Mathematical foundations of event trees

A mathematical foundation from first principles of event trees is presented. The main objective of this formulation is to offer a formal basis for developing automated computer assisted construction techniques for event trees. The mathematical theory of event trees is based on the correspondence between the paths of the tree and the elements of the outcome space of a joint event. The concept of a basic cylinder set is introduced to describe joint event outcomes conditional on specific outcomes of basic events or unconditional on the outcome of basic events. The concept of outcome space partition is used to describe the minimum amount of information intended to be preserved by the event tree representation. These concepts form the basis for an algorithm for systematic search for and generation of the most compact (reduced) form of an event tree consistent with the minimum amount of information the tree should preserve. This mathematical foundation allows for the development of techniques for automated generation of event trees corresponding to joint events which are formally described through other types of graphical models. Such a technique has been developed for complex systems described by functional blocks and it is reported elsewhere. On the quantification issue of event trees, a formal definition of a probability space corresponding to the event tree outcomes is provided. Finally, a short discussion is offered on the relationship of the presented mathematical theory with the more general use of event trees in reliability analysis of dynamic systems.     

A logical model for quantification of occupational risk

Functional block diagrams (FBDs) and their equivalent event trees are introduced as logical models in the quantification of occupational risks. Although a FBD is similar to an influence diagram or a belief network it provides a framework for introduction in a compact form of the logic of the model through the partition of the paths of the equivalent event tree. This is achieved by consideration of an overall event which has as outcomes the outmost consequences defining the risk under analysis. This event is decomposed into simpler events the outcome space of which is partitioned into subsets corresponding to the outcomes of the initial joint event. The simpler events can be further decomposed into simpler events creating a hierarchy where the events in a given level (parents) are decomposed to a number of simpler events (children) in the next level of the hierarchy. The partitioning of the outcome space is transferred from level to level through logical relationships corresponding to the logic of the model.Occupational risk is modeled trough a general FBD where the undesirable health consequence is decomposed to “dose” and “dose/response”; “dose” is decomposed to “center event” and “mitigation”; “center event” is decomposed to “initiating event” and “prevention”. This generic FBD can be transformed to activity—specific FBDs which together with their equivalent event trees are used to delineate the various accident sequences that might lead to injury or death consequences.The methodology and the associated algorithms have been computerized in a program with a graphical user interface (GUI) which allows the user to input the functional relationships between parent and children events, corresponding probabilities for events of the lowest level and obtain at the end the quantified corresponding simplified event tree.The methodology is demonstrated with an application to the risk of falling from a mobile ladder. This type of accidents has been analyzed as part of the Workgroup Occupational Risk Model (WORM) project in the Netherlands aiming at the development and quantification of models for a full range of potential risks from accidents in the workspace.     

Genetic adaptive coding optimization applied to fractal image compression

This paper presents a fractal image compression method that utilized a genetic optimization algorithm for optimal domain block selection. The technique successfully addresses the problem of finding an optimal domain block pool for a given range partition, one of the most important issues in fractal image compression. This technique utilizes a genetic optimization algorithm that starts with a source image and generates both a random range partition and a random set of candidate domain blocks for each element of the range partition. Each member of the candidate domain block set was mapped to the corresponding element of the range partition. It was subsequently tested via a quantitative objective function, ranked using a linear fitness scheme and modified, as required, using crossover and mutation operators. This evolutionary process converged to produce an optimal iterated function system (IFS) representation of the source image within a few generations in a robust and efficient manner. © 1999 John Wiley & Sons, Inc. Int J Imaging Syst Technol 10, 369–378, 1999     

基于NIOSII的红外图像实时非均匀性校正

实时红外图像非均匀性校正是红外热成像系统的基础.采用Altera公司的NIOSII嵌入式软核CPU技术,提出了一种基于非线性拟合的实时校正方法以及利用FPGA为核心的硬件实现途径.针对校正中耗时的算法用FPGA中模块完成,采用NIOSII处理器的自定制指令,使FPGA的并行性和DSP的灵活性完美结合在一起,极大的提高了系统的性能.该方法动态范围大,系统仅采用一片FPGA芯片,使得系统小型化成为可能.介绍了硬件电路的原理图以及工作过程并给出实验结果.实验证明了这种方法的优越性,并取得了满意的实验结果.     

执行器受限空间机器人的模糊神经网络控制

空间机器人关节执行器输出力矩幅值及幅值变化率受限的情况,是其在太空应用中不可避免要面临的实际问题。为此该文讨论了关节执行器输出力矩幅值及幅值率受限情况下参数未知空间机器人系统协调运动的动力学控制问题。依据系统动量守恒关系和拉格朗日第二类方程,推导了漂浮基空间机器人系统的动力学方程。以此为基础,针对关节执行器输出力矩幅值及幅值率受限的情况,设计了一种自适应模糊神经网络控制器,以使空间机器人系统的本体姿态和机械臂关节铰协调地跟踪各自在关节空间的期望运动轨迹。该控制方案由自适应模糊神经网络控制器及抗饱和参数自适应律构成。首先利用有限差分法将幅值率受限条件转化为幅值受限条件,并与该文预设的力矩受限条件比较以确定每个采样时刻的力矩动态受限范围;然后再通过设计一个抗饱和参数自适应律来确保执行器的输出力矩在动态受限范围内。基于Lyapunov稳定性理论证明了该控制器可确保控制系统是渐近稳定的。仿真对比实验证明了该控制方案的有效性。     

A Survey of Lower Limb Rehabilitation Systems and Algorithms Based on Functional Electrical Stimulation

Functional electrical stimulation is a method of repairing a dysfunctional limb in a stroke patient by using low-intensity electrical stimulation. Currently, it is widely used in smart medical treatment for limb rehabilitation in stroke patients. In this paper, the development of FES systems is sorted out and analyzed in a time order. Then, the progress of functional electrical stimulation in the field of rehabilitation is reviewed in details in two aspects, i.e., system development and algorithm progress. In the system aspect, the development of the first FES control and stimulation system, the core of the lower limb-based neuroprosthesis system and the system based on brain-computer interface are introduced. The algorithm optimization for control strategy is introduced in the algorithm. Asynchronous stimulation to prolong the function time of the lower limbs and a method to improve the robustness of knee joint modeling using neural networks. Representative applications in each of these aspects have been investigated and analyzed.     

Representing cognitive activities and errors in HRA trees

A graphic representation method is presented herein for adapting an existing technology—human reliability analysis (HRA) event trees, used to support event sequence logic structures and calculations—to include a representation of the underlying cognitive activity and corresponding errors associated with human performance. The analyst is presented with three potential means of representing human activity: the NUREG/CR-1278 HRA event-tree approach; the skill-, rule- and knowledge-based paradigm; and the slips, lapses, and mistakes paradigm. The above approaches for representing human activity are integrated in order to produce an enriched HRA event tree—the cognitive event tree system (COGENT)—which, in turn, can be used to increase the analyst's understanding of the basic behavioral mechanisms underlying human error and the representation of that error in probabilistic risk assessment. Issues pertaining to the implementation of COGENT are also discussed.     

CAD-based integrated tolerancing system

Assembly tolerance analysis involves the determination of tolerances of critical dimensions. This paper addresses two basic areas in tolerance analysis and allocation. (1) Dimension normalization, which identifies the relevant functional dimensions. A new algorithm called the dimension block diagram (DBD) algorithm for dimension normalization is presented. (2) Dimension representation, which provides a robust framework for representing the tolerance chain. A new dimension representation framework using Assembly Dimensional Tolerance (ADT) tree is presented. The two methodologies are automated and integrated within the framework of a CAD system using an Expert System. A computer test bed software has been developed demonstrating the viability of this approach.     

The analysis of the transmission-type optical smoke detector threshold sensitivity to the high rate temperature variations

Reliability of the transmission-type optical smoke detectors is limited by the high sensitivity of optical components to parasitic effects, especially to contamination and temperature. Influences of the high rate temperature variations cannot be eliminated by filtering, as their spectral range partially overlaps with the spectral range of a smoke absorption index. Hence, sensitivity to these effects has to be eliminated through the mutual cancellation of the corresponding components of the output signal. First determining the temperature dependence of the light source and the receiver in the generalized block diagram of the transmission-type optical smoke detector, transfer functions are derived, specifying the detector output signal as a function of the temperature variations of the blocks considered. Using the second-order thermal model for the thermal system of the optoelectronic diodes, an expression is given for the steady-state solution of the difference of the source and the receiver diode junction temperatures, when the ambient temperature is a ramp function of time. On the basis of the thermal system analysis, a block diagram is shown to be equivalent to RC low-pass (LP) filters that model the pn junction temperature dependence on ambient temperature. For the completed block diagram, with the help of the expressions derived, an analysis is performed to establish how to eliminate the detector threshold sensitivity to ambient temperature variations, or to adjust it to realize a multicriteria fire detector.     

基于拓扑降维法路径规划的状态空间划分原则

在拓扑降维法理论的基础上，提出了划分状态空间的一个原则，即用机器人肘关节运动禁止区划分机器人腰关节角度集合，并对状态空早分原则做了归纳和总结。     

摄像头自动平视玻璃量器标线算法研究

介绍了一种摄像头自动平视玻璃量器标线的算法,该算法基于像平面标线开口大小与运动系摄像头高度的变化关系,给出了自动平视的程序框图.实验研究结果表明:图像处理误差是影响重复性的主要不确定因素,算法为实现摄像头自动平视标线提供了一种高效的解决方案.     

A parameter tree approach to estimating system sensitivities to parameter sets

A post-processing technique for determining relative system sensitivity to groups of parameters and system components is presented. It is assumed that an appropriate parametric model is used to simulate system behavior using Monte Carlo techniques and that a set of realizations of system output(s) is available. The objective of our technique is to analyze the input vectors and the corresponding output vectors (that is, post-process the results) to estimate the relative sensitivity of the output to input parameters (taken singly and as a group) and thereby rank them. This technique is different from the design of experimental techniques in that a partitioning of the parameter space is not required before the simulation. A tree structure (which looks similar to an event tree) is developed to better explain the technique. Each limb of the tree represents a particular combination of parameters or a combination of system components. For convenience and to distinguish it from the event tree, we call it the parameter tree.To construct the parameter tree, the samples of input parameter values are treated as either a “+” or a “−” based on whether or not the sampled parameter value is greater than or less than a specified branching criterion (e.g., mean, median, percentile of the population). The corresponding system outputs are also segregated into similar bins. Partitioning the first parameter into a “+” or a “−” bin creates the first level of the tree containing two branches. At the next level, realizations associated with each first-level branch are further partitioned into two bins using the branching criteria on the second parameter and so on until the tree is fully populated. Relative sensitivities are then inferred from the number of samples associated with each branch of the tree.The parameter tree approach is illustrated by applying it to a number of preliminary simulations of the proposed high-level radioactive waste repository at Yucca Mountain, NV. Using a Total System Performance Assessment Code called TPA, realizations are obtained and analyzed. In the examples presented, groups of five important parameters, one for each level of the tree, are used to identify branches of the tree and construct the bins. In the first example, the five important parameters are selected by more traditional sensitivity analysis techniques. This example shows that relatively few branches of the tree dominate system performance. In another example, the same realizations are used but the most important five-parameter set is determined in a stepwise manner (using the parameter tree technique) and it is found that these five parameters do not match the five of the first example. This important result shows that sensitivities based on individual parameters (i.e. one parameter at a time) may differ from sensitivities estimated based on joint sets of parameters (i.e. two or more parameters at a time).The technique is extended using subsystem outputs to define the branches of the tree. The subsystem outputs used in this example are the total cumulative radionuclide release (TCR) from the engineered barriers, unsaturated zone, and saturated zone over 10,000 yr. The technique is found to be successful in estimating the relative influence of each of these three subsystems on the overall system behavior.     

Extended block diagram method for a multi-state system reliability assessment

The presented method extends the classical reliability block diagram method to a repairable multi-state system. It is very suitable for engineering applications since the procedure is well formalized and based on the natural decomposition of the entire multi-state system (the system is represented as a collection of its elements). Until now, the classical block diagram method did not provide the reliability assessment for the repairable multi-state system. The straightforward stochastic process methods are very difficult for engineering application in such cases due to the “dimension damnation”—huge number of system states. The suggested method is based on the combined random processes and the universal generating function technique and drastically reduces the number of states in the multi-state model.     

Phase-error-free quadrature sampling technique in the ultrasonic B-scan imaging system and its application to the synthetic focusing system

The quadrature sampling technique as a means of detecting the envelope of RF waveform in the baseband is well known. If this technique is applied to a focused ultrasound imaging system using an array transducer, whether it is a synthetic or nonsynthetic focusing system, unwanted phase terms appear in the expressions of the inphase and quadrature components of the baseband signal when an appropriate delay time is introduced to each channel signal for the purpose of focusing. The expressions of the inphase and quadrature components from the point of focusing are derived and analyzed in detail, and a scheme to eliminate the unwanted phase terms is proposed. The resulting phase-error-free quadrature sampling technique is applied to the synthetic focusing system; a system block diagram together with the simulation and experimental results are presented.     

一起精氩塔氮塞的处理与分析

由于投用液氩贮槽气相回精氩塔阀，导致参与精氩塔精馏的气体氮含量偏高，从而发生精氩塔氮塞。通过减量生产，并采取相应操作，系统工况恢复正常。     

一起精氩塔氮塞的处理与分析

由于投用液氩贮槽气相回精氩塔阀,导致参与精氩塔精馏的气体氮含量偏高,从而发生精氩塔氮塞。通过减量生产,并采取相应操作,系统工况恢复正常。     

A generic and efficient Taylor series–based continuation method using a quadratic recast of smooth nonlinear systems

This paper is concerned with a Taylor series–based continuation algorithm, the so-called Asymptotic Numerical Method (ANM). It describes a generic continuation procedure to apply the ANM principle at best, in other words, that presents a high level of genericity without paying the price of this genericity by low computing performances. The way to quadratically recast a system of equation is now part of the method itself, and the way to handle elementary transcendental function is detailed with great attention. A sparse tensorial formalism is introduced for the internal representation of the system, which, when combined with a block condensation technique, provides a good computational efficiency of the ANM. Three examples are developed to show the performance and the versatility of the implementation of the continuation tool. Its robustness and its accuracy are explored. Finally, the potentiality of this method for complex nonlinear finite element analysis is enlightened by treating 2D elasticity problems with geometrical nonlinearities.     

Code design using deterministic annealing

We address the problem of designing codes for specific applications using deterministic annealing. Designing a block code over any finite dimensional space may be thought of as forming the corresponding number of clusters over the particular dimensional space. We have shown that the total distortion incurred in encoding a training set is related to the probability of correct reception over a symmetric channel. While conventional deterministic annealing make use of the Euclidean squared error distance measure, we have developed an algorithm that can be used for clustering with Hamming distance as the distance measure, which is required in the error correcting scenario.     

A Wiener path integral technique for determining the stochastic response of nonlinear oscillators with fractional derivative elements: A constrained variational formulation with free boundaries

A technique based on the concept of Wiener path integral (WPI) is developed for determining approximately the joint response probability density function (PDF) of nonlinear oscillators endowed with fractional derivative elements. Specifically, first, the dependence of the state of the system on its history due to the fractional derivative terms is accounted for, alternatively, by augmenting the response vector and by considering additional auxiliary state variables and equations. In this regard, the original single-degree-of-freedom (SDOF) nonlinear system with fractional derivative terms is cast, equivalently, into a multi-degree-of-freedom (MDOF) nonlinear system involving integer-order derivatives only. From a mathematics perspective, the equations of motion referring to the latter can be interpreted as constrained. Second, to circumvent the challenge of increased dimensionality of the problem due to the augmentation of the response vector, a WPI formulation with mixed fixed/free boundary conditions is developed for determining directly any lower-dimensional joint PDF corresponding to a subset only of the response vector components. This can be construed as an approximation-free dimension reduction approach that renders the associated computational cost independent of the total number of stochastic dimensions of the problem. Thus, the original SDOF oscillator joint PDF corresponding to the response displacement and velocity is determined efficiently, while circumventing the computationally challenging task of treating directly equations of motion involving fractional derivatives. Two illustrative numerical examples are considered for demonstrating the reliability of the developed technique. These pertain to a nonlinear Duffing and a nonlinear vibro-impact oscillators with fractional derivative elements subjected to combined stochastic and deterministic periodic loading. Note that alternative standard approximate techniques, such as statistical linearization, need to be significantly modified and extended to account for such cases of combined loading. Remarkably, it is shown herein that the WPI technique exhibits the additional advantage of treating such types of excitation in a straightforward manner without the need for any ad hoc modifications. Comparisons with pertinent Monte Carlo simulation data are included as well.