failure data becomes available. This preliminary modeling framework enables accurate estimation even with limited historical data, improving estimation accuracy without requiring complex real-time analysis.
Solution Approach 2:
The patent introduces the cumulative time-varying failure rate as an intermediary concept that bridges simple failure rate assessment and complex reliability analysis. This intermediary model captures the effects of varying operation states and loads while maintaining a relatively simple calculation framework, thus improving estimation accuracy without proportionally increasing complexity.
3Reliability
If historical failure records are used for statistical analysis, then failure patterns can be identified, but diagnosis cannot reflect present situation when operation states change
Solution Approach 1:
The patent addresses information loss by transforming the static historical failure rate into a dynamic time-varying failure rate λ(t) that incorporates current operation states. The cumulative time-varying failure rate integrates this dynamic information over time, ensuring that the diagnosis reflects both historical patterns and present conditions, thereby maintaining reliability while preventing information loss.
Solution Approach 2:
The patent implements feedback by continuously updating the failure probability assessment based on current operation states and comparing it with historical failure patterns. The cumulative time-varying failure rate model incorporates real-time operational information, creating a feedback loop that ensures the diagnosis remains relevant to the current situation while learning from historical data.
Data Source
AI summary
The problem of the present invention is to establish how to more accurately estimate the failure probabilities of the components of a machine system that has a small number of failure records. A failure probability assessment system 100 is a system for assessing a failure probability of a component composing a machine system and includes: a failure probability density function parameter database 4 for storing a parameter that determines the failure probability density function of the component; a failure probability density function identification unit 12 for calculating the failure probability density function of the component; and a damage model generation/update unit 7 for generating survival analysis data that has a minimum variation defined by the failure probability density function using failure history data and the time series operation data, wherein the failure probability density function identification unit 12 estimates a failure probability density function parameter from a past failure probability density function parameter stored in the failure probability density function parameter database 4 and the latest survival analysis data using the Bayes estimation.