Multivariate Nonlinear Regression Method Research Articles

3D simulation estimation and experimental validation of droplet generation in CFD-based flow-focusing microfluidic chips

Abstract Microdroplets generated using microfluidic techniques offer significant advantages over those generated using conventional methods, including high accuracy and excellent monodispersity. However, there remains a paucity of literature regarding the influence of fluid operating conditions and physical properties on droplet generation, specifically in relation to size and frequency, using computational fluid dynamics (CFD) techniques. In this study, we present a simplified microfluidic chip capable of flexibly adjusting the structure and size of the microchannels based on specific requirements. Subsequently, three-dimensional numerical simulations of this chip were conducted using CFD techniques and fitted a dimensionless model to estimate the droplet generation size and frequency through multivariate nonlinear regression methods. The experimental validation results demonstrated a strong correlation between the fitted data and the experimental observations, with size differences not exceeding 8% and good monodispersity, indicated by a coefficient of variation of less than 2.4%. This study provides valuable insights and a reference for future research.

Investigation of hydrodynamic characteristics of an oyster reef under regular waves

Oyster reef living shorelines are popular solutions to mitigate coastal hazards while providing ecosystem services, and their hydrodynamic characteristics deserve further examination. This paper reports an experimental and numerical study of the hydrodynamic behavior of a bagged oyster shell (BOS) reef under regular waves. The dependence of the pore pressure within the reef and the hydrodynamic coefficients on the reef height, length, porosity, and wave parameters are investigated. The results show that the normalized maximum pore pressure ps_m∗ decreases from the seaside of the BOS reef to its leeside and decreases with increasing dimensionless reef length. With increasing wave steepness, ps_m∗ fluctuates with an overall increasing trend. With increasing BOS reef porosity, ps_m∗ decreases at seaside locations and increases at leeside locations; simultaneously, the wave reflection coefficient Kr and the wave dissipation coefficient Kd decrease, and the wave transmission coefficient Kt increases. With increasing wave steepness for a given wave period, Kr and Kt tend to increase, but Kd exhibits the opposite trend. As the dimensionless reef height and length increase, Kt decreases and Kd increases. Multivariate nonlinear regression and genetic programming-based symbolic regression methods are individually used to derive two formulas for predicting the wave transmission coefficient, with the formula from the latter method being found to give a higher prediction accuracy.

Experimental and modelling studies on static sag of solid weighting powders in Polysulfonate workover fluids at high temperature and high pressure

The solid weighting material in a high-density workover fluid is prone to static sag. Existing experimental methods cannot predict the parameters of the settling stability of workover fluids at high temperature and high pressure (HTHP). Therefore, in this study, static settlement experiments were carried out using a novel experimental setup. The experimental setup enables the measurement of the density profile of heavy workover fluids at HTHP. A multi-parameter correlation equation between the sag factor and particle diameter, particle density, base fluid density, workover fluid density and rheological parameters, aging time, temperature, and pressure was obtained using dimensional analysis and multivariate nonlinear regression methods. The results reveal that the settlement stability of the workover fluid decreases with the increase in temperature and pressure. Based on the multi-parameter correlation, the predicted and the measured values were compared and verified. The error between the predicted value and the measured value was within 5%. The average prediction error was 1.68%, and the maximum prediction error was 3.8%. These results reveal that the model proposed in this study can effectively predict the static sedimentation stability of the solid weighted Polysulfonate workover fluids. Furthermore, the proposed correlation can guide the properties adjustment of the workover fluids to achieve the required sag stability. This work provides a new approach to predict and control the sag stability of the solid weighted workover fluids.

Numerical study of wave run-up on sea dikes with vegetated foreshores

Integrating coastal vegetation into sea dikes is a nature-based approach aimed at combining disaster prevention with ecological sustainability in coastal areas. This study investigates the impact of vegetation on the wave run-up on dikes through numerical analysis. The numerical model used in the study solves the Reynolds-averaged Navier–Stokes equations by adding a vegetation resistance force to account for momentum loss. A stabilized k–ω shear stress transport model considering the vegetation effect was adopted for turbulence closure. A series of numerical simulations was carried out on the wave run-up (Ru) on dikes, focusing on the effects of different vegetation heights, densities, zone lengths, and dike slopes under various wave conditions. The results indicate that vegetation can significantly decrease Ru and may cause the wave to change from breaking to nonbreaking on dikes. The Ru behaviors depend on whether waves break and can be well characterized by the Iribarren number and dimensionless wave momentum flux parameter under breaking and nonbreaking conditions, respectively. Finally, the multivariate non-linear regression (MNLR) and artificial neural network (ANN) methods were adopted to explore a prediction model for evaluating Ru. Comparisons showed that the prediction performance of the ANN model is superior to that of the MNLR model. The ANN model has the potential as a promising predictive tool for obtaining wave run-up on dikes with vegetated foreshores under breaking and nonbreaking conditions.

Proposing a novel mathematical model for hospital pneumatic system

Hospital Pneumatic Systems, specializing in pneumatic systems, are among the most essential components for hospitals. It offers efficient and cost-effective solutions to problems related to the transportation of various materials in hospitals. However, in existing systems, the need for compressed air is met without worrying about cost control and without depending on the sample transported, and this not only makes the system inefficient but also may cause sample degradation. The main purpose of this study is to provide speed/pressure control according to the type of material transported to eliminate the disadvantages of existing systems such as energy use and sample degradation. In this study, a new mathematical model is presented that can be used to make more energy-efficient hospital pneumatic systems. Although there are many studies on various pneumatic systems in the literature, there is not enough for the control of hospital pneumatic systems. According to the results obtained in this study, the system parameters were determined and the mathematical model of the system was obtained by using the Multivariate nonlinear regression method. A genetic algorithm was used to test the validity of the obtained mathematical model and to optimize the coefficient of the input parameters of the model. It is expected that this proposed model will contribute to the use of hospital pneumatic systems and provide a scientific and practical solution to the proposed mathematical model. The proposed mathematical model provides up to %43 more efficient transportation over the currently used system that has been tested.

Structural Characteristics and Improved Thermal Stability of HDPE/Calcium Pimelate Nanocomposites

In the present research work, calcium pimelate (CaPim) was synthesized and investigated as an additive for high-density polyethylene (HDPE). HDPE/CaPim nanocomposites were prepared by melt-mixing, with CaPim content ranging from 0.1% to 1%, affording white homogeneous materials. The chemical structure of the nanocomposites and the incorporation of CaPim was confirmed by infrared spectroscopy. The surficial morphology and the additive distribution were examined by scanning electron microscopy. Differential scanning calorimetry and X-ray diffraction measurements showed that the thermal transitions and crystal structure of HDPE are not affected by the incorporation of CaPim, while the mechanical properties are retained overall. This study focuses on the thermal degradation of HDPE nanocomposites, investigating the degradation mechanism and kinetic parameters through various analytical methods. Isoconversional techniques, including the Friedman method, Vyazovkin analysis, and Ozawa Flynn Wall analysis, were employed to calculate activation energies (Eα). The degradation mechanism and kinetic triplet were determined based on a multivariate non-linear regression method (model-fitting). Finally, the presence of a CaPim additive was shown to increase the Eα of thermal degradation, consistent with the calculated dependence of Eα on the degree of conversion and the improved thermal stability of the HDPE matrix.

Direct solar-driven calcination kinetics for Ca-looping thermochemical energy storage

Ca-looping thermochemical energy storage is considered to be an efficient and low-cost thermal energy storage technology for third-generation concentrated solar thermal power generation. However, the limitation of conventional kinetic studies cannot satisfy the direct solar driven calcination reaction mechanism. Therefore, a direct solar-driven calcination kinetics function of calcium carbonate particles based on multivariate nonlinear regression method is proposed. This scheme driven by full-wavelength solar energy has widely universality and application taking the effects of particle size, porosity, doping composition, temperature and CO2 concentration into account, which intuitively reflects the essence of photothermal conversion characteristics and reveals the mechanisms of photothermal calcination reactions. The heat storage efficiency of Fe:Mn:Al modified calcium carbonate particles after 20 cycles is 93.03%, the spectral absorption rate is 84.27%. This work provides a new idea for the in-depth study of the decomposition kinetics of solar-driven calcium-based particles.

Investigating the Phase Transition Kinetics of 1-Octadecanol/Sorbitol Derivative/Expanded Graphite Composite Phase Change Material with Isoconversional and Multivariate Non-Linear Regression Methods.

Organic composite phase change materials (PCMs) have been extensively studied, and it is important to investigate the effect of added components on the phase change process of the organic matrix. Herein, the phase transition process of the composite PCM with 1-octadecanol (OD) as the matrix adsorbed by a network framework composed of 1,3:2,4-di-(3,4-dimethyl) benzylidene sorbitol (DMDBS) and expanded graphite (EG) was measured using differential scanning calorimetry (DSC) at several linear heating rates. Using isoconversional and multivariate non-linear regression methods, a two-step consecutive reaction model for the composite PCM was established, while the apparent activation energies and pre-exponential factors were determined. The reaction mechanism of the first step was altered compared to pure OD, while the activation energies significantly decreased at the initial stage of the phase transition process and increased at the later stage. Combined with microscopic morphology analysis, the main reasons were the size and nanoconfinement effect. The predictions of the composite PCM under various conditions suggested that the composite PCM had a wider available temperature range compared to pure OD. This research provided a new idea for the in-depth study of the phase transition process of organic composite PCMs, which was helpful for the evaluation of organic composite PCMs.

Performance Optimization of a Spoon Precision Seed Metering Device Based on a Maize Seed Assembly Model and Discrete Element Method

To improve the sowing performance of the spoon wheel maize seeding machinery, in this paper, two varieties of maize seed are selected as examples. The maize spoon precision seed metering device, a core component of the spoon wheel seeding machinery, is used as the research object. The maize seed assembly model is first established based on the maize seed assembly modeling method. Its validity is verified by the sowing experiment and corresponding DEM simulation under the different revolving speeds of the seed metering wheel. Secondly, the performance of the spoon precision seed metering device is optimized by integrating the maize seed assembly model and multivariate nonlinear regression method. Therefore, the number of sub-spheres of the horse tooth, spherical cone, and spheroid maize seed model are 10–14, 18, and 6, respectively. The results show that the performance of the seed metering device improved when the revolving speed of the seed metering wheel, handing angle, and seed spoon radius are 25 r/min, 40°, and 7 mm, respectively. There is good agreement between the expected results and experimental ones with relative errors of less than 5%, and the optimized seed metering device facilitates the process of seed guiding and seed delivery during the sowing process.

Empirical formulas for predicting the energy attenuation behavior of primary stress waves in 1D composite chain of viscoelastic spheres

One-dimensional composite chain of viscoelastic spheres are potential candidates for novel impact buffers. Understanding the energy attenuation behavior of primary stress waves in the composite chain of viscoelastic spheres is the premise for high-performance impact buffers design. Although the current research included viscoelasticity into the motion equations of spheres, most of them were limited to homogeneous chains. Moreover, the models of discrete system could not give the explicit expressions of the key factors governing the energy attenuation of primary stress waves. The absence of explicit formulas for the key factors hindered efficient optimization design of impact buffers constructed by one-dimensional composite chain of viscoelastic spheres. In this study, empirical formulas for predicting the input amplitude, the attenuation coefficient of the contact force and the transmission coefficient at the interface were constructed. Multivariate nonlinear regression method and dimensional constraint were applied to ensure that all the empirical formulas only employ the impact velocity and the parameters of the used spheres as independent variables. Intermediate factor was introduced for individual key factor to evaluate the accuracy of the empirical formula. Though the groups of empirical formulas have degraded performance in the low range of the intermediate factors, their accuracy in quantitatively predicting the energy attenuation behavior of the stress waves in one-dimensional composite chain of viscoelastic spheres deserves satisfactory.

An efficient calculation method of large-region dynamic traffic noise maps based on hybrid modeling

The construction of noise maps is of great significance for the management and control of urban noise and the protection of residents’ physical and mental health. The European Noise Directive recommends using computational methods to construct strategic noise maps when possible. The current noise maps based on model calculation rely on complex noise emission and propagation models, and their huge number of regional grids needs to consume a lot of calculation time. This seriously restricts the update efficiency of noise maps, making it difficult to realize large-scale application and real-time dynamic update of noise maps. In order to improve the computational efficiency of noise maps, based on big data-driven technology, this paper combines the traditional CNOSSOS-EU noise emission modeling method with the multivariate nonlinear regression modeling method, and proposes an efficient calculation method of large-region dynamic traffic noise maps based on hybrid modeling method. First, this paper constructs the (daily and nightly) noise contribution prediction models of road sources with different classes, considering the daily and nightly periods and different urban road classes. Parameters of the proposed model are evaluated by using the multivariate nonlinear regression method to replace the complex nonlinear acoustic mechanism modeling. On this basis, in order to further improve the computational efficiency, noise contribution attenuations of the constructed models are parameterized and evaluated quantitatively. And then, the database containing the index table of the road noise sources-receivers and the corresponding noise contribution attenuations is constructed. The experimental results show that compared with the traditional calculation methods based on acoustic mechanism model, the noise map calculation method based on hybrid model proposed in this paper greatly reduces the model computations of noise map, improves the efficiency of noise mapping. It will provide technical support for constructing dynamic noise maps of large urban regions.

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.

Crystallization kinetics of GdYScAlCo high-entropy bulk metallic glass

The thermal stability and non-isothermal crystallization of a new bulk-amorphous high-entropy (HE-BMG) equiatomic GdYScAlCo alloy were studied by differential scanning calorimetry (DSC). The alloy shows a four-stage crystallization process. The kinetic parameters (activation energy (Eα)), the pre-exponential factor (logA) and glass-forming ability indicators (kinetic fragility index, characteristic temperatures) for the GdYScAlCo alloy were obtained. The Eα values obtained by isoconversional methods indicate a nonlinear Arrhenian behaviour and a complex process. The Avrami equation modification proposed by Jeziorny and the multivariate nonlinear regression method were applied on the nonisothermal crystallization. In the case of primary crystallization of the amorphous GdYScAlCo alloy under nonisothermal conditions, the kinetics of the nucleation process is best described by an autocatalytic reaction.

Hydrodynamic and aeration characteristics of an aerator of a surging water tank with a vertical baffle under a horizontal sinusoidal motion

To address the hypoxia problem in seawater, this paper proposes an aerator for a surging water tank with a vertical baffle and experimentally and numerically investigates its hydrodynamic and aeration characteristics under a horizontal sinusoidal motion. The intrinsic relationships of the dimensionless maximum wave surface run-up, maximum air pressure, and airflow rate are examined with the ratios of tank surging amplitude to still water depth, tank surging frequency to natural frequency, water exchange height to still water depth, and air hole area to plan area of the sub-tank, respectively. In particular, the dimensionless maximum wave surface run-up reaches its peak when the tank surging frequency fe approaches the natural frequency f1 of the individual sub-tank sloshing mode, and the maximum dimensionless airflow rate appears when the tank surging frequency fe approaches the natural frequency fs of the U-tube sloshing mode. The ratio of the tank surging amplitude to the still water depth and fe/fs play minor roles in the dimensionless maximum air pressure. Furthermore, two methods are used to deduce the prediction formulas for the dimensionless airflow rate. The symbolic regression method performs better than the multivariate non-linear regression method.

Prediction model of strength properties of marine gas-bearing sediments based on compressional wave velocity

The strength properties of marine sediments are closely related to the spudcan penetration and jacket installation of offshore oil platforms. However, gas affects the properties of sediments to a certain extent and poses certain hidden dangers to the operation. Therefore, rapid and accurate determination of the strength properties of gas-bearing sediments has become an important issue. In this study, a series of acoustic and mechanical experiments were conducted in the laboratory by replicating marine gas-bearing sediments. Based on the two acoustic wave propagation theories, the calculated compressional wave velocity was compared with the measured wave velocity, and it was found that the result of the porous media model (P-M) is consistent with the actual situation. Laboratory mechanical property tests showed that cohesion and internal friction angle were positively correlated with density and negatively correlated with water content. The bubble fractional volume affects the undrained shear strength of the sediment, and the multi-parameter equation of the strength properties and physical properties of the marine sediment is fitted by the multivariate nonlinear regression method. On this basis, a single-parameter strength property prediction model of marine gas-bearing sediments based on compressional wave velocity was established with physical properties as a bridge, and the strength properties of gas-bearing sediments were accurately predicted. This prediction model avoids the disturbance of sediments measured by in-situ sampling and improves the accuracy of the strength properties of gas-bearing sediments in marine areas that cannot be sampled.

A Contrast Analysis of Deformation Characteristics and Critical Dynamic Stress of Natural and Fiber-Binder Reinforced Subgrade Filler after Different Freeze-Thaw Cycles

To investigate the dynamic stability of natural subgrade filler (NSF) and fiber-binder reinforced subgrade filler (RSF) under cyclic load after freeze-thaw (FT) cycles, a triaxial test was conducted to determine the correlation between cumulative plastic strain (CPS) and the quantity of loading cycles, as well as the evolution law of dynamic strength and critical dynamic stress (CDS) with different FT cycles. The CPS change in the NSF and RSF shows three states (stable, critical, and destructive) with increasing vibration times. However, both fillers have different failure forms, and the curve shapes of the CPS with loading cycle quantities before and after failure are also different. With the number of FT cycles increasing, the requisite dynamic stress threshold for NSF specimen failure decreases continuously. After three FT cycles, the anti-cumulative deformation ability of the NSF decreases by approximately 32%. The anti-cumulative deformation abilities of the NSF after seven and nine FT cycles, respectively, are similar. The amelioration measures could significantly enhance the FT resistance of the NSF. After zero, one, three, five, seven, and nine FT cycles, the requisite dynamic stress threshold for the RSF to reach destruction is increased 1.52, 1.89, 1.98, 2.32, 2.2, and 2.45 times, respectively, compared to that of the NSF. A mechanical model of critical dynamic stress of the NSF and RSF that considers the FT cycle was obtained using a multivariate nonlinear regression method.

A Mathematical Model for Predicting the Sauter Mean Diameter of Liquid-Medium Ultrasonic Atomizing Nozzle Based on Orthogonal Design

As a new type of atomizing nozzle with superior atomizing performance, the liquid-medium ultrasonic atomization nozzle has been widely applied in the field of spray dust reduction. In this study, in order to establish a mathematical model for predicting the Sauter mean diameter (SMD) of such nozzles, the interaction between the SMD of the nozzle and the three influencing factors, i.e., air pressure, water pressure, and outlet diameter were investigated based on the custom-designed spraying experiment platform and orthogonal design methods. Through range analysis, it was obtained that the three parameters affecting the SMD of the nozzle are in the order of air pressure > water pressure > outlet diameter. On this basis, using the multivariate nonlinear regression method, the mathematical model for predicting the SMD of the nozzle was constructed. Comparison of the experimental results with the predicted values of the SMD of the nozzle by the multivariate nonlinear regression mathematical model, showed strong similarity with an average relative error of only about 5%. Therefore, the established mathematical model in this paper can be used to predict and calculate the droplet size for liquid-medium ultrasonic atomizing nozzles.

Predicting adulteration of grated Parmigiano Reggiano cheese with Ricotta using electrophoresis, multivariate nonlinear regression and computational intelligence methods

Urea polyacrylamide gel electrophoresis combined with statistical methods was used to detect the addition of Ricotta to grated Parmigiano Reggiano cheese. The adulterated samples were prepared by adding grated Ricotta to grated Parmigiano Reggiano cheese in six different ratios. The logistic regression and rank correlation performed worse than the naïve Bayes classifier at identifying samples of grated Parmigiano Reggiano containing more than 20% Ricotta in terms of area under the receiver operating characteristic curve and classification accuracy. This work can be considered a pilot study to investigate the potential of machine‐learning methods to predict the authenticity of Parmigiano Reggiano cheese.

Nonisothermal Crystallization Kinetics: Studying the Validity of Different Johnson–Mehl–Avrami–Erofeev–Kolmogorov (JMAEK) Based Equations

The Johnson–Mehl–Avrami–Erofeev–Kolmogorov (JMAEK) equation modifications proposed by Jeziorny, by Atiqullah and by Ruitenberg and Woldt were applied on the nonisothermal crystallization data of Poly(ethylene 2,5-furandicarboxylate)/2.5 wt. % Carbon Nanotubes (PEF/2.5 CNTs) nanocomposite. The classic JMAEK equation and the JMAEK model using the multivariate nonlinear regression method were also used to evaluate the cold crystallization's kinetic parameters of PEF/2.5 CNTs. Differential Scanning Calorimetry (DSC) measurements were carried out at heating rates of 1, 2.5, 5, 10 and 15 K/min. The effective activation energy (Eα) of the process was calculated using the isoconversional method of Vyazovkin. The Eα values indicate a nonlinear Arrhenian behavior and a complex process. The multivariate nonlinear regression method suggested a consecutive two-mechanism reaction model described by the JMAEK equation for both mechanisms. This method provided better fitting results of the experimental data for all the heating rates simultaneously and kinetic parameters' values within the limits of physical meaning. In any case, Jeziorny's modification of the JMAEK model was the most inadequate since the extracted Avrami exponents exceed in value those with a physical meaning.

Real-time regulation of filling speed based on multiparameter synergistic coupling effect in fused deposition modeling

This paper aimed to perform a preliminary study on real-time regulation of filling speed by considering multiparameter synergistic coupling effect in fused deposition modeling. Bivariate experiments and sampling printing tests on designed samples, under different parameter combinations which are made up by filling speed, layer thickness, nozzle temperature and corner angle, were carried out to build and validate a real-time regulation model of filling speed by employing error analysis and multivariate nonlinear regression method. Results showed that the equivalent dimensional deviation values and area deviation values of Sample A, Sample B, Sample C by using real-time regulation algorithm of filling speed are lower than or close to the concentrated averages by using the optimal constant filling speed, with the maximum of 0.32 mm and 0.46 mm2. Actual and theoretical build time of Sample D at real-time regulated filling speed are less than those at 20 mm/s (“low speed”), and close to those at 45 mm/s (“medium speed”) or 70 mm/s (“high speed”), which indicates that the method of real-time dynamic adjusting filling speed can not only improve printing accuracy, but also give a full consideration to printing efficiency at the same time.