Nonlinear Regression Fuzzy Analysis of Real Variable and Fuzzy Parameter

As far as the nonlinear regression method is concerned, the condition when both independent and dependent variable take the Fuzzy value, while the parameter, θ∈ΘR m the real value, have been discussed in . But for most of actual conditions, the independent variable generally takes the real value, while both parameter and dependent variable take the Fuzzy value. This paper propounded a method for the latter and its relevant Fuzzy regreession model. In addition the Fuzzy observation, matrix distribution and the rational estimation of modeling parameter have also been discussed. Furthermore, the Max min estimation of modeling parameter and its corresponding calculating sequence have also been offered to and the calculating example shows the method is feasible.

Regression analysis and its application to oil and gas exploration:A case study of hydrocarbon loss recovery and porosity prediction,China

In oil and gas exploration,elucidating the complex interdependencies among geological variables is paramount.Our study introduces the application of sophisticated regression analysis method at the forefront,aiming not just at predicting geophysical logging curve values but also innovatively mitigate hydrocarbon depletion observed in geochemical logging.Through a rigorous assessment,we explore the efficacy of eight regression models,bifurcated into linear and nonlinear groups,to accommodate the multifaceted nature of geological datasets.Our linear model suite encompasses the Standard Equation,Ridge Regression,Least Absolute Shrinkage and Selection Operator,and Elastic Net,each presenting distinct advantages.The Standard Equation serves as a foundational benchmark,whereas Ridge Regression implements penalty terms to counteract overfitting,thus bolstering model robustness in the presence of multicollinearity.The Least Absolute Shrinkage and Selection Operator for variable selection functions to streamline models,enhancing their interpretability,while Elastic Net amalgamates the merits of Ridge Regression and Least Absolute Shrinkage and Selection Operator,offering a harmonized solution to model complexity and comprehensibility.On the nonlinear front,Gradient Descent,Kernel Ridge Regression,Support Vector Regression,and Piecewise Function-Fitting methods introduce innovative approaches.Gradient Descent assures computational efficiency in optimizing solutions,Kernel Ridge Regression leverages the kernel trick to navigate nonlinear patterns,and Support Vector Regression is proficient in forecasting extremities,pivotal for exploration risk assessment.The Piecewise Function-Fitting approach,tailored for geological data,facilitates adaptable modeling of variable interrelations,accommodating abrupt data trend shifts.Our analysis identifies Ridge Regression,particularly when augmented by Piecewise Function-Fitting,as superior in recouping hydrocarbon losses,and underscoring its utility in resource quantification refinement.Meanwhile,Kernel Ridge Regression emerges as a noteworthy strategy in ameliorating porosity-logging curve prediction for well A,evidencing its aptness for intricate geological structures.This research attests to the scientific ascendancy and broad-spectrum relevance of these regression techniques over conventional methods while heralding new horizons for their deployment in the oil and gas sector.The insights garnered from these advanced modeling strategies are set to transform geological and engineering practices in hydrocarbon prediction,evaluation,and recovery.

Evaluation of the seismic behavior of reinforced concrete structures with flat slab-column gravity frame and shear walls through nonlinear analysis methods

This paper presents an investigation of the seismic behavior of reinforced concrete(RC)structures in which shear walls are the main lateral load-resisting elements and the participation of flat slab floor systems is not considered in the seismic design procedure.In this regard,the behavior of six prototype structures(with different heights and plan layouts)is investigated through nonlinear static and time history analyses,implemented in the OpenSees platform.The results of the analyses are presented in terms of the behavior of the slab-column connections and their mode of failure at different loading stages.Moreover,the global response of the buildings is discussed in terms of some parameters,such as lateral overstrength due to the gravity flat slab-column frames.According to the nonlinear static analyses,in structures in which the slab-column connections were designed only for gravity loads,the slab-column connections exhibited a punching mode of failure even in the early stages of loading.However,the punching failure was eliminated in structures in which a minimum transverse reinforcement recommended in ACI 318(2019)was provided in the slabs at joint regions.Furthermore,despite neglecting the contribution of gravity flat slab-column frames in the lateral load resistance of the structures,a relatively significant overstrength was imposed on the structures by the gravity frames.

Composition Analysis and Identification of Ancient Glass Products Based on L1 Regularization Logistic Regression

In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluster analysis, hyper-parameter test and other models, and SPSS, Python and other tools were used to obtain the classification rules of glass products under different fluxes, sub classification under different chemical compositions, hyper-parameter K value test and rationality analysis. Research can provide theoretical support for the protection and restoration of ancient glass relics.

Multiple Nonlinear Regression Analysis for the Stability of Non-overtopping Perforated Quarter Circle Breakwater

Breakwaters have been built throughout the centuries for the coastal protection and the port development,but changes occurred in their layout and criteria used for the design.Quarter circle breakwater(QBW)is a new type evolved having advantages of both caisson type and perforated type breakwaters.The present study extracts the effect of change in the percentage of perforations on the stable conditions of seaside perforated QBW by using various physical models.The results were graphically analyzed using dimensionless parameters and it was concluded that there is a reduction in dimensionless stability parameter with an increase in steepness of the wave and change in water depth to the height of breakwater structure.Multiple non–linear regression analysis was done and the equation for the best fit curve with a higher regression coefficient was obtained by using Excel statistical software—XLSTAT.

Logistic Regression Analysis of Catheter Fixation Defects and Their Influencing Factors

[Objectives] To analyze the influencing factors of fixed defects in patients with catheter fixation in clinical nursing work, in order to provide the best catheter fixation nursing plan for patients.[Methods] 176 inpatients with indwelling catheter from surgical system of Taihe Hospital in Shiyan City from August 2022 to March 2023 were selected. Using a retrospective analysis method, the influencing factors of catheter fixation defects in the study subjects were divided into two categories based on objective characteristics: type I non modifiable influencing factors and type II modifiable influencing factors. Using the standard for catheter fixation defects, whether the patient had catheter fixation defects was determined. After classified and statistically analyzed item by item, binary Logistic multiple regression analysis was used to identify the influencing factors.[Results] The occurrence of catheter fixation defects in patients with catheter fixation was related to factors such as whether the patient was evaluated before fixation, whether the fixation method was standardized and systematic, whether there was sufficient communication between nurses and patients, and the patient s knowledge of catheter fixation. It was also influenced by factors such as the patient s age, catheterization site, catheterization number, catheterization duration, where there was a consciousness disorder, educational level, and external environmental temperature.[Conclusions] Early attention to the key factors affecting patients with catheter fixation defects can effectively prevent adverse factors and provide patients with the best catheter fixation nursing plan to improve nursing quality.

Nonlinear Time History Analysis for the Different Column Orientations under Seismic Wave Synthetic Approach

The significant impact of earthquakes on human lives and the built environment underscores the extensive human and economic losses caused by structural collapses. Over the years, researchers have focused on improving seismic design to mitigate earthquake-induced damages and enhance structural performance. In this study, a specific reinforced concrete (RC) frame structure at Kyungpook National University, designed for educational purposes, is analyzed as a representative case. Utilizing SAP 2000, the research conducts a nonlinear time history analysis to assess the structural performance under seismic conditions. The primary objective is to evaluate the influence of different column section designs, while maintaining identical column section areas, on structural behavior. The study employs two distinct seismic waves from Abeno (ABN) and Takatori (TKT) for the analysis, comparing the structural performance under varying seismic conditions. Key aspects examined include displacement, base shear force, base moment, joint radians, and layer displacement angle. This research is anticipated to serve as a valuable reference for seismic restraint reinforcement work on RC buildings, enriching the methods used for evaluating structures through nonlinear time history analysis based on the synthetic seismic wave approach.

Nonlinear Pushover Analysis of the Influences on RC Footing for the External Elevator Well

In contemporary society, reducing carbon dioxide emissions and achieving sustainable development are paramount goals. One effective approach is to preserve existing RC (Reinforced Concrete) buildings rather than demolishing them for new construction. However, a significant challenge arises from the lack of elevator designs in many of these existing RC buildings. Adding an external elevator becomes crucial to solving accessibility issues, enhancing property value, and satisfying modern residential buildings using convenient requirements. However, the structural performance of external elevator wells remains understudied. This research is designed by the actual external elevator project into existing RC buildings in Jinzhong Rd, Shanghai City. Specifically, this research examines five different external elevator wells under nonlinear pushover analysis, each varying in the height of the RC (Reinforced Concrete) footing. By analyzing plastic hinge states, performance points, capacity curves, spectrum curves, layer displacement, and drift ratio, this research aims to provide a comprehensive understanding of how these structures of the external elevator well respond to seismic events. The findings are expected to serve as a valuable reference for future external elevator projects, ensuring the external elevator designs meet the seismic requirements. By emphasizing seismic resistance in the design phase, the research aims to enhance the overall safety and longevity of external elevator systems integrated into existing RC buildings.

Attenuation Parameters of Blasting Vibration by Fuzzy Nonlinear Regression Analysis

In order to reduce the influence of outliers on the parameter estimate of the attenuation formula for the blasting vibration velocity,a fuzzy nonlinear regression method of Sadov’s vibration formula was proposed on the basis of the fuzziness of blasting engineering,and the algorithm was described in details as well.In accordance with an engineering case,the vibration attenuation formula was regressed by the fuzzy nonlinear regression method and the nonlinear least square method,respectively.The calculation results showed that the fuzzy nonlinear regression method is more suitable to the field test data.It differs from the nonlinear least square method because the weight of residual square in the objective function can be adjusted according to the membership of each data.And the deviation calculation of least square estimate of parameters in the nonlinear regression model verified the rationality of using the membership to assign the weight of residual square.The fuzzy nonlinear regression method provides a calculation basis for estimating Sadov’s vibration formula’s parameters more accurately.

Application of cluster analysis and stepwise regression in predicting the traffic volume of lanes

Because of the difficulty to obtain the traffic flow information of lanes at non-detector intersections in most metropolises of the world,based on the relationships between the lanes of signal-controlled intersections,cluster analysis and stepwise regression are integrated to predict the traffic volume of lanes at non-detector isolated controlled intersections.First cluster analysis is used to cluster the lanes of non-detector isolated signal-controlled intersections and the lanes of all signal-controlled intersections with detectors.Then, by the results of cluster analysis,the traffic volume samples are selected randomly and stepwise regression is used to predict the traffic volume of lanes at non-detector isolated signal-controlled intersections.The method is tested by the traffic volume data of lanes of the road network of Nanjing city.The problem of predicting the traffic volume of lanes at non-detector isolated signal-controlled intersections was resolved and can be widely used in urban traffic flow guidance and urban traffic control in cities without enough intersections equipped with detectors.

DIFFERENTIAL QUADRATURE FOR AXISYMMETRIC GEOMETRICALLY NONLINEAR ANALYSIS OF CIRCULAR PLATES

New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bending stresses of circular plates with movable and immovable edges under uniform pressures or a central point load.The shortcomings existing in the earlier analysis by the DQ method have been overcome by a new approach in applying the boundary conditions. The accuracy and the efficiency of the newly developed method for solving nonlinear problems are demonstrated.

Population Quantity Variations of Oriental Fruit Fly (Bactrocera dorsalis Hendel) on the Basis of Stepwise Regression Analysis

[Objective] The research aimed to study the significant influence factors of the population variations of oriental fruit fly. [Method] Using stepwise regression analysis, the population variations law of oriental fruit fly in Jianshui County of Yunnan province and the meteorological factors that caused its occurrence were analyzed. And the regression model was built. Finally, the regression model was tested on the basis of the data in Jianshui County of Yunnan Province during 2004-2006.[Result] The main meteorological factors that influenced the occurrence of oriental fruit fly were relative humidity, the lowest monthly temperature and rainfall. [Conclusion] This study will provide certain reference for the prediction researches on the time, quantity and occurrence peak of oriental fruit fly.

A Cross-Reference Method for Nonlinear Time Series Analysis in Semi-Blind Case

In this paper, we propose a cross reference method for nonlinear time series analyzing in semi blind case, that is, the dynamic equations modeling the time series are known but the corresponding parameters are not. The tasks of noise reduction and parameter estimation which were fulfilled separately before are combined iteratively. With the positive interaction between the two processing modules, the method is somewhat superior. Some prior work can be viewed as special cases of this general framework. The simulations for noise reduction and parameter estimation of contaminated chaotic time series show improved performance of our method compared with previous work.

Constitutive equations of 1060 pure aluminum based on modified double multiple nonlinear regression model

In order to study the work-ability and establish the optimum hot formation processing parameters for industrial 1060 pure aluminum, the compressive deformation behavior of pure aluminum was investigated at temperatures of 523?823 K and strain rates of 0.005?10 s?1 on a Gleeble?1500 thermo-simulation machine. The influence rule of processing parameters (strain, strain rate and temperature) on flow stress of pure aluminum was investigated. Nine analysis factors consisting of material parameters and according weights were optimized. Then, the constitutive equations of multilevel series rules, multilevel parallel rules and multilevel series &parallel rules were established. The correlation coefficients (R) are 0.992, 0.988 and 0.990, respectively, and the average absolute relative errors (AAREs) are 6.77%, 8.70% and 7.63%, respectively, which proves that the constitutive equations of multilevel series rules can predict the flow stress of pure aluminum with good correlation and precision.

Geometric and material nonlinear analysis of tensegrity structures

A numerical method is presented for the large deflection in elastic analysis of tensegrity structures including both geometric and material nonlinearities.The geometric nonlinearity is considered based on both total Lagrangian and updated Lagrangian formulations,while the material nonlinearity is treated through elastoplastic stress-strain relationship.The nonlinear equilibrium equations are solved using an incremental-iterative scheme in conjunction with the modified Newton-Raphson method.A computer program is developed to predict the mechanical responses of tensegrity systems under tensile,compressive and flexural loadings.Numerical results obtained are compared with those reported in the literature to demonstrate the accuracy and efficiency of the proposed program.The flexural behavior of the double layer quadruplex tensegrity grid is sufficiently good for lightweight large-span structural applications.On the other hand,its bending strength capacity is not sensitive to the self-stress level.

Combined influence of nonlinearity and dilation on slope stability evaluated by upper-bound limit analysis

The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem.The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soil blocks with the nonlinear Mohr–Coulomb failure criterion and nonassociated flow rule.The multipoint tangent(multi-tangent) technique was used to analyze the slope stability by linearizing the nonlinear failure criterion.A general expression for the slope safety factor was derived based on the virtual work principle and the strength reduction technique,and the global slope safety factor can be obtained by the optimization method of nonlinear sequential quadratic programming.The results show better agreement with previous research result when the nonlinear failure criterion reduces to a linear failure criterion or the non-associated flow rule reduces to an associated flow rule,which demonstrates the rationality of the presented method.Slope safety factors calculated by the multi-tangent inclined-slices technique were smaller than those obtained by the traditional single-tangent inclined-slices technique.The results show that the multi-tangent inclined-slices technique is a safe and effective method of slope stability limit analysis.The combined effect of nonlinearity and dilation on slope stability was analyzed,and the parameter analysis indicates that nonlinearity and dilation have significant influence on the result of slope stability analysis.

DDM regression analysis of the in-situ stress field in a non-linear fault zone

A multivariable regression analysis of the in-situ stress field, which considers the non-linear deformation behavior of faults in practical projects, is presented based on a newly developed three-dimensional displacement discontinuity method （DDM） program. The Bar- ton-Bandis model and the Kulhaway model are adopted as the normal and the tangential deformation model of faults, respectively, where the Mohr-Coulomb failure criterion is satisfied. In practical projects, the values of the mechanical parameters of rock and faults are restricted in a bounded range for in-situ test, and the optimal mechanical parameters are obtained from this range by a loop. Comparing with the traditional finite element method （FEM）, the DDM regression results are more accurate.

Nonlinear Mathematical Modeling and Sensitivity Analysis of Hydraulic Drive Unit

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

Nonlinear Bend Stiffener Analysis Using A Simple Formulation and Finite Element Method

Flexible marine risers are commonly used in deepwater floating systems. Bend stiffeners are designed to protect flexible risel against excessive bending at the connection with the hull. The structure is usually analyzed as a cantilever beam subjected to an inclined point load. As deflections are large and the bend stiffener material exhibits nonlinear stress-strain characteristics, geometric and material nonlinearities are important considerations. A new approach has been developed to solve this nonlinear problem. Its main advantage is its simplicity; in fact the present method can be easily implemented on a spreadsheet. Finite element analysis using ABAQUS is performed to validate the method. Solid elements are used for the bend stiffener and flexible pipe. To simulate the near inextensibility of flexible risers, a simple and original idea of using truss elements is proposed. Through a set of validation studies the present method is found to be in a good agreement with the finite element analysis. Further, parametric studies are performed by using both methods to identify the key parameters and phenomena that are most critical in design. The most important finding is that the common practice of neglecting the internal steel sleeve in the bend stiffener analysis is non-conservative and therefore needs to be reassessed.

Modified scaled distance regression analysis approach for prediction of blast-induced ground vibration in multi-hole blasting

The blast-induced ground vibration prediction using scaled distance regression analysis is one of the most popular methods employed by engineers for many decades. It uses the maximum charge per delay and distance of monitoring as the major factors for predicting the peak particle velocity(PPV). It is established that the PPV is caused by the maximum charge per delay which varies with the distance of monitoring and site geology. While conducting a production blasting, the waves induced by blasting of different holes interfere destructively with each other, which may result in higher PPV than the predicted value with scaled distance regression analysis. This phenomenon of interference/superimposition of waves is not considered while using scaled distance regression analysis. In this paper, an attempt has been made to compare the predicted values of blast-induced ground vibration using multi-hole trial blasting with single-hole blasting in an opencast coal mine under the same geological condition. Further,the modified prediction equation for the multi-hole trial blasting was obtained using single-hole regression analysis. The error between predicted and actual values of multi-hole blast-induced ground vibration was found to be reduced by 8.5%.