Modeling of Flexural Strength of Fiber Reinforced Concretes Containing Silica Fume or Fly Ash by GEP

In this paper, a mathematical equation based on the gene expression programming (GEP) model has been developed to predict the flexural strength (ffs) of steel fiber reinforced concretes (SFRCs) containing silica fume (SF) or fly ash (FA). In order to obtain a mathematical equation of this model, the training, testing and validation sets using the experimental results for 175 specimens produced with 118 different mixtures were gathered from different literatures. The data used in the input variables of GEP model are arranged in a format of eleven input parameters that cover the age of specimen, the amounts of concrete mixtures and the properties of steel fibers. According to these input parameters, the ffs values of SFRCs were predicted in the GEP model. The training, testing and validation results in the model have shown that the model has strong potential to predict the ffs values of SFRCs containing SF or FA

Estimación de propiedades mecánicas de roca utilizando inteligencia artificial

This paper discusses how two artificial intelligence techniques were combined, neural networks and genetic algorithms for the development of a computational tool used for the estimation of mechanical properties such as tensile strength, uniaxial compressive strength and triaxial compressive strength in sandstones, from petrophysical properties using data from tests of Rock Mechanics Laboratory of the Colombian Petroleum Institute - Ecopetrol SA as training data, to improve the design of non-destructive testing with some degree of confidence and resulting in cost reduction.PACS: 91.60.Ba, 91.60.DcMSC: 82C32Este artículo presenta la forma como fueron combinadas dos técnicas de inteligencia artificial, redes neuronales y algoritmos genéticos, para el desarrollo de una herramienta computacional utilizada para la estimación de propiedades mecánicas tales como la resistencia a la tensión, la resistencia a la compresión uniaxial y la resistencia a la compresión triaxial en areniscas, a partir de propiedades petrofísicas utilizando datos de pruebas del Laboratorio de Mecánica de Rocas del Instituto Colombiano del Petróleo - Ecopetrol S.A. como datos de entrenamiento facilitando el diseño de ensayos no destructivos con cierto grado de confianza y dando lugar a una reducción de costos.PACS: 91.60.Ba, 91.60.DcMSC: 82C3

Geotechnical Properties Of the Travis Peak (Hosston) Formation in East Texas: A Compressive and Tensile Strength Analysis using Regression Analysis.

The estimation of rock mass strength is a key parameter in geotechnical engineering which is used in the design of geotechnical structures like tunnels, dams and slopes. Geotechnical engineering is the branch of civil engineering which works on the principles of soil and rock mechanics to evaluate subsurface conditions, stability of slopes, foundations of structures and construction of earthworks. The main focus of this study was to calculate the strength of Lower Cretaceous Travis Peak Formation rocks of East Texas and to check the accuracy by comparing it with Regression analysis. The parameters which were used were the Uniaxial Compression Test (UCS) and tensile strength. Core samples were collected at Stephen F. Austin State University Core Lab Repository. Strength tests were conducted at the lab facilities of University of Houston. Parameters such as load for UCS and tensile strength were experimentally determined using procedures outlined by the International Society of Rock Mechanics (ISRM, Rock characterization testing and monitoring, 1981). In this study, a linear regression analysis was also performed to predict and compare the strength values of the core rock samples from the Travis Peak Formation. Based on previous studies, it was shown that regression analysis is accurate in providing the strength of rocks. The results obtained from the tests are useful in predicting the strength of rocks from the Travis Peak Formation. Uniaxial compression and tensile strength tests were performed for 12 samples at the Department of Civil Engineering’s Laboratory at the University of Houston. Before the tests, the samples were cut before into the size of 7.2 to 3.6 in ratio of length to diameter to maintain a 2:1 ratio. The average value of UCS for the 12 samples was 27.43 MPa. Similarly, the average value for tensile strength for 12 samples was 4.05 MPa. Based on the values which were calculated, these samples were classified as medium strength rocks which belongs to Class D. Linear Regression analysis was performed using MATLAB software for predicting the strength of core rock samples. The equation for linear regression was in the form of , where y is the tensile strength and x is UCS. The root mean square generated for regression analysis was 0.6378

Quantifying of impact breakage of cylindrical rock particles on an impact load cell

The detailed understanding of rock impact breakage represents a key challenge in the development of comminution models. Semi-empirical properties have been used to describe ore competencies, such as the JK breakage index t10 and Axb values, but are not able to estimate mechanical properties linked with particle fracture. The information derived from particle breakage testing on impact load cells devices, have the potential estimates such mechanical properties. However, the large intrinsic natural variability of rocks and ores composition and shape makes the results difficult to analyze and difficult to compare against each other for particles with similar properties. This study investigates the effect of rock shape on the variability of the impact breakage test conducted on impact load cells. The test methodology was modified to account for shape when testing regular shape samples such as drilled mini-cores, with objective of reducing the intrinsic variability caused by rock shape, using a controlled shaped sample. The promising results open new avenues for establishing relationships between rock composition, texture and mechanical properties

Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensors

In this study we put forth a modular approach for distilling hidden flow physics in discrete and sparse observations. To address functional expressiblity, a key limitation of the black-box machine learning methods, we have exploited the use of symbolic regression as a principle for identifying relations and operators that are related to the underlying processes. This approach combines evolutionary computation with feature engineering to provide a tool to discover hidden parameterizations embedded in the trajectory of fluid flows in the Eulerian frame of reference. Our approach in this study mainly involves gene expression programming (GEP) and sequential threshold ridge regression (STRidge) algorithms. We demonstrate our results in three different applications: (i) equation discovery, (ii) truncation error analysis, and (iii) hidden physics discovery, for which we include both predicting unknown source terms from a set of sparse observations and discovering subgrid scale closure models. We illustrate that both GEP and STRidge algorithms are able to distill the Smagorinsky model from an array of tailored features in solving the Kraichnan turbulence problem. Our results demonstrate the huge potential of these techniques in complex physics problems, and reveal the importance of feature selection and feature engineering in model discovery approaches

Modeling Asphalt Pavement Overlay Transverse Cracks and High Performance Concrete Using Levenberg-Marquardt Genetic Operation Tree

為實驗數據建立模型一般是使用類神經演算法與非線性迴歸，然而類神經演算法被批評是一種黑盒子，無法提供研究者了解變數之間明確的關係及物理意義。而非線性迴歸則是需要研究者預先決定正確的方程式結構方能調整係數以達 RMSE( Root of Mean Square Error )誤差最小值，可惜的是，一組明確可定義的方程式不容易預先猜測。為解決這些難處，近期研究採用基因運算樹( Genetic Operation Tree; GOT )自動擬定方程式結構，然其過低的係數搜尋效率致使在染色體迭代過程中，往往把『差係數值配好方程式結構』的可行解淘汰，並導向以更多運算子、運算元去磨合實驗數據，其成果是公式冗長且 RMSE 較大。本研究提出一創新技術，結合二種最佳化方法： Levenberg-Marquardt 演算法與 GOT ，我們稱之 LMGOT 。 GOT 用基因演算法求解離散問題，以找尋較佳的運算樹結構。一株運算樹結構可代表一組方程式，同時再利用 LM 方法求解出方程式係數的最佳值，有了係數值後，實驗數據代入方程式所得到的預估值可與實驗真值相較，其 RMSE 誤差值就是 GOT 的適存值，結合 GOT 的迭代技巧，可逐代逼近最佳的運算樹結構。本研究將 LMGOT 方法應用在美國德州交通部收集十五年的路面服務性能實驗數據及兩種不同實驗室來源的高性能混凝土數據，實驗數據可在 http://em.nchu-cm.com/ 下載。成果顯示 LMGOT 可產生具預測性的簡潔公式，且能有效率地建立低 RMSE 的瀝青鋪面橫向裂縫總長度及高性能混凝土抗壓強度的預測模型。The Artificial Neural Network ( ANN ) and the nonlinear regression method ( NRM ) are commonly used to build models from experimental data. However, the ANN has been criticized for incapable of providing clear relationships and physical meanings, and is usually regarded as a black box. The NRM needs predefined and correct formula structures to process parameter search in terms of the minimal sum of square errors. Unfortunately, the formula structures of these models are often unclear and cannot be defined in advance. To overcome these challenges, recent studies have applied genetic operation tree ( GOT ) to automatically set a formula structures. The shortcoming of GOT is so low efficiency on search coefficient. It usually eliminates a feasible solution with composition of wrong coefficient and good structure in the iteration process of chromosomes and directs to use more operators and operands to build model that has tedious expression and higher RMSE. This study proposes a novel approach, called “ LMGOT ”, that integrates two optimization techniques: the Levenberg–Marquardt ( LM ) Method and the genetic operation tree. The GOT borrows the concept from the genetic algorithm, a famous algorithm for solving discrete optimization problems, to generate operation trees ( OTs ), which represent the structures of the formulas. Meanwhile, the LM takes advantage of its merit for solving nonlinear continuous optimization problems, and determines the coefficients in the GOTs that best fit the experimental data. This paper uses the LMGOT to investigate the data sets of pavement cracks from a 15-year experiment conducted by the Texas Departments of Transportation. Results show a concise formula for predicting the length of asphalt pavement transverse cracks, and indicate that the LMGOT is an efficient approach to building an accurate crack model. In the other two HPC compress strength cases from difference sources, it also shows the same result.1 前言 13 2 文獻回顧 19 2.1 實驗數據模型之應用方法 19 2.2 運算樹( Operation Tree ) 22 2.3 基因運算樹( Genetic Operation Tree ) 24 2.3.1 浮動層級式運算樹結構 25 2.4 求解非線性函數係數值 27 2.4.1 陡降法(The Steepest Descent method) 29 2.4.2 牛頓法( Newton method ) 30 2.4.3 高斯-牛頓法( Gauss-Newton method ) 30 2.4.4 Levenberg-Marquardt method 31 3 LMGOT 方法 33 3.1 LMGOT 流程說明 34 3.1.1 設定執行參數值 34 3.1.2 初始化運算樹 35 3.1.3 最佳化方程式係數值 37 3.1.4 評估運算樹的適存值 40 3.1.5 評估 GOT 是否收斂 40 3.1.6 依適存值選擇菁英 41 3.1.7 運算樹繁殖 41 3.1.8 產生子代並進行係數最佳化 47 3.1.9 運算樹最佳解輸出 48 3.2 LMGOT 方法小結 48 4 案例實作 49 4.1 案例 1: SPS-5 的 A502-509 鋪面資料 49 4.1.1 表面處理 53 4.1.2 加鋪厚度 53 4.1.3 再生材料 53 4.1.4 基因編碼說明 53 4.1.5 SPS-5 之橫向裂縫總累積長度模型 55 4.1.6 探討公式內變數關係 65 4.1.7 SPS-5 案例小結 67 4.2 案例 2: Lim Chul-Hyun(2004) 的高性能混凝土資料 69 4.2.1 LMGOT 之抗壓強度模型 71 4.2.2 Adil(2009) 之抗壓強度模型 76 4.2.3 Lim(2004) 數據之抗壓強度模型小結 77 4.2.4 Lim(2004) 實驗數據的坍度模型 80 4.3 案例 3: Yeh I-Cheng(2006) 的高性能混凝土數據 82 4.3.1 Yeh(2006) 實驗數據之抗壓強度模型 82 4.3.2 Yeh(2006) 案例小結 86 5 結論 89 6 未來方向與建議 93 7 參考文獻 95 8 附錄 10

Prediction of compressive and tensile strength of Gaziantep basalts via neural networks and gene expression programming

In this paper, two soft computing approaches, which are known as artificial neural networks and Gene Expression Programming (GEP) are used in strength prediction of basalts which are collected from Gaziantep region in Turkey. The collected basalts samples are tested in the geotechnical engineering laboratory of the University of Gaziantep. The parameters, "ultrasound pulse velocity", "water absorption", "dry density", "saturated density", and "bulk density" which are experimentally determined based on the procedures given in ISRM (Rock characterisation testing and monitoring. Pergamon Press, Oxford, 1981) are used to predict "uniaxial compressive strength" and "tensile strength" of Gaziantep basalts. It is found out that neural networks are quite effective in comparison to GEP and classical regression analyses in predicting the strength of the basalts. The results obtained are also useful in characterizing the Gaziantep basalts for practical applications