Failure Probability Evaluation Using Tail-Specific Density Estimation
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Solution Overview
Problem
Existing methods for evaluating failure probabilities in mechanical systems, such as wind power generators, inaccurately estimate the end portions of stress and strength distributions, leading to reduced accuracy in failure probability calculations when central and end portions do not follow the same probability distribution.
Innovation Solution
A failure probability evaluation device and method that utilize an extreme value statistical model to estimate the probability density function of the end portion and a separate model for the central portion, connecting these to compute the entire probability density function for improved accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a single probability density function is used to estimate the entire frequency distribution of generated stress, then the estimation is simple and unified, but the accuracy of estimating the end portion is reduced when the central portion and end portion do not follow the same probability distribution
Solution Approach 1:
The patent divides the frequency distribution of generated stress into two distinct segments: the central portion and the end portion. Each segment is modeled using a separate probability density function (PDF) - the central portion using a normal distribution and the end portion using an extreme value distribution. This segmentation allows each region to be estimated with the most appropriate statistical model, thereby improving the accuracy of end portion estimation without excessive complexity.
Solution Approach 2:
The patent applies different probability density functions to different regions of the stress distribution based on their local characteristics. The central portion, where stress values occur most frequently, is modeled with a normal distribution, while the end portion, representing extreme stress values, is modeled with an extreme value distribution. This local quality approach ensures that each region is estimated with the most suitable statistical model for its specific behavior.
2Reliability
If the entire frequency distribution is modeled with one probability distribution, then the model is simple, but it cannot accurately represent cases where central and end portions follow different distributions
Solution Approach 1:
The patent segments the stress frequency distribution into central and end portions, each modeled with appropriate PDFs. This segmentation improves reliability by ensuring that the failure probability evaluation accurately represents the true stress distribution, particularly in the critical end region where extreme values determine failure likelihood.
Solution Approach 2:
The patent creates a composite probability distribution model that combines a normal distribution for the central portion and an extreme value distribution for the end portion. This composite model accurately represents the heterogeneous nature of stress distributions, where different regions follow different statistical patterns, thereby improving the reliability of failure probability predictions.
3Measurement precision
If measurement data is used to accurately estimate the probability density function, then the failure probability evaluation becomes more accurate, but the complexity of data processing and model selection increases
Solution Approach 1:
The patent simplifies data analysis by segmenting the stress data into central and end portions based on predefined criteria (e.g., percentile thresholds). This segmentation makes it easier to apply appropriate statistical models to each region, reducing the overall complexity of data processing while maintaining high estimation accuracy.
Solution Approach 2:
The patent transforms the complex problem of estimating a single PDF for the entire distribution into a simpler problem of estimating two separate PDFs for different regions. By changing the parameterization approach from one unified model to two region-specific models, the patent reduces the difficulty of detecting and measuring the appropriate distribution characteristics from the measurement data.
Data Source
AI summary
Provided are: a technique for improving failure probability evaluation precision, even when the center and tails of an occurrence frequency distribution for stress or strength, or a physical quantity associated with stress or strength, such as load, for example, do not conform to the same probability distribution, by precisely estimating a tail probability density function; and a high-precision failure probability evaluation device. This results in a failure probability evaluation device comprising: a probability density estimation function estimation unit comprising a storage unit for storing a failure model, which computes the probability of failure in a mechanical system, and a probability variable occurrence frequency distribution used in the failure model, a tail estimation unit for estimating a probability density function for the tails of the occurrence frequency distribution on the basis of an extreme-value statistical model, a center estimation unit for estimating a probability density function for the parts of the occurrence frequency distribution other than the tails, and a connection unit for using the probability density function for the tails and the probability density function for the parts other than the tails to estimate an overall probability density function for the occurrence frequency distribution; and a failure probability computation unit for computing the probability of failure in the mechanical system on the basis of the overall probability density function and the failure model.