Monte Carlo Simulation for Electric Circuit Yield Analysis
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Solution Overview
Problem
Complex systems require significant computing resources and time for simulation, often resulting in impractically long processing times, especially when analyzing distributions greater than or equal to 6σ relative to the center value, even with supercomputing.
Innovation Solution
A simulation method using a computing system with processors that runs different simulations based on input distribution boundaries, generating samples, and applying machine learning to determine worst-case points, shifting boundaries until a minimum critical value is reached, thereby improving analysis speed and reliability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a standard Monte Carlo simulation is used to analyze complex systems with large distribution ranges (≥6σ), then the simulation coverage is comprehensive, but the computing time and resources increase significantly, often exceeding practical limits
Solution Approach 1:
The simulation process is divided into two distinct phases: a preliminary analysis phase that identifies critical regions using a small number of samples, and a main simulation phase that concentrates computational effort on those critical regions. This segmentation allows the system to achieve comprehensive coverage with significantly reduced total computing time by avoiding uniform sampling across the entire distribution range.
Solution Approach 2:
Before conducting the full simulation, the system performs a preliminary analysis using a small initial sample set to identify worst-case points and critical regions in the input space. This preliminary action guides the subsequent main simulation, ensuring that computational resources are allocated efficiently to regions that most impact simulation reliability, rather than uniformly sampling the entire ≥6σ distribution range.
2Productivity
If the distribution boundary is reduced to decrease simulation time, then the computing resources are reduced, but the simulation may miss critical worst-case scenarios
Solution Approach 1:
The system uses its own simulation results to guide further simulation. By identifying worst-case points from initial simulations and using those points to define the boundaries for subsequent simulations, the system automatically adapts its sampling strategy. This self-service mechanism ensures that the simulation boundary dynamically contracts to the most critical regions, maintaining detection accuracy while reducing the overall distribution range that requires extensive sampling.
Solution Approach 2:
The system implements a feedback loop where simulation results from one iteration inform the configuration of the next iteration. The identified worst-case points and their function values feed back into determining the new simulation boundary, creating a closed-loop system that continuously refines its focus on critical regions. This feedback mechanism ensures that even as the boundary reduces, the simulation maintains precision in detecting worst-case scenarios.
Data Source
AI summary
In a simulation system and method thereof, the simulation includes, when a function value for a nominal point (NP) of an input is a first value, running a first simulation on the input; and when the function value for the NP of the input is a second value different from the first value, running a second simulation on the input. Here, the running of the second simulation may include (a) setting a boundary of an input distribution for the second value as a first distribution value, (b) generating input samples within the set boundary of the input distribution, (c) obtaining a worst case point (WCP) for the input by performing machine learning on the generated input samples, and (d) repeatedly performing the steps (a) to (c) while shifting the boundary of the input distribution until the boundary of the input distribution reaches a minimum critical value.