Bayesian Network Learning for Data-Driven Design

2018 ◽  
Vol 4 (4) ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Conditional Probability ◽  
Probability Learning ◽  
Learning Algorithms ◽  
Engineering Application ◽  
Gaussian Mixture ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Practical Applications ◽  
Analysis And Design ◽  
Engineering Design Problems

Bayesian networks (BNs) are being studied in recent years for system diagnosis, reliability analysis, and design of complex engineered systems. In several practical applications, BNs need to be learned from available data before being used for design or other purposes. Current BN learning algorithms are mainly developed for networks with only discrete variables. Engineering design problems often consist of both discrete and continuous variables. This paper develops a framework to handle continuous variables in BN learning by integrating learning algorithms of discrete BNs with Gaussian mixture models (GMMs). We first make the topology learning more robust by optimizing the number of Gaussian components in the univariate GMMs currently available in the literature. Based on the BN topology learning, a new multivariate Gaussian mixture (MGM) strategy is developed to improve the accuracy of conditional probability learning in the BN. A method is proposed to address this difficulty of MGM modeling with data of mixed discrete and continuous variables by mapping the data for discrete variables into data for a standard normal variable. The proposed framework is capable of learning BNs without discretizing the continuous variables or making assumptions about their conditional probability densities (CPDs). The applications of the learned BN to uncertainty quantification and model calibration are also investigated. The results of a mathematical example and an engineering application example demonstrate the effectiveness of the proposed framework.

Bayesian Network Learning for Uncertainty Quantification

2017 ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Uncertainty Quantification ◽  
Probability Learning ◽  
Learning Algorithms ◽  
Engineering Application ◽  
Gaussian Mixture ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Practical Applications ◽  
Analysis And Design ◽  
Engineering Design Problems

Bayesian Networks (BNs) are being studied in recent years for system diagnosis, reliability analysis, and design of complex engineered systems. In several practical applications, BNs need to be learned from available data before being used for design or other purposes. Current BN learning algorithms are mainly developed for networks with only discrete variables. Engineering design problems often consist of both discrete and continuous variables. This paper develops a framework to handle continuous variables in BN learning by integrating learning algorithms of discrete BNs with Gaussian mixture models (GMMs). We first make the topology learning more robust by optimizing the number of Gaussian components in the univariate GMMs currently available in the literature. Based on the BN topology learning, a new Multivariate Gaussian Mixture (MGM) strategy is developed to improve the accuracy of conditional probability learning in the BN. A method is proposed to address this difficulty of MGM modeling with data of mixed discrete and continuous variables by mapping the data for discrete variables into data for a standard normal variable. The proposed framework is capable of learning BNs without discretizing the continuous variables or making assumptions about their CPDs. The applications of the learned BN to uncertainty quantification and model calibration are also investigated. The results of a mathematical example and an engineering application example demonstrate the effectiveness of the proposed framework.

scholarly journals Neural Population Coding and Approximations of Mutual Information for Discrete Variables

2018 ◽  
Author(s):  
Wentao Huang ◽  
Kechen Zhang
Keyword(s):  
Information Theory ◽  
Mutual Information ◽  
Population Coding ◽  
Neural Population ◽  
Asymptotic Formulas ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Practical Applications ◽  
Leibler Divergence ◽  
Approximation Formulas

Information theory is widely used in various disciplines, and effective calculation of Shannon mutual information is typically not an easy task for many practical applications, including problems of neural population coding in computational and theoretical neuroscience. Asymptotic formulas based on Fisher information may provide accurate approximations to mutual information but this approach is restricted to continuous variables because the calculation requires derivatives with respect to the encoded variables. In this paper, we consider information-theoretic bounds and approximations based on Kullback-Leibler divergence and Rényi divergence. We propose several information metrics to approximate Shannon mutual information in the context of neural population coding, and these asymptotic formulas hold true for discrete variables as there is no requirement for differentiability. In particular, one of our approximation formulas has consistent performance and good accuracy regardless of whether the encoded variables are discrete or continuous. We performed numerical simulations and confirmed that our approximation formulas were highly accurate for approximating mutual information between the discrete variables or stimuli and the responses of a large neural population. These approximation formulas may potentially bring convenience to the applications of information theory to many practical and theoretical problems.

Ultrasonic Transducer Design via APDL Optimization

2010 ◽  
Vol 34-35 ◽  
pp. 1076-1081
Author(s):  
Xiang Hui Zhang ◽  
Gui Hua Li
Keyword(s):  
Vibration Amplitude ◽  
Optimization Problem ◽  
Ultrasonic Transducer ◽  
Optimization Method ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Ultrasonic Machine ◽  
Practical Applications ◽  
Design Variables ◽  
Transducer Design

The design of ultrasonic transducer is used to achieve the desired value of terminal vibration amplitude. However, in many practical applications of ultrasonic transducer, the maximum vibration amplitude failed to achieve that value such as ultrasonic machine and bonding. For that matter, the design of ultrasonic transducer used APDL optimization method. In this paper the optimal design of a sandwich ultrasonic transducer is investigated. The design problem is formulated mathematically as a constrained single-objective optimization problem. The maximum vibration amplitude is considered as optimization objective. Design variables involve continuous variables and discrete variables. What is more, the behavior of ultrasonic transducer is modeled using ANSYS based on models of the transfer matrix method. In this paper, the optimized results are analyzed and the vibration amplitude is determined.

scholarly journals A Multimodal Smart Quantum Particle Swarm Optimization for Electromagnetic Design Optimization Problems

Energies ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4613
Author(s):  
Shah Fahad ◽  
Shiyou Yang ◽  
Rehan Ali Khan ◽  
Shafiullah Khan ◽  
Shoaib Ahmed Khan
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Quantum Particle ◽  
Particle Swarm ◽  
Continuous Variables ◽  
Design Problems ◽  
Swarm Optimization ◽  
Electromagnetic Design ◽  
Quantum Particle Swarm Optimization ◽  
Engineering Design Problems

Electromagnetic design problems are generally formulated as nonlinear programming problems with multimodal objective functions and continuous variables. These can be solved by either a deterministic or a stochastic optimization algorithm. Recently, many intelligent optimization algorithms, such as particle swarm optimization (PSO), genetic algorithm (GA) and artificial bee colony (ABC), have been proposed and applied to electromagnetic design problems with promising results. However, there is no universal algorithm which can be used to solve engineering design problems. In this paper, a stochastic smart quantum particle swarm optimization (SQPSO) algorithm is introduced. In the proposed SQPSO, to tackle the premature convergence problem in order to improve the global search ability, a smart particle and a memory archive are adopted instead of mutation operations. Moreover, to enhance the exploration searching ability, a new set of random numbers and control parameters are introduced. Experimental results validate that the adopted control policy in this work can achieve a good balance between exploration and exploitation. Finally, the SQPSO has been tested on well-known optimization benchmark functions and implemented on the electromagnetic TEAM workshop problem 22. The simulation result shows an outstanding capability of the proposed algorithm in speeding convergence compared to other algorithms.

Numerical Study of Viscous Flows Inside Partially Filled Spinning and Coning Cylinders

1996 ◽  
Vol 118 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Mohamed Selmi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Center Of Mass ◽  
Steady Motion ◽  
Practical Interest ◽  
Nonlinear Effects ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Practical Applications ◽  
Analysis And Design

This paper is concerned with the solution of the 3-D-Navier-Stokes equations describing the steady motion of a viscous fluid inside a partially filled spinning and coning cylinder. The cylinder contains either a single fluid of volume less than that of the cylinder or a central rod and a single fluid of combined volume (volume of the rod plus volume of the fluid) equal to that of the cylinder. The cylinder rotates about its axis at the spin rate ω and rotates about an axis that passes through its center of mass at the coning rate Ω. In practical applications, as in the analysis and design of liquid-filled projectiles, the parameter ε = τ sin θ, where τ = Ω/ω and θ is the angle between spin axis and coning axis, is small. As a result, linearization of the Navier-Stokes equations with this parameter is possible. Here, the full and linearized Navier-Stokes equations are solved by a spectral collocation method to investigate the nonlinear effects on the moments caused by the motion of the fluid inside the cylinder. In this regard, it has been found that nonlinear effects are negligible for τ ≈ 0.1, which is of practical interest to the design of liquid-filled projectiles, and the solution of the linearized Navier-Stokes equations is adequate for such a case. However, as τ increases, nonlinear effects increase, and become significant as ε surpasses about 0.1. In such a case, the nonlinear problem must be solved. Complete details on how to solve such a problem is presented.

Low Resistivity Pay Carbonates: A Practical Approach to Quantify Water Saturation Using a Modified Archie's Model

2021 ◽  
Author(s):  
Ramsin Eyvazzadeh ◽  
Abdullatif Al-Omair ◽  
Majed Kanfar ◽  
Achong Christon
Keyword(s):  
Machine Learning ◽  
Water Saturation ◽  
Pore Space ◽  
Learning Algorithms ◽  
Machine Learning Algorithms ◽  
Theoretical Research ◽  
Low Contrast ◽  
Practical Applications ◽  
Low Resistivity ◽  
New Models

Abstract A detailed description of a modified Archie's equation is proposed to accurately quantify water saturation within low resistivity/low contrast pay carbonates. The majority of previous work on low resistivity/low contrast reservoirs focused on clastics, namely, thin beds and/or clay effects on resistivity measurements. Recent publications have highlighted a "non-Archie" behavior in carbonates with complex pore structures. Several theoretical models were introduced, but new practical applications were not derived to solve this issue. Built upon previous theoretical research in a holistic approach, new models and workflows have been developed. Specifically, utilizing a combination of machine learning algorithms, nuclear magnetic resonance (NMR), core and geological data, field specific calibrated equations to compute water saturation (Sw) in complex carbonate formations are presented. Essentially, these new models partition the porosity into pore spaces and calculate their relative contribution to water saturation in each pore space. These calibrated equations robustly produce results that have proven invaluable in pay identification, well placement, and have greatly enhanced the ability to manage these types of reservoirs. This paper initially explains the theory behind the development of the analysis illustrating workflows and validation techniques used to qualify this methodology. A key benefit performing this research is the utilization of machine-learning algorithms to predict NMR derived values in wells that do not have NMR data. Several examples explore where results of this analysis are compared to dynamic testing, formation testing and laboratory measured samples to validate and demonstrate the utility of this new analysis.

scholarly journals Machine Learning and Cryptographic Algorithms – Analysis and Design in Ransomware and Vulnerabilities Detection

2020 ◽  
Author(s):  
Nandkumar Niture
Keyword(s):  
Machine Learning ◽  
Intelligent System ◽  
Learning Algorithms ◽  
Machine Learning Algorithms ◽  
System Level ◽  
Management Systems ◽  
System Response ◽  
Hard Part ◽  
Analysis And Design ◽  
Password Management

The AI, deep learning and machine learning algorithms are gaining the ground in every application domain of information technology including information security. In formation security domain knows for traditional password management systems, auto-provisioning systems and user information management systems. There is another raising concern on the application and system level security with ransomware. On the existing systems cyber-attacks of Ransomware asking for ransom increasing every day. Ransomware is the class of malware where the goal is to gain the data through encryption mechanism and render back with the ransom. The ransomware attacks are mainly on the vulnerable systems which are exposed to the network with weak security measures. With the help of machine learning algorithms, the pattern of the attacks can be analyzed. Create or discuss a workaround solution of a machine learning model with combination of cryptographic algorithm which will enhance the effectiveness of the system response to the possible attacks. The other part of the problem, which is hard part to create an intelligence for the organizations for preventing the ransomware attacks with the help of intelligent system password management and intelligent account provisioning. In this paper I elaborate on the machine learning algorithms analysis for the intelligent ransomware detection problem, later part of this paper would be design of the algorithm.

Probability Density Methods for Smooth Function Approximation and Learning in Populations of Tuned Spiking Neurons

1998 ◽  
Vol 10 (6) ◽  
pp. 1567-1586 ◽  
Author(s):  
Terence David Sanger
Keyword(s):  
Unsupervised Learning ◽  
Learning Algorithms ◽  
External Input ◽  
Spiking Neurons ◽  
Intermediate Cell ◽  
Continuous Variables ◽  
Neural Firing ◽  
Tuning Curves ◽  
Cell Firing ◽  
Density Methods

This article proposes a new method for interpreting computations performed by populations of spiking neurons. Neural firing is modeled as a rate-modulated random process for which the behavior of a neuron in response to external input can be completely described by its tuning function. I show that under certain conditions, cells with any desired tuning functions can be approximated using only spike coincidence detectors and linear operations on the spike output of existing cells. I show examples of adaptive algorithms based on only spike data that cause the underlying cell-tuning curves to converge according to standard supervised and unsupervised learning algorithms. Unsupervised learning based on principal components analysis leads to independent cell spike trains. These results suggest a duality relationship between the random discrete behavior of spiking cells and the deterministic smooth behavior of their tuning functions. Classical neural network approximation methods and learning algorithms based on continuous variables can thus be implemented within networks of spiking neurons without the need to make numerical estimates of the intermediate cell firing rates.

Nonlinear Mixed Integer-Discrete-Continuous Programming and its Application to Engineering Design Problems

1989 ◽  
Author(s):  
J.-F. Fu ◽  
R. G. Fenton ◽  
W. L. Cleghorn
Keyword(s):  
Nonlinear Programming ◽  
Objective Function ◽  
Engineering Design ◽  
Optimization Algorithm ◽  
Mixed Integer ◽  
Continuous Variables ◽  
Design Problems ◽  
Continuous Programming ◽  
Engineering Design Problems ◽  
Standard Values

Abstract An algorithm for solving nonlinear programming problems containing integer, discrete and continuous variables is presented. Based on a commonly employed optimization algorithm, penalties on integer and/or discrete violations are imposed on the objective function to force the search to converge onto standard values. Examples are included to illustrate the practical use of this algorithm.

Discrete Optimal Design Formulations: Application to Gear Train Design

1992 ◽  
Author(s):  
Leonard P. Pomrehn ◽  
Panos Y. Papalambros
Keyword(s):  
Optimal Design ◽  
Spur Gear ◽  
Gear Train ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Interesting Aspect ◽  
Model Formulation ◽  
Design Models ◽  
Different Types

Abstract The use of discrete variables in optimal design models offers the opportunity to deal rigorously with an expanded variety of design situations, as opposed to using only continuous variables. However, complexity and solution difficulty increase dramatically and model formulation becomes very important. A particular problem arising from the design of a gear train employing four spur gear pairs is introduced and formulated in several different ways. An interesting aspect of the problem is its exhibition of three different types of discreteness. The problem could serve as a test for a variety of optimization or artificial intellegence techniques. The best known solution is included in this article, while its derivation is given in a sequel article.

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