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16th IFAC Symposium on Advanced Control of Chemical Processes (ADCHEM)

作者： Kusumo, Kennedy P. Morrissey, James Mitchell, Hamish Shah, Nilay Chachuat, Benoit Imperial Coll London Dept Chem Engn Sargent Ctr Proc Syst Engn London England

The use of mathematical models for design space characterization has become commonplace in pharmaceutical quality-by-design, providing a systematic risk-based approach to assurance of quality. This paper presents a methodology to complement sampling algorithms by computing the largest box inscribed within a given probabilistic design space at a desired reliability level. Such an encoding of the samples yields an operational envelope that can be conveniently communicated to process operators as independent ranges in process parameters. The first step involves training a feed-forward multi-layer perceptron as a surrogate of the sampled probability map. This surrogate is then embedded into a design centering problem, formulated as a semi-infinite program and solved using a cutting-plane algorithm. Effectiveness and computational tractability are demonstrated on the case study of a batch reactor with two critical process parameters. Copyright (C) 2021 The Authors.

关键词： quality-by-design probabilistic design space sampling algorithm design centering multi-layer perceptron

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Motion Planning of Planar Closed Chains Based on Structural Sets

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IEEE ACCESS 2020年 8卷 117203-117217页

作者： Liu, Guanfeng Trinkle, Jeff Yang, Yong Luo, Shaoming Guangdong Polytech Normal Univ Sch Mechatron Engn Guangzhou 510665 Peoples R China Lehigh Univ Dept Comp Sci Bethlehem PA 18015 USA

This paper investigates the motion planning problem of planar m-link (m >= 4) closed chains among point obstacles with extension to arbitrary convex 2-D obstacles. The configuration space (C-space) of closed chains is embedded into two copies of m-3 dimensional tori. Two structural sets, the C-boundaries and the C-obstacles, are analyzed based upon the C-spaces of recursively constructed lower-dimensional closed chains. They contain essential structural information about the connectivity of the collision-free portion (C-free) of the C-space. By approximating each workspace obstacle by a set of points on the boundary after dilation, its corresponding C-obstacle is guaranteed to be covered by the C-obstacle of the convex hull of the point set. This permits a resolution-complete roadmap algorithm that puts specific bias for sampling the structural sets. Several benchmark examples are presented that compare the performance between our algorithm and the traditional algorithms. Animation videos and source codes are also provided which demonstrate the effectiveness of our method for closed chains of up to 20 links.

关键词： Path planning closed chains boundary variety bifurcation narrow passages sampling algorithm

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Fast One-to-Many Reliability Estimation for Uncertain Graphs 31st

Fast One-to-Many Reliability Estimation for Uncertain Graphs

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31st International Conference on Database and Expert Systems Applications (DEXA)

作者： Yanagisawa, Junya Shiokawa, Hiroaki Univ Tsukuba Grad Sch Sci & Technol Tsukuba Ibaraki Japan Univ Tsukuba Ctr Computat Sci Tsukuba Ibaraki Japan

ISBN: (纸本)9783030590031;9783030590024

Uncertain graphs commonly represent noisy and unreliable real-world datasets in various applications. One fundamental primitive on uncertain graphs is reliability, which evaluates the connection robustness between two specific nodes. Although reliability is helpful to analyzeuncertain graphs, it is computationally expensive because (1) the reliability estimation is #P-hard problem and (2) many applications require reliability computations among all possible pairs of nodes. To overcome the aforementioned problems, we present a novel algorithm called Sharing RCSS+, which efficiently computes the reliability among all possible pairs of nodes. Our extensive experiments on both real-world and synthetic uncertain graphs clarified that Sharing RCSS+ achieves a more efficient estimation than the state-of-the-art methods.

关键词： Uncertain graphs Reliability sampling algorithm

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Estimating Normalizing Constants for Log-Concave Distributions: algorithms and Lower Bounds 2020

Estimating Normalizing Constants for Log-Concave Distributio...

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52nd Annual ACM SIGACT Symposium on Theory of Computing (STOC)

作者： Ge, Rong Lee, Holden Lu, Jianfeng Duke Univ Durham NC 27708 USA

ISBN: (纸本)9781450369794

Estimating the normalizing constant of an unnormalized probability distribution has important applications in computer science, statistical physics, machine learning, and statistics. In this work, we consider the problem of estimating the normalizing constant Z = f(Rd) e(-f(x)) dx to within a multiplication factor of 1 +/- epsilon for a mu-strongly convex and L-smooth function f, given query access to f(x) and del f(x). We give both algorithms and lowerbounds for this problem. Using an annealing algorithm combined with a multilevel Monte Carlo method based on underdamped Langevin dynamics, we show that (O) over tilde (d(4/3)kappa+d(7/6)kappa(7/6)/epsilon(2)) queries to del f are sufficient, where kappa = L/mu is the condition number. Moreover, we provide an information theoretic lowerbound, showing that at least d(1-o(1))/epsilon(2-o(1)) queries are necessary. This provides a first nontrivial lowerbound for the problem.

关键词： Langevin Monte Carlo multilevel Monte Carlo normalizing constant partition function log-concave distribution sampling algorithm

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A Design Centering Methodology for Probabilistic Design Space

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IFAC-PapersOnLine 2021年第3期54卷 79-84页

作者： Kennedy P. Kusumo James Morrissey Hamish Mitchell Nilay Shah Benoît Chachuat The Sargent Centre for Process Systems Engineering Department of Chemical Engineering Imperial College London London UK

关键词： quality-by-design probabilistic design space sampling algorithm design centering multi-layer perceptron

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Semi-constrained Path Planning for Industrial Robot with External Axis

Semi-constrained Path Planning for Industrial Robot with Ext...

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Chinese Automation Congress (CAC)

作者： Sun, Yu Meng, Xiangqun Yu, Miaocheng Tang, Houjun Shanghai Jiao Tong Univ Dept Elect Engn Shanghai Peoples R China Shanghai Fangling Comp Software Co Ltd Shanghai Peoples R China

ISBN: (纸本)9781728176871

To solve the problem that the working space of the industrial robot is limited by the arm length, and the flexibility is limited by the number of joints, the robot system with external axes is necessary. This paper proposes a novel sampling-based path planning method to control the industrial robot and external axes simultaneously. An external axis space is proposed for sampling external axis value to solve task-constrained path planning problems in practical industrial applications. The configuration space of a robot system with external axes is decoupled to extract task space independent of external axis space, based on the semi-constrained characteristic of typical Cartesian curve tracking tasks. The task space is defined by the position and orientation parameter of the robot's end-effector. As a result, a sampling space, which meets the task-constraint, can he found. Analytical Inverse Kinematics (IK) algorithm is used to map the samples back to the task-constrained configuration space without iterative modifications. Simulation studies on practical path planning tasks under constraints prove the effectiveness of the proposed method.

关键词： industrial robot external axis task-constrained path planning sampling algorithm

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Geometrically stable tracking for depth images based 3D reconstruction on mobile devices

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ISPRS JOURNAL OF PHOTOGRAMMETRY AND REMOTE SENSING 2018年 143卷 222-232页

作者： Liu, Yangdong Gao, Wei Hu, Zhanyi Chinese Acad Sci Inst Automat Natl Lab Pattern Recognit Beijing 100190 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China

With the development of hardwares such as mobile devices and portable depth cameras, on-line 3D reconstruction on the mobile devices with depth streams as input turns to be possible and promising. Most existing systems use volumetric representation methods to fuse the depth images and use ICP algorithm to estimate the poses of cameras. However, ICP tracker suffers from large drift in scenes containing insufficient geometric information. To deal with this problem, we propose a stability based sampling method which select different number of point-pairs in different windows according to their geometric stability. In addition, we fuse the ICP tracker with the IMU information through an analysis of the condition number. Then we apply the stability based sampling method to the spatially hashed volumetric representation. Qualitative and quantitative evaluations of tracking accuracy and 3D reconstruction results show that our method outperforms the current state-of-the-art systems, especially in scenes lacking sufficient geometric information. In total, our method achieves frame rates 20 Hz on an Apple iPad Air 2 and 200 Hz on a Nvidia GeForce GTX 1060 GPU. (C) 2018 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights reserved.

关键词： Visual-SLAM Dense mapping ICP algorithm sampling algorithm On-line Mobile device

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A Fill Estimation algorithm for Sparse Matrices and Tensors in Blocked Formats 32

A Fill Estimation Algorithm for Sparse Matrices and Tensors ...

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27th International Heterogeneity in Computing Workshop in conjunction with 32nd IEEE International Parallel and Distributed Processing Symposium (IPDPS)

作者： Ahrens, Willow Xu, Helen Schiefer, Nicholas MIT Comp Sci & Artificial Intelligence Lab 77 Massachusetts Ave Cambridge MA 02139 USA

ISBN: (纸本)9781538643686

Many sparse matrices and tensors from a variety of applications, such as finite element methods and computational chemistry, have a natural aligned rectangular nonzero block structure. Researchers have designed high-performance blocked sparse operations which can take advantage of this sparsity structure to reduce the complexity of storing the locations of nonzeros. The performance of a blocked sparse operation depends on how well the block size reflects the structure of nonzeros in the tensor. Sparse tensor structure is generally unknown until runtime, so block size selection must be efficient. The fill is a quantity which, for some block size, relates the number of nonzero blocks to the number of nonzeros. Many performance models use the fill to help choose a block size. However, the fill is expensive to compute exactly. We present a sampling-based algorithm called PHIL to estimate the fill of sparse matrices and tensors in any format. We provide theoretical guarantees for sparse matrices and tensors, and experimental results for matrices. The existing state-of-the-art fill estimation algorithm, which we will call OSKI, runs in time linear in the number of elements in the tensor. The number of samples PHIL needs to compute a fill estimate is unrelated to the number of nonzeros and depends only on the order (number of dimensions) of the tensor, desired accuracy of the estimate, desired probability of achieving this accuracy, and number of considered block sizes. We compare PHIL and OSKI on a suite of 42 matrices. On most inputs, PHIL estimates the fill at least 2 times faster and often more than 20 times faster than OSKI. PHIL consistently produced accurate estimates-in all cases that we tested PHIL was faster and/or more accurate than OSKI. Finally, we find that PHIL and OSKI produce comparable speedups in multicore blocked sparse matrix-vector multiplication (SpMV) when the block size was chosen using fill estimates in a model due to Vuduc et al.

关键词： Fill Estimation Sparse Matrix Sparse Tensor Block Sparse Block Size Selection Randomized algorithm sampling algorithm Autotuning Performance Engineering Performance Model Numerical Linear Algebra Phil

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Efficient sampling Methods for Discrete Distributions

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algorithmICA 2017年第2期79卷 484-508页

作者： Bringmann, Karl Panagiotou, Konstantinos Max Planck Inst Informat Saarbrucken Germany Univ Munich Munich Germany

We study the fundamental problem of the exact and efficient generation of random values from a finite and discrete probability distribution. Suppose that we are given n distinct events with associated probabilities p(1,)...,p(n) First, we consider the problem of sampling from the distribution where the i-th event has probability proportional to p(i). Second, we study the problem of sampling a subset which includes the i-th event independently with probability . For both problems we present on two different classes of inputs-sorted and general probabilities-efficient data structures consisting of a preprocessing and a query algorithm. Varying the allotted preprocessing time yields a trade-off between preprocessing and query time, which we prove to be asymptotically optimal everywhere.

关键词： sampling algorithm Subset sampling Distribution Proportional sampling Data structures

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A comparison of pivotal sampling and unequal probability sampling with replacement

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STATISTICS & PROBABILITY LETTERS 2017年 121卷 1-5页

作者： Chauvet, Guillaume Ruiz-Gazen, Anne ENSAI IRMAR Campus Ker Lann F-35170 Bruz France Toulouse Sch Econ 21 Allee Brienne F-31000 Toulouse France

We prove that any implementation of pivotal sampling is more efficient than multinomial sampling. This yields the weak consistency of the Horvitz Thompson estimator and the existence of a conservative variance estimat... 详细信息

关键词： Cube method Mean-square consistency sampling algorithm Unequal probabilities Variance estimator With-replacement sampling

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