Large Number Of Input Variables Research Articles

Multivariate projection methods applied to flotation columns

On line monitoring and diagnosis systems of process operating performance are becoming important part of industrial programs, leading to improve process operation and therefore product quality over time. In processes, such as flotation, a large number of input variables, highly correlated, are presented. These characteristics usually pose more difficulties in modelling the process for monitoring and diagnosis purposes. Multivariate statistical projection methods have been proposed to effectively deal with these situations. The application of these ideas to a column flotation process is discussed here. In this work, the detection of measurement problems in relevant variables, and the identification of the set of variables responsible for driving the process outside its normal operating region, are demonstrated. Furthermore, the use of these techniques gave considerable information for the correction of the operating problem.

Selective descriptor pruning for QSAR/QSPR studies using artificial neural networks.

Selection of optimal descriptors in quantitative structure-activity-property relationship (QSAR/QSPR) studies has been a perennial problem. Artificial Neural Networks (ANNs) have been used widely in QSAR/QSPR studies but less widely in descriptor selection. The current study used ANNs to select an optimal set of descriptors using large numbers of input variables. The effects of clean, noisy, and random input descriptors with linear, nonlinear, and periodic data on synthetic and real data QSAR/QSPR sets were examined. The optimal set of descriptors could be determined using a signal-to-noise ratio method. The optimal values for the rho parameter, which relates sample size to network architecture, were found to vary with the type of data. ANNs were able to detect meaningful descriptors in the presence of large numbers of random false descriptors.

Fundamentals of Slurry Design for CMP of Metal and Dielectric Materials

AbstractThe formulation of slurries for chemical–mechanical planarization (CMP) is currently considered more of an art than a science, due to the lack of understanding of the wafer, slurry, and pad interactions involved. Several factors, including the large number of input variables for slurries and the synergistic interplay among input variables and output parameters, further complicate our ability to understand CMP phenomena. This article provides a fundamental basis for the choice of chemical additives and particles needed for present-day and next-generation slurry design. The effect of these components on nanoscale and microscale interaction phenomena is investigated. Methodologies are suggested for the development of next-generation slurries required to overcome CMP challenges related to defectivity and the surface topography of soft materials such as Low-κ dielectrics and copper.

High Dimensional Model Representations

In the chemical sciences, many laboratory experiments, environmental and industrial processes, as well as modeling exercises, are characterized by large numbers of input variables. A general objective in such cases is an exploration of the high-dimensional input variable space as thoroughly as possible for its impact on observable system behavior, often with either optimization in mind or simply for achieving a better understanding of the phenomena involved. An important concern when undertaking these explorations is the number of experiments or modeling excursions necessary to effectively learn the system input → output behavior, which is typically a nonlinear relationship. Although simple logic suggests that the number of runs could grow exponentially with the number of input variables, broadscale evidence indicates that the required effort often scales far more comfortably. This paper considers an emerging family of high dimensional model representation concepts and techniques capable of dealing with such input → output problems in a practical fashion. A summary of the state of the subject is presented, along with several illustrations from various areas in the chemical sciences.

Ranking importance of input parameters of neural networks

Artificial neural networks have been used for simulation, modeling, and control purposes in many engineering applications as an alternative to conventional expert systems. Although neural networks usually do not reach the level of performance exhibited by expert systems, they do enjoy a tremendous advantage of very low construction costs. This paper addresses the issue of identifying important input parameters in building a multilayer, backpropagation network for a typical class of engineering problems. These problems are characterized by having a large number of input variables of varying degrees of importance; and identifying the important variables is a common issue since elimination of the unimportant inputs leads to a simplification of the problem and often a more accurate modeling or solution. We compare three different methods for ranking input importance: sensitivity analysis, fuzzy curves, and change of MSE (mean square error); and analyze their effectiveness. Simulation results based on experiments with simple mathematical functions as well as a real engineering problem are reported. Based on the analysis and our experience in building neural networks, we also propose a general methodology for building backpropagation networks for typical engineering applications.

Modelling runoff and sediment transport in catchments using GIS

The application of geographical information systems (GIS) in modelling runoff and erosion in catchments offers considerable potential. Several examples illustrate simple GIS techniques to produce erosion hazard indices or erosion estimates using USLE-type models. Existing erosion models can also be loosely coupled to a GIS, such as the ANSWERS model. Furthermore, models can be fully integrated into a GIS by embedded coupling, such as the LISEM model. However, GIS raster-based erosion models do not necessarily produce better results than much simpler and partly lumped erosion models with ‘representative elements’, although they reproduce topography in more detail. The reasons for the disappointing results of spatial models must be sought in the uncertainty involved in estimating and measuring the large number of input variables at a catchment scale. There is a need for much simpler loosely coupled or embedded GIS erosion models simulating only the dominant processes operating in the catchment. © 1998 John Wiley & Sons, Ltd.

Evolutionary design of a fuzzy knowledge base for a mobile robot

This paper presents a learning method which automatically designs fuzzy logic controllers (FLCs) by means of a genetic algorithm (GA). A messy coding scheme is proposed which allows a compact and flexible representation of the fuzzy rules in the genotype. It reduces the complexity and size of the rule base, through which the GA is able to solve the design task even for FLCs with a large number of input variables. A dynamically weighted objective function is proposed for control problems with multiple conflicting goals, which prevents the GA from premature convergence on FLCs that are specialized exclusively in the easier subtasks. In order to achieve a robust control behavior for a broad spectrum of control states, a second GA coevolves a set of training situations to evaluate the performance of the FLCs. We employed the method to train an FLC which implements a behavior of a mobile robot. The robot obtains the task of reaching an aiming point and avoiding collisions with obstacles on its way. It perceives its environment by means of ultrasonic sensors, which provide the measured distances to objects as input to the FLC. The knowledge base of the FLC is learnt in a simulation based on a simplified model of the sensors and the environment. The adapted control behavior is tested afterwards in real world experiments with the mobile robot.

Genetic algorithms for the optimization of piecewise linear discriminants

The application of genetic algorithms (GAs) to the optimization of piecewise linear discriminants is described. Piecewise linear discriminant analysis (PLDA) is a supervised pattern recognition technique employed in this work for the automated classification of Fourier transform infrared (FTIR) remote sensing data. PLDA employs multiple linear discriminants to approximate a nonlinear separating surface between data categories defined in a vector space. The key to the successful implementation of PLDA is the positioning of the individual discriminants that comprise the piecewise linear discriminant. For the remote sensing application, the discriminant optimization is challenging due to the large number of input variables required and the corresponding tendency for local optima to occur on the response surface of the optimization. In this work, three implementations of GAs are configured and evaluated: a binary-coded GA (GAB), a real-coded GA (GAR), and a Simplex-GA hybrid (SGA). GA configurations are developed by use of experimental design studies, and piecewise linear discriminants for acetone, methanol, and sulfur hexafluoride are optimized (trained). The training and prediction classification results indicate that GAs area viable approach for discriminant optimization. On average, the best piecewise linear discriminant optimized by a GA is observed to classify 11% more analyte-active patterns correctly in prediction than an unoptimized piecewise linear discriminant. Discriminant optimization problems not used in the experimental design study are employed to test the stability of the GA configurations. For these cases, the best piecewise linear discriminant optimized by SGA is shown to classify 19% more analyte-active patterns correctly in prediction than an unoptimized discriminant. These results also demonstrate that the two real number coded GAs (GAR and SGA) perform better than the GAB. Real number coded GAs are also observed to execute faster and are simpler to implement.

DESIGN OF EXPERIMENTS FOR MULTI‐STAGE PROCESSES

Many industrial processes involve large numbers of input variables so that a complete factorial design would require prohibitively many experimental runs. This is particularly the case with multi-stage processes. We offer a view of multi-stage processes, in terms of autoregressive models, which can help in the sensible reduction in the size of experiments and can also allow different stages of the process to be investigated separately.

DESIGN OF EXPERIMENTS FOR MULTI-STAGE PROCESSES

Many industrial processes involve large numbers of input variables so that a complete factorial design would require prohibitively many experimental runs. This is particularly the case with multi-stage processes. We offer a view of multi-stage processes, in terms of autoregressive models, which can help in the sensible reduction in the size of experiments and can also allow different stages of the process to be investigated separately.

Selecting Input Variables for Fuzzy Models

We present an efficient method for selecting important input variables when building a fuzzy model from data. Past methods for input variable selection require generating different models while searching for the optimal combination of variables; our method requires generating only one model that employs all possible input variables. To determine the important variables, premises in the fuzzy rules of this initial model are systematically removed to search for the best simplified model without actually generating any new models. We also present an efficient method for generating the initial model that typically must incorporate a large number of input variables. These methods are illustrated through application to the benchmark Box and Jenkins gas furnace data; the results are compared with those of other fuzzy models found in literature.

Sensitivity and uncertainty analyses for performance assessment modeling

Sensitivity and uncertainty analyses methods for computer models are being applied in performance assessment modeling in the geologic high-level radioactive-waste repository program. The models used in performance assessment tend to be complex physical/chemical models with large numbers of input variables. There are two basic approaches to sensitivity and uncertainty analyses: deterministic and statistical. The deterministic approach to sensitivity analysis involves numerical calculation or employs the adjoint form of a partial differential equation to compute partial derivatives; the uncertainty analysis is based on Taylor series expansions of the input variables propagated through the model to compute means and variances of the output variable. The statistical approach to sensitivity analysis involves a response surface approximation to the model with the sensitivity coefficients calculated from the response surface parameters; the uncertainty analysis is based on simulation. The methods each have strengths and weaknesses.

Representation of Multivalued Functions Using the Direct Cover Method

An efficient method for representing multivalued functions is described. The method employs an algorithm which generates an efficient cover for a given function directly, i.e., without resorting to the intermediate step of creating a table of prime implicants. Data are presented to show that the covers generated are as efficient in terms of cover size as prime implicant based methods. More importantly, however, the direct cover method is shown to require much less computation time than prime implicant based methods, thus making it practical for functions with a large number of input variables and/or as the radix of implementation increases. The algorithm is introduced by applying it to functional representations employing the traditional max and min operation. Next, a modified form of the algorithm is presented for use with the sum and product operators more appropriate to I2L and other current summation technologies.

Small sample sensitivity analysis techniques for computer models.with an application to risk assessment

As modeling efforts expand to a broader spectrum of areas the amount of computer time required to exercise the corresponding computer codes has become quite costly (several hours for a single run is not uncommon). This costly process can be directly tied to the complexity of the modeling and to the large number of input variables (often numbering in the hundreds) Further, the complexity of the modeling (usually involving systems of differential equations) makes the relationships among the input variables not mathematically tractable. In this setting it is desired to perform sensitivity studies of the input-output relationships. Hence, a judicious selection procedure for the choic of values of input variables is required, Latin hypercube sampling has been shown to work well on this type of problem. However, a variety of situations require that decisions and judgments be made in the face of uncertainty. The source of this uncertainty may be lack ul knowledge about probability distributions associated with input variables, or about different hypothesized future conditions, or may be present as a result of different strategies associated with a decision making process In this paper a generalization of Latin hypercube sampling is given that allows these areas to be investigated without making additional computer runs. In particular it is shown how weights associated with Latin hypercube input vectors may be rhangpd to reflect different probability distribution assumptions on key input variables and yet provide: an unbiased estimate of the cumulative distribution function of the output variable. This allows for different distribution assumptions on input variables to be studied without additional computer runs and without fitting a response surface. In addition these same weights can be used in a modified nonparametric Friedman test to compare treatments, Sample size requirements needed to apply the results of the work are also considered. The procedures presented in this paper are illustrated using a model associated with the risk assessment of geologic disposal of radioactive waste.

The application of map-entered variables to the use of multiplexers in the synthesis of logic functions

This paper describes a simple and fast design method for using multiplexers in the synthesis of logic functions. The method relies on the use of map-entered variables, whereby only a single Karnaugh map needs to be drawn for each function. The method is shown to be particularly useful for the implementation of control algorithms, especially those having a large number of input variables.