研究目的
To estimate the uncertainty in the maximal vibration amplitude of a beam system with piezo-elastic supports due to manufacturing variations, by developing an improved surrogate model that combines experimental and simulation data using neural networks.
研究成果
The proposed method, which combines experimental and simulation data using neural networks, outperforms classical density estimation approaches in most simulated cases, reducing L1 errors significantly. However, when applied to real data with dependent input variables, the results were less satisfactory, indicating a need for better modeling of dependencies. The approach shows promise for uncertainty quantification in complex technical systems but requires refinement for real-world applications.
研究不足
The small sample size of experimental data (n=10) limits the reliability of nonparametric estimates. The assumption of independence and normal distribution for input parameters may not hold, as dependencies were later identified. The computational model is imperfect, introducing errors. Time and cost constraints prevent increasing the experimental sample size.
1：Experimental Design and Method Selection:
The methodology involves using neural networks to create a surrogate model that integrates experimental data (n=10 samples) and simulation data (Ln=200 samples) to estimate the density of the maximal vibration amplitude. The neural network is trained using least squares estimation with the Levenberg-Marquardt algorithm.
2：Sample Selection and Data Sources:
Experimental data from ten built systems of a beam with piezo-elastic supports, measuring parameters like stiffness and height, and corresponding vibration amplitudes. Simulation data generated from a physical model based on these parameters.
3：List of Experimental Equipment and Materials:
A beam with circular cross-section, piezo-elastic supports (including elastic membrane-like spring elements, piezoelectric stack transducers, disc springs, and axial extensions), and electrical shunt circuits for vibration attenuation. Specific equipment not detailed beyond general descriptions.
4：Experimental Procedures and Operational Workflow:
Construct and assemble the piezo-elastic supports multiple times, measure the five parameters (lateral and rotatory stiffnesses, height) and the maximal vibration amplitude for each system. Use these measurements to estimate distributions and generate simulation data.
5：Data Analysis Methods:
Use kernel density estimation (via MATLAB's ksdensity routine) on the surrogate model outputs to estimate the density of Y. Compare different density estimates using L1 error metrics from simulations.
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