Nonlinear time series analysis using Bayesian recurrence plot quantification to analyse the dynamics of friction-induced vibrations, in particular wear and damping in artificial synovial joints.

使用贝叶斯递归图量化的非线性时间序列分析来分析摩擦引起的振动的动力学，特别是人工滑膜关节中的磨损和阻尼。

• 批准号: 314996946
• 负责人: Dr. Sebastian Oberst
• 金额: --
• 依托单位: Institut für Strukturdynamik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/314996946?language=en
• 关键词: Nonlinear; time; series; analysis; using

Unwanted vibrations particularly owing to friction are encountered in various industries. While vibrations usually decay with time owing to damping, friction-induced instabilities cause positive and energy providing positive system damping. Positive damping lets vibration amplitudes grow, leading to excessive wear and premature product failure. These positive feedback loops, once established, also lead to audible noises, which are also problematic in artificial synovial joints, as found in total knee or hip replacements. In the past most research concentrated on reducing wear particles or improving their biocompatibility using experimental testing. However, damping and lubrication considering the cartilage or synovial fluid and their effect on artificial synovial joints friction has never been studied numerically or from the dynamics point of view. Here, nonlinear dynamics as output quantity is employed to develop highly innovative Bayesian recurrence plot quantification analysis measures based on recurrence plots and Bayesian updating in combination with the Maximum Entropy Theory. Dynamic variants with credibility bounds, embedding parameters, and unstable periodic orbits are estimated. Attractor-based templates are used to generate inversely reduced-order models to explore the nonlinear dynamics. The basin of attraction and its linear stability boundary is estimated using the templates and analytical models. The influence of noise on invariant estimations in practical measurements is considered. This novel methodology is applied to nonlinear benchmark systems and then to a large database of experimental biomechanical tests of hip and knee implants, considering different driving parameters, various lubricants and running times. By using sophisticated vibration testing over laser vibrometry and kinematics determined over Roentgen stereo photogrammetric analysis, in a bottom up process, a high-fidelity finite element model coupled to computational fluid dynamics simulations is setup to study artificial synovial hip joint with focus on lubrication and squeeze film damping considering the synovial fluid. Modern methods of uncertain parameter identification are employed taking into account the component, the subassembly and the assembly level with and without fluid. Numerical time traces are then analysed by applying the novel Bayesian recurrence plot quantification measures and invariant estimations which allow the numerical model being further updated, both evidence- and response-based and in a top-down approach. Different stages according to the gate cycle are analysed rendering the model updating as a multi-stage process and allow finally to study the effect of the synovial fluids thin film on damping and dissipation. Findings will lead to significant insights of underlying the physics in friction and wear in artificial synovial joints which can be used to design quieter hip inserts by making use of optimised thin film or squeeze film damping.

在许多行业中，由于摩擦而产生的不必要的振动是常见的。由于阻尼，振动通常随时间衰减，而摩擦引起的不稳定性导致正能量和正能量提供系统阻尼。正阻尼使振动幅度增大，导致过度磨损和产品过早失效。这些正反馈回路一旦建立，也会导致可听到的噪音，这在人工滑膜关节中也是有问题的，就像在全膝关节或髋关节置换术中发现的那样。过去的研究大多集中在减少磨损颗粒或通过实验测试来提高其生物相容性。然而，考虑软骨或滑膜液的阻尼和润滑及其对人工滑膜关节摩擦的影响尚未从数值或动力学角度进行研究。本文以非线性动力学作为输出量，结合最大熵理论，基于递归图和贝叶斯更新，开发了极具创新性的贝叶斯递归图量化分析方法。估计了具有可信边界、嵌入参数和不稳定周期轨道的动态变量。利用基于吸引子的模板生成逆降阶模型来研究非线性动力学。利用模板和解析模型对引力盆地及其线性稳定边界进行了估计。考虑了实际测量中噪声对不变估计的影响。在考虑不同驱动参数、不同润滑剂和运行时间的情况下，将这种新方法应用于非线性基准系统，然后应用于髋关节和膝关节植入物实验生物力学测试的大型数据库。通过激光振动测量和伦琴立体摄影测量分析确定的复杂振动测试，在自下而上的过程中，建立了高保真有限元模型，并结合计算流体动力学模拟，重点研究了滑膜人工髋关节的润滑和挤压膜阻尼。采用现代的不确定参数辨识方法，考虑了有流体和无流体情况下的组件、子组件和组件水平。然后通过应用新的贝叶斯递归图量化措施和不变估计来分析数值时间轨迹，这些措施和不变估计允许数值模型进一步更新，既基于证据，也基于响应，并采用自上而下的方法。分析了闸门周期的不同阶段，使模型更新成为一个多阶段的过程，并最终研究了滑液薄膜对阻尼和耗散的影响。研究结果将对人工滑膜关节摩擦和磨损的潜在物理原理产生重要的见解，通过使用优化的薄膜或挤压膜阻尼，可用于设计更安静的髋关节植入物。