Active learning for adaptive surrogate model improvement in high-dimensional problems.

This paper investigates a novel approach to efficiently construct and improve surrogate models in problems with high-dimensional input and output. In this approach, the principal components and corresponding features of the high-dimensional output are first identified. For each feature, the active subspace technique is used to identify a corresponding low-dimensional subspace of the input domain; then a surrogate model is built for each feature in its corresponding active subspace. A low-dimensional adaptive learning strategy is proposed to identify training samples to improve the surrogate model. In contrast to existing adaptive learning methods that focus on a scalar output or a small number of outputs, this paper addresses adaptive learning with high-dimensional input and output, with a novel learning function that balances exploration and exploitation, i.e., considering unexplored regions and high-error regions, respectively. The adaptive learning is in terms of the active variables in the low-dimensional space, and the newly added training samples can be easily mapped back to the original space for running the expensive physics model. The proposed method is demonstrated for the numerical simulation of an additive manufacturing part, with a high-dimensional field output quantity of interest (residual stress) in the component that has spatial variability due to the stochastic nature of multiple input variables (including process variables and material properties). Various factors in the adaptive learning process are investigated, including the number of training samples, range and distribution of the adaptive training samples, contributions of various errors, and the importance of exploration versus exploitation in the learning function.

Online monitoring and control of a cyber-physical manufacturing process under uncertainty.

Recent technological advancements in computing, sensing and communication have led to the development of cyber-physical manufacturing processes, where a computing subsystem monitors the manufacturing process performance in real-time by analyzing sensor data and implements the necessary control to improve the product quality. This paper develops a predictive control framework where control actions are implemented after predicting the state of the manufacturing process or product quality at a future time using process models. In a cyber-physical manufacturing process, the product quality predictions may be affected by uncertainty sources from the computing subsystem (resource and communication uncertainty), manufacturing process (input uncertainty, process variability and modeling errors), and sensors (measurement uncertainty). In addition, due to the continuous interactions between the computing subsystem and the manufacturing process, these uncertainty sources may aggregate and compound over time. In some cases, some process parameters needed for model predictions may not be precisely known and may need to be derived from real time sensor data. This paper develops a dynamic Bayesian network approach, which enables the aggregation of multiple uncertainty sources, parameter estimation and robust prediction for online control. As the number of process parameters increase, their estimation using sensor data in real-time can be computationally expensive. To facilitate real-time analysis, variance-based global sensitivity analysis is used for dimension reduction. The proposed methodology of online monitoring and control under uncertainty, and dimension reduction, are illustrated for a cyber-physical turning process.

Fast Surrogate Modeling using Dimensionality Reduction in Model Inputs and Field Output: Application to Additive Manufacturing.

A novel approach to surrogate modeling motivated by recent advancements in parameter dimension reduction is proposed. Specifically, the approach aims to speed-up surrogate modeling for mapping multiple input variables to a field quantity of interest. Computational efficiency is accomplished by first identifying principal components (PC) and corresponding features in the output field data. A map from inputs to each feature is considered, and the active subspace (AS) methodology is used to capture their relationship in a low-dimensional subspace in the input domain. Thus, the PCAS method accomplishes dimension reduction in the input as well as the output. The method is demonstrated on a realistic problem pertaining to variability in residual stress in an additively manufactured component due to the stochastic nature of the process variables and material properties. The resulting surrogate model is exploited for uncertainty propagation, and identification of stress hotspots in the part. Additionally, the surrogate model is used for global sensitivity analysis to quantify relative contributions of the uncertain inputs to stress variability. Our findings based on the considered application are indicative of enormous potential for computational gains in such analyses, especially in generating training data, and enabling advancements in control and optimization of additive manufacturing processes.

Optimization of fused filament fabrication process parameters under uncertainty to maximize part geometry accuracy.

This work presents a novel process design optimization framework for additive manufacturing (AM) by integrating physics-informed computational simulation models with experimental observations. The proposed framework is implemented to optimize the process parameters such as extrusion temperature, extrusion velocity, and layer thickness in the fused filament fabrication (FFF) AM process, in order to reduce the variability in the geometry of the manufactured part. A coupled thermo-mechanical model is first developed to simulate the FFF process. The temperature history obtained from the heat transfer analysis is then used as input for the mechanical deformation analysis to predict the dimensional inaccuracy of the additively manufactured part. The simulation model is then corrected based on experimental observations through Bayesian calibration of the model discrepancy to make it more accurately represent the actual manufacturing process. Based on the corrected prediction model, a robustness-based design optimization problem is formulated to optimize the process parameters, while accounting for multiple sources of uncertainty in the manufacturing process, process models, and measurements. Physical experiments are conducted to verify the effectiveness of the proposed optimization framework.

Network Reconfiguration for Increasing Transportation System Resilience Under Extreme Events.

Evacuating residents out of affected areas is an important strategy for mitigating the impact of natural disasters. However, the resulting abrupt increase in the travel demand during evacuation causes severe congestions across the transportation system, which thereby interrupts other commuters' regular activities. In this article, a bilevel mathematical optimization model is formulated to address this issue, and our research objective is to maximize the transportation system resilience and restore its performance through two network reconfiguration schemes: contraflow (also referred to as lane reversal) and crossing elimination at intersections. Mathematical models are developed to represent the two reconfiguration schemes and characterize the interactions between traffic operators and passengers. Specifically, traffic operators act as leaders to determine the optimal system reconfiguration to minimize the total travel time for all the users (both evacuees and regular commuters), while passengers act as followers by freely choosing the path with the minimum travel time, which eventually converges to a user equilibrium state. For each given network reconfiguration, the lower-level problem is formulated as a traffic assignment problem (TAP) where each user tries to minimize his/her own travel time. To tackle the lower-level optimization problem, a gradient projection method is leveraged to shift the flow from other nonshortest paths to the shortest path between each origin-destination pair, eventually converging to the user equilibrium traffic assignment. The upper-level problem is formulated as a constrained discrete optimization problem, and a probabilistic solution discovery algorithm is used to obtain the near-optimal solution. Two numerical examples are used to demonstrate the effectiveness of the proposed method in restoring the traffic system performance.

A Bio-Inspired Approach to Traffic Network Equilibrium Assignment Problem.

Finding an equilibrium state of the traffic assignment plays a significant role in the design of transportation networks. We adapt the path finding mathematical model of slime mold Physarum polycephalum to solve the traffic equilibrium assignment problem. We make three contributions in this paper. First, we propose a generalized Physarum model to solve the shortest path problem in directed and asymmetric graphs. Second, we extend it further to resolve the network design problem with multiple source nodes and sink nodes. At last, we demonstrate that the Physarum solver converges to the user-optimized (Wardrop) equilibrium by dynamically updating the costs of links in the network. In addition, convergence of the developed algorithm is proved. Numerical examples are used to demonstrate the efficiency of the proposed algorithm. The superiority of the proposed algorithm is demonstrated in comparison with several other algorithms, including the Frank-Wolfe algorithm, conjugate Frank-Wolfe algorithm, biconjugate Frank-Wolfe algorithm, and gradient projection algorithm.

Predictive Model Markup Language (PMML) Representation of Bayesian Networks: An Application in Manufacturing.

Bayesian networks (BNs) represent a promising approach for the aggregation of multiple uncertainty sources in manufacturing networks and other engineering systems for the purposes of uncertainty quantification, risk analysis, and quality control. A standardized representation for BN models will aid in their communication and exchange across the web. This paper presents an extension to the Predictive Model Markup Language (PMML) standard, for the representation of a BN, which may consist of discrete variables, continuous variables, or their combination. The PMML standard is based on Extensible Markup Language (XML) and used for the representation of analytical models. The BN PMML representation is available in PMML v4.3 released by the Data Mining Group. We demonstrate the conversion of analytical models into the BN PMML representation, and the PMML representation of such models into analytical models, through a Python parser. The BNs obtained after parsing PMML representation can then be used to perform Bayesian inference. Finally, we illustrate the developed BN PMML schema for a welding process.

PhysarumSpreader: A New Bio-Inspired Methodology for Identifying Influential Spreaders in Complex Networks.

Identifying influential spreaders in networks, which contributes to optimizing the use of available resources and efficient spreading of information, is of great theoretical significance and practical value. A random-walk-based algorithm LeaderRank has been shown as an effective and efficient method in recognizing leaders in social network, which even outperforms the well-known PageRank method. As LeaderRank is initially developed for binary directed networks, further extensions should be studied in weighted networks. In this paper, a generalized algorithm PhysarumSpreader is proposed by combining LeaderRank with a positive feedback mechanism inspired from an amoeboid organism called Physarum Polycephalum. By taking edge weights into consideration and adding the positive feedback mechanism, PhysarumSpreader is applicable in both directed and undirected networks with weights. By taking two real networks for examples, the effectiveness of the proposed method is demonstrated by comparing with other standard centrality measures.

A biologically inspired network design model.

A network design problem is to select a subset of links in a transport network that satisfy passengers or cargo transportation demands while minimizing the overall costs of the transportation. We propose a mathematical model of the foraging behaviour of slime mould P. polycephalum to solve the network design problem and construct optimal transport networks. In our algorithm, a traffic flow between any two cities is estimated using a gravity model. The flow is imitated by the model of the slime mould. The algorithm model converges to a steady state, which represents a solution of the problem. We validate our approach on examples of major transport networks in Mexico and China. By comparing networks developed in our approach with the man-made highways, networks developed by the slime mould, and a cellular automata model inspired by slime mould, we demonstrate the flexibility and efficiency of our approach.

Dependence Assessment in Human Reliability Analysis Using Evidence Theory and AHP.

Dependence assessment among human errors in human reliability analysis (HRA) is an important issue. Many of the dependence assessment methods in HRA rely heavily on the expert's opinion, thus are subjective and may sometimes cause inconsistency. In this article, we propose a computational model based on the Dempster-Shafer evidence theory (DSET) and the analytic hierarchy process (AHP) method to handle dependence in HRA. First, dependence influencing factors among human tasks are identified and the weights of the factors are determined by experts using the AHP method. Second, judgment on each factor is given by the analyst referring to anchors and linguistic labels. Third, the judgments are represented as basic belief assignments (BBAs) and are integrated into a fused BBA by weighted average combination in DSET. Finally, the CHEP is calculated based on the fused BBA. The proposed model can deal with ambiguity and the degree of confidence in the judgments, and is able to reduce the subjectivity and improve the consistency in the evaluation process.

A belief-based evolutionarily stable strategy.

As an equilibrium refinement of the Nash equilibrium, evolutionarily stable strategy (ESS) is a key concept in evolutionary game theory and has attracted growing interest. An ESS can be either a pure strategy or a mixed strategy. Even though the randomness is allowed in mixed strategy, the selection probability of pure strategy in a mixed strategy may fluctuate due to the impact of many factors. The fluctuation can lead to more uncertainty. In this paper, such uncertainty involved in mixed strategy has been further taken into consideration: a belief strategy is proposed in terms of Dempster-Shafer evidence theory. Furthermore, based on the proposed belief strategy, a belief-based ESS has been developed. The belief strategy and belief-based ESS can reduce to the mixed strategy and mixed ESS, which provide more realistic and powerful tools to describe interactions among agents.

An improved Physarum polycephalum algorithm for the shortest path problem.

Shortest path is among classical problems of computer science. The problems are solved by hundreds of algorithms, silicon computing architectures and novel substrate, unconventional, computing devices. Acellular slime mould P. polycephalum is originally famous as a computing biological substrate due to its alleged ability to approximate shortest path from its inoculation site to a source of nutrients. Several algorithms were designed based on properties of the slime mould. Many of the Physarum-inspired algorithms suffer from a low converge speed. To accelerate the search of a solution and reduce a number of iterations we combined an original model of Physarum-inspired path solver with a new a parameter, called energy. We undertook a series of computational experiments on approximating shortest paths in networks with different topologies, and number of nodes varying from 15 to 2000. We found that the improved Physarum algorithm matches well with existing Physarum-inspired approaches yet outperforms them in number of iterations executed and a total running time. We also compare our algorithm with other existing algorithms, including the ant colony optimization algorithm and Dijkstra algorithm.

Box-covering algorithm for fractal dimension of weighted networks.

Box-covering algorithm is a widely used method to measure the fractal dimension of complex networks. Existing researches mainly deal with the fractal dimension of unweighted networks. Here, the classical box covering algorithm is modified to deal with the fractal dimension of weighted networks. Box size length is obtained by accumulating the distance between two nodes connected directly and graph-coloring algorithm is based on the node strength. The proposed method is applied to calculate the fractal dimensions of the "Sierpinski" weighted fractal networks, the E.coli network, the Scientific collaboration network, the C.elegans network and the USAir97 network. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks. We find that the fractal property is influenced by the edge-weight in weighted networks. The possible variation of fractal dimension due to changes in edge-weights of weighted networks is also discussed.

Hyper-competition, collusion, free riding or coopetition: basins of attraction when firms simultaneously compete and cooperate.

Using a dyad in a homogeneous market, facing investment decisions, we investigate simultaneous competition and cooperation behavior of firms under the effects of (a) government policies that send signals regarding incentives for different levels of competition and cooperation and (b) two different 'states of nature' for the market, i.e., one that rewards firms for building on their existing strategic path and another that rewards firms for exploring new strategies. We conceptualize the dyad and the external environment as a complex adaptive system and formulate simultaneous competition and cooperation as a dynamic duopoly game with variable demand and supply curves. Employing a simulation-based methodology, we investigate the attractors of this two-firm system. We find that in markets that reward firms for building on their existing strategic path, coopetition (sustained simultaneous competition and cooperation) is a common attractor and the system is not affected by imbalances in governmental policies. On the other hand, in markets that reward firms for exploring new strategy, competition is rare; rather, the system frequently exhibits hyper-coopetition, collusion or freeridership. Additionally, we find that the market share of firms as well as a firm's initial disposition toward competition and cooperation are important factors that affect the outcome.