Low Relative Error Research Articles

A novel deep learning-based automatic search workflow for CO2 sequestration surrogate flow models

Numerical simulation can significantly enhance subsurface resource utilisation's efficiency and economic benefits by multiphase flow in heterogeneous porous media. However, numerical simulation brings enormous computational demands and time consumption due to high-dimensional nonlinearity, heterogeneity, and coupling of multiple physical processes. Surrogate models can accelerate the establishment of complex models without sacrificing accuracy. However, creating well-performing surrogate models requires extensive human intervention and trial-and-error processes, even for cross-domain experts. This study proposes an automated surrogate flow model workflow based on deep learning called Surrogate Flow Model Search (SFMS). By incorporating neural architectures and loss functions into joint hyperparameter optimisation, SFMS automates many complex and time-consuming tasks involved in model development, such as designing neural architectures and loss functions. The automated surrogate model construction workflow enables researchers to develop high-quality surrogate models without extensive deep-learning expertise. We demonstrate the effectiveness of SFMS using saline aquifer CO2 injection as an example. The results show that SFMS can automatically generate a highly accurate surrogate flow model in a short time (<1300 s), capable of accurately predicting 120-time steps under different well controls and placements with a low average relative error (<0.4%). Therefore, SFMS can significantly reduce the time and effort required to develop accurate and reliable surrogate models, providing a new approach to building surrogate models.

Potentiometric Sensing of Nonsteroidal Painkillers by Acyclic Squaramide Ionophores.

We report here a small library of a new type of acyclic squaramide receptors (L1-L5) as selective ionophores for the detection of ketoprofen and naproxen anions (KF- and NS-, respectively) in aqueous media. 1H NMR binding studies show a high affinity of these squaramide receptors toward KF- and NS-, suggesting the formation of H-bonds between the two guests and the receptors through indole and -NH groups. Compounds L1-L5 have been tested as ionophores for the detection of KF- and NS- inside solvent PVC-based polymeric membranes. The optimal membrane compositions were established through the careful variation of the ligand/tridodecylmethylammonium chloride (TDMACl) anion-exchanger ratio. All of the tested acyclic squaramide receptors L1-L5 have high affinity toward KF- and NS- and anti-Hofmeister selectivity, with L4 and L5 showing the highest sensitivity and selectivity to NS-. The utility of the developed sensors for a high precision detection of KF- in pharmaceutical compositions with low relative errors of analysis (RSD, 0.99-1.4%) and recoveries, R%, in the range 95.1-111.8% has been demonstrated. Additionally, the chemometric approach has been involved to effectively discriminate between the structurally very similar KF- and NS-, and the possibility of detecting these analytes at concentrations as low as 0.07 μM with R2 of 0.947 and at 0.15 μM with R2 of 0.919 for NS- and KF-, respectively, was shown.

Effects of cluster plot design parameters on landscape fragmentation estimates: A case study using data from the Swedish national forest inventory

Forest fragmentation is commonly characterized using indices derived from analyses of classified land cover maps. An alternative is to use data obtained from sampling, such as those from a national forest inventory (NFI). The main objective of the current study is fill knowledge gaps on the performance of sample-based forest fragmentation metrics calculated with different cluster plot designs and under different forest conditions. A set of NFI cluster plot designs, each with different geometric properties, was created from Swedish NFI data. Each member of the set was used to calculate the fragmentation metrics mean patch size (MPS) and perimeter-area ratio (PA). Impacts of plot design parameters on metric estimates and their precision were assessed.Important differences in metric values were observed both within and between regions under different plot design scenarios; within regions, ranges of PA and MPS values were large, and confidence intervals for the minimum and maximum metric values did not overlap. Weighted least squares regression significance testing results suggest that subplot separation distance was an impactful design factor whereas number of subplots and cluster shape were less important. However, cluster plots with more and widely-separated subplots yielded estimates that were more precise (lower relative sampling errors) than smaller, more compact clusters. We suggest that care should be taken when interpreting the physical meaning of the metrics under study.

Predicting characteristics of cracks in concrete structure using convolutional neural network and image processing

The degradation of infrastructures such as bridges, highways, buildings, and dams has been accelerated due to environmental and loading consequences. The most popular method for inspecting existing concrete structures has been visual inspection. Inspectors assess defects visually based on their engineering expertise, competence, and experience. This method, however, is subjective, tiresome, inefficient, and constrained by the requirement for access to multiple components of complex structures. The angle, width, and length of the crack allow us to figure out the cause of the propagation and extent of the damage, and rehabilitation can be suggested based on them. This research proposes an algorithm based on a pre-trained convolutional neural network (CNN) and image processing (IP) to obtain the crack angle, width, endpoint length, and actual path length in a concrete structure. The results show low relative errors of 2.19%, 14.88%, and 1.11%, respectively for the crack angle, width, and endpoint length from the CNN and IP methods developed in this research. The actual path length is found to be 14.69% greater than the crack endpoint length. When calculating the crack length, it is crucial to consider its irregular shape and the likelihood that its actual path length will be greater than the direct distance between the endpoints. This study suggests measurement methods that precisely consider the crack shape to estimate its actual path length.

Low-Cost Wideband Interrogation System for Fiber Optic Sensors

The interrogation of optical fiber sensors (OFS) often relies on complex devices such as Optical Spectrum Analyzers (OSA) which are expensive with low portability and mainly suited to laboratory measurements or dedicated interrogation systems with limited spectral range. An interrogation unit was designed and fabricated using a photodetector combined with a Micro Electro-mechanical System and a Fabry-Pérot Interferometer (MEMS-FPI) working as a tunable filter with a response in the range 1350 to 1650nm. Deconvolution techniques were applied to mitigate the effect of the broadband response of the tunable filter on the measured signal. The performance of the unit was validated with the interrogation of Long Period Fiber Gratings (LPFG) as temperature, refractive index (RI) and relative humidity (RH) sensors. For the temperature a sensitivity of 0.135 ± 0.007nm/°C was obtained, which showed a 4.9% relative error when compared to the same measurement with an OSA. For the RI a sensitivity of 147 ± 11 nm/RIU was obtained which showed a relative error lower than 1% when compared to the OSA. For the humidity, sensitivities of 0.742 ± 0.005 nm/%RH and 0.056 ± 0.006 nm/%RH were obtained, with errors of 2.75% and 6.67% respectively, when compared to a commercial dedicated interrogation system. The low relative error obtained when compared to commercial alternatives, shows the potential of the system to be used in real-time applications that require portability, low-cost, energy efficiency and capacity for integration in dedicated systems.

Genetic-Algorithm-Based Inverse Optimization Identification Method for Hot-Temperature Constitutive Model Parameters of Ti6Al4V Alloy.

A precise constitutive model is the foundation and key to finite element simulation in material volume forming and the optimization of the hot working process. Hence, to build a precise constitutive model, a method based on a genetic algorithm (GA) for the inverse optimization identification of parameters is presented in this paper. The idea of this method is to continuously adjust the model parameters through GA until the objective function reaches the minimum value. In this study, hot compression experiments were performed on the Gleeble-1500D thermal simulator at temperatures ranging from 800 °C to 1000 °C and strain rates of 0.01 s-1 to 1 s-1. The Arrhenius-type (A-T) model considering strain compensation and the Johnson-Cook (JC) model considering the coupling effects of strain, temperature and strain rate were constructed, respectively, by using the regression method and the parameter inverse optimization identification method. For the purposes of comparing and verifying the reliability of the predictions of the two established constitutive models, the correlation coefficient (R), average absolute relative error (AARE), and relative error (RE) were adopted. The results show that both the optimized A-T model and the optimized JC model have high prediction accuracy. Compared to the optimized JC model, the optimized A-T model demonstrated a higher correlation coefficient, by 0.003, and a lower average absolute relative error, by 1.43%. Furthermore, the relative error distribution of the optimized A-T model was found to be more concentrated than that of the optimized JC model. These results suggest that the A-T model is more appropriate than the JC model for characterizing the high-temperature deformation behavior of Ti6Al4V alloy.

High-precision sugarcane yield prediction by integrating 10-m Sentinel-1 VOD and Sentinel-2 GRVI indexes

Developing accurate models of sugarcane yield mapping at fine-scale is of paramount importance and will benefit many aspects of managing growth and harvest of sugarcane crops. Here, we combined high-spatial-resolution multi-sensor (optical and microwave) remote sensing data to estimate sugarcane yield using two approaches. First, we retrieved the 10 m resolution vegetation optical depth (VOD) using C-band Sentinel-1 synthetic aperture radar data via the water cloud model, then derived a combined VOD and Sentinel-2 derived green–red vegetation index (GRVI, a traditional vegetation index) time series. Second, we adopted the eXtreme Gradient Boost (XGBoost) machine learning algorithm to estimate total sugarcane production based on the aggregated mean monthly VOD and GRVI time series at the county scale. County-scale sugarcane yield data from 81 counties across Guangxi, China (2018–2020) were used for model training and testing. We then kept the trained best-performance model unchanged to re-predict pixel-scale (10-m resolution) yield using VOD and GRVI images. A SHapley Additive exPlanations (SHAP) approach was employed to test XGBoost knowledge regarding the mechanisms affecting yield. The main outcomes from this study were as follows. (1) The XGBoost model and VOD and GRVI time series unequivocally provided reliable and precise estimates of sugarcane yield, with a low relative error both at the county scale and at the pixel scale. (2) Predictions of sugarcane yield in the growing season using combined VOD and GRVI data yields high accuracy (R2 = 0.815) with specific spatial patterns of sugarcane yields for Guangxi province, and were feasible up to two months prior to harvest. (3) The SHAP model revealed that Sentinel-1 derived VOD data are important for predicting yield. This research portrays the benefits of combining VOD and GRVI data in automatic machine learning models for estimating sugarcane yield at high spatial and temporal resolutions.

Quantitative Analysis of Steel Alloy Elements Based on LIBS and Deep Learning of Multi-Perspective Features

The Si and Mn contents in steel alloys are important characteristic indexes that influence the plasticity and welding properties of these alloys. In this work, the quantitative analysis methods for trace elements under complex alloy matrices by laser-induced breakdown spectroscopy (LIBS) are studied, which provide a foundation for utilizing LIBS technology in the rapid online detection of steel alloy properties. To improve the quantitative analysis accuracy of LIBS, deep learning algorithm methods are introduced. Given the characteristics of LIBS spectra, we explore multi-perspective feature extraction and backward differential methods to extract the spatio-temporal characteristics of LIBS spectra. The Text Convolutional Neural Network (TextCNN) model, combined with multi-perspective feature extraction, displays good stability and lower average relative errors (6.988% for Si, 6.280% for Mn) in the test set compared to the traditional quantitative analysis method and deep neural network (DNN) model. Finally, the backward differential method is employed to optimize the two-dimensional LIBS spectral input matrix, and the results indicate that the average relative errors of Si and Mn elements in the test set decrease to 5.139% and 3.939%, respectively. The method proposed in this work establishes a theoretical basis and technical support for precise prediction and online quality monitoring.

An inverse analysis to estimate the thermal properties of nanoporous aerogel composites using the particle swarm optimized deep neural network

To understand the transient heat transfer characteristics of nanoporous aerogel insulating composites, solving the inverse heat transfer problem would be crucial for identifying the temperature-dependent thermal properties of composites. In this study, with constructed a forward model to numerically investigate the heat transfer in composites, a deep neural network (DNN) model and a particle swarm optimized deep neural network (PSO-DNN) model are conducted to rapidly estimate the effective temperature-dependent thermal conductivity of the desiccated and moist composites from the temperature response measurements. With the DNN model, the retrieved thermal conductivities for desiccated composites possess low deviation to experimental measurements (<3.2%) and constantly low errors (<5.2%) from 280 K to 1080 K. The precision of the DNN solver could be enhanced by adjusting the hyperparameters of the neural networks using PSO. The retrieved thermal conductivities possess low deviation from experiments (<2.5%) and low relative errors within 1.5%. Furthermore, the robustness of the PSO-DNN solver is discussed when commercial thermocouple measurement errors are considered, within retrieving the thermal properties of desiccated and moist aerogel composites.

Optimized Design and Fabrication of Polyethylene Glycol 1000/Polyamide 6 (PEG1000/PA6) Nanofibers for Phase Change Materials (PCMs) Application

Ultrafine phase change nanofibers based on polyethylene glycol 1000 (PEG1000) as phase change material (PCM) and polyamide 6 (PA6) as a supporting material were prepared in a systematic manner planned by the Design-Expert® software using the uniaxial electros-pinning. Research surface methodology (RSM) was carried out to optimize the parameters and conditions leading to minimize the fiber diameter. The effect of PEG content, applied voltage, needle gauge, and flow rate on the fiber characteristics was studied by a central composite design (CCD). The minimum diameter of nanofibers was predicted by a quadratic model to be 64.33 nm and the actual fibers diameter prepared under optimal condition showed a very low relative standard error (RSE). It was shown that the PEG/PA6 mass ratio has the dominant effect on the fibers diameter. The results from FTIR and FE-SEM images confirmed well encapsulated PEG in PA6 and no leakage and morphology alterations were observed after heating tests. To further investigate morphological structure and the quality of PEG1000 encapsulation in PA6 matrices, the composite fibers underwent a solvent treatment using ethanol. The results proposed a new innovative method to control operational electrospinning conditions for encapsulating phase change materials in polymer matrices which is very important in thermal energy saving/retrieving applications.

Study the effect of different shapes of plume rise on Gaussian plume models and its maximum in unstable conditions

Exposure to radioactive pollutants such as Iodine-135 I135 seriously threatens public health and environmental balance. Monitoring and managing these pollutants require expensive economic equipment that is not suitable for low-income countries such as Egypt. Therefore, trying to derive a mathematical model that estimates the concentrations of these radioactive pollutants with high accuracy and a low relative error coefficient compared to the actually measured values ​​is very important. Therefore a mathematical Gaussian model was received to estimate the concentrations of I135 emitted from the research nuclear reactor in the Inshas region in Egypt using different shapes of plume rise in unstable conditions. A comparison between the derived model and its maximum values with observed concentrations data measuring on Egyptian Atomic Energy Authority for I135 in unstable conditions has been found. The derived model may be applied to estimate and predict the emissions of any radioactive pollutant for any similar area and similar type of used reactor, which provides high-precision technology with zero economic cost. The statistical technique shows that the entire Gaussian model and its maximum inside a factor of two with observed concentration data achieved 98%. In addition, the statistics show that all the Gaussian plume models and their maximum have a correlation coefficient of about 0.95%. Also, the normalized mean square error. And the fraction bias. are near-zero values in all Gaussian models and their maximum.

UtilityAware: A framework for data privacy protection in e-health

Data privacy in e-health deals with the protection of sensitive medical information that is collected, stored, and analyzed in electronic health systems. Several organizations publish sensitive person-specific data for research purposes. E-health data and related domains are the loci of research. First, in publishing sensitive person-specific datasets, ensuring the privacy of user sensitive information is an issue. Secondly, ascertaining both privacy-preservation and data utility simultaneously are contradictory to each other. In addition, all transactions have the same prior belief that may result in erroneous modeling and privacy breaches. To refrain from the belief of an adversary and to solve the above discussed issues, a semantic privacy guarantee must be ensured before publishing data by any organization. This paper proposes a solution to the former issue, a framework for privacy preservation of structured datasets in ascertaining that an adversary has low confidence in extrapolation. The latter problem is also tackled by the proposed framework that combines stratified sampling with generalization to achieve representative semantic privacy-preservation with high data utility. Moreover, this study presents a mathematical proof that the proposed framework achieves differential privacy. Our experimental results show that our algorithm provides better data utility and privacy simultaneously. The proposed framework achieves 3% and 0.04% higher classification accuracy and low relative error, respectively, compared to state-of-the-art existing privacy-preservation approaches.

Synthesis, characterization and application of BR@Ag nanocomposite material for high degree reduction of p-nitro phenol under a suitable condition

ABSTRACT One of the most essential chemical processes that is utilized in the manufacturing of a great deal of contemporary goods is called heterogeneously catalyzed reactions, and it is also one of the most fascinating. Metallic nanostructures are heterogeneous catalysts for range reactions due to their huge surface area, large assembly of active surface sites, and quantum confinement effects. Unprotected metal nanoparticles suffer from irreversible agglomeration, catalyst poisoning, and limited life cycle. To circumvent these technical disadvantages, catalysts are frequently spread on chemically inert materials like as mesoporous Al2O3, ZrO2, and different types of ceramic material. In this research, plentiful bauxite residue is used to create a low-cost alternative catalytic material. We have hydrogenated p-Nitrophenol to p-Aminophenol on bauxite residue (BR) supported silver nanocomposites (Ag NCs). The phase and crystal structure, bond structure and morphological analysis of the developed material will be done XRD, FTIR, and SEM-EDX respectively. The ideal conditions were 150 ppm of catalyst, 0.1 mM of p-NP, and 10 minutes overall up-to 99% conversion of p-NP to p-AP. A multi-variable predictive model created using Response Surface Methodology (RSM) and a data-based Artificial Neural Network (ANN) model were found to be the best ways to predict the maximum conversion efficiency. ANN models predicted efficiency more accurately than RSM models, and the strong agreement between model predictions and experimental data was indicated by their low relative error (RE0.10), high regression coefficient (R2>0.97), and Willmott-d index (dwill-index > 0.95) values.

Thermo-economic and drying kinetic analysis of Oleaster using a solar dryer integrated with phase change materials and recirculation system

Drying of agricultural products is a good way to store wet products. In recent decades, using solar dryers has received much attention due to the environmental problems of using fossil fuels. However, one of the main problems of solar drying system is the low thermal efficiency and inhomogeneous distribution of temperature in the drying chamber. In this work, the increase of heat efficiency of flat plate collector has been investigated using phase change materials and air recirculation mechanism. Copper pipes containing phase change material, at the top of the collector plate vertically at three 5, 10 and 15 cm intervals. Drying process of Oleaster fruit was used to evaluate the drying performance of the solar dryer. The results revealed that using air recirculation system and thermal storage systems improved the drying efficiency and thermal efficiency it was about 43.42% and 16.75 %, respectively. The average thermal efficiency for distances of 5, 10 and 15 cm was 53.26, 54.89 and 56.29 %, respectively. Using return air flow increased the thermal efficiency at least 11.65 %. By economical optimization about 8.6 %. The best mathematical to predict the drying was Henderson and pabis. Moreover, the results indicated that applied CFD model predicted the thermal performance of the dryer at acceptable range (with low relative error 2.56 ± 0.32%). Based on the optimization process the proper arrangement of PCM tubes inside of the collector was obtained.

Factors affecting uniaxial compressive strength and ultrasonic pulse velocity of meso-scale heterogeneous concrete

Ultrasonic pulse velocity test (UPV) and uniaxial compressive strength (UCS) is widely used for building conversion model in concrete non-destructive test. However, the stability and accuracy of test results is always a questionable issue because concrete is heterogeneous on the meso-scale. In this study, a meso-scale simulation methodology aimed at specifying the influencing factors of UCS and UPV is proposed. Firstly, a meso-scale finite element model of concrete consisting of mortar, interfacial transition zone (ITZ) and randomly distributed aggregates is developed. Furtherly, by using L18 orthogonal array, the effects of significant influencing factors were analyzed: aggregate content, aggregate type, maximum aggregate size, thickness and porosity of ITZ, and water-cement ratio. The analysis of variance (ANOVA) results show water-cement ratio is the only significant influence of UCS. But significant factors for UPV including water-cement ratio, aggregate type and ITZ porosity. In addition, the rationality of the simulation methodology is validated with low relative errors (4.72% for UCS and 3.21% for UPV) is achieved on the experimental data and theoretical formulations.

Forecasting the GDP in the United States by Using ARIMA Model

This paper aims to give an overall view of the Gross Domestic Product (GDP) in the United States and determine the optimal model to predict the growth of GDP by using the Autoregressive Integrated Moving Average Model (ARIMA). The ARIMA model was performed for 93 years from 1929 to 2022 of Gross Domestic Product, Billions of Dollars, Annually from Federal Reserve Economic Data (https://fred. stlouisfed.org). The researcher conclude that the estimated model of the first-order difference for the logarithm of GDP (DLGDP) series is ARIMA (1,1,1) with coefficients: C = 0.057064, AR (1) = 0.489046 &amp; MA (1) = 0.265583 where S.E. of regression equals 0.051529, R-squared value is about 0.412974, Durbin-Waston statistic (1.961008) and the probability of F-statistic equals (0.000000), which gives the forecast value 0.10436 of LGDP in 2022, while the actual value equals 0.8818 with very low relative error 1.617%, therefore, the forecast value is close to the actual value and indicates that the ARIMA (1,1,1) model has a good fitting effect.

Effect of adding dimethyl carbonate and gasoline to diesel fuel + corn oil blend on performance and combustion characteristics of a diesel engine.

Diesel fuel and corn oil are mixed in the 80:20 volumetric ratio. Dimethyl carbonate and gasoline are added to diesel fuel + corn oil blend in 4:96, 6:94, 8:92, and 10:90 volumetric ratios to obtain ternary blends. Effects of ternary blends on the performance and combustion characteristics of a diesel engine are investigated under different engine speeds (1000-2500 rpm). 3D Lagrange interpolation method is applied to measured data of dimethyl carbonate blends to predict the engine speed, blending ratio, and crank angle giving maximum peak pressure and peak heat release rate. On average, dimethyl carbonate blends and gasoline blends show 4.3642-12.1578% and 1.0323-8.6843% reduction in effective power, and 1.4938-3.4322% and 4.3357-8.7188% reduction in effective efficiency, respectively, relative to diesel fuel. On average, there is a reduction in cylinder peak pressure (4.6701-7.3418%; 4.0457-6.2025%) and peak heat release rate (0.8020-4.5627%; 0.4-1.2654%) for dimethyl carbonate blends and gasoline blends, respectively, compared to diesel fuel. Because of low relative errors (1.0551% and 1.4553%), 3D Lagrange provides well accuracy in the prediction of maximum peak pressure and peak heat release rate. On average, dimethyl carbonate blends produce less CO (7.4744-17.5424%), HC (15.5410-29.5501%) and smoke (14.1767-25.2834%) emissions, compared with diesel fuel.

Artificial Neural Network Modeling and Genetic Algorithm Multiobjective Optimization of Process of Drying-Assisted Walnut Breaking.

This study combined an artificial neural network (ANN) with a genetic algorithm (GA) to obtain the model and optimal process parameters of drying-assisted walnut breaking. Walnuts were dried at different IR temperatures (40 °C, 45 °C, 50 °C, and 55 °C) and air velocities (1, 2, 3, and 4 m/s) to different moisture contents (10%, 15%, 20%, and 25%) by using air-impingement technology. Subsequently, the dried walnuts were broken in different loading directions (sutural, longitudinal, and vertical). The drying time (DT), specific energy consumption (SEC), high kernel rate (HR), whole kernel rate (WR), and shell-breaking rate (SR) were determined as response variables. An ANN optimized by a GA was applied to simulate the influence of IR temperature, air velocity, moisture content, and loading direction on the five response variables, from which the objective functions of DT, SEC, HR, WR, and SR were developed. A GA was applied for the simultaneous maximization of HR, WR, and SR and minimization of DT and SEC to determine the optimized process parameters. The ANN model had a satisfactory prediction ability, with the coefficients of determination of 0.996, 0.998, 0.990, 0.991, and 0.993 for DT, SEC, HR, WR, and SR, respectively. The optimized process parameters were found to be 54.9 °C of IR temperature, 3.66 m/s of air velocity, 10.9% of moisture content, and vertical loading direction. The model combining an ANN and a GA was proven to be an effective method for predicting and optimizing the process parameters of walnut breaking. The predicted values under optimized process parameters fitted the experimental data well, with a low relative error value of 2.51-3.96%. This study can help improve the quality of walnut breaking, processing efficiency, and energy conservation. The ANN modeling and GA multiobjective optimization method developed in this study provide references for the process optimization of walnut and other similar commodities.

EESD special issue: AI and data‐driven methods in earthquake engineering – (Part 1)

EESD special issue: AI and data‐driven methods in earthquake engineering – (Part 1)

Fractal Geometric Model for Statistical Intermittency Phenomenon.

The phenomenon of intermittency has remained a theoretical concept without any attempts to approach it geometrically with the use of a simple visualization. In this paper, a particular geometric model of point clustering approaching the Cantor shape in 2D, with a symmetry scale θ being an intermittency parameter, is proposed. To verify its ability to describe intermittency, to this model, we applied the entropic skin theory concept. This allowed us to obtain a conceptual validation. We observed that the intermittency phenomenon in our model was adequately described with the multiscale dynamics proposed by the entropic skin theory, coupling the fluctuation levels that extended between two extremes: the bulk and the crest. We calculated the reversibility efficiency γ with two different methods: statistical and geometrical analyses. Both efficiency values, γstat and γgeo, showed equality with a low relative error margin, which actually validated our suggested fractal model for intermittency. In addition, we applied the extended self-similarity (E.S.S.) to the model. This highlighted the intermittency phenomenon as a deviation from the homogeneity assumed by Kolmogorov in turbulence.