# An ANN Model for Predicting the Compressive Strength of Concrete
## 1 Introduction  
Due to the high compressive strength and the capability of being casted into any shape and size, concrete is the most used construction material in the world. The compressive strength is related to the proportioning of its ingredients, such as water, cement, coarse aggregates, sand, and other admixtures. How to predict the compressive strength according to the proportioning design is a very practical topic. For example, with a prediction model one can estimate the compressive strengths of dozens of mix designs and just choose those that achieve the required strength for further physical tests. This can reduce the number of trials for a specific compressive strength requirement and can save a lot of money and time. Furthermore, one can determine the most inexpensive choice among those that required compressive strength for economical consideration. Conventionally, statistics are a useful tool for evaluating the results of strength tests. For instance, one can obtain a regression equation using data of water-cement ratio versus the compressive strengths [1]. However, there are not just one or two factors that affect compressive strength. The predicted results by just using the water-cement ratio could be very poor in many cases. In recent decades, the artificial neural networks (ANNs) have drawn more and more attention because of the capability of dealing with multivariable analysis. Several authors have used the ANNs to determine the compressive strength of concrete [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. An ANN is like a black box. After training the ANN, one can input several numerical values and the ANN will prompt another numerical value which represents the predicted compressive strength of the concrete. The components for the input can be factors such as the proportioning of water, cement, sand, etc. Recently, more and more new types of ANN structures, such as the Support Vector Machines [17; 18], Deep Learning Neural Network [19; 20; 21; 22; 23], Radial Basis Function Network [24; 25; 26; 27; 28; 29] for various research areas have popped out, as wellas other algorithms like tabu and genetic [15; 19; 26; 28; 29; 30] are newly applied for training the ANN. In [16], data of real concrete mix proportioning listed in [12] were used to establish a database. With that database, the ANN of back-propagation type (BP) with single hidden layer was employed to establish the prediction models of strength and slump of concrete. Cylindrical test samples of 12 additional mix designs were also casted and their compressive strengths were examined in the laboratory to verify the established ANN model. In this study, we use the same database for establishing our new ANN model. However, we think data for establishing a concrete slump prediction model are insufficient due to 39% of slump records being missing from the database. Therefore, we just focus on establishing a prediction model for the compressive strength of concrete in this study. Typically, the database has to be divided into two parts, one for training and the other for testing. This is for the sake of avoiding over-training and over-fitting. In [16], most of the data were used for training the ANN while only 20 pieces of data were used in the testing process. There are 482 pieces of data in the database, so data for testing were about 4% of the whole. In our opinion, that is inadequate, though the results of verification were still acceptable. Consequently, we contrive an improvement by using fewer data for training and more data for testing, for the reason that the over-fitting can be alleviated. There are so many choices for establishing the ANN model but for comparison with [16], we still use the BP-ANN with single hidden layer. The final result of the synaptic weights and the thresholds in the ANN are all listed in this paper. Therefore, anyone can use them accompanied with the formulae expressed in the article to predict the concrete compressive strength according to the mix proportioning on his/her own.