P1: GCR Natural Resources Research (NRR)
pp873-narr-466261
June 12, 2003
10:19
Style file version Nov. 07, 2000
C 2003) Natural Resources Research, Vol. 12, No. 2, June 2003 (°
Use of a Probabilistic Neural Network to Reduce Costs of Selecting Construction Rock Donald A. Singer1 and James D. Bliss2 Received 14 November 2002; accepted 6 December 2002
Rocks used as construction aggregate in temperate climates deteriorate to differing degrees because of repeated freezing and thawing. The magnitude of the deterioration depends on the rock’s properties. Aggregate, including crushed carbonate rock, is required to have minimum geotechnical qualities before it can be used in asphalt and concrete. In order to reduce chances of premature and expensive repairs, extensive freeze-thaw tests are conducted on potential construction rocks. These tests typically involve 300 freeze-thaw cycles and can take four to five months to complete. Less time consuming tests that (1) predict durability as well as the extended freeze-thaw test or that (2) reduce the number of rocks subject to the extended test, could save considerable amounts of money. Here we use a probabilistic neural network to try and predict durability as determined by the freeze-thaw test using four rock properties measured on 843 limestone samples from the Kansas Department of Transportation. Modified freeze-thaw tests and less time consuming specific gravity (dry), specific gravity (saturated), and modified absorption tests were conducted on each sample. Durability factors of 95 or more as determined from the extensive freeze-thaw tests are viewed as acceptable—rocks with values below 95 are rejected. If only the modified freeze-thaw test is used to predict which rocks are acceptable, about 45% are misclassified. When 421 randomly selected samples and all four standardized and scaled variables were used to train a probabilistic neural network, the rate of misclassification of 422 independent validation samples dropped to 28%. The network was trained so that each class (group) and each variable had its own coefficient (sigma). In an attempt to reduce errors further, an additional class was added to the training data to predict durability values greater than 84 and less than 98, resulting in only 11% of the samples misclassified. About 43% of the test data was classed by the neural net into the middle group— these rocks should be subject to full freeze-thaw tests. Thus, use of the probabilistic neural network would mean that the extended test would only need be applied to 43% of the samples, and 11% of the rocks classed as acceptable would fail early. KEY WORDS: Probabilistic neural network; classification; aggregate; industrial minerals.
INTRODUCTION
(i.e., limestone, dolostone), is required to have minimum geotechnical qualities before it can be used in asphalt and concrete construction. The best aggregate is strong, chemically inert, and readily adheres to the bonding paste, whether it is asphalt or Portland cement. Geotechnical qualities are measures of the chemical and physical properties of aggregate samples determined in the laboratory. The laboratory test results are believed to result in reasonable approximations of how the aggregate is likely to behave during use. Specific gravity, absorption, and freeze-thaw
Carbonate rocks have been the most important bedrock sources of crushed aggregate in the USA accounting for about 70% of total production (Langer and Glanzman, 1993). Aggregate, including that which is created from crushing carbonate rocks 1
U.S. Geological Survey, 345 Middlefield Road, Menlo Park, California 94025, USA. email:
[email protected] 2 U.S. Geological Survey, Tucson, Ariz.
135 C 2003 International Association for Mathematical Geology 1520-7439/03/0600-0135/1 °
P1: GCR Natural Resources Research (NRR)
pp873-narr-466261
June 12, 2003
10:19
136 (Marek, 1991) are examples of geotechnical qualities that may be considered. Performance of aggregate over the life of the structure in which it is used is important because aggregate typically comprises well over 90% of the volume of asphalt and concrete. In temperate climates susceptibility of roads and buildings to frost action is a critical concern. A standardized test of the durability of aggregate subject to frost action takes between three and five months to conduct on each sample. The long time for each test indicates that the testing procedure is expensive—a less time consuming way to predict the results of the durability test could save substantial amounts of money. In a previous study to address this problem, a feedforward neural network was used by Najjar and Basheer (1997) to try to predict the results of the durability and percent expansion tests with five basic physical properties of aggregate. They opted to use a neural network because linear statistical methods seemed to be inadequate to explain the variation and interdependence of the variables. In their evaluation of predicting durability with the neural network, about 63% of the test samples were correctly classified. Although better than linear statistical methods, these results were not compelling enough to consistently apply by the Kansas Department of Transportation (KDOT). The results however, are used as a limited screen on production samples (Rodney Montney, written comm, 1 November 2002). The results suggest that some form of neural network might be able to reduce the costs of testing aggregate by basing the classification on other testing (Bliss, 1999; Bliss and Singer, 2001). Here we examine if probabilistic neural networks, which are designed for classification, can be trained with four less time consuming measurements to classify aggregate into samples that pass the durability test and those that do not. We do not consider expansion, the other KDOT requirement for acceptance. First, we provide a short description of probabilistic neural networks, followed by information about the samples and variables used. Finally, the results of several tests are presented and discussed.
PROBABILISTIC NEURAL NETWORK The goal here is to be able to make an estimate of the probability that an unknown rock will pass the durability test. Standard statistical classification meth-
Style file version Nov. 07, 2000
Singer and Bliss ods assume some knowledge of the distributions of the variables used to classify. Typically a multivariate normal distribution is assumed and the training data are used to estimate the means and variances. Large deviations from normality or multimodal distributions cause these methods to fail. Neural networks can typically handle complex distributions and are not adversely affected by correlated variables. Probabilistic neural networks were designed to be classifiers (Specht, 1990). In the present study, the algorithms for a probabilistic neural network developed by Masters (1995) were employed. Masters’ algorithms find the scale weights, σ , that minimize the error of misclassification of the training data using the standard statistical technique termed jackknifing, in which every case is sequentially held back from training. Details about the algorithm used and probabilistic neural networks in general is given in Masters (1993, 1995). Probabilistic neural networks require no assumptions about distributions of random variables used to classify; they even can handle multimodal distributions. They train quickly and as well as, or better than, multiple-layer feedforward networks. They have the ability to provide mathematically sound confidence levels and are relatively insensitive to outliers. Mathematically sound Bayesian confidence levels require that the classes are mutually exclusive and exhaustive (i.e., no situation can possibly fall into more than one population and the training set encompasses all populations fairly). When these conditions exist, Bayes’ Theorem can be used to compute the probability that an observation is the member of a population. Each density estimate could be multiplied by prior probabilities and cost constants, if desired. These features are not used in this study, however. In many practical situations, the mutually exclusive and exhaustive class conditions might not exist. The unknown sample used in testing might be from a population different from any of the training classes. In this study, this should not be a problem because we only have pass and fail durability classes. The neural network program will estimate the probabilities that the unknown rock belongs to the classes it has been taught; thus, careless use of a neural network could lead to mistaken classifications. The success of probabilistic neural networks depends on determining weight functions (scale factors), σ , that minimize misclassification errors of training data. For this reason, it is critical that the data used to train the neural network be representative of the data in the neural network application.
P1: GCR Natural Resources Research (NRR)
pp873-narr-466261
June 12, 2003
10:19
Style file version Nov. 07, 2000
Use of a Probabilistic Neural Network to Reduce Costs of Selecting Construction Rock THE DATA Laboratory tests on aggregate for concrete are conducted because the tests are significantly less expensive than trial and error of observing highway or building failures. The test results are believed to be reasonable approximations of how aggregate is likely to behave during use in the field. Where concrete is exposed to freezing and thawing a durability test is commonly used. Durability is measured by preparing a concrete beam containing the aggregate, curing it for up to 90 days, and repeatedly freezing and thawing the beam for 300 cycles. After the 300 cycles, which take a total of a little more than four months including the curing time, the beam’s durability is calculated from physical measurements. A modified freeze-thaw test, which takes about two weeks, is run on aggregate only and is stopped after 25 freeze and thaw cycles. Other laboratory tests of the aggregate that might be useful in predicting durability are specific gravity (dry), specific gravity (saturated), acid insoluble residue, and absorption. Using 843 limestone samples, we try to predict durability as estimated by the 300-cycle freezethaw test using these rock properties measured by the Kansas Department of Transportation. The modified freeze-thaw test, and less time consuming specific gravity (dry), specific gravity (saturated), acid insoluble residue, and modified absorption tests were conducted on each sample. Durability factors of 95 or more as determined from the extensive freeze-thaw test are viewed as acceptable—rocks with values below 95 are rejected. A plot of modified freeze-thaw results versus durability for all 843 samples shows how well the modified test used alone can be used to predict the durability results (Fig. 1). It is instructive to examine histograms of the modified freeze-thaw samples that pass the durability test and those that do not (Fig. 2). Clearly there is considerable overlap in the two histograms demonstrating that the modified test is not a robust predictor of the final durability results when used alone. If only the modified freeze-thaw test is used to predict which rocks are acceptable (Table 1), about 45% are misclassified. The numbers of modified freeze-thaw samples in agreement with the durability test results are in the diagonal elements and the number in disagreement in off-diagonal elements. Each of the variables was transformed by taking its logarithm to reduce the effects of skewness. Because some of the variables were negatively skewed, specific gravity dry and specific gravity saturated were
137
Table 1. Number of Samples Classed Into Those That Pass the Durability Test (≥95) and Those That Do Not Based on the Modified Freeze-Thaw Test Value ≥0.95 Predicted class
Known class
