Simulating Prosthetic Gait ‐ Lessons to Learn

Modern computer assisted above knee prostheses currently available on the market (e.g. C‐Leg from Otto‐Bock) allow the patients to choose their walking speed freely during level walking. Due to energy reasons it is only possible to change the passive mechanical characteristics of the prosthetic limb but no active actuators can be used to influence the knee joint movement. The control strategies for level walking act on the damping of the knee joint during swing phase of gait. During walking down ramps or descending stairs the control strategies are switched off in current designs. Based on a measured reference kinematics it should be possible to study the influence and behaving of technical devices in combination with the whole body biomechanical system. For this purpose we use a combined inverse‐forward‐dynamics approach. Kinematics parameters that are not critical in the inverse‐dynamics approach (leading to physiological reasonable forces and moments) and that are not influenced by the other parameters in the model are prescribed as in the classical inverse‐dynamics approach. To follow the other kinematics parameters (joint‐angles) control elements are used where the associated joint‐moments are determined by the goal trajectory and physiological boundary conditions. The so called “controlled joints” of the model and the applied technical device (prosthesis) are formulated as a forward‐dynamics system. In contrast to experimental studies a simulation study offers the advantage, that parameters can be varied in a wide range. Different ramp and stair inclinations can be implemented and different control strategies can be tested without any risk for the patient. The disadvantage lies in the fact, that there are only few reference sets for the kinematics of real patients. The modification of a reference kinematics for different situations (level walking, ramp or stair descent) is a big challenge and needs further investigation. On the other hand the combined inverse‐forward‐dynamics approach with its well balanced simplicity and complexity offers a flexible tool to reach this aim. This approach can also be used to investigate the interaction of the biomechanical system with other technical systems like sports equipment.     

Modelling and identifying the parameters of a magneto-rheological damper with a force-lag phenomenon

In this study a model based on the Bouc–Wen–Baber–Noori (BWBN) method was proposed to describe the distorted hysteretic behaviour of a self-constructed magneto-rheological (MR) damper whose mechanical performance was measured with an Instron test machine. The experimental results indicated that the MR damper exhibited a force-lag phenomenon. The parameters of the modified BWBN model were identified with the MATLAB SIMULINK Design and Optimisation toolbox. A comparison between the experimental results and modelling predictions revealed that the proposed model could well present the force-lag phenomenon.     

Hybrid modeling approach for vehicle frame coupled with nonlinear dampers

The vehicle frame system comprises frame structure and nonlinear dampers. In order to investigate the effects of frame flexibility and nonlinear hysteresis, a hybrid modeling approach for vehicle frame coupled with nonlinear dampers will be proposed. Before that, a complex model for nonlinear damper is developed consisting of knowledge-based model and support vector machine (SVM) model. The frame structure is modeled by FEM where the SVM complex model of damper is embedded in. Thus a hybrid model for vehicle frame system is established and successfully validated via a dummy vehicle riding in different conditions. The results show that the hybrid model can capture the nonlinear dynamic characteristics accurately. The hybrid model can also provide a basis for structural design with the existing of FEM model.     

OPTIMAL CONTROL THEORY APPLIED TO JOINT PRODUCTION OF TIMBER AND FORAGE

Renewable natural resource systems often represent examples of joint production. Optimal control theory is employed using the linear variational method to derive the general solution to the timber-forage joint production problem, with the objective of maximizing present value of revenue. The results indicate that optimal control theory can successfully solve such problems. The functional forms of the solution provide insight into how changes in parameters will influence the optimal joint production system.     

A novel adaptive spectrum reservation strategy in CRNs and its performance optimization

Spectrum reservation strategy is an effective technology for conserving communication resources in Cognitive Radio Networks. In order to better adapt to changes of the system load, we present an adaptive control approach to determine the reservation ratio of the licensed spectrum for secondary users and propose a novel adaptive spectrum reservation strategy. We then establish a three-dimensional discrete time Markov Chain model to capture the stochastic behavior of users. By using a method similar to that of the matrix geometric solution, we obtain the steady-state probability distribution for the system model, and derive the formulas for some required performance measures of two types of users. Numerical experiments and simulation experiments indicate that the system performance is sensitive to system parameters like the adaptive control factor and the admission threshold. Finally, we construct a system cost function to balance different performance measures, and present an intelligent searching algorithm to optimize the system parameters with the global minimum system cost.     

A generalized activity network model

In recent years activity networks for projects with both random and deterministic alternative outcomes in key nodes have been considered. The developed control algorithm chooses an optimal outcome direction at every deterministic alternative node which is reached in the course of the project's realization. At each routine decision-making node, the algorithm singles out all the subnetworks (the so-called joint variants) which correspond to all possible outcomes from that node. Decision-making results in determining the optimal joint variant and following the optimal direction up to the next decision-making node. However, such models cover a limited class of alternative networks, namely, only fully-divisible networks which can be subdivided into nonintersecting fragments. In this paper, a more generalized activity network is considered. The model can be applied to a broader spectrum of R&D projects and can be used for all types of alternative networks, for example, for non-divisible networks comprising nodes with simultaneously ‘must follow’, random ‘exclusive OR’ and deterministic ‘exclusive or’ emitters. The branching activities of the third type refer to decision-making outcomes; choosing the optimal outcome is the sole prerogative of the project's management. Such a model is a more universal activity network; we will call it GAAN—Generalized Alternative Activity Network. The problem is to determine the joint variant optimizing the mean value of the objective function subject to restricted mean values of several other criteria. We will prove that such a problem is a NP-complete one. Thus, in general, the exact solution of the problem may be obtained only by looking through all the joint variants on the basis of their proper enumeration. To enumerate the joint variants we will use the lexicographical method in combination with some techniques of discrete optimization. A numerical example will be presented. Various application areas are considered.     

Optimisation of road vehicle passive suspension systems. Part 1. Optimisation algorithm and vehicle model

Numerous problems have in the past been experienced during the development of military vehicle suspension systems. In order to solve some of these problems a two-dimensional multi-body vehicle dynamics simulation model has been developed for computer implementation. This model is linked to a mathematical optimisation algorithm in order to enable the optimisation of vehicle design parameters through the minimisation of a well defined objective function. In part 1 of this paper the concept of multi-disciplinary design optimisation is discussed. This is followed by the presentation of the up to six degrees of freedom vehicle model developed for this study, and a discussion of the specific gradient-based optimisation algorithm selected for the optimisation. In particular the derivation of the set of second-order differential equations, describing the acceleration of the different solid bodies of the vehicle model, is presented. In order to perform the optimisation of the non-linear suspension component characteristics, a six piece-wise continuous and linear approximation is used which is also described in this paper. Part 2 of this study will outline the simulation programme and the qualification of the programme. It will also present a typical case study where the proposed optimisation methodology is applied to improve the damper characteristics of a specific vehicle.     

The availability model and parameters estimation method for the delay time model with imperfect maintenance at inspection

The delay time model (DTM) is widely used to model the two-stage failure process and is helpful for developing cost-effective inspection/maintenance plans. Imperfect maintenance is common in practice, but seldom considered in DTM. An improved DTM with imperfect maintenance at inspection has been developed based on the assumption of imperfect inspection maintenance and perfect failure maintenance. The model of the long-run availability for the improved DTM is established. Parameters estimation method and the test for goodness of fit method are given. Numerical simulations are performed to study the influence of imperfect maintenance on the long-run availability and to validate the credibility of the parameters estimation method. The results show that imperfect maintenance will decrease the long-run availability. The existence of the optimal inspection interval regarding the maximum long-run availability is tightly related to the improvement factor, which denotes the maintenance effect. The parameters estimation method proves credible. The maximum likelihood estimations of the reliability parameters can be easily achieved by the Genetic Algorithms (GAs) searching tool.     

几何耦合对直升机桨叶液压减摆器等效线性阻尼的影响研究

建立了直升机前飞时,计入变距/挥舞/摆振几何耦合和力-速度非线性关系的液压减摆器分析模型;用4阶龙格-库塔法在时域内计算减摆器的轴向速度;根据减摆器轴向速度的瞬态响应成分,利用基于富里叶级数的移动矩形窗方法计算了减摆器等效线性阻尼。结果表明,存在变距/挥舞/摆振几何耦合的液压减摆器,在直升机前飞时其等效线性阻尼将大幅度下降。     

Simultaneous price and due date settings for multiple customer classes

Extending the model of [Eur. J. Oper. Res. 116 (2) (1999) 305] that, under contingent capacity, simultaneously optimizes the bidding price and due date for each incoming order, we propose a bidding model with multiple customer segments classified based on parameters of willingness to pay, sensitivity to short delivery time, quality level requirement, and intensity of competition. The winning probability function was also modified to be of more practical and robust model in reflecting stochastic nature of customer's decision. Two sequencing rules, namely the early-due-date (EDD) for time-critical orders and first-come-first-serve (FCFS) for regular orders, were applied to determine the sequencing position of each incoming order, and a simplified pattern search algorithm was used to improve the efficiency in searching for optimal price and due date. The simulation results show that, in general, our proposed model and method can significantly increase the marginal revenue to the firm.     

Identification of Finite-Motion Parameters of Serial Chains via Measurement of 6 × 6 Stiffness Matrices

This paper describes a procedure for identifying geometric and stiffness parameters of a mechanical serial chain of know structure by measuring spatial 6×6 stiffness matrices at different positions. The method uses standard optimization routines to determine model parameters such that the model stiffness matrix features in the Frobenius norm the closest distance possible to the measured matrix. From this local identification, a rough model of parameters of finite-motion is created, from which new measuring positions are guessed. By applying this step repeatedly, a model for finite-displacement parameters can be obtained by a sequence of small force-displacement tests. The method is tested with a dummy device consisting of a revolute joint connecting two rigid links dressed with soft material to mimic for example muscle masses of a surrogate mechanism for the elbow joint of a human arm. Two robots grasping the upper and lower arm generate the motion while the force measurement is carried out by a six-axis force sensor. This makes the method potentially suitable for detecting anatomical parameters by in-vivo measurements. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulated annealing for financing cost distribution based project payment scheduling from a joint perspective

Based on the distribution of the project financing cost over the contractor and the client, this paper involves the project payment scheduling problem from a joint perspective of the two parties. In the problem, the project financing cost is defined as the expense for raising money from the outside or the opportunity cost of the capital devoted into the project and the objective is to find the project payment schedule that can not only maximize the joint revenue of the two parties but also be accepted by them. Based on the characteristics of the problem, an optimization model consisting of two submodels is constructed using the activity-based method. For the strong NP-hardness of the problem, two simulated annealing algorithms with different searching structures are developed and compared with the multi-start iterative improvement method on the basis of a computational experiment performed on a data set generated randomly. The results show that the simulated annealing algorithm with the nested loop module seems to be the most promising algorithm for solving the defined problem especially when the scale of the problem becomes larger. In addition, the influences of some key parameters on the computational results are investigated through the full factorial experiment and a few useful conclusions are drawn.     

Sequential order statistics with an order statistics prior

In the model of sequential order statistics, prior distributions are considered for the model parameters, which, for example, describe increasing load put on remaining components. Gamma priors are examined as well as priors out of a class of extended truncated Erlang distributions (ETED), which is introduced along with some properties. The choice of independent priors in both set-ups leads to respective independent, conjugate posterior distributions for the model parameters of sequential order statistics. Since, in practical applications, the model parameters will often be increasingly ordered, a multivariate prior is applied being the joint distribution of common ETED-order statistics. Whatever baseline distribution of the sequential order statistics is chosen, the joint posterior distribution turns out to be a Weinman multivariate exponential distribution. Posterior moments are given explicitly, and HPD credible sets for the model parameters are stated.     

Physiological loading of cartilage replacement materials in a bioreactor environment

Trying to replace injured cartilage by implants is a common practice in biomedical engineering. These implants can be non-seeded or seeded with human cartilage cells. To initiate cell multiplication and oriented cell growth in cell seeded implants, the implants are cultivated and usually stimulated electrically or mechanically in a bioreactor before implanting. In the present study, a knee testing bench combined with a bioreactor environment is developed. Doing so, it is possible to stimulate such implants controlled in a physiologically consistent, multi-dimensional way. The implants are placed in a recreated human knee joint and stimulated with several physiological load cycles of reproduced walking. After some days, the implanted material can be removed and mechanically and biologically evaluated in cooperation with the RWTH Aachen University Hospital. The new experimental set-up enables us for the first time to study the remodelling effect, the efficiency of the preconditioning as well as the influence of the body-conformable load on the material. Furthermore, the need of cell colonisation in the implants shall be investigated. To understand the correlation between tissue remodelling and mechanical load history, the experiment is also numerically investigated, based on a geometrically realistic FE model of the recreated human knee and appropriate material models for the involved structures. Doing so, the strains and stresses, as well as the shear forces in the implant can be evaluated. The results will be compared to experimental data. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A template for the exploration of chaotic locomotive patterns

Inverted pendulum and spring-mass models have been successfully used to explore the dynamics of the lower extremity for animal and human locomotion. These models have been classified as templates that describe the biomechanics of locomotion. A template is a simple model with all the joint complexities, muscles and neurons of the locomotor system removed. Such templates relate well to the observed locomotive patterns and provide reference points for the development of more elaborate dynamical systems. In this investigation, we explored if a passive dynamic double pendulum walking model, that walks down a slightly sloped surface (γ<0.0189 rad), can be used as a template for exploring chaotic locomotion. Simulations of the model indicated that as γ was increased, a cascade of bifurcations were present in the model's locomotive pattern that lead to a chaotic attractor. Positive Lyapunov exponents were present from 0.01839 rad <γ<0.0189 rad (Lyapunov exponent range=+0.002 to +0.158). Hurst exponents for the respective γ confirmed the presence of chaos in the model's locomotive pattern. These results provide evidence that a passive dynamic double pendulum walking model can be used as a template for exploring the biomechanical control parameters responsible for chaos in human locomotion.     

Reconstructing the knee joint mechanism from kinematic data

The interpretation of joint kinematics data in terms of displacements is a product of the type of movement, the measurement technique and the underlying model of the joint implemented in optimization procedures. Kinematic constraints reducing the number of degrees of freedom (DOFs) are expected to compensate for measurement errors and noise, thus, increasing the reproducibility of joint angles. One approach already successfully applied by several groups approximates the healthy human knee joint as a compound hinge joint with minimal varus/valgus rotation. Most of these optimizations involve an orthogonality constraint. This contribution compares the effect of a model with and without orthogonality constraint on the obtained joint rotation angles. For this purpose, knee joint motion is simulated to generate kinematic data without noise and with normally distributed noise of varying size. For small noise the unconstrained model provides more accurate results, whereas for larger noise this is the case for the constrained model. This can be attributed to the shape of the objective function of the unconstrained model near its minimum.     

Joint replenishment model with substitution

When products are coupled to the same cycle, the joint replenishment model (JRM) is used to determine optimal inventory levels, where the amount to order (for each item) is designed to minimize the joint holding and ordering costs based on a given demand. JRM studies assume that there is no substitution between items. However, this assumption is unrealistic in some settings where substitution cannot be ignored. This paper combines the separate works on substitution and joint replenishment and proposes a solution procedure for solving the joint replenishment model with substitution (JRMS) for two products within the framework of the classical economic order quantity model. We determine the optimal order quantities for each product taking into consideration substitution between them so that demand is partially met and the total cost associated with the delivery, holding, and shortage of the products is minimized. We also provide an extensive scenario analysis and draw insights. In particular, we shed some light on the role of substitution in reducing the fixed cost. We show that JRMS can result in substantial cost savings compared to the ordinary JRM.     

Development of a chaotic nonlinear tuned mass damper for optimal vibration response

In this article an efficient method is developed for optimal design of a nonlinear tuned mass damper (N-TMD) system. Using several horizontal linear springs coming into action sequentially, system nonlinearity can be achieved with ease as a novel method. Friction force between tuned mass and the structure is variably produced by a vertical linear spring that follows a specified controlling curved path allowing reduction of the desired tuned mass. Chaotic behavior of the introduced tuned mass is investigated in terms of the existing parameters in the system. Lyapunov characteristic exponents are determined to demonstrate the chaotic behavior of the system. It is confirmed by comparison that the proposed scheme is able to retrofit structures in a superior way than some other devices such as multiple tuned mass damper systems. The optimization procedure is performed by sequential Simplex algorithm, while Newmark’s beta method for step by step integration is used to find the dynamic response of the structure.     

基于人工免疫网络的药代动力学参数优化方法

提出了基于人工免疫网络优化药代动力学参数的PKAIN算法．新增的分组并发单纯形变异用以提高人工免疫网络的局部搜索能力．通过PKAIN人工免疫网络中网络细胞的进化得到给定药代动力学模型的一组优化参数．应用Laplace变换求解瑞芬太尼(remifentanil)及其代谢产物瑞芬太尼酸的联合代谢动力学模型的微分方程组,通过PKAIN算法优化导出房室模型参数A·D2实验表明,对伴有轻度肾损伤病人可以应用二室模型描述瑞芬太尼酸的药代动力学特征．     

A revised and generalized model with improved discrimination for finding most efficient DMUs in DEA

In this paper we first propose a generalized model which in its special case revises a recently proposed model for finding most BCC-efficient DMU. Then, by explaining about the drawbacks of existing approaches, an algorithm will be developed to consider all possible alternative optimal solutions and determine the set of most efficient DMUs. Another model also will be proposed to provide more discrimination which can be used to select a single most efficient DMU, when it is desirable. The proposed approaches of this paper are applicable for all assumptions about returns-to-scale, and can be utilized to select a DMU or provide a full ranking of DMUs. The contents of the paper are illustrated through numerical examples.