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.

在各种行业中都会遇到不必要的振动，特别是由于摩擦。虽然振动通常会因阻尼而随时间衰减，但摩擦引起的不稳定性会产生正能量，从而提供系统的正阻尼力。正阻尼会使振动幅度增大，导致过度磨损和产品过早损坏。这些正反馈环一旦建立，也会导致可听到的噪音，这在人工滑膜关节中也是问题，如在全膝关节或髋关节置换中发现的。过去的研究大多集中在通过实验测试来减少磨粒或改善其生物相容性。然而，考虑软骨或滑液的阻尼力和润滑力以及它们对人工滑膜关节摩擦的影响，还没有从数值或动力学的角度进行研究。本文以非线性动力学为输出量，结合最大熵理论，提出了基于递归图和贝叶斯修正的贝叶斯递归图量化分析方法。估计了具有可信界、嵌入参数和不稳定周期轨道的动态变量。基于吸引子的模板被用来生成逆降阶模型以探索非线性动力学。利用模板和分析模型估计了吸引域及其线性稳定边界。考虑了实际测量中噪声对不变估计的影响。这种新的方法被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的大型实验生物力学测试数据库，考虑了不同的驱动参数、不同的润滑剂和运行时间。通过激光测振仪的精密振动测试和Roentgen立体摄影测量的运动学分析，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，重点研究了人工滑膜髋关节的润滑和考虑滑液的挤压膜阻尼。采用了现代不确定参数识别方法，考虑了部件、组件和有、无流体的组件水平。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，这使得数值模型能够以证据和响应为基础并以自上而下的方法进行进一步更新。根据闸门周期分析了不同的阶段，使模型修正成为一个多阶段的过程，并最终研究了滑液薄膜对阻尼力和耗散力的影响。这些发现将对人工滑膜关节的摩擦和磨损的潜在物理学有重要的见解，这些人工滑膜关节可以通过利用优化的薄膜或挤压薄膜减震来设计更安静的髋关节插入件。

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.