Uncertainty is the inseparable part of the engineering analysis. These uncertainties have different Distributions. SOBOL decomposition method is one of the most well-known methods of sensitivity analysis. SOBOL decomposition as a robust sensitivity analysis method can only be used for uniform distribution. In the present paper, we generalize SOBOL sensitivity method for all continuous and discrete distributions. Hence it can be used for wide Varity models in engineering and science of different distributions. The capability of the generalized method for precise numerical values presentation, the results of the sensitivity analysis of the Tehran seismic hazard is given. Due to the variability of materials and earthquakes, Structural and geosciences are full of uncertainties. Calculating the role of the uncertainty of each parameter in the overall uncertainty can be to optimize the efforts and costs necessary for outputs precision, so, it is possible to provide a precise values of sensitivities. The results are satisfactory.

Background: Accurate computation of the radiation dose to the breast is essential to mammography. Various the thicknesses of breast, the composition of the breast tissue and other variables affect the optimal breast dose. Furthermore, the glandular fraction, which refers to the composition of the breasts, as partitioned between radiation-sensitive glandular tissue and the adipose tissue, also has an effect on this calculation. Fatty or fibrous breasts would have a lower value for the glandular fraction than dense breasts.Breast tissue composed of half glandular and half adipose tissue would have a glandular fraction in between that of fatty and dense breasts. Therefore, the use of a computational code for average glandular dose calculation in mammography is a more effective means of estimating the dose of radiation, and is accurate and fast.Methods: In the present work, the SOBOL-Wu beam quality parameters are used to write a FORTRAN code for glandular dose calculation in molybdenum anode-molybdenum filter (Mo-Mo), molybdenum anode-rhodium filter (Mo-Rh) and rhodium anode-rhodium filter (Rh-Rh) target-filter combinations in mammograms. The input parameters of code are: tube voltage in kV, half-value layer (HVL) of the incident x-ray spectrum in mm, breast thickness in cm (d), and glandular tissue fraction (g).Results: The average glandular dose (AGD) variation against the voltage of the mammogram X-ray tube for d = 4 cm, HVL = 0.34 mm Al and g=0.5 for the three filter target combinations, as well as its variation against the glandular fraction of breast tissue for kV=25, HVL=0.34, and d=4 cm has been calculated. The results related to the average glandular absorbed dose variation against HVL for kV = 28, d=4 cm and g= 0.6 are also presented. The results of this code are in good agreement with those previously reported in the literature.Conclusion: The code developed in this study calculates the glandular dose quickly, and it is complete and accurate. Furthermore, it is user friendly and useful for dose optimizing in mammography imaging.

Bone drilling process is indispensable in orthopedic surgeries and treating bone breakages. It is also very important in dentistry and bone sampling operations. Therefore, bone drilling is one of the most important, common and sensitive processes in biomedical engineering field. Orthopedic surgeries can be improved using robotic bone drilling systems and also mechatronic bone drilling process can be promoted using automatic drilling machines and surgery-assisting robots. Furthermore, imposing higher forces to bone might lead breaking or cracking and consequently serious damage in bone. In this paper a mathematical second order linear regression model is introduced to predict process force behavior during bone drilling process as a function of tool drilling speed, feed rate, tool diameter and effective interactions. Design of experiments using response surface methodology is followed. Then second linear governing equation is assigned to the model and its accuracy is evaluated. Later, SOBOL Statistical sensitivity analysis is used to ascertain the effect of process input parameters on process force. Results show that among all effective input parameters tool rotational speed, feed rate and tool diameter have the highest influence on process force respectively. The behavior of each output parameters with variation in each input parameter is further investigated.

Water quality indicators are a standard for classifying surface water based on the use of standard parameters and are a mathematical tool that converts a large amount of data used to describe water properties into a number and obtains a water quality level. This study aimed to assess and compare the sensitivity of NSFWQI and IRWQISC water quality indicators to quality parameters using variance-based methods on Haraz River with monthly sampling in 2022 in 7 selected stations in the range of Panjab to Haraz Reservoir Dam in the province Mazandaran. The results of the present study have shown that the water quality in S1 (upstream) and S2-1 stations are relatively good at best, and bad at worst. Water quality in stations of S2, S3, S4, S5-1, and S5 (downstream), in the best case, is moderate and in the worst case in September has poor quality. SRC method was used to analyze the uncertainty and sensitivity of the NSFWQI index and FAST and SOBOL methodologies were used for the IRWQISC index. The results of sensitivity analysis based on the Factor Prioritization approach showed that in NSFWQI index, DO, BOD, CF, T, and P parameters respectively and in IRWQISC index after DO parameter, BOD, P, and N parameters had the most impact on output. In the uncertainty analysis, the results of applying the SOBOL methodology for different stations of Haraz River were consistent with the FAST method, but the results of sensitivity analysis obtained from these two methods were different from each other. Considering the obtained results and despite the similarity of the results of the two methods, it can be said that the SOBOL methodology has been more successful than the FAST methodology in this study due to unconditional convergence.

One of the common treatments in orthopedic surgery is machining of knee joints to attach the artificial joint. In this surgery preparation of tibia and femur surfaces is necessary to obtain proper joint kinematics and ligament balancing. For this purpose milling is involved in surgery requiring accurate machining of bone surfaces and creation of accurate slots. In this paper, milling process was carried out on polymethylmethacrylate as workpiece and suitable substitute for bone and for the first time, it is focused on modeling and optimizing the effective parameters in milling namely cutting speed, feed rate, tool diameter and cutting depth for analyzing the surface roughness using the surface response methodology. The second-order regression equation governing the model is drived and the influence of the input parameters and their interaction on the surface roughness as the output parameter is carefully investigated. Also, SOBOL statistical sensitivity analysis is used to ascertain the effect of process input parameters quantitatively. The results show that in order to achieve the desirable surface quality, minimum of feed, minimum rotational speed, smaller tool diameter and low cutting depth should be considered. Results show that among all effective input parameters tool rotational speed, feed rate, tool diameter and ctting depth have the highest influence on process roughness respectively. The behavior of each output parameters with variation in each input parameter is further investigated.

Background and Objectives: In recent decades following the massive increase in computational power, considerable progress has been made in hydrological models. As the complexity of the model increases, model parameters increases and this lead to increasing the chances of overfitting and difficulty in identifying both model parameter values and model structure. One possible way to mitigate over-parameterization/non-identifiability is reducing the number of parameters to a small number that can be sufficiently calibrated with limited data.Sensitivity analysis (SA) is a commonly used approach for identifying important parameters that dominate model behaviors. Overall, they can be categorized into two groups: local SA and global SA. The local SA explores the changes of model response by varying one parameter while keeping other parameters constant. On the other hand, the global SA examines the changes of model response by varying all parameters at the same time. No general rule has yet been defined for verifying the convergence of the General SA methods. In order to fill this gap this paper presents a convergence analysis of three widely used SA methods (Morris screening, SOBOL and Entropy index) for two rainfall-runoff models, TOPMODEL and HBV. The simulations are carried out over ChehlChay watershed within Gorganrood River Basin.Materials and Methods: The sensitivity and interaction analysis based onSOBOL, Morris screen and Entropy methods were applied. The Morris method has been proposed as a screening method to identify a subset of inputs that have the greatest influence on the outputs.SOBOL SA is a global, variance-based method that attributes variance in the model output to individual parameters and their interactions.Mutual entropy analysis is a sensitivity analysis method in which the mutual entropy of two variables is regarded as the correlative extent between these two variables. The distribution character of data (X, Y) can be expressed by contingency tables.The HBV model and TOPMODEL are used as a test problem. There are thirteen and nine parameters in the HBV model and TOPMODEL models, respectively. In each model, samples of the model parameter space are obtained using a latin-hypercube. The convergence analysis has been performed by increasing the number of simulations until there was no significant change of the sensitivity measure. In addition, the three SA methods are evaluated and compared in terms of convergence, the related evolution of the parameter ranking results and required computation cost.Results: Results of the quantitative convergence analysis for Morris screen was achieved at 700 and 1000 number of simulations for HBV and TOPMODEL models, respectively. Results for the SOBOL method deviated considerably from the other methods by 22000 and 28000 for the TOPMODEL and HBV models, respectively. In Entropy method need about 6000 samples for the same purpose in both hydrological models. The ranking of parameters sensitivity indices in TOPMODEL for the first two most sensitive parameters for the three methods are similar. In general, the ranks of sensitive parameters are the same for all methods. Meanwhile for Entropymethod, M and Srmax as the third and fourth ranking are vice versa than other two methods.In HBV model, SOBOL and Morris screen methods provide similar results for those model parameters having the highest influence. For the parameter P, the sensitivity obtained from Entropy method was 3rd rank but in two other methods the parameter ranking varies from 3rd to sixth. In Entropy parameter FC becomes the most important parameter but in Morris screen and SOBOL methods, the model parameter BETA selected as the parameter with the highest importance.Conclusion: There is no single best strategy for all problems. Therefore in general use of two or more methods, preferably with dissimilar theoretical foundations, may be needed to increase confidence in the ranking of the key inputs.This study conducted a comprehensive evaluation of the effectiveness and efficiency of three SA methods by using the HBV and TOPMODEL models as test problem. The strengths and limitations of qualitative and quantitative SA methods are explored.For the SOBOL method, a comparatively large number of simulations (>20 000) were required to sufficiently cover the parameter space. Hence, performing SOBOL method for complex models is often becoming problematic. The Morris method, instead, is computationally cheap and needed only<1000 simulations to obtain stable results.

Introduction: To write a computational program to calculate the average glandular dose in Mammography with Rh-Rh target-filter and also use it as an accurate and fast method of dose calculation founder different situations.Materials and Methods: In this research, the SOBOL-Wu parameters are used to write a FORTRAN code for glandular dose calculation in Rh-Rh target-filter mammograms. The code calculates the glandular dose for Rh-Rh target-filter mammograms for the input parameters such as tube voltage in kV scale, half-value layer (HVL) of the incident x-ray spectrum in mm Al, breast thickness in cm and glandular tissue fraction (g).Results: The average glandular dose variation has been calculated against the voltage of mammogram X-ray tube for d = 5 cm, HVL = 0.35 mm Al and different value of g. Also the results related to the average glandular absorbed dose variation per unit roentgen against the glandular fraction of breast tissue for kV=28, HVL = 0.387 mm Al and different value of d are presented. Discussion and Conclusion: The results of this research are in good agreement with the computational results of J. M. Boone and the experimental results of E. L. Gingold et al. Also the code is fast, accurate and user friendly, that can be used for dose optimization in mammography imaging.

In this paper, using the SOBOL sensitivity analysis method, which is based on variance, 11 factors affecting the optimization of the loading path of the hydroforming process are investigated, then the feasibility and validation of the results with other optimization methods such as finite element and experimental method are reported. Is Input factors include, expansion pressure, final pressure, yield time, end of expansion time, intermediate mandrel displacement, final mandrel displacement, intermediate mandrel displacement time, initial position of reciprocating mandrel, final position of reciprocating mandrel, start time of reciprocating mandrel and time The stops of the reciprocating mandrels are considered, then the effect of each of them on the minimum thickness and maximum height in the loading path of the hydroforming process to produce T-joints is investigated and reported in detail. Quantitatively and qualitatively, the optimal values are obtained for each of the 11 input factors and are calculated based on the loading paths.

Background: The widespread adoption of a sedentary lifestyle characterized by the consumption of a high-energy diet combined with a lack of physical activity has resulted in a rise in the prevalence of metabolic disorders like type 2 diabetes (T2D) globally. The data published by the International Diabetes Federation (IDF) every year catches the attention of the world. Insulin resistance results in the dysregulation of the control mechanism that leads to T2D. In addition to metformin as a globally prescribed drug, physical exercise is recommended for the treatment of T2D as an alternative therapy. In today’s systems biology era, sensitivity analysis plays a major role in providing deeper insights into the metabolic insulin signalling pathways (ISPs). Methods: Here, the complex in silico dynamic model of the effect of alternative therapies on T2D was examined. In order to obtain more quantitative information about the signal transduction network of the ISPs and their interaction, a global sensitivity analysis of the in silico model was carried out using the MATLAB tool. Results: This study sheds light on the effect of parameter perturbation on the ISP via GLUT4 translocation in T2D patients performing physical exercise and using metformin. It also allows for the selection of a variety of parameters for in vivo or in vitro studies in the future on the basis of the impact of parameter variations on each component of the pathway. Conclusion: The SOBOL index for each condition was noted after introducing perturbations in the most sensitive parameters. These results can provide experimental guidance on how the variations in model inputs have affected the model outputs.

In the present study, the effect of different parameters including of tool rotational speed, feed rate and tool diameter on the damage caused by drilling operations near the drilling hole in the E-glass/epoxy composite laminates with twelve layers of plain woven fabric manufactured using hand lay-up method was investigated and the experimental tests conducted on them. Then, using the SOBOL statistical sensitivity analysis method, the effect of the above-mentioned parameters on the induced damage near the drilling hole was investigated. The statistical and experimental results show that for analyzing the damage variable, the simultaneous effect of rotational velocity in conjunction with feed rate of the drilling tool should be taken into account in order to minimize the damage variable, so that in the low velocities, the reduction of feed rate along with the reduction of the rotational speed causes the damaged variable to be minimized, while at the same time, in the high diameters, the simultaneous increase of the two mentioned parameters, minimizes delamination induced damage in laminated composites. The Sobel sensitivity analysis shows that the diameter of the tool, the velocity, and the rotational speed will have the greatest effect on damage variable in laminated composites, respectively.