Research Projects
Adaptive Methods for Coordinate Metrology Using Support Vectors
The larger objective of this Sensors and Sensors Networks (Sensors) research project is to develop sturdy, consistent and adaptive methods for sensing in manufacturing. Within this framework, the focus of primary research is in prudent and yet accurate feature verification using coordinate measuring machines. The processing of parts results in surface errors that will be quantified using process physics prior to feature verification. Sensing will be guided by the geometry of the part and these prior process models. Support Vector Machine (SVM) represents a new type of learning machine based on statistical learning theory. Methodologies based on the SVMs and learning theory will be applied to integrate sampling and zone determination in part verification. Research will focus efforts on developing and evaluating search methods for sample reduction using SVM, and on quantifying errors generated during processing. Methodologies for non-linear forms and profile metrology will follow. Extensions will be investigated for full-part metrology and Reverse Engineering (RE). Suitability of proposed sensing concepts to surface metrology and tribology will also be investigated. Research will be deployed to classrooms and computer modules prepared for wider dissemination. The success of this research for an adaptive procedure will lend itself for use to a wider domain of sensing, but the principal focus for this research is in coordinate metrology for part verification. Successful application will improve product and process designs and interchangeability. New generation software for coordinate metrology incorporating learning will also result. This research will lead to metrology standards as well as present improved solutions to the inspection enterprise. The two principal concepts embedded in this project are knowledge-based sensing and mathematical search. These concepts can be extended to other manufacturing sensing applications. Introduction of SVMs to manufacturing is also expected to lead to other applications. Significant potential exists in education and training in each area of manufacturing, metrology, and operations research/data mining.
A Real Time Mining of Integrated Weather Data
The mission of our multidisciplinary group is to build systems and develop theory for extracting information and identifying patterns that are useful for making decisions in real time. In the context of this project, real-time signifies analysis of a stream of data so that the results of the processing can be distributed in time for critical decisions to be made even as more data are streaming in. Initial research will support real- time weather analysis and forecasting; in the future, we anticipate applying emerging techniques to data rich environments in other disciplines. Over the past few years, the volume of data available for weather forecasts has increased greatly. However, the techniques that are being used to process the data and provide useful information to the public and to forecasters have not kept pace. We at the Oklahoma Weather Center (OWC), for example, have data streaming in from nine different Doppler weather radars, a phased array radar, an extensive Mesonet, two GOES satellites, a micronetwork of rainfall observations around a research polarimetric radar, a 3D lightning mapper, and Terminal Doppler Weather Radar data. We have been working with researchers from Georgia Tech on a NSF-funded project to integrate these various data feeds in a four-dimensional display system. The results underscore the importance of algorithms that process multiple sensor data. The algorithms and techniques that are currently used to process the data are based on a single data source, with no integration of the information from various data sources. The OWC is unique in this abundance of weather data sources; however, experience gained in this project and software developed will be transferable to states such as Georgia and Mississippi which require analysis of multiple radars, mesonet stations, and satellites. As the CRAFT project makes real-time access to base data from multiple radars possible for much of the country, the benefits of automated algorithms that process data from multiple sensors will become more widespread.
In this proposal, we request funding to build pattern recognition techniques that will exploit multi-sensor data in an integrated manner to provide information such as the presence or absence of tornadoes, supercells and mesocyclones; estimate precipitation; predict the occurrence of flash floods; assimilate and display large volumes of multi-sensor data and trigger the archive of selected data sets. We propose to accomplish these tasks by customizing and developing techniques for real-time data mining. Our approaches will include traditional data reduction methods such as PCA and clustering; Procrustes analysis; Kalman filters and non-linear time series analysis with regime switching; and, decomposition and robust optimization methods for training support vector machines.
Globally Optimal Neural Computing: Algorithms and Applications
In collaboration with Dr. Sahinidis, University of Illinois.
The application of neural networks to all aspects of technology has escalated recently as engineers and scientists have widely embraced neural computing in their quest for deeper understanding of complex phenomena and systems. Finding the best possible neural network for a particular application requires choosing the network parameters in a way that minimizes learning errors. Even for simple learning problems, the error function possesses a large number of local minima (isolated valleys). Despite the enormous amount of attention devoted to neural networks, there is currently no efficient method that can identify with certainty the global minimum of the error function. Current approaches, such as back-propagation and stochastic search methods, may get trapped at local minima corresponding to large learning errors and suboptimal neural networks. This may lead to incorrect inferences and devastate decision makers. To overcome the multiple minima difficulty in machine learning, this project will develop efficient global optimization algorithms for neural computing. The algorithms are based on the branch and bound principle and incorporate a number of bounding techniques which provide sharp lower and upper bounds. The main feature of the proposed algorithms is that they can approximate the global minimum arbitrarily well in a finite number of iterations.
Preliminary computations with many benchmark machine learning problems demonstrate that the proposed techniques identify neural networks that are more accurate than those in the open literature. More important, our solutions have simpler network structures leading to neural networks that are easier to interpret and faster to simulate.
The research deals with:
- development of guaranteed global optimization algorithms for neural network training, topology design, and optimization;
- development of novel machine learning algorithms that scale well with problem size;
- development of systematic approaches to avoid over-training and generate networks that are robust to uncertainty in the training data;
- development of an approach to choose kernel parameters for support vector machines;
- application of the proposed algorithms to a broad set of challenging data mining problems.
Globally optimal neural computing holds the promise of an enabling technology that could significantly improve learning in many diverse application domains. The results of the proposed research will be implemented in our widely distributed global optimization software package and will be made available to the research community.
Robust and Interior Point Optimization Methods in Support Vector Machine Training
This research investigates new algorithms for training Support Vector Machines based on Interior Point Methods (IPMs). Training a Support Vector Machine (SVM) requires the solution of a very large quadratic programming (QP) optimization problem. Our objective is to handle very large training sets for analyzing massive data. We use Benders decomposition and column generation techniques. We also investigate a robust convex optimization approach to uncertainty with applications to SVM learning with noisy data. This approach deals with a “decision environment” which is characterized by crude knowledge of the uncertainty: all that is known about the uncertain data vector v is that it belongs to a given uncertainty set U. We show that in the case that the set U is an ellipsoid the SVM learning is equivalent to a convex quadratic optimization problem with conic quadratic constraints. The proposed project is multidisciplinary, integrating state of the art techniques of mathematical programming and machine learning to solve large scale data mining problems with applications to meteorology, seismology, high energy physics, astronomy, finance and credit card fraud. It will have a significant effect on infrastructure of science and engineering since it presents a new approach for training large scale SVMs.