关于抽样时间独立识别放松时间和频率光谱 粘性弹性材料模型使用应力放松实验数据
Anna Stankiewicz1, Sławomir Juściński2, Marzena Błażewicz-Woźniak3
1Department of Technology Fundamentals, Faculty of Production Engineering, University of Life Sciences in Lublin, 20-612 Lublin, Poland.
Materials (Basel, Switzerland)
|September 27, 2025
概括
这项研究引入了一种分析材料机械性能的新方法,通过创建独立于实验采样时间的放松光谱模型来分析材料的机械性质. 随机抽样时间导致准确和稳定的模型,即使有噪音数据.
科学领域:
- 材料科学 材料科学 材料科学
- 类风病学 类风病学 类风病学
- 计算力学 计算力学 计算力学
背景情况:
- 粘弹性放松时间和频谱对于描述材料机械性质至关重要.
- 获得这些光谱的传统方法依赖于应力或振荡剪切测量.
- 现有的频谱识别数学模型和算法在材料特异性和对测量条件的依赖性方面存在局限性.
研究的目的:
- 开发一种可靠的方法来识别放松光谱模型,这些模型在实验采样时间上是异常独立的.
- 为了确保鉴定模型的稳定性和准确性,尽管在放松模量测量中的噪声.
- 呈现一个完整的算法,用于放松光谱的识别,适用于各种类风学材料.
主要方法:
- 放松光谱的近似使用直角 (莱根德,拉盖尔,切比舍夫) 和非直角 (权指数,修改贝塞尔) 基础函数的有限序列.
- 在应力放松实验中随机选择采样时间,以实现采样时间独立性.
- 应用提霍诺夫规范化来稳定不良的识别问题.
- 解决一系列加权最小平方放松模量近似问题.
主要成果:
- 证明采样时间随机化能够独立于采样时间的最佳光谱模型的确定,即使对于未知的真实光谱.
- 恢复的光谱模型是对真实模型的强烈一致的估计.
- 通过规范化,实现了对错误的识别问题的稳定解决方案.
- 随机收分析显示,收的速度是指数级的.
- 模拟研究证实了各种已知的光谱 (科尔劳施 - 威廉姆斯 - 沃茨,高斯式,姆盖尔特 - 绍斯伯格 - 温特) 的有效性.
结论:
- 提出的方法有效地识别稳定和准确的放松光谱模型,独立于实验采样时间.
- 抽样时间的随机化是实现可靠和可概括的风湿学模型的关键策略.
- 开发的算法提供了一种可靠的方法来分析材料粘弹性特性,提高模型的可预测性和适用性.
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