Nonlinear Regression Relationship Research Articles

Eastern oyster (Crassostrea virginica) nursery production in tropical coastal lagoons in Yucatán, Mexico: nonlinear regression modeling and relationships with environmental variables

Eastern oyster (Crassostrea virginica) nursery production in tropical coastal lagoons in Yucatán, Mexico: nonlinear regression modeling and relationships with environmental variables

Experimental investigation and application of soft computing models for predicting flow energy loss in arc-shaped constrictions

Abstract This investigation focuses on flow energy, a crucial parameter in the design of water structures such as channels. The research endeavors to explore the relative energy loss (ΔEAB/EA) in a constricted flow path of varying widths, employing Support Vector Machine (SVM), Artificial Neural Network (ANN), Gene Expression Programming (GEP), Multiple Adaptive Regression Splines (MARS), M5 and Random Forest (RF) models. Experiments span a Froude number range from 2.85 to 8.85. The experimental findings indicate that the ΔEAB/EA exceeds that observed in a classical hydraulic jump with constriction section. Within the SVM model, the linear kernel emerges as the best predictor of ΔEAB/EA, outperforming polynomial, radial basis function (RBF), and sigmoid kernels. In addition, in the ANN model, the MLP network was more accurate compared to the RBF network. The results indicate that the relationship proposed by the MARS model can play a significant role resulting in high accuracy compared to the non-linear regression relationship in predicting the target parameter. Upon comprehensive evaluation, the ANN method emerges as the most promising among the candidates, yielding superior performance compared to the other models. The testing phase results for the ANN-MLP are noteworthy, with R = 0.997, average RE% = 0.63%, RMSE = 0.0069, BIAS = −0.0004, DR = 0.999, SI = 0.0098 and KGE = 0.995.

The rainfall threshold of forest cover for regulating extreme floods in mountainous catchments

Floods frequently occur in mountainous regions and threaten lives and property worldwide. Forest cover usually plays an important role in regulating and preventing floods. However, the rainfall thresholds for forest cover to effectively regulate extreme flood are still unclear. In this study, we developed the topography-based subsurface storm flow hydrological (Top-SSF) model, which generally exhibited precise simulation performances in five typical mountainous catchments in southwest China. Then, the Top-SSF model was combined with a frequency analysis method to set different forest cover scenarios, investigating the relationship between rainfall threshold and forest cover in mountainous catchments. The results showed that under the control of soil saturated hydraulic conductivity (Ks) and maximum soil water storage capacity (Szm), the rainfall threshold of an extreme flood (the 100-year return period) increased significantly, especially when forest cover was larger than 70% of a catchment. Under the same forest cover, high initial soil water content (Swi) weakened the mitigating effect of forest cover on the extreme flood. In addition, a non-linear regression relationship between forest cover and rainfall threshold of a catchment was developed considering the impacts of Ks, Swi and annual mean precipitation (P¯) of the catchment. The significant impact of forest cover change on extreme floods was not only due to changing the amount of forest cover but also the soil properties. These results contribute to the understanding of the impact of forest cover changes on extreme floods and may provide valuable insights for flood defence in mountainous catchments.

Hierarchical Bayesian calibration of regional moment magnitude predictive models

Onsite Earthquake Early Warning (EEW) applications require robust predictive models that can relate the early part of the recorded seismic waves to seismicity and/or ground shaking characteristics, the latter representing the variables used to make decisions about raising or not an alarm. The use of limited information to establish these models within a real-time estimation setting, typically corresponding to the first few seconds after the identification of the seismic wave arrival, introduces significant uncertainty (variability) in the predictions. To increase the number of historical observations available for the model calibration, data from multiple seismic stations within the same geographic region are utilized for the latter task. Unfortunately, this introduces additional sources of variability in the predictive model development, originating from local geographical effects and site conditions that affect differently the underlying physics at each station. This paper introduces a hierarchical Bayesian model updating framework to address this challenge. To better focus the research effort, the calibration of earthquake magnitude nonlinear regression models based on the seismic maximum predominant period is investigated, though underlying principles can be extended to other type of decision variables and intensity measures used in EEW applications. Within the hierarchical updating framework, the predictive models for each station are separately calibrated (first level), while sharing information across the stations by selecting common calibration hyper-parameters (second level). This facilitates a reduction of the variability of the estimates originating from regional wave propagation effects while simultaneously providing sufficient amount of data for calibrating the predictive models even for stations with scarce available records. To support computational efficiency in the hierarchical calibration, conjugate priors are utilized, while for accommodating nonlinear regression relationships samples from the posterior distribution, representing the model calibration, are obtained using Metropolis-within-Gibbs sampling. As illustrative case study, the application to the Sichuan region of Southwestern China is examined, with extensive comparisons performed for the accuracy and robustness of the resultant probabilistic predictive models.

GROSS DOMESTIC PRODUCT AS A PREDICTOR OF THE BIRTH RATE IN UKRAINE

The paper conducts an information-analytical study of correlations between the fertility rate in Ukraine and the level of the gross domestic product (hereinafter referred to as – GDP), expressed in US dollars, per person of the population. Preliminary calculations based on the official statistical data for 1990-2021 indicated the absence (R2 = 0.0089) of both linear and non-linear regression relationships between the studied indicators. However, a more detailed analysis of the correlation field made it possible to trace three time intervals with a fairly close linear relationship between the birth rate in Ukraine and the general state of the national economy. The combined regression model of the birth rate built as a result of such an analysis turned out to be adequate, and all its parameters were statistically significant at the confidence level of p = 0.95.At the same time, similar statistical estimates of the unknown parameters of the model were also obtained when investigating the presence of inertia in the reactions of the values of the endogenous variable, taking into account a lag delay of one year. The change in the specification of the model, as a result of the introduction to consideration of an additional indicator of the global financial crisis, led to an improvement in its correlation indicators and interpolation accuracy, both in the presence of a lag shift (R∆=1=0.960, MAPE∆=1 = 3.89%), and in its absence (R∆=0=0.982, MAPE∆=0 = 2.68%). According to estimates made on the basis of a combined fertility model, it was established that before the beginning of the military aggression of the russian federation in 2014, the birth rate in the country had a direct linear relationship with the level of GDP, expressed in US dollars, per person of the population. However, the regression coefficient observed during the economic crisis of 1990-1999 was significantly higher than the corresponding indicator calculated for the economic recovery period of 2000-2014. That is, the process of reducing the birth rate, which was provoked by the economic crisis, turned out to be more significant than the process of its recovery during the economic growth of the country. On the other hand, for the period of the military aggression of the russian federation, a feedback relationship between these indicators becomes characteristic, namely, a decrease in the birth rate is accompanied by an increase in the level of the country’s GDP.

BUILDING PREDICTIVE MODELS TO ASSESS DEGRADATION OF SOIL ORGANIC MATTER OVER TIME USING REMOTE SENSING DATA

Agricultural fields near Rabia district, northwest of Nineveh Governorate/Iraq, were selected for study, as the study area is located between longitudes (36°31'51.34'' and 36°43'40.343'') north and two latitudes (42°16'14.475'' and 42°34'50.99'') east, with an area of approximately 52.5 hectares. The predictive model is built from the integration of multiple linear and nonlinear regression relationships between remote sensing data and laboratory-measured organic matter concentration values. The predictive model was applied to Satellite data for three years (2002, 2012, and 2022), producing three maps to describe the soil content of organic matter (a map for each year). The results of the study showed the possibility of applying predictive models to Satellite data for a particular area and for previous years to give results with high spatial accuracy (R2 = 0.9581). Spatial maps were possible for each of the three years studied (2002, 2012, and 2022), and fertility maps were drawn by projecting spectral evidence values into the predictive model equation in the ENVI program. The resulting images were then processed using ArcGIS 10.8 to color them and perform a Reclassify operation and take them out with the values of percentages of organic matter concentrations. The results showed a clear deterioration in the soil's organic matter content over time, especially between 2012 and 2022

Effects of 3D Roughness Parameters of Sandblasted Surface on Bond Strength of HVOF Sprayed WC-12Co Coatings

This work aims to reveal the effects of 3D roughness parameters of sandblasted surfaces on bond strength between thermal spray coatings and substrates. The investigation was carried out on the surface of AISI 4140, which were pretreated with automatic-sandblasting system. 3D topography and roughness parameters were analyzed by a 3D optical profiler. The bond strength of WC-12Co coatings was measured using a pull-off test method. Scanning electron microscope revealed that the morphology of the surface after sandblasting was rough. Furthermore, the surface topography was characterized by several irregular peaks and pits with different directions and no fixed orientation randomly distributed on sandblasted surface. The average values for surface roughness Sa = 4.84 ± 0.34 μm and bond strength = 32.8 ± 2.8 MPa were obtained. In terms of 3D roughness parameters, Sa, Sdr, Sdq and Sq were found to have more significant impact on affecting the bond strength, showing a nonlinear regression relationship. Furthermore, bond strength was positively correlated with Sa, Sdr and Sdq, while inversely proportional to Sq. This confirmed that a greater surface roughness of a sandblasted surface was not more conducive to the improvement of bond strength. The influence mechanism of each parameter was discussed, which was consistent with the regression mathematical model.

Optimal sliding friction coefficients for isolated viaducts and bridges: A comparison study

The aim of this work is to evaluate the influence of the pier–abutment–deck interaction on the seismic response of bridges isolated by single concave sliding pendulum isolators (friction pendulum system [FPS]) through a comparison with the results of the seismic response of isolated bridges without considering the presence of the rigid abutment (i.e., isolated viaducts). Two different multidegree-of-freedom (mdof) models are properly defined to carry out this comparison. In the both mdof models, five vibrational modes are considered to describe the elastic behavior of the reinforced concrete pier, and an additional degree of freedom is adopted to analyze the response of the infinitely rigid deck isolated by the seismic devices. The FPS isolator behavior is described through a widespread velocity-dependent model. By means of a nondimensional formulation of the motion equations with respect to the seismic intensity, a parametric analysis for several structural properties is performed in order to investigate the differences between the two mdof models in relation to the relevant response parameters. The uncertainty in the seismic input is taken into account by means of a set of natural records with different characteristics. Finally, multivariate nonlinear regression relationships are provided to estimate the optimum values of the sliding friction coefficient able to minimize the pier displacements relative to the ground as a function of the structural properties considering or neglecting the presence of the abutment.

Prediction Model for Spontaneous Combustion of Coal around Boreholes Using Bedding Gas Drainage

To accurately and reliably predict the time of spontaneous combustion of fractured coal around a borehole induced by gas drainage along the seam, this study performed an orthogonal test taking the No. 10 Coal Mine of Pingdingshan as the research object, in terms of the suction negative pressure and coal seam buried depth. COMSOL Multiphysics was used to model the orthogonal test results, and a multielement statistical analysis of four factors and their relationships with the spontaneous combustion of coal around the borehole and a single-factor analysis in line with the site conditions were performed on the modeling results through multiple regression. The results showed a nonlinear regression relationship between the sealing hole length, sealing hole depth, negative pressure, and coal seam depth and the spontaneous combustion of the coal around the gas drainage borehole; the prediction regression model is significant. Taking the field gas drainage in the No. 10 Coal Mine of Pingdingshan as an example, the relationship between the time of spontaneous combustion of gas drainage and the drainage pressure follows a power of two. When the drainage negative pressure is less than 45 kPa, the coal around the borehole is more likely to undergo spontaneous combustion with increasing pressure, and the sealing hole length has a positive linear correlation with the time of spontaneous combustion of the coal around the borehole. When the sealing hole length is 23 m, the time of spontaneous combustion of the coal around the gas drainage hole is >500 days, and the coal around the borehole does not easily undergo spontaneous combustion. When the sealing depth is 15 m, the time of spontaneous combustion of the coal around the gas drainage hole is 76 days, which is most likely to cause spontaneous combustion.

Evaluating Parameter Estimation Effect on the Polynomial Profile Monitoring Methods’ Phase II Performance

In some statistical process monitoring applications, the quality of a product or process can be determined by a linear or nonlinear regression relationship called profile. Basically, standard monitoring methods involve two phases: Phase I and Phase II. Usually, it is assumed that the process parameters are known, however this condition in many applications is not met and parameters are estimated using the in-control data set collected in Phase I. The present study evaluates and compares some Phase II control chart approaches for monitoring the second order polynomial profiles when the process parameters are estimated. These methods includes Orthogonal, MEWMA and dEWMA-OR control charts. The performance of each control chart is measured in terms of ARL, SDRL, AARL and SDARL metrics using Monte Carlo simulation approach. The results showed that the in-control and out-of-control performance of control charts is strongly affected by parameter estimation, especially when only a few Phase I samples are used to estimate the parameters. Moreover, the superior overall performance of the Orthogonal method rather than the other competing methods is shown. Furthermore, we concluded that F estimation method leads to better performance of control charts in Phase II.

Soil nitrogen sequestration in a long-term fertilizer experiment in central China

Aim of study: To evaluate the effects of a long-term manuring and fertilization experiment on the soil total N concentration and its storage and sequestration rates in the rice-wheat cropping system.Area of study: A rice-wheat rotation area in central China.Material and methods: A 35-yr long-term fertilizer experiment was conducted with 9 treatments: unfertilized (Control), N, P, and K fertilizers, manure (M) and M combined with N, P, and K fertilizers treatments. Soil total N input amount, total N concentration, total N storage amount and N sequestration rate in soil were calculated.Main results: The soil total N input amount, N concentration, N storage amount and N sequestration rate were significantly influenced by M and chemical fertilizers. In total, 0.017-0.021 g N/kg soil accumulated in the organic M plots, whereas only 0.005-0.007 g in chemical fertilizer alone plots. The highest soil total N storage amount was 6.09 t/hain the M alone plot, and the lowest value was 4.46 tN/ha in the N fertilizer alone plot. The highest N sequestration rate in soil was 0.061 t N/ha/yr in the high amount M plus NPK fertilizers plot, and the lowest value was 0.002 tN/ha/yr in the N fertilizer alone plot. A significant nonlinear regression relationship existed between the total N sequestration rate in soil and annual total N input amount. Moreover, the average soil total N concentration was significantly positively correlated with the average grain yield of crop and soil organic C concentration. The soil total N sequestration rate in M alone or M combined with inorganic fertilizer treatments were increased compared with inorganic fertilizer alone treatments.Research highlights: Considering crop yields and total N sequestration rate in soil, the use of manure combined with inorganic fertilizer should be recommended in the rice-wheat cropping system.

Predicting seepage from unlined earthen channels using the finite element method and multi variable nonlinear regression

Seepage losses from unlined channels are a major contributor to water loss in the agricultural sector. Quantification of seepage losses can improve water conveyance efficiency and provide solutions to water scarcity. In this study, a numerical simulation method is applied to investigate the factors that affect seepage from earthen channels. SEEP/W software was used to generate finite element method (FEM) solutions of the seepage flow equations. 246 numerical models, including different sections of trapezoidal, rectangular, and triangular earthen channels were studied using FEM. Numerical results are compared to available observation data from Zayandeh-Rud irrigation channels in Iran. Non-linear regression equations for the four empirical seepage equations are obtained from the SPSS statistical software. The results show that nonlinear multivariate regression relationships provide a suitable match for estimating seepage discharge. The accuracy of the suggested nonlinear regression equation in terms of R2 and RE are 0.928 and -2.42 %, respectively. Comparison of the seepage discharge with the empirical relationships showed that the empirical relationships have excessive error.

Numerical investigation on geometric configurations affecting seepage from unlined earthen channels and the comparison with field measurements

In this study, a numerical simulation is applied to investigate the effective factors on the seepage from the earthen channels. To authenticate the information at hand, some of the earthen channels in the Zayandeh-Rud irrigation network in Iran and Gediz watershed in Turkey were studied. 246 numerical models, including different sections of trapezoidal, rectangular and triangular earthen channels, were performed using the finite elements method (FEM). The results showed that, for a numerical simulation, a width of 15 times wider than the top width of the water surface in the channel would be required for the modelling of the left and right lateral boundaries. The comparison of the seepage with empirical relationships showed that the empirical relationships have too much error in the seepage estimation, however, Moritz’s relation with the coefficient of determination (R2) of 0.373 was better than the others. The linear and nonlinear multivariate regression relationships provide a suitable match for the seepage discharge estimation. The wetted perimeter has been distinguished as an effective parameter in the seepage from the channels, yet the channels side slope has a low impact on the seepage.

Random forest, M5P and regression analysis to estimate the field unsaturated hydraulic conductivity

Hydraulic conductivity of soil reveals its influencing role in the studies related to management of surface and subsurface flow, e.g. irrigation and drainage projects, and solute mass transport models. Direct measurements of hydraulic conductivity have many difficulties due to spatial variation of the property in the field. Pertaining to this problem, in this study, estimation models have been developed using machine learning methods (M5 tree model and random forest model) in an attempt to estimate the accurate values of unsaturated hydraulic conductivity related to basic soil properties (clay, silt and sand content, bulk density and moisture content). Data set was collected from the experimental measurements of cumulative infiltration using mini disc infiltrometer at the study area (Kurukshetra, India). A multivariate nonlinear regression (MNLR) relationship was derived, and the performance of this model was compared with the machine learning-based models. The evaluation of the results, based on statistical criteria (R2, RMSE, MAE), suggested that random forest regression model is superior in accurate estimations of the unsaturated hydraulic conductivity of field data relative to M5 model tree and MNLR.

Site-Specific Relationships between Bedrock Depth and HVSR Fundamental Resonance Frequency Using KiK-NET Data from Japan

It is commonly accepted that the horizontal-to-vertical spectral ratio (HVSR) technique enables the detection of the fundamental resonance frequency ($$f_{\text{HVSR}}$$) of a given site. The utility of this $$f_{\text{HVSR}}$$ is analyzed using the nonlinear regression relationships between $$f_{\text{HVSR}}$$ and bedrock depth ($$h$$). The derived relationships are mostly site-specific, so that the present paper consists of two main parts. The first is a literature review for the available empirical relationships between $$f_{\text{HVSR}}$$ and $$h$$. The aim of this part is to highlight the practical limitations of these established relationships and to make fair comparisons. The second is to generate new relationships, taking advantage of the very wide range of available lithological, geophysical, and geotechnical borehole drilling data of the 697 KiK-NET seismic stations in Japan. For this purpose, HVSR are calculated using 10,000 weak earthquakes or linear events recorded at KiK-NET stations to determine the $$f_{\text{HVSR}}$$ and correlate it with the corresponding $$h$$. The overlying layers/bedrock interface falling within sedimentary, igneous, or metamorphic layers significantly affect the derived frequency–depth relationships. In addition, these relationships are strongly reproduced by the $$V_{\text{p}} /V_{\text{s}}$$ ratio of the bedrock in the range of 1.6–2.2. Interestingly, it is found that $$f_{\text{HVSR}}$$ less than 1 Hz corresponding to $$h$$ more than 100 m leads the trend of the overall frequency–depth relationship.

A new method to estimate cloud effective radius using Meteosat Second Generation SEVIRI over Middle East

The cloud particle size distribution varies with height and the phase may change from water to mixed phase to ice through the vertical profile of the cloud, giving rise to different radiative characteristics. Researchers suggested an empirical equation for an approximation of the relation between cloud-particle effective radius and reflectance of channel IR3.7 for Advanced Very High Resolution Radiometer (AVHRR) and Multi-Functional Transport Satellite (MTSAT)-1R satellites. However, when we examined this empirical equation for MSG satellites, there was no correlation between the cloud particle effective radius and those from the Terra and Aqua/MODIS (Moderate Resolution Imaging Spectrometers) products. Given the fact that this relationship is empirical and not applicable for Meteosat satellites with 3.9 µm wavelength cloud properties, we need to introduce a new nonlinear equation that is independent from other cloud properties, to retrieve the cloud effective radius from MSG satellite over Middle East. Thus, in this study, a development of the mentioned method, based on a nonlinear regression model, was introduced to estimate the water/ice-cloud particle effective radius from the 3.9 µm wavelength reflectivity of the Meteosat Second Generation Indian Ocean Data Coverage (MSG-1(IODC)) satellite over the Middle East region. For this purpose, the LibRadTran radiative transfer model was used. This approach is almost independent from other cloud properties, which makes this relationship more efficient for retrieving a cloud’s effective radius. To evaluate this approach, the results have been compared to the effective-radius product of the MODIS on board the Terra and Aqua satellites, and cloud effective radius parameter from the MSG-1 satellite’s optimal cloud analysis (OCA) data. The average of correlation coefficient, standard deviation, and RMSE (root mean square error) of this retrieved algorithm method for 29 randomly selected case studies, in comparison to the corresponding MODIS product, are 0.93, 3.093, and 3.639, and compared with OCA product, 0.88, 4.015, and 4.51, respectively. Therefore, the results of analysis in the Middle East region show that the retrieved effective particle radius from Meteosat satellites corresponds strongly with MODIS data from the Terra and Aqua satellites, and also with the OCA products of the MSG-1. Furthermore, using the algorithm that is presented in this paper, a nonlinear regression relationship can be made for retrieving cloud effective radius in the intended place.

Research on the correlation between mechanical signaling molecules of hypertrophic scar and post injury time in burn patients in scar remodeling stage

Objective: To analyze the correlation between integrin β1, focal adhesion kinase (FAK), extracellular signal-regulated kinase 1/2 (ERK1/2) of hypertrophic scar (HS) and post injury time in burn patients in scar remodeling stage. Methods: Thirty-four patients with 34 HS specimens admitted to Department of Burns and Plastic Surgery of Chengdu No.2 Hospital and Institute of Burn Research of the First Affiliated Hospital of Army Medical University (originally the Third Military Medical University) from May 2013 to April 2016 were recruited by convenient sampling method, and normal skin specimens were obtained from donor sites of another 6 patients from the above-mentioned departments who had scar resection and skin grafting for this cross-sectional and observational study. Vancouver Scar Scale (VSS) was used to assess the height, vascularity, pigmentation, and pliability of scars. Diasonograph was used to assess scar thickness. Immunohistochemical method was used to observe the expressions of integrin β1, FAK, and ERK1/2 in dermis and epidermis of scar and normal skin. Correlations between the post injury time and the scar thickness, the post injury time and the expressions of integrin β1, FAK, and ERK1/2 in epidermis of scar, the post injury time and the expressions of integrin β1, FAK, and ERK1/2 in dermis of scar, the expressions of integrin β1, FAK, and ERK1/2 in dermis and those in epidermis of scar were analyzed by Pearson correlation analysis. Locally estimated scatterplot smoothing curve fitting line was used to demonstrate the non-linear regression relationship between the expressions of integrin β1, FAK, and ERK1/2 in dermis and those in epidermis of scar, the scar thickness and the post injury time. Results: (1) The total VSS score of scars of patients was (8.3±2.3) points, with height scored (2.2±0.7) points, vascularity scored (2.0±0.8) points, pigmentation scored (2.3±0.7) points, and pliability scored (1.9±0.7) points. The thickness of scar was (2.8±1.1) mm. (2) The expressions of integrin β1, FAK, and ERK1/2 in dermis and epidermis of scar were more than those in normal skin. (3) There was significantly positive correlation between the scar thickness and the post injury time (r=0.39, P<0.05). There was significantly positive correlation between the expression of integrin β1 in epidermis of scar and the post injury time (r=0.33, P<0.05). There were no significantly correlations between the expressions of FAK and ERK1/2 in epidermis of scar and the post injury time (r=-0.03, -0.04, P>0.05). There was significantly negative correlation between the expression of FAK in dermis of scar and the post injury time (r=-0.34, P<0.05). There were no significantly correlations between the expressions of integrin β1 and ERK1/2 in dermis of scar and the post injury time (r=0.07, -0.23, P>0.05). There were significantly positive correlation between the expressions of integrin β1, FAK, and ERK1/2 in dermis and those in epidermis of scar (r=0.70, 0.60, 0.64, P<0.01). (4) The expressions of integrin β1, FAK, and ERK1/2 in dermis and epidermis of scar were changed from downtrend in 1 to 2 months post injury to uptrend in 2 to 3 months post injury, which reached the peak around 3 to 4 months post injury. Hereafter the expressions of mechanical signaling molecules in epidermis of scar were gradually declined, while the expressions of mechanical signaling molecules in dermis of scar were at a quite high level within half a year post injury. Scar thickness was steadily increased after 1 month post injury. Conclusions: In scar remodeling stage of burn patients, the HS thickness increases continuously along with the increasing post injury time in the early stage of scar formation. The vulnerability of integrin β1, FAK, and ERK1/2 of HS to external mechanical stimuli increases gradually within 4 months post injury.

A Monte Carlo simulation technique for assessment of earthquake-induced displacement of slopes

The dynamic response of slopes against earthquake is commonly characterized by the earthquake-induced displacement of slope (EIDS). The EIDS value is a function of several variables such as the material properties, slope geometry, and earthquake acceleration. This work is aimed at the prediction of EIDS using the Monte Carlo simulation method (MCSM). Hence, the parameters height, unit specific weight, cohesion, friction angle, vibration duration, and maximum horizontal acceleration are used to predict the EIDS values. To do this, a multiple non-linear regression relationship is first derived between EIDS and the independent variables. Then MCSM is performed based on the developed regression equation. The results obtained demonstrate that the stochastic approach used is able to successfully reproduce the EIDS values and calculate the confidence intervals. The average of the measured and simulated values for EIDS was 4.34 cm and 4.48 cm, respectively. Eventually, the results of a performed correlation sensitivity analysis revealed that the maximum horizontal acceleration had the greatest impact on EIDS.

Influence of soil conditions on the optimal sliding friction coefficient for isolated bridges

The aim of this work is to evaluate the optimal properties of friction pendulum system (FPS) bearings for the seismic protection of bridge piers under earthquake excitations having different frequency characteristics representative of different soil conditions in order to reduce the seismic vulnerability of infrastructures increasing their safety level. A two-degree-of-freedom model is adopted to describe, respectively, the response of the infinitely rigid deck isolated by the FPS devices and the elastic behaviour of the pier. The FPS isolator behaviour is modeled through a widespread velocity-dependent rule. By means of a non-dimensional formulation of the motion equations, proposed in this study, a wide parametric analysis considering several structural parameters is performed to investigate their influence on the response parameters relevant to the performance assessment. Seismic excitations, modeled as time-modulated filtered Gaussian white noise random processes having different intensities and frequency contents, are considered. Specifically, the filter parameters, which control the frequency contents, are properly calibrated to reproduce stiff, medium and soft soil conditions, respectively. Finally, multi-variate non-linear regression relationships are derived to estimate the optimum values of the sliding friction coefficient able to minimize a percentile of the pier displacements relative to the ground as a function of the structural properties, of the seismic input intensity and of the soil condition.

Cautionary note on the use of genetic programming in statistical downscaling

The selection of inputs (predictors) to downscaling models is an important task in any statistical downscaling exercise. The selection of an appropriate set of predictors to a downscaling model enhances its generalization skills as such set of predictors can reliably explain the catchment‐scale hydroclimatic variable (predictand). Among the predictor selection procedures seen in the literature, the use of genetic programming (GP) can be regarded as a unique approach as it not only selects a set of predictors influential on the predictand but also simultaneously determines a linear or nonlinear regression relationship between the predictors and the predictand. In this short communication, the details of an investigation on the assessment of effectiveness of GP in identifying a unique optimum set of predictors influential on the predictand and its ability to generate a unique optimum predictor–predictand relationship are presented. In this investigation, downscaling models were evolved for relatively wet and dry precipitation stations pertaining to two study areas using two different sets of reanalysis data for each calendar month maintaining the same GP attributes. It was found that irrespective of the climate regime (i.e., wet and dry) and reanalysis data set used, the probability of identification of a unique optimum set of predictors influential on precipitation by GP is quite low. Therefore, it can be argued that the use of GP for the selection of a unique optimum set of predictors influential on a predictand is not effective. However, when run repetitively, GP algorithm selected certain predictors more frequently than others. Also, when run repetitively, the structure of the predictor–predictand relationships evolved by GP varied from one run to another, indicating that the physical interpretation of the predictor–predictand relationships evolved by GP in a downscaling exercise can be unreliable.