Physics-based modeling and simulation of human walking: a review of optimization-based and other approaches

A review of human walking modeling and simulation is presented. This review focuses on physics-based human walking simulations in the robotics and biomechanics literature. The gait synthesis methods are broadly divided into five categories: (1) inverted pendulum model; (2) passive dynamics walking; (3) zero moment point (ZMP) methods; (4) optimization-based methods; and (5) control-based methods. Features of various methods are discussed, and their advantages and disadvantages are delineated. The modeling, formulation, and computation aspects of each method are reviewed.     

The spectrum of mathematical modeling and systems simulation

The methodology involved in the modeling and simulation of physical, life and social science systems is viewed in perspective. A critical factor determining the validity of a model is the extent to which it can be derived from basic laws and insights into the internal structure of the system using deductive methods, rather than relying upon observations and measurements of the system input and outputs. Accordingly, the mathematical models as they arise in various application disciplines are arranged along a spectrum according to the relative amount of deduction and induction involved in their construction. This provides an insight into the ultimate validity of simulations and to what use they can properly be put.     

Electrocardiogram simulation using a personal computer

A personal computer with a digital-to-analog converter is used as an electrocardiogram simulator. A TurboPascal procedure, given the heart rate, rhythm, and ST segment levels, generates the voltages for Leads II and V5. A simple circuit reduces the voltages to the physiologic range and smoothes the waveforms, removing the staircase effects of digitalization. The procedure can be manually controlled using a software interface or driven by other programs for use in a full-scale operating room simulator.     

Two approaches to the mathematical modeling of detonation waves

The work is dedicated to the numerical investigation of different propagation regimes of a gaseous pulsating detonation wave using two approaches. In the first one, the problem is solved in the laboratory frame and the detonation is initiated near the closed end of the channel. In the second approach, the simulation is carried out in the shock-attached frame. For this purpose, a second approximation order algorithm for the integration of the shock evolution equation using the grid-characteristic method is proposed. The stable, weakly unstable, and irregular regimes of detonation wave propagation are investigated using both approaches. The qualitative and quantitative differences between the two approaches are put forward.     

Integration of simulation modeling and computer aided production management in computer integrated enterprise

Designing efficient and integrated manufacturing systems is the first step in attaining computer integrated enterprises (CIE). Integration of planning and implementation phases of manufacturing is essential for taking full advantage of the CIE. In order to design reliable and efficient manufacturing systems, the designers must consider the impacts of planning decisions made by computer aided production management (CAPM) modules on implementations held in manufacturing cells.

This paper focuses on two issues. The first issue is importance and necessity of integrating CAPM modules with manufacturing cells. The second issue includes major features of the object-oriented approach and their relevance to our objective of modeling a design framework which focuses on integration of CAPM modules and simulation models which emulate the manufacturing cells in the CIE environment.     

Backward walking simulation of humans using optimization

The objective of this study is to formulate, simulate and study the backward walking motion of a full-body skeletal digital human model using an optimization approach. Predictive dynamics is used to simulate the task in which joint angle profiles are treated as primary unknowns in the formulation. The joint torques are treated as dependent variables that are evaluated directly from the equations of motion. For the performance measure, the normalized dynamic effort represented by the integral of the squares of all the normalized joint torques is minimized subject to the associated physical constraints. Backward walking at different speeds is simulated and analyzed. The backward walking is validated with motion capture data and the available data in the literature. The results of the backward walking motion are compared to those of the forward walking motion in order to study the differences between the two walking patterns. It is seen that the joint torque profiles for hip and knee of backward walk are quite similar to those of forward walk with reverse sequence, but with different time duration of flexion and extension activations. These findings can impact many fields, such as improvement of human performance, rehabilitation from injuries, and others.     

Environmental effects on WBGT and HSI using a computer simulation

A computer simulation was used to investigate environmental effects on Wet Bulb Globe Temperature (WBGT) and to compare WBGT to Heat Stress Index (HSI). Constant values of WBGT (isometrics) were straight lines on a psychrometric chart with a slope of −1.17 mmHg/dgC. The intercept on the dry bulb axis (zero water vapor pressure) changed with WBGT value, air velocity (v), and mean wall temperature expressed as an increment above air temperature (ΔT_w); there was also an interaction between v and ΔT_w on changes in intercept. For a given target value of WBGT, HSI changed with environmental conditions, especially with v. Using effective air velocity (adding a component of air movement associated with activity) reduced much of the variation in HSI. Comparisons between WBGT and HSI suggested that the effect of increasing metabolism was either overestimated by HSI or underestimated by recommended WBGT action levels.     

An FCM modeling for using a priori knowledge: application study in modeling quadruped walking

Fuzzy cognitive map (FCM) is well established as a decision-making mechanism with many applications. This paper presents a new strategy for realistic FCM-based inference named input-sensitive FCM. The problem of lack of influence from initial concepts’ weights or priory knowledge on decision outputs is resolved. The results and comparisons with the existing inference models are included to evaluate the strength of the new strategy. The quadruped walking cycle is simulated as a case study for sanity testing and validation of the developed model in terms of realistic decision outputs.     

Mathematical modeling and computer simulation of elevated foundations supporting vibrating machinery

Structures supporting machines which give rise to dynamic loads must be carefully analyzed and designed to assure satisfactory performance. These highly complex systems must be reduced to mathematical and computer models which will behave in a similar fashion as the structure-machine-soil prototype. Four models are considered and a comparison of significant results is given. A lumped-mass model with complete soil-structure interaction (Model D) is recommended for best overall results provided a high speed digital computer and software is available.     

Physically-based modeling,simulation and rendering of fire for computer animation

We give an up-to-date survey on techniques and methods for fire simulation in computer graphics. Physically-based method prevails over traditional non-physical methods for realistic visual effect. In this paper, we explore visual simulation of fire-related phenomena in terms of physically modeling, numerical simulation and visual rendering. Firstly, we introduce a physical and chemical coupled mathematical model to explain fire behavior and motion. Several assumptions and constrains are put forward to simplify their implementations in computer graphics. We then give an overview of present methods to solve the most complicated processes in numerical simulation: velocity advection and pressure projection. In addition, comparisons of these methods are also presented respectively. Since fire is a participating medium as well as a visual radiator, we discuss techniques and problems of these issues as well. We conclude by addressing several open challenges and possible future research directions in fire simulation.     

Construction of nonlocal linear vibration models using a computer algebra system

In the paper, on the examples of a string and beam, resonance vibrations in linear elastic systems that result from nonlocal boundary conditions (even if external forces are lacking) are considered. Formulas of exact solutions of the corresponding boundary-value problems are presented. These formulas are used for evaluation of the solutions and for construction of plots. Computer algebra system Mathematica was used for derivation and analysis of the exact solutions and for development of software packages designed for evaluation of the derived formulas and solution visualization. The authors believe that results of this study can be used to explain the causes for the vibration of the Tacoma and Volgograd bridges in 1940 and 2010, respectively.     

Validation of multibody modeling and simulation using an instrumented bicycle: from the computer to the road

This paper describes the use of an instrumented bicycle and its computational model for teaching multibody dynamics. The presented approach employs the Whipple model for the kinematic and inverse dynamic simulation of a bicycle ride using as an input three generalized coordinates registered with digital sensors. During the experimental phase, students ride the instrumented bicycle to collect the necessary sensor data. The kinematic and inverse dynamic simulations based on these signals provide a full picture of the motion of the system in different positions and at a range of velocities and accelerations. In addition, they estimate the traction, control, and tire-to-road contact forces during the ride. To validate the simulated results, the simulated velocity and accelerations are compared with the data acquired with an inertial measurement unit (IMU) installed on the bicycle. The paper describes the experimental setup of the instrumented bicycle, enabling readers to build the very same system for their own educational use. The instrumented bicycle system is based on open-source software and as much as possible on open hardware.     

Generalised computer routines for the simulation of linear multi-compartment systems

Multi-compartmental models with constant coefficients for the transfer of material between compartments are much used to describe the distribution and retention of radionuclides in biological systems. In this paper a general method for analysis of the properties of such systems is discussed and simple computer-based routines implementing this method are described. All code presented is written in MICROSOFT FORTRAN 80. The routines are readily transferable between differing micro- and mini-computers, with minimal alteration of code for compatibility with FORTRAN 77.     

A combination of linear and nonlinear activation functions in neural networks for modeling a de-superheater

This paper deals with modeling a power plant component with mild nonlinear characteristics using a modified neural network structure. The hidden layer of the proposed neural network has a combination of neurons with linear and nonlinear activation functions. This approach is particularly suitable for nonlinear system with a low grade of nonlinearity, which can not be modeled satisfactorily by neural networks with purely nonlinear hidden layers or by the method of least square of errors (the ideal modeling method of linear systems). In this approach, two channels are installed in a hidden layer of the neural network to cover both linear and nonlinear behavior of systems. If the nonlinear characteristics of the system (i.e. de-superheater) are not negligible, then the nonlinear channel of the neural network is activated; that is, after training, the connections in nonlinear channel get considerable weights. The approach was applied to a de-superheater of a 325 MW power generating plant. The actual plant response, obtained from field experiments, is compared with the response of the proposed model and the responses of linear and neuro-fuzzy models as well as a neural network with purely nonlinear hidden layer. A better accuracy is observed using the proposed approach.     

A homogeneous computer network Analysis and simulation

A network of minicomputers to support transaction processing against a distributed data base is described. This paper gives a brief overview of the design based on a loop communications subnetwork and then describes analytic and simulation models that have been used to predict performance.Service demands in this network are assumed to have the following characteristics.Transaction: Users at on-line terminals enter messages that invoke short computations, a few accesses to the data base and a response message that is then sent back to the terminal.Locality of reference: Transactions entering at one node in the network can almost always be serviced locally, the fraction requiring remote service is expected to be in the 10% to 30% range.The network has been modelled analytically as a network queues. The predictions of this model have been compared to those of a large simulation of the network in an attempt to validate that simulation model. Agreement is good for a two host network over a broad range of network loading. The simulation program has been used to study a large number of problems where we varied: transaction characteristics, remote traffic fraction, host configuration and communications subnetwork speed. One such experiment is described here in detail.     

Optimization of a complex flow line for printed circuit board fabrication by computer simulation

The complex operations and considerable process time variability of printed circuit board (PCB) fabrication create difficulties in finding effective and efficient planning techniques for today's PCB production management. A great deal of money is involved. By modeling and testing a real world PCB fabrication facility, this paper shows that computer simulation can provide a viable planning tool to estimate production capacity and to explore optimum arrangement in batch work size of key bottleneck machines to minimize product throughput time. Many simulation experiments are performed and the results analyzed as a response surface. The general characteristic of product throughput time is found to be that its minimal value exists when batch job numbers of subsequential key machines are matched in batch size or in multiples thereof. A nonlinear empirical equation to estimate product throughput time has been derived from the simulation results.     

The solution of linear equations on a SIMD computer using a parallel iterative algorithm

Techniques for solving linear equations on a single instruction multiple data (SIMD) computer such as the ICL DAP have so far been confined to simple methods such as the Successive Overrelaxation and Alternating Direction Implicit algorithms. While these techniques are adequate for simple finite difference problems require more complex algorithms. Preconditioned conjugate gradient methods have solved difficult problems successfully on serial machines. This paper describes a preconditioning technique suitable for parallel machines and numerical results obtained from a series of problems of varying degrees of difficulty.     

Predictive simulation of human walking transitions using an optimization formulation

A general optimization formulation for transition walking prediction using 3D skeletal model is presented. The formulation is based on a previously presented one-step walking formulation (Xiang et al., Int J Numer Methods Eng 79:667–695, 2009b). Two basic transitions are studied: walk-to-stand and slow-to-fast walk. The slow-to-fast transition is used to connect slow walk to fast walk by using a step-to-step transition formulation. In addition, the speed effects on the walk-to-stand motion are investigated. The joint torques and ground reaction forces (GRF) are recovered and analyzed from the simulation. For slow-to-fast walk transition, the predicted ground reaction forces in step transition is even larger than that of the fast walk. The model shows good correlation with the experimental data for the lower extremities except for the standing ankle profile. The optimal solution of transition simulation is obtained in a few minutes by using predictive dynamics method.