Improved algorithm for tolerance allocation based on Monte Carlo simulation and discrete optimization

The allocation of design and manufacturing tolerances has a significant effect on both manufacturing cost and quality. This paper considers nonlinearly constrained tolerance allocation problems. The purpose is to minimize the ratio between the sum of the manufacturing costs (tolerances costs) and the risk (probability of the respect of geometrical requirements). The techniques of Monte Carlo simulation and genetic algorithm are adopted to solve these problems. As the simplest and the popular method for non-linear statistical tolerance analysis, the Monte Carlo simulation is introduced into the frame. Moreover, in order to make the frame efficient, the genetic algorithm is improved according to the features of the Monte Carlo simulation. An illustrative example (hyperstatic mechanism) is given to demonstrate the efficiency of the proposed approach.     

Interval approach challenges Monte Carlo simulation

Intervals are used to represent imprecise numerical values. Modelling uncertain values with precise bounds without considering their probability distribution is infeasible in many applications. As a solution, this paper proposes the use of probability density functions instead of intervals; we consider evaluation of an arithmetical function of random variables. Since the result density cannot in general be solved algebraically, an interval method for determining itsguaranteed bounds is developed. This possibility challenges traditional Monte Carlo methods in which only stochastic characterizations for the result distribution, such as confidence bounds for fractiles, can be determined.     

A Monte Carlo simulation approach for effective assessment of flyrock based on intelligent system of neural network

One of the undesirable phenomena in the surface mines, which results in various hazards for human and facilities, is flyrock. It seems that the careful study of the subject and its effects on the environment can affect the control of flyrock hazards in the studied area. Therefore, the use of intelligent models and methods which are capable of predicting and simulating the risk of flyrock can be considered as an appropriate solution in this regard. The current research was conducted using nonlinear models and Monte Carlo (MC) simulation. The data used in this study consist of 260 samples of rock thrown from a mine in Malaysia. The parameters used in these models include hole’s diameter (D), hole’s depth (HD), burden to spacing (BS), stemming (ST), maximum charge per delay (MC), and powder factor (PF). At first, multiple regression analysis (MRA) and artificial neural network (ANN) models were used in order to develop a non-linear relationship between dependent and independent parameters. The ANN model was an appropriate predictor of flyrock in the mine. Then using the best implemented model of ANN, the flyrock environmental phenomenon was simulated using MC technique. MC simulation showed a proper level of accuracy of flyrock ranges in the mine. Using this simulation, it can be concluded with 90% accuracy that the Flyrock phenomenon does not exceed 331 m. Under these conditions, this simulation can be used for various areas requiring risk assessment. Finally, a sensitive analysis was carried out on data. This analysis showed MC has the greatest effect on flyrock.     

Tolerance analysis based on Monte Carlo simulation: a case of an automotive water pump design optimization

Successful products are those presenting the highest quality at a fair cost. Although different approaches can be used to define the concept of quality, functional reliability is always a major requirement, due to implications such as safety and user losses regarding maintenance expenses, and product availability. Intelligent designs are robust and result in a fair cost. Robust designs are those insensitive to sources of variation occurring during the product life, keeping their performance under variable use conditions, like thermal and stress effects. The robustness approach is a function of two main design criteria: low complexity and tolerance design. Design for manufacture and assembly is closely related to decreasing complexity. Tolerance design is a tool in which the unavoidable manufacturing variations are considered during product development. This work presents a proposal for an intelligent design in an actual application by considering design simplification through the reduction of parts for an automotive water pump. The tolerance analysis is performed by means of a powerful statistical approach—a Monte Carlo simulation—in which process behavior is randomly simulated representing a high production volume. Additionally, service thermal effects are also contemplated, and assembly tests are proposed for automatic rejection of non-conforming parts, assuring high reliability and full compliance with functional requirements. This is an example of integrated design–manufacturing work aiming at both cost saving and improved reliability.

     

A reliability-based optimization method using sequential surrogate model and Monte Carlo simulation

This paper presents a sequential surrogate model method for reliability-based optimization (SSRBO), which aims to reduce the number of the expensive black-box function calls in reliability-based optimization. The proposed method consists of three key steps. First, the initial samples are selected to construct radial basis function surrogate models for the objective and constraint functions, respectively. Second, by solving a series of special optimization problems in terms of the surrogate models, local samples are identified and added in the vicinity of the current optimal point to refine the surrogate models. Third, by solving the optimization problem with the shifted constraints, the current optimal point is obtained. Then, at the current optimal point, the Monte Carlo simulation based on the surrogate models is carried out to obtain the cumulative distribution functions (CDFs) of the constraints. The CDFs and target reliabilities are used to update the offsets of the constraints for the next iteration. Therefore, the original problem is decomposed to serial cheap surrogate-based deterministic problems and Monte Carlo simulations. Several examples are adopted to verify SSRBO. The results show that the number of the expensive black-box function calls is reduced exponentially without losing of precision compared to the alternative methods, which illustrates the efficiency and accuracy of the proposed method.

     

基于Monte Carlo仿真的降低光谱散射方法比较研究

散射是影响光谱分析与检测技术精度的主要因素,使光谱分析的基本线性定律——朗伯比尔定律不再成立。基于Monte Carlo仿真对3种常用的降低光散射的方法进行比较分析,即偏振差法、附加吸收剂法和空间滤波法。3种方法都是通过提取出弱散射光,线性化光强衰减度与吸收系数关系。提出线性度可以由透射光的光程方差判断。弱散射光的光程更短,光程均值更接近介质厚度,光程方差更低,但是光强也更弱。对3种方法在不同散射系数的透射光时间响应、光强衰减度与吸收系数关系、光程方差以及光强进行比较,表明偏振差法相比其他两种方法效果更佳。     

A Monte Carlo approach for Galerkin radiosity

Galerkin radiosity solves the integral rendering equation by projecting the illumination functions into a set of higher-order basis functions. This paper presents a Monte Carlo approach for Galerkin radiosity to compute the coefficients of the basis functions. The new approach eliminates the problems with edge singularities between adjacent surfaces present in conventional Galerkin radiosity, the time complexity is reduced fromO(K ⁴) toO(K ²) for aK-order basis, and ideally specular energy transport can be simulated. As in conventional Galerkin radiosity, no meshing is required even for large or curved surfaces, thus reducing memory requirements, and no a posteriori Gouraud interpolation is necessary. The new algorithm is simple and can be parallelized on any parallel computer, including massively parallel systems.     

A metamodel-based Monte Carlo simulation approach for responsive production planning of manufacturing systems

Production planning is concerned with finding a release plan of jobs into a manufacturing system so that its actual outputs over time match the customer demand with the least cost. For a given release plan, the system outputs, work in process inventory (WIP) levels and job completions, are non-stationary bivariate time series that interact with time series representing customer demand, resulting in the fulfillment/non-fulfillment of demand and the holding cost of both WIP and finished-goods inventory. The relationship between a release plan and its resulting performance metrics (typically, mean/variance of the total cost and the fill rate) has proven difficult to quantify. This work develops a metamodel-based Monte Carlo simulation (MCS) method to accurately capture the dynamic, stochastic behavior of a manufacturing system, and to allow real-time evaluation of a release plan's performance metrics. This evaluation capability is then embedded in a multi-objective optimization framework to search for near-optimal release plans. The proposed method has been applied to a scaled-down semiconductor fabrication system to demonstrate the quality of the metamodel-based MCS evaluation and the results of plan optimization.     

基于序贯蒙特卡洛算法的交通流事件重构

针对交通数据重构应用性差、缺乏对交通事件重构的研究等问题,结合交通流非线性非高斯的特点,提出一个基于序贯蒙特卡洛方法的交通流堵塞事件重构模型。该模型不断同化道路上的传感器数据,使仿真中的交通状态不断逼近真实路况,通过分析仿真数据以探测真实路网中存在的堵塞事件。模型能够对探测到的堵塞进行多粒子模拟来实现对真实道路上堵塞事件的重构。实验结果表明,该模型能够推测并重构出道路上的堵塞事件,对堵塞起始位置重构的平均误差为17m,对堵塞范围重构的平均覆盖率为82%。     

Machining accuracy reliability analysis of multi-axis machine tool based on Monte Carlo simulation

Although machine tool can meet the specifications while it is new, after a long period of cutting operations, the abrasion of contact surfaces and deformation of structures will degrade the accuracy of machine tool due to the increase of the geometric errors in six freedoms. Therefore, how to maintain its accuracy for quality control of products is of crucial importance to machine tool. In this paper, machining accuracy reliability is defined as the ability to perform its specified machining accuracy under the stated conditions for a given period of time, and a new method to analyze the sensitivity of geometric errors to the machining accuracy reliability is proposed. By applying Multi-body system theory, a comprehensive volumetric model explains how individual geometric errors affect the machining accuracy (the coupling relationship) was established. Based on Monte Carlo mathematic simulation method, the models of the machining accuracy reliability and sensitivity analysis of machine tools were developed. By taking the machining accuracy reliability as a measure of the ability of machine tool and reliability sensitivity as a reference of optimizing the basic parameters of machine tools, an illustrative example of a three-axis machine tool was selected to demonstrate the effectiveness of the proposed method.     

Error measures for fuzzy linear regression: Monte Carlo simulation approach

The focus of this study is to use Monte Carlo method in fuzzy linear regression. The purpose of the study is to figure out the appropriate error measures for the estimation of fuzzy linear regression model parameters with Monte Carlo method. Since model parameters are estimated without any mathematical programming or heavy fuzzy arithmetic operations in fuzzy linear regression with Monte Carlo method. In the literature, only two error measures (E₁ and E₂) are available for the estimation of fuzzy linear regression model parameters. Additionally, accuracy of available error measures under the Monte Carlo procedure has not been evaluated. In this article, mean square error, mean percentage error, mean absolute percentage error, and symmetric mean absolute percentage error are proposed for the estimation of fuzzy linear regression model parameters with Monte Carlo method. Moreover, estimation accuracies of existing and proposed error measures are explored. Error measures are compared to each other in terms of estimation accuracy; hence, this study demonstrates that the best error measures to estimate fuzzy linear regression model parameters with Monte Carlo method are proved to be E₁, E₂, and the mean square error. One the other hand, the worst one can be given as the mean percentage error. These results would be useful to enrich the studies that have already focused on fuzzy linear regression models.     

基于RMC的蒙特卡罗程序性能优化

蒙特卡罗MC方法是核反应堆设计和分析中重要的粒子输运模拟方法.MC方法能够模拟复杂几何形状且计算结果精度高,缺点是需要耗费大量时间进行上亿规模粒子模拟.如何提高蒙特卡罗程序的性能成为大规模蒙特卡罗数值模拟的挑战.基于堆用蒙特卡罗分析程序RM C,先后开展了基于TCMalloc动态内存分配优化、OpenMP线程调度策略优...     

基于多假设粒子群优化的蒙特卡罗定位算法

针对传统蒙特卡罗定位(MCL)算法在结构化相似环境中容易出现定位失败的问题,提出一种基于多假设粒子群优化的改进蒙特卡罗定位方法(MPSO-CL).以激光传感器的观测信息作为适应度函数,对MCL算法的采样粒子进行多假设粒子群优化更新,使得采样粒子向当前群体中多个最优粒子方向移动,从而使得粒子迅速收敛到后验概率密度分布取值较大的区域,实现了移动机器人高效精确自主定位.实验结果表明,MPSO-MCL算法克服了相似环境中定位的粒子匮乏问题,并且提高了定位的精确度.     

Monte Carlo simulation program for ecosystems

A Monte Carlo computer simulation program is designed in order to describe the spatial and time evolution of a population of living individuals under preassigned environmental conditions of energy. The simulation is inspired by previous techniques developed in physics--in particular, in molecular dynamics and simulations of liquids--and it already provides some new insights regarding macroscopic deterministic models in ecology and concerning eventual control of artificial biomass production plants.     

Reliable kinetic Monte Carlo simulation based on random set sampling

Kinetic Monte Carlo (KMC) method has been widely used in simulating rare events such as chemical reactions or phase transitions. Yet lack of complete knowledge of transitions and the associated rates is one major challenge for accurate KMC predictions. In this paper, a reliable KMC (R-KMC) mechanism is proposed in which sampling is based on random sets instead of random numbers to improve the robustness of KMC results. In R-KMC, rates or propensities are interval estimates instead of precise numbers. A multi-event algorithm based on generalized interval probability is developed. The weak convergence of the multi-event algorithm towards the traditional KMC is demonstrated with a generalized Chapman–Kolmogorov equation.     

Monte Carlo simulation on transputer arrays

A Monte Carlo simulation of a simple statistical physics model is decomposed onto a multi-processor (transputer) array in two essentially different ways: using ‘geometric’ and ‘algorithmic’ concurrency. The geometric decomposition (in which each processor handles a small sector of the physical system) is characterized by high efficiency in utilization of processors, and relative simplicity in programming. The algorithmic decomposition (in which each processor handles a small sub-task of the full algorithm, typically in a pipelined mode) is characterized by greater flexibility in the data-size (size of the physical system) and minimal memory requirements for a majority of the processors in the array. These assertions are made concrete in relation to our specific problem (a two-dimensional spin system simulation) which is, in many respects representative of a wide class of problems of interest to theoretical physicists.     

结合先验知识与蒙特卡罗模拟的麻将博弈研究

针对内陆麻将缺乏统一平台和大量牌谱数据,难以设计出基于监督学习的博弈算法的问题,本文设计了一系列将规则、经验与蒙特卡罗方法相结合的博弈算法.首先,分别针对麻将博弈的弃牌模块、听牌模块、吃牌模块提出了弃牌优先级、听牌有效数、吃牌优先级的方法,完善了麻将AI的知识体系,设计了基础版博弈算法Fanfou_ba和优化版博弈算法...     

A very high speed Monte Carlo simulation on DAP

The Ising ferromagnet is a well-known model of a system of interacting spins which is amenable to Monte Carlo calculation involving:

• 1.(a) Boolean work and low precision counting;
• 2.(b) conditional choice of transition probabilities;
• 3.(c) high quality 24-bit random number generation (RNG);
• 4.(d) comparison of transition probabilities with random numbers.

An assembler implementation on the 64 × 64 DAP has achieved 42 × 10⁶ spin updates per second on a 64 × 64 × 64 problem using a standard DAP random number generator (RNG) that has recently been speeded up by a factor of eight. A later implementation involves:

• 1.(a) a new RNG that is an order of magnitude faster still, mainly achieved by producing data in greater bulk;
• 2.(b) a rewrite of the code including a form of parallel table look up for the transition probabilities;
• 3.(c) an increase in the problem size to 128 × 128 × 144. The performance is 218 × 10⁶ spin updates per second. This compares with 22 × 10⁶ on a CYBER 205 and 24 × 10⁶ on special purpose hardware built by a group in Santa Barbara, both on 64 × 64 × 64 problems.

Our results can be extrapolated to about 40 × 10⁶ spin updates per second for a possible 32 × 32 DAP which would be about two times faster than a CYBER 205 and two orders of magnitude cheaper.     

基于Monte Carlo随机模拟的综合交通网络布局评价与决策方法

针对综合交通网络评价指标权重及属性值具有主观性和随机性的特点,提出了基于模拟运算的布局规划方案排序选优的群体随机决策方法.仿真生成满足集结的多个专家对指标重要性偏好排序统计分布的权重,同时考虑交通需求的不确定性对指标值的影响,结合客观熵权计算方案的综合评价值,由多次模拟得到的排序优势度确定方案的优劣差异.根据设计的仿真流程通过算例说明了方法应用的有效性,评价中考虑了主客观因素及随机性特征,可以为网络布局提供科学决策依据.