Multivariate Nonlinear Regression Model Research Articles

Serum cystatin C as a biomarker to predict all-cause mortality in geriatrics hip fracture

BackgroundCystatin C, a low-molecular-weight protein, belongs to cysteine protease inhibitors produced primarily by nucleated cells. Its serum concentration, independent of sex, age, or muscle mass, is a good predictor of renal dysfunction in older adults. This study evaluated the association between all-cause mortality and preoperative cystatin C levels in hip fractures. Materials and methodsData describing the demographic and clinical characteristics of the patients were gathered specifically from older individuals who had suffered hip fractures. The study used linear and non-linear multivariate Cox regression models to investigate the association between preoperative cystatin C levels and mortality. The analyses were conducted using the R and EmpowerStats software. ResultsIn total, two thousand three hundred and ninety-four patients were included in this study. A total of 790 patients (33 %) died of all causes. The mean follow-up was 37.62 months. The preoperative cystatin C was 0.91 ± 0.41 mg/L. Linear multivariate Cox regression analysis revealed a significant association between preoperative cystatin C level and death, with a hazard ratio (HR) of 2.19 (95 % confidence interval [CI]: 1.72–2.79, P < 0.0001). Nevertheless, the correlation between the variables was inconsistent. A cystatin C concentration of 1.62 mg/L marked a significant change in the non-linear relationship. A preoperative cystatin C level below 1.62 mg/L was found to be significantly linked with an increased risk of mortality (HR = 2.60, 95 % CI: 1.92–3.52, P < 0.0001). The mortality reached its highest point when the preoperative cystatin C level was greater than 1.62 mg/L. After that, the mortality risk did not increase further (HR = 1.54, 95 % CI: 0.98–2.42, P = 0.0588). The non-linear relationship remained consistent in the propensity score-matching sensitive analysis. ConclusionsThe study found a non-linear relationship between preoperative cystatin C levels and mortality in geriatric hip fractures. This suggests that preoperative cystatin C can be used as a predictor of the risk of death. The registration number is ChiCTR2200057323.

A study on the influence of network environment on college students’ ideological and political attitudes

Abstract The network environment is gradually formed and developed under the impetus of information technology, and it plays an important role in transmitting political concepts, forming political attitudes, and cultivating political identity. After exploring the dilemma of ideological and political education in the network environment, this paper uses polynomial least squares approximation to construct polynomial regressions to solve various nonlinear regression problems. Then, the network environment factors such as bad guidance, network technology, cultural penetration, and false information are taken as independent variables. College students’ ideological and political attitudes are taken as dependent variables to construct a multivariate nonlinear regression model, observe the polynomial regression parameters according to the principle of least-squares estimation, and take 489 college students of the University of R as the research subjects to explore the influence of network environment on college students’ ideological and political attitudes. The results show that the correlation coefficients of four factors, namely, poor guidance of network environment, network technology, cultural penetration, and false information, with students’ ideological and political attitudes range from 0.178 to 0.531, which is a significant positive correlation. Meanwhile, compared with political cognition and political emotion, network environment factors explain the strongest tendency of political behavior (54.9%), and different network environment factors have various degrees of influence on college students’ ideological and political attitudes. The study offers data to support the cultivation and strengthening of college students’ ideological and political attitudes.

Prediction of wetting pattern dimensions under moistube irrigation with a multivariate nonlinear model

Moistube irrigation is a new micro-irrigation technology. Accurately estimating its wetting pattern dimensions presents a challenge. Therefore, it is necessary to develop models for efficient assessment of the wetting transport pattern in order to design a cost-effective moistube irrigation system. To achieve this goal, this study developed a multivariate nonlinear regression model and compared it with a dimensional model. HYDRUS-2D was used to perform numerical simulations of 56 irrigation scenarios with different factors. The experiments showed that the shape of the wetting soil body approximated a cylinder and was mainly affected by soil texture, pressure head, and matric potential. A multivariate nonlinear model using a power function relationship between wetting size and irrigation time was developed, with a determination coefficient greater than 0.99. The model was validated for cases with six soil texture types, with mean average absolute errors of 0.43–0.90 cm, root mean square errors of 0.51–0.95 cm, and mean deviation percentage values of 3.23%–6.27%. The multivariate nonlinear regression model outperformed the dimensional model. It can therefore provide a scientific foundation for the development of moistube irrigation systems.

Estimation of grassland aboveground biomass and its response to climate changes based on remote sensing inversion in Three-River-Source National Park, Tibet Plateau, China

Three-River-Source (TRS) National Park stands as one of China’s earliest established national parks, dedicated to significant ecological responsibilities that include conserving soil and water resources in the Tibetan Plateau region. Research on climate change’s influence on the TRS region’s grasslands is of great significance in our efforts to comprehend and conserve the grassland ecosystem. The most effective random forest (RF) model was chosen to invert the aboveground biomass (AGB) of grassland in the previous 6 years (2015−2020) and predict the grassland AGB in the following 20 years (2021−2040) by comparing linear regression and multivariate nonlinear regression models such as RF, support vector machine, decision tree, and artificial neural network. A Theil–Sen median trend analysis and a Mann–Kendal test were then used to examine the trends of grassland AGB. The results showed that (1) RF outperformed other models in estimating grassland AGB, with a test set decision coefficient of multiple determination (R2) of 0.722, a root mean square error of 42.596 g/m2, and a mean absolute error of 35.619 g/m2; (2) over 6 years, the grassland AGB in TRS National Park had a spatial trend of a steady rise from the northwest to the southeast. The average annual grassland AGB was 247.333 g/m2, with averages of 44.836 g/m2, 92.601 g/m2, and 120.217 g/m2 in the Yangtze River, Yellow River, and Lancang River source parks respectively. The trend of the grassland AGB was primarily stabilized and slightly recovered, with a small portion of the slightly deteriorated areas; (3) climate change significantly affected grassland AGB, and when temperature and precipitation conditions were adequate, grassland AGB values increased with temperature and precipitation. In the scenarios of ssp119, ssp245, and ssp585, grassland AGB is projected to exhibit a dynamic upward trend over the next 20 years. Global warming is expected to boost grassland AGB. Comprehensive measures are essential to maintain grassland health and ensure a positive impact on global carbon and ecological balance. The study’s findings hold great importance for the ecological security of the TRS region and contribute to our global understanding of sustainable grassland development.

Multivariate nonlinear regression analysis of hydraulic fracturing parameters based on hybrid FEM–DEM

PurposeThis paper aims to employ a multivariate nonlinear regression analysis to establish a predictive model for the final fracture area, while accounting for the impact of individual parameters.Design/methodology/approachThis analysis is based on the numerical simulation data obtained, using the hybrid finite element–discrete element (FE–DE) method. The forecasting model was compared with the numerical results and the accuracy of the model was evaluated by the root mean square (RMS) and the RMS error, the mean absolute error and the mean absolute percentage error.FindingsThe multivariate nonlinear regression model can accurately predict the nonlinear relationships between injection rate, leakoff coefficient, elastic modulus, permeability, Poisson’s ratio, pore pressure and final fracture area. The regression equations obtained from the Newton iteration of the least squares method are strong in terms of the fit to the six sensitive parameters, and the model follow essentially the same trend with the numerical simulation data, with no systematic divergence detected. Least absolutely deviation has a significantly weaker performance than the least squares method. The percentage contribution of sensitive parameters to the final fracture area is available from the simulation results and forecast model. Injection rate, leakoff coefficient, permeability, elastic modulus, pore pressure and Poisson’s ratio contribute 43.4%, −19.4%, 24.8%, −19.2%, −21.3% and 10.1% to the final fracture area, respectively, as they increased gradually. In summary, (1) the fluid injection rate has the greatest influence on the final fracture area. (2)The multivariate nonlinear regression equation was optimally obtained after 59 iterations of the least squares-based Newton method and 27 derivative evaluations, with a decidability coefficient R2 = 0.711 representing the model reliability and the regression equations fit the four parameters of leakoff coefficient, permeability, elastic modulus and pore pressure very satisfactorily. The models follow essentially the identical trend with the numerical simulation data and there is no systematic divergence. The least absolute deviation has a significantly weaker fit than the least squares method. (3)The nonlinear forecasting model of physical parameters of hydraulic fracturing established in this paper can be applied as a standard for optimizing the fracturing strategy and predicting the fracturing efficiency in situ field and numerical simulation. Its effectiveness can be trained and optimized by experimental and simulation data, and taking into account more basic data and establishing regression equations, containing more fracturing parameters will be the further research interests.Originality/valueThe nonlinear forecasting model of physical parameters of hydraulic fracturing established in this paper can be applied as a standard for optimizing the fracturing strategy and predicting the fracturing efficiency in situ field and numerical simulation. Its effectiveness can be trained and optimized by experimental and simulation data, and taking into account more basic data and establishing regression equations, containing more fracturing parameters will be the further research interests.

An Exploratory Study of Laser Scribing Quality through Cross-Section Scribing Profiles.

This article presents a novel approach for evaluating laser scribing quality through cross-section profiles generated from a three-dimensional optical profiler. Existing methods for assessing scribing quality only consider the width and depth of a scribe profile. The proposed method uses a cubic spline model for cross-section profiles. Two quality characteristics are proposed to assess scribing accuracy and consistency. Accuracy is measured by the ratio of the actual laser-scribed area to the target area (RA), which reflects the deviation from the desired profile. The mean square error (MSE) is a measure of how close each scribed cross-section under the same scribing conditions is to the fitted cubic spline model. Over 1370 cross-section profiles were generated under 171 scribing conditions. Two response surface polynomial models for RA and MSE were built with 18 scribing conditions with acceptable scribing depth and RA values. Both RA and MSE were considered simultaneously via contour plots. A scatter plot of RA and MSE was then used for Pareto optimization. It was found that the cross-sectional profile of a laser scribe could be accurately represented by a cubic spline model. A multivariate nonlinear regression model for RA and MSE identified pulse energy and repetition rate as the two dominant laser parameters. A Pareto optimization analysis further established a Pareto front, where the best compromised solution could be found.

Preoperative Serum Calcium Level Predicts Postoperative Mortality in Older Adult Patients with Hip Fracture: A Prospective Cohort Study of 2333 Patients

ObjectivesHip fractures are a significant cause of mortality among older adults. However, predictive markers for an unfavorable prognosis are still lacking. Serum calcium is an essential element in several biochemical reactions in the body. This study investigated the role of the preoperative serum calcium level as a prognostic parameter for postoperative mortality in older adult patients with hip fractures. DesignWe conducted a prospective cohort study at the trauma center in our hospital, from January 1, 2015, to September 30, 2019. A total of 2333 older patients with hip fractures were recruited. This prospective cohort study was conducted in accordance with the criteria of STROCSS. Setting and ParticipantsOlder adult patients with hip fractures were screened between January 2015 and September 2019 at the trauma center of our hospital. MethodsDemographic and clinical characteristics of the patients were collected. Linear and nonlinear multivariate Cox regression models were used to identify the association between preoperative serum calcium level and all-cause mortality. All analyses were performed using EmpowerStats and the R software. ResultsA total of 2333 older adult patients with hip fractures were included in the study. The mean follow-up was 37.5 months. Overall, 770 patients (33%) died of all causes. The preoperative serum calcium concentrations were 2.18 ± 0.13 mmol/L. Linear multivariate Cox regression models showed that preoperative serum calcium levels were associated with mortality [hazard ratio (HR) 0.37, 95% CI 0.21-0.67; P = .0009] after adjusting for confounders. However, the linear association was unstable, and nonlinearity was identified. A preoperative serum calcium level of 2.3 mmol/L was an inflection point for prediction. When the preoperative serum calcium concentration was below 2.3 mmol/L, serum calcium concentration increased by 1 mmol/L, and mortality risk decreased by 77% (HR 0.23, 95% CI 0.13-0.43, P < .0001). In contrast, when the preoperative serum calcium concentration was more significant than 2.3 mmol/L, the mortality risk increased with serum calcium concentration (HR 6.27, 95% CI 1.65-23.74, P = .0069). Conclusions and ImplicationsThe preoperative serum calcium level is nonlinearly associated with mortality in older adults with hip fractures, with a U-shaped association, and could be used as a potential predictor of prognosis.

Bivariate and Multivariate Data Cloning through Non Linear Regression Models

Nonlinear regression analysis holds significant popularity in mathematical, engineering, and social science domains. Disciplines like financial matters, biology, and natural chemistry have broadly utilized nonlinear regression models (NLRMs). Cloned datasets have their own importance in such areas which provide the same fit of bivariate and multivariate nonlinear regression models for the actual datasets. This article presents a sequence of cloned datasets that give exactly the same fit of bivariate and multivariate nonlinear regression models.

The Association Between Red Cell Distribution Width (RDW) and All-Cause Mortality in Elderly Patients with Hip Fractures: A Retrospective Cohort Study.

Red cell distribution width (RDW) may be related to the prognosis of hip fractures. The purpose of this study was to evaluate the association between (RDW) and all-cause mortality in elderly hip fractures. Elderly patients aged ≥65 years who had a hip fracture were screened between January 1, 2015, and September 30, 2019. The age, gender of patients and other demographics, as well as history of allergy, injury mechanism, underlying illnesses at the time of admission, fracture classification, time from admission to operation, RDW, operation time, blood loss, infusion, transfusion, treatment strategy, and length in hospital stay and follow-up and other clinical characteristics were collected. Linear and nonlinear multivariate Cox regression models were used to identify the association between RDW and mortality in these patients. Analyses were performed using EmpowerStats and the R software. A total of 2587 patients were included in this retrospective cohort study. The mean follow-up period was 38.92 months. A total of 873 (33.75%) patients died due to all-cause mortality. The RDW was linearly associated with mortality in elderly patients with hip fractures. Linear multivariate Cox regression models showed that RDW was associated with mortality (hazard ratio [HR]=1.03, 95% confidence interval [CI]:1.02-1.05, P < 0.0001) after adjusting for confounding factors. The mortality risk increased by 3% when RDW increased by 1 fL. RDW is associated with mortality in elderly patients with hip fractures, and RDW could be considered a predictor of mortality risk. ChiCTR2200057323.

The serum NT-proBNP is associated with all-cause mortality in geriatric hip fracture: a cohort of 1354 patients.

To explore the relationship between N-terminal prohormone of brain natriuretic peptide (NT-proBNP) level and all-cause mortality in geriatric hip fractures and evaluate the possible predictive role of NT-proBNP level. Consecutive older adult patients with hip fractures were screened between January 2015 and September 2019. Demographic and clinical characteristics of the patients were collected. Linear and nonlinear multivariate Cox regression models were used to identify the association between NT-proBNP levels and mortality. All analyses were performed using EmpowerStats and the R software. One thousand three hundred fifty-four patients were included in the study. The mean follow-up was 34.35 ± 15.82 months. Four hundred twenty-nine (31.68%) patients died due to all-cause mortality. The preoperative NT-proBNP was median 337.95 (range 16.09-20,123.00) ng/L. Multivariate Cox regression models showed a nonlinearity association between NT-proBNP levels and mortality in elderly hip fractures. An NT-proBNP of 781 ng/L was an inflection point in the saturation effect. When < 781 ng/L, NT-proBNP was associated with mortality (hazard ratio [HR] = 1.12, 95% confidence interval [CI]: 1.06-1.18, P < 0.0001), whereas at > 781 ng/L, NT-proBNP was not associated with mortality (HR = 1.00, 95% CI: 0.98-1.01, P = 0.4718). In the stratification analysis, the result was stable. The NT-proBNP levels were nonlinearly associated with mortality in elderly hip fractures, and NT-proBNP of 781 ng/L was a valuable indicator of all-cause mortality. ChiCTR2200057323.

Test research on flexural strength of soil-cement reinforced with carbon fibers

In order to verify the feasibility of using chopped carbon fibers to reinforce soil-cement, the orthogonal test and verification test of flexural strength had been carried out and the correctness and effectiveness of the test results had been clarified. The test results indicated that the addition of carbon fibers could make the flexural strength of soil-cement improved effectively and change the brittle failure of soil-cement into plastic failure. The flexural strength of carbon fiber soil-cement (CFSC) could reach 0.509 MPa, that was 31.5 % higher than that (0.387 MPa) of the plain soil-cement in the standard condition. All the first extreme flexural strength (e.g. the flexural strength), yield strength, second extreme flexural strength and residual strength increased first and then decreased with the increase of either fiber content or fiber length. Thus, excessive fiber content and fiber length were not better and the optimum values were existent with 0.6 % and 15 mm respectively under the test conditions agreed in this study. The change magnitude of the yield strength, second extreme flexural strength and residual strength was much greater than that of the first extreme flexural strength. So the strengthening effect of the carbon fibers on soil-cement was better for its toughness and ductility than for its flexural strength. The order of soil type corresponding with the flexural strength of CFSC from high to low was clay, silty clay, mucky silty clay, silt and fine sand. The flexural strength of CFSC increased linearly with the increase of cement content and the economical cement content was obtained as 15 %. The flexural strength of CFSC increased quickly between the 3 d and 14 d, slowly between the 14 d and 28 d and very slowly after 28 d, but still was increasing. The interaction mechanism between carbon fibers and soil-cement had been analyzed from a macro and a micro perspective respectively. The modified multivariate nonlinear regression model was proposed. The results and conclusions above could provide reference and basis for the application and popularization of CFSC in actual engineering.

Association of a lifestyle score with cardiometabolic markers among individuals with diabetes: a cross-sectional study

IntroductionTo investigate the associations of a lifestyle score with various cardiovascular risk markers, indicators for fatty liver disease as well as MRI-determined total, subcutaneous and visceral adipose tissue mass in...

Slurry-ability mathematical modeling of microwave-modified lignite: A comparative analysis of multivariate non-linear regression model and XGBoost algorithm model

In the preparation of microwave-modified lignite (ML) water slurry (MLWS), its specific surface area, oxygen functional groups and oxygen-carbon atomic ratio are important factors affecting the slurry ability. Based on the relationship between the physicochemical properties of 23 ML samples and their maximum solid concentrations, a multivariate nonlinear regression (MNR) model and a machine learning model based on XGBoost algorithm were established to predict the slurry ability. The determination coefficient (R2), the mean average error (MAE) and the mean squared errors (MSE) for MNR mode is 0.928, 0.507 and 0.391, respectively. The R2, MAE and MSE for XGBoost model is 0.582, 0.619 and 0.667, respectively. Hence, the MNR model with less error percentage has a higher accuracy than the XGBoost model, but the XGBoost model is highly efficient, flexible and portable with strong generalization ability to unknown data. Overall, the proposed models in this study have a good effect on the prediction of the slurry ability of ML, and serve as a technical reference for future predicting the slurry ability of other types of coal.

Two sides of the same coin: Kernel partial least-squares (KPLS) for linear and non-linear multivariate calibration. A tutorial

A tutorial is presented on the operation and properties of the non-linear multivariate regression model kernel partial least-squares (KPLS). After the discussion of a simple non-linear univariate problem, solved by regressing a dependent variable on the projection of an independent variable onto a set of Gaussian functions, the principles of KPLS are introduced for processing non-linear multivariate data. The following aspects are covered: (1) the estimation of the model sensitivity as a function of analyte concentration from error propagation concepts, (2) the proposal of a parameter measuring the degree of non-linearity, to avoid a black-and-white description of data sets as either linear or non-linear, (3) the use of the model parameters for variable selection. The application of KPLS to both simulated and experimental data sets is discussed, in the latter case involving near infrared spectra employed for the determination of quality parameters in foodstuff samples and fluorescence spectroscopic data for the study of systems of biological relevance. Computer codes written in the popular MATLAB and R environments are also provided.

Cadmium, lead, and mercury interactions on obstructive lung function in pre- and postmenopausal women.

There was a dearth of information on how heavy metals affect women's lung function. To assess the effects of cadmium, lead, and mercury and their interactions on obstructive lung function in pre- and postmenopausal women. The associations between an individual heavy metal and its mixtures and the first second of forced expiration (FEV1)/forced vital capacity (FVC) were studied using multivariate non-linear, linear, and logistic regression models, Bayesian kernel machine regression (BKMR), and marginal effects in 1821 women. Serum cadmium and lead levels and the percentage of FEV1/FVC < 70% were substantially higher in postmenopausal women than in premenopausal women. Cadmium (β = - 0.84, 95%, - 1.63 to - 0.05) and lead (β = - 0.43, 95%CI, - 1.62 to - 0.04) were found to be inversely associated with the FEV1/FVC ratio in premenopausal women, while a combination of cadmium and mercury showed a negative association with the FEV1/FVC ratio in postmenopausal women (β = - 0.65, 95%CI, - 1.27 to - 0.03). In the non-linear regression model, an inverted U-shape association of mercury with FEV1/FVC indicator was found in postmenopausal women (β = - 0.78, 95%CI, - 1.41 to - 0.15). In BKMR model, a mixture of three heavy metals was negatively associated with the FEV1/FVC ratio. Cadmium was identified as an important substance associated with lung function decline (posterior inclusion probabilities (PIPs) = 0.731 in premenopausal and PIPs = 0.514 in postmenopausal women). Cadmium appeared linear; an inverted U-shape association of mercury with the FEV1/FVC indicator and slightly positive associations of lead with the FEV1/FVC indicator in postmenopausal women were found. Threshold cutoff values for the studied substances related to clinical lung function decline were established. In conclusion, the presence of mixed heavy metals (cadmium, lead, and mercury) and their association with obstructive lung function showed worse results than separate associations. These findings have important implications for policy and future research about how heavy metals affect women's lungs.

Numerical simulation of wave propagation through rigid vegetation and a predictive model of drag coefficient using an artificial neural network

Coastal vegetation has been widely recognized as an effective nature-based measure for coastal protection. Numerous studies based on macroscopic models have been performed to simulate vegetation-induced wave attenuation. The modeling accuracy is closely related to a key input parameter, the drag coefficient (CD). To date, however, no reliable prediction method is available for determining CD, limiting the practical application of the macroscopic models. In this study, vegetation-induced wave attenuation was investigated using a macroscopic model that solved Reynolds-averaged Navier-Stokes equations by introducing a vegetation resistance force to account for momentum loss. A stabilized k-ε turbulence model considering vegetation effects was developed for turbulence closure. The volume-of-fluid technique was used to capture the free surface. Using a calibration method to determine CD, the numerical model was validated based on several laboratory experiments. A correlation analysis was performed to reveal the potential contributions of dimensionless parameters about waves and vegetation to the calibrated CD. Multivariate non-linear regression (MNLR) and artificial neural network (ANN) methods were adopted to develop a CD predictive model. Comparisons indicated that the prediction performance of ANN model is superior to that of the MNLR model. The ANN model has the potential as a promising predictive tool for obtaining CD when simulating wave propagation through rigid vegetation.

Non-destructive determination of soluble solids content in intact apples using a self-made portable NIR diffuse reflectance instrument

The soluble solids content (SSC) is an important internal quality parameter of fruits that is monitored on the fruit market to meet different consumer demands. The aim of this study was to develop a self-made portable near-infrared (NIR) diffuse reflectance instrument to evaluate and monitor the SSC of intact apples. The visible and near-infrared (Vis-NIR) spectra of 118 ‘Fuji’ apples were collected using a Vis-NIR diffuse reflectance spectroscopic measurement system in the spectral range of 450–1100 nm. Savitzky-Golay convolution smoothing and first derivative methods were subsequently applied to eliminate noise interference and baseline shift. Successive projections algorithm (SPA) was performed to extract feature wavelengths from the pretreatment spectra, and the back-propagation artificial neural network (BP-ANN) and multivariate nonlinear regression (MNLR) models were employed to evaluate the predictive ability of the extracted and selected feature wavelengths for the SSC of apples. Seven wavelengths (881, 890, 901, 926, 941, 951, 978 nm) were selected as optimal feature wavelengths from the extracted feature wavelengths (18 wavelengths). The MNLR model (R2 = 0.953, RMSE = 0.391 %) exhibited a high prediction accuracy compared to the BP-ANN model (R2 = 0.865, RMSE = 0.754 %). Based on the results, NIR combined with the MNLR model could be applied in the self-made portable instrument to innovatively monitor the SSC of apples. Finally, a self-made portable NIR diffuse reflectance instrument was designed and developed, and the spectral information of 298 ‘Fuji’ apples was collected using the instrument. According to the results, the MNLR model could well predict the SSC of apples (R2 = 0.871, RMSE = 0.687 %). The overall results also revealed that the developed portable NIR instrument is a promising device for rapid non-destructive monitoring of fruit SSC, thereby meeting the practical application requirement of postharvest commercial processing systems. This instrument could also be beneficial to customers, growers, and producers.

A machine-learning-based model for seismic performance assessment of interior slab-column connections

Slab-column connections are the most critical components in flat plate systems under seismic actions due to their brittle failure mode. Finite element analysis (FEA) can be adopted as an extension of experimental testing to potentially lead to the development of modern design codes by providing significant information on the punching shear failure process of connections. However, the available concrete constitutive models in FEA packages fail in simulating the hysteretic response of the connections under cyclic loads. Moreover, it is shown that the available design code recommendations and empirical models are not accurate tools for assessing the seismic performance of these connections (e.g., unbalanced moment and/or drift capacity). In an effort to overcome these limitations, a dataset of previously tested experiments is compiled to predict the ultimate load and drift of the connections using the multi-variate non-linear regression model. Additionally, there is a need to develop a new constitutive material model for seismic performance assessment of the connections to capture the complete hysteretic response of the connection using numerical FEA. Consequently, a deep neural network is trained over the accumulated dataset and integrated into the OpenSees source code to determine the seismic performance of the connections. For data augmentation, a generative neural network model of autoencoders known as Generative Adversarial Networks (GANs) is constructed to generate synthetic data. The proposed material model is found to have significantly improved precision in capturing the hysteretic response of flat plates. The developed models showed higher accuracy than the design code estimations and empirical models.

Research on Water Resources Development and Utilization Based on Linear Regression and Multiple Nonlinear Regression

With the further development of industrialization and urbanization, China's water resources will be more severe. In order to study the synergy of the three red line targets, we predicted the total water consumption in 2030 by establishing the total water consumption model and using the linear regression prediction method. It is assumed that the water consumption of 10,000 yuan of industrial added value and the effective utilization coefficient of agricultural irrigation water all reached the red line value in 2030. Next, a multivariate nonlinear regression model of total water consumption is established, and the indirect substitution method is used to obtain the function of the internal relationship among the water consumption of 10,000 yuan GDP, the actual water consumption per mu of cultivated land for irrigation, and the water consumption of 10,000 yuan industrial added value, which includes time variables, and then the sensitivity analysis of the above functions are carried out. The following conclusions are drawn: China's overall water resources development and utilization should adopt the policy of improving the effective utilization coefficient of farmland irrigation water and reducing the industrial added value water consumption of 10,000 yuan as a supplement.

Process Parameters and Modeling Study of Thermosonic Flip Chip Bonding

Thermosonic flip chip (TSFC) bonding technology has become a developing area of chip packaging technology due to its advantages of low bonding temperature and bonding pressure. To explore the appropriate bonding parameters and to understand the relationship between each parameter and the stress/strain at the bonding interface. Bonding tests were carried out and then simulated orthogonal tests were conducted using the finite element model. The bonding test results show that: The initial position of the bumps does not affect the strength after bonding. But, an unreasonable selection of bonding pressure and ultrasonic parameters can lead to different degrees of cracks at the bonding interface after bonding and destroy the bonding strength. Simulation results show that: The order of influence of the three bonding parameters on von Mises stress/(shear stress) is: bonding pressure> ultrasonic amplitude>bonding temperature/(ultrasonic amplitude>bonding temperature>bonding pressure). Based on the simulation results, a multivariate nonlinear regression model between von Mises stress/shear stress and bonding parameters was constructed. Some recommendations for the selection of bonding parameters are given: 1 ) the bonding pressure was selected in the range of 9-11MPa, 2)the bonding temperature was chosen to be less than 200 °C and 3) the ultrasonic amplitude was 1.1μm(power about 22w). At the same time, the ultrasonic power can be increased by increasing the ultrasonic frequency to achieve better results in bonding. This study can provide some theoretical basis for the selection of bonding parameters for TSFC bonding.