Precipitation Normalization via Gradient-Based Parameter Optimization

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Solution Overview

Problem

Current methods for analyzing precipitation data struggle to accurately adapt to different climatic conditions due to their reliance on empirically set transformation parameters, which can lead to suboptimal results in statistical analysis.

Innovation Solution

A method and system for gradient-based parameter optimization in precipitation normalization, which involves constructing a normal transformation model, optimizing likelihood functions using analytic gradients, and updating parameters to maximize the likelihood function, thereby adapting to specific precipitation distribution features.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of manufacture

If empirical parameter setting is used in normal transformation methods, then the modeling analysis process is simpler, but the accuracy of analysis results deteriorates due to inability to adapt to different climatic conditions

Engineering Contradiction:

Improvesimplicity of modeling analysis processVSAvoidaccuracy of analysis results

Core Design Contradiction:

Ease of manufactureVSMeasurement precision

Solution Approach 1:

The patent changes the parameter setting approach from fixed empirical values to dynamically optimized parameters. By using gradient-based optimization algorithms, the transformation parameters are automatically adjusted to maximize the likelihood function, allowing the model to adapt to different precipitation distribution characteristics under various climatic conditions while maintaining computational efficiency.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent implements self-service by allowing the model to automatically determine optimal transformation parameters through maximum likelihood estimation. The gradient-based optimization process enables the system to self-adjust and self-optimize without requiring manual intervention or empirical rule application, thereby improving accuracy while maintaining process simplicity.

Inventive Principle:

Principle #25Self-service

2Measurement precision

If gradient-based parameter optimization is implemented, then the accuracy of precipitation data analysis is improved, but the computational complexity increases

Engineering Contradiction:

Improveaccuracy of precipitation data analysisVSAvoidcomputational complexity of parameter optimization

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent replaces complex manual parameter tuning mechanisms with automated gradient-based optimization algorithms. By using mathematical gradients and likelihood functions, the system automatically computes optimal parameters through iterative processes, reducing the need for complex manual adjustments and empirical trial-and-error approaches.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent optimizes computational complexity by changing the parameter optimization approach to gradient-based methods. These methods use calculated gradients to efficiently navigate the parameter space and converge to optimal solutions, avoiding the need for exhaustive search or complex heuristic algorithms while maintaining high accuracy.

Inventive Principle:

Principle #35Parameter changes

3Ease of operation

If transformation parameters are set as matter of experience, then the implementation is easier, but the adaptability to different climatic conditions deteriorates

Engineering Contradiction:

Improveease of implementationVSAvoidadaptability to different climatic conditions

Core Design Contradiction:

Ease of operationVSAdaptability or versatility

Solution Approach 1:

The patent implements self-service by enabling the system to automatically determine and optimize transformation parameters based on the actual precipitation data characteristics. The gradient-based optimization process allows the model to self-adjust to different climatic conditions without requiring manual reconfiguration or empirical knowledge, thereby maintaining ease of implementation while significantly improving adaptability.

Inventive Principle:

Principle #25Self-service

Solution Approach 2:

The patent changes the parameter setting mechanism from static empirical values to dynamic optimized parameters. The gradient-based optimization allows transformation parameters to automatically adapt to different climatic conditions by maximizing the likelihood function for each specific dataset, thereby achieving both ease of operation and high adaptability.

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS20250021617A1Method and system for analyzing precipitation normalization by gradient-based parameter optimization

Publication Date: 2025.01.16 SUN YAT SEN UNIV

AI summary

The present invention provides a method and system for analyzing precipitation normalization by gradient-based parameter optimization. The method includes the following steps: acquiring precipitation data to be analyzed; constructing a normal transformation model to perform normal transformation on the precipitation data, to obtain a normal variable Z; letting the normal variable Z to obey normal distribution to construct a joint probability density function of the normal variable Z; constructing a likelihood function for parameter optimization based on the normal transformation model and the joint probability density function; deducing an analytic gradient vector of the likelihood function to optimize the likelihood function till a predetermined termination condition is satisfied, to obtain the optimum parameter enabling the maximum value of the likelihood function; and updating the normal transformation model based on the optimum parameter, and performing normal transformation and modeling analysis on the precipitation data to obtain a precipitation normalization analysis result.