Nonlinear Response Surface Model Research Articles

Modeling stream baseflow nitrate concentration in an agricultural watershed using neural network and bootstrap method

The evaluation of water resource vulnerability to nonpoint source pollution in the presence of uncertainty remains a crucial concern. To enhance the accuracy of the assessment and pinpoint the key factors that affect watershed water quality, the integration of an artificial neural network (ANN) into the evaluation process is imperative. The research involved the collection of streams baseflow samples from thirty-eight sites between 1994 and 1999 in the Tomorrow-Waupaca River Watershed in central Wisconsin, USA, with a focus on examining the relationship between nitrate concentrations and a range of environmental and land use variables extracted from the watershed GIS database. This study utilized ANN methodology, combined with a bootstrap technique that employed a random resampling approach from a single input dataset, to simulate monthly stream baseflow nitrate concentrations. The effectiveness and predictive ability of the ANN model were assessed by comparing it to conventional multivariate regression methods. Through the use of ANN, more precise outcomes can be achieved while taking into account the uncertainty associated with the analysis. The findings demonstrated that the ANN outperformed both the multivariate linear regression and nonlinear quadratic response surface models in explaining the variance of stream nitrate and in external prediction consistency. This study also highlighted several key variables, such as the areal percentage of agricultural land and grassland, stream order, and the average slope of the groundwater flow path, that significantly impacted the stream baseflow nitrate concentrations in this watershed that was dominated by dairy farming and groundwater. Of these variables, the percentage of agricultural land emerged as the most significant factor.

Probabilistic Analysis of Shallow Foundations on c-φ Soils Using 2nd Order Response Surface Methods

The HL-Reliability Index is utilized to investigate the applicability of several linear and nonlinear response surface models based on design experiments techniques to evaluate the safety under random loading, against bearing capacity failure of shallow foundations resting on c-φ soils with multivariate correlated variables. The reliability results obtained using FORM/SORM coupled with these models, are checked by Monte Carlo simulation method. It is demonstrated that the application of these models significantly reduces the execution time and memory requirements, with the central composite design scheme being the most accurate. It is also concluded, that consideration of correlation, significantly affects the reliability index for large values of soil friction angle uncertainty. The reliability index is found to be highly sensitive to uncertainties of soil friction angle more than the cohesion and the loading which have approximately the same influence, especially for the case of lognormally distributed variables. In addition, the probabilistic results show that reliability index decreases substantially with the increase of the applied pressure, and that there is significant difference between the reliability indices values computed, based on the assumption of normal distribution as compared to lognormal distribution, especially for the lower ranges of applied loading.

Design and Employing of a Non-Linear Response Surface Model to Predict the Microbial Loads in Anaerobic Digestion of Cow Manure: Batch Balloon Digester

Biogas is among the sources of renewable energy with a great potential to mitigate global energy challenges by virtue of the ease of implementation of the technology. The study focused on monitoring the total viable bacteria counts with the number of days, daily average ambient temperature and pH from a balloon type biodigester fed with 2500 L of cow manure (500 L of slurry each day for five successive days) with six months retention time using data acquisition system, standard methods and mathematical model. A non-linear response surface model was developed to predict the total viable bacteria counts with the predictors. The predictors were ranked by weights of importance to the desired targets by reliefF test. At the end of the anaerobic digestion cycle the cumulative volume of biogas was 6.75 m3 with 65.8% methane and 31.2% carbon dioxide. The ranking by weights of the predictors revealed that all the input parameters were primary factors and number of days contributed the most. Based on the testing data set, the response surface model was capable of predicting the total viable bacteria counts with high accuracy as the determination coefficient, root mean square error and p-value were 0.959, 0.197 and 0.602.

Modeling photocatalytic hydrogen production from ethanol over copper oxide nanoparticles: a comparative analysis of various machine learning techniques

The production of hydrogen is one way to meet the ever-increasing demand for cleaner and renewable energy sources. In this study, various machine learning techniques such as Levenberg–Marquardt neural networks (LMNN), scaled conjugate gradient descent neural networks (SCDNN), and support vector machine (SVM) in comparison with nonlinear regression model (NLM) and response surface model (RSM) were employed for modeling photocatalytic hydrogen production from ethanol using copper oxide (CuO) nanoparticles as photocatalyst. The effects of input parameters such as the irradiation time, the CuO content, the catalyst dosage, and the ethanol concentration on hydrogen production were considered in the modeling process. Optimized network configurations of 4-12-1 and 4-5-1 representing the input nodes, hidden neurons, and output node were used for the LMNN and SCDNN, respectively. Both the LMNN and SCDNN show superior prediction of hydrogen production compared with the SCDNN, SVM, NLM, and RSM as indicated by the high R values of 0.998 and 0.997 for LMNN and SCDNN, respectively. The LMNN displayed the best prediction of hydrogen production with R value of 0.998. The sensitivity analysis shows that all the input parameters influenced the LMNN model output. However, the predicted hydrogen from the LMNN model was best influenced by the irradiation time.

Nonlinear regression analysis and response surface modeling of Cr (VI) removal from synthetic wastewater by an agro-waste Cocos Nucifera: Box-Behnken Design (BBD)

In this study mixture of coconut shell and coir was used for Cr (VI) removal from synthetic wastewater and statistical tool Response Surface Modeling (RSM) was applied to optimize process parameters. The solution pH (2–6), reaction time (20–100 minutes) and adsorbent quantity (0.03–0.2 g) was optimized to find the maximum response of Cr (VI) removal using statistical Box-Behnken design (BBD) software. The equilibrium data obtained by the batch experiment were analyzed by ANOVA and found fitted in a second-order polynomial equation through multiple regression analysis. The optimum value of pH, adsorbent quantity and reaction time for 99% of Cr(VI) was found as 2, 0.1 g and 100 minutes, respectively. By using non-linear regression method it was found that Freundlich isotherm and Pseudo-second-order kinetic with high correlation coefficient (R 2), low Chi-square (χ 2) and root mean squares errors (RMSE), best describe the adsorption of Cr (VI) on mixture of coconut shell and coir (MCSC) surface. Positive enthalpy (ΔH°) and negative Gibbs free energy (ΔGo) values confirm the endothermic and spontaneous nature of adsorption process. Pre and post adsorption phenomenon was confirmed by characterization of adsorbent using AFM, FTIR, SEM, and EDX analysis. The adsorbent MCSC has regenerative property and can be reused 3–4 times after treating with alkaline medium (0.2 N NaOH) and offered more than 60% removal of Cr (VI) at the fourth cycle. It can be inferred based on this study that MCSC is an effective adsorbent for Cr (VI) removal and can be used on an industrial scale for social and environmental benefit. Novelty statement An agriculture waste mixture of coconut shell and coir (MCSC) without the addition of any chemical reagent, was used for Cr(VI) removal. As per literature survey and best of our knowledge, the adsorbent MCSC has not been reported for Cr (VI) removal. In the previous study, authors reported either coconut coir pith or coconut shell or coconut charcoal as adsorbent for Cr (VI) removal. The adsorbent MCSC is efficient even at very low doses (0.1 g) as compared to the reported adsorbent.

Multi-objective optimization of the shell in autonomous intelligent argo profiling float

To improve the performance of the first-generation profiling float and ensure that the float smoothly completes the profile motion, a shell optimization method based on response surface approximation model and multi-objective genetic algorithm is proposed. The second-order nonlinear response surface models of resistance, mass and envelope volume of the shell are established based on the data from Design of Experiments (DOE). Taking the minimum resistance, the minimum mass and the maximum envelope volume of the shell as optimization objectives, the Pareto Front is obtained based on the fast elitist Non-dominated Sorting Genetic Algorithm II (NSGA-II). The influence rule and degree of each design variable on the optimization objective are gained through the main effect analysis. A set of solutions are selected as the design scheme of the shell for second-generation profiling float. The hydrodynamic performance, endurance and carrying capacity of the profiling float have been greatly improved compared with the first-generation. Finally, the feasibility and effectiveness of the optimization results are verified through simulation analysis and high pressure test. The proposed optimization process can greatly improve the performance of Argo profiling float, shorten the optimization period of shell design and improve the optimization efficiency. Therefore, it has a good reference value for the design optimization of other similar submarines. • To improve the hydrodynamic performance, endurance and carrying capacity of the first-generation Argo profiling float, a shell optimization method based on response surface approximation model and (NSGA-II) is proposed. The Pareto Front is obtained based on the NSGA-II. A set of solutions are selected as the design scheme of the shell for second-generation profiling float. • The feasibility and effectiveness of the optimization results are verified through hydrodynamic analysis by FLUENT and buckling analysis by ABAQUS. In order to prove the feasibility of the final optimization scheme and the reliability of the simulation analysis, 48 M P a high pressure test is carried out by the high pressure experimental device. • Through the analysis of the main effect plots, we can get the influence law and degree of each design variable on the optimization objective. In the design of the shell, the range of design variables can be determined according to the requirements of design indicators. • The proposed optimization process can greatly improve the performance of the second-generation Argo profiling float, shorten the optimization period of shell design and improve the optimization efficiency. Therefore, it has a good reference value for the design optimization of other similar submarines.

Optimal Design of Experiments for Non-Linear Response Surface Models

SummaryMany chemical and biological experiments involve multiple treatment factors and often it is convenient to fit a non-linear model in these factors. This non-linear model can be mechanistic, empirical or a hybrid of the two. Motivated by experiments in chemical engineering, we focus on D-optimal designs for multifactor non-linear response surfaces in general. To find and study optimal designs, we first implement conventional point and co-ordinate exchange algorithms. Next, we develop a novel multiphase optimization method to construct D-optimal designs with improved properties. The benefits of this method are demonstrated by application to two experiments involving non-linear regression models. The designs obtained are shown to be considerably more informative than designs obtained by using traditional design optimality algorithms.

Patient response prediction with logistic regression in gastrointestinal endoscopy under midazolam-alfentanil sedation performed as well as response surface model

BackgroundResearchers have used logistic regression (LR) and non-linear response surface models (RSMs) to predict patient responses to sedation. The reduced Greco and hierarchy RSMs have proven to be more appropriate than other RSMs in gastrointestinal endoscopies using midazolam and alfentanil. In this study, we evaluate the performance of a simpler model, LR, and compared it with that of RSM. MethodsThirty-three patients who received esophagogastroduodenoscopy (EGD) and colonoscopy sedation with midazolam and alfentanil were enrolled in the study. LR was performed for the EGD group and validated using the colonoscopy group. The two RSMs were performed using the same process, and performances and receiver operating characteristic (ROC) curves of the models were evaluated. ResultsThe native EGD LR model had an ROC curve area of 0.94. For external validation, the ROC curves were 0.92, 0.94, and 0.94 for the reduced Greco, hierarchy, and LR models, respectively. Pairwise comparison between models was not significant. ConclusionThe LR model performed as well as RSM in generalizing the predicted sedative effect of midazolam and alfentanil during gastrointestinal endoscopies. LR may be used for generalization across patients experiencing procedures with similar stimulus intensities.

Optimization of Double Pivot Suspension Kingpin Axis during Steering

A double pivot suspension used for in-wheel motor electric vehicle was designed, and the virtual prototype model of the suspension assembly was build. The suspension parameters changed greatly during steering. In order to solve this problem, this paper proposed a non-linear response surface model to fit the relationship of suspension parameters and design variables. An optimization scheme was designed based on the response surface model. The suspension performance was improved significantly using optimized variables.

Active learning to understand infectious disease models and improve policy making.

Modeling plays a major role in policy making, especially for infectious disease interventions but such models can be complex and computationally intensive. A more systematic exploration is needed to gain a thorough systems understanding. We present an active learning approach based on machine learning techniques as iterative surrogate modeling and model-guided experimentation to systematically analyze both common and edge manifestations of complex model runs. Symbolic regression is used for nonlinear response surface modeling with automatic feature selection. First, we illustrate our approach using an individual-based model for influenza vaccination. After optimizing the parameter space, we observe an inverse relationship between vaccination coverage and cumulative attack rate reinforced by herd immunity. Second, we demonstrate the use of surrogate modeling techniques on input-response data from a deterministic dynamic model, which was designed to explore the cost-effectiveness of varicella-zoster virus vaccination. We use symbolic regression to handle high dimensionality and correlated inputs and to identify the most influential variables. Provided insight is used to focus research, reduce dimensionality and decrease decision uncertainty. We conclude that active learning is needed to fully understand complex systems behavior. Surrogate models can be readily explored at no computational expense, and can also be used as emulator to improve rapid policy making in various settings.

A Novel Approach to Establishing the Design Space for the Oral Formulation Manufacturing Process

A novel approach to establishing the design space for the oral formulation manufacturing process was investigated. A response surface method incorporating multivariate spline interpolation was applied to overcome the nonlinear problem, which is always problematic in pharmaceutical development studies, and a bootstrap resampling technique, polynomial approximation technique, and 95% confidence intervals based on a nonparametric approach were applied to estimate the reliability of the established design space derived from the nonlinear response surface model. The critical quality attributes (CQAs) of intermediate material rather than the critical process parameters (CPPs) were chosen as the causal factors for the response variables, which were CQAs of the final product to avoid scale-gap and equipment-gap. This enabled the effective use of data sets accumulated during all pharmaceutical development studies. It was confirmed that a conservative border as well as an optimistic border of the design space for practical use was obtained considering the variability of the border of the design spaces on nonlinear response surfaces. Furthermore, the nonlinear response surface model using CQAs of intermediate material derived from data sets of a laboratory scale study and pilot scale studies could predict the CQA of the final product (2.5 h dissolution of commercial-scale study) with high accuracy. Consequently, the proposed novel approach overcame all of the difficulties for the manufacturing process development of oral formulations and this is the first study to demonstrate the effectiveness of the design space using CQA of intermediate material for the oral formulation manufacturing process.

Modeling, Simulation, and Kinetic Studies of Solvent‐Free Biosynthesis of Benzyl Acetate

Solvent‐free biosynthesis of benzyl acetate through immobilized lipase‐mediated transesterification has been modeled and optimized through statistical integrated artificial intelligence approach. A nonlinear response surface model has been successfully developed based on central composite design with transesterification variables, namely, molarity of alcohol, reaction time, temperature, and immobilized lipase amount as input variables and molar conversion (%) as an output variable. Statistical integrated genetic algorithm optimization approach results in an optimized molar conversion of 96.32% with the predicted transesterification variables of 0.47 M alcohol molarity in a reaction time of 13.1 h, at 37.5°C using 13.31 U of immobilized lipase. Immobilized lipase withstands more than 98% relative activity up to 6 recycles and maintains 50% relative activity until 12 recycles. The kinetic constants of benzyl acetate, namely, Km and Vmax were found to be 310 mM and 0.10 mmol h−1 g−1, respectively.

Ochratoxin A quantification: Newly developed HPLC conditions

Ochratoxin A (OTA) is a mycotoxin that has been classified as a Group 2B carcinogen, which means that it belongs to a group of possible carcinogens to humans. The main objective of the present study was to optimize the High Performance Liquid Chromatography (HPLC) parameters including pH (X1), temperature (X2) and flow rate (X3) for quantitative analysis of OTA (Y4) in spiked peanuts. Significant nonlinear response surface model with high coefficient of determinations (R2) was fitted to evaluate the effect of HPLC parameters on the quantification level of OTA. All HPLC variables had significant (p < 0.05) effect on the quantification level of OTA. The highest quantification value for OTA was obtained with the following HPLC conditions: mobile phase consisting of 5 mM sodium acetate (acidified to pH 2.36 with acetic acid)/ACN/MeOH (40:30:30); excitation of 333 nm; emission of 467 nm; flow rate of 0.4 mL/min; and temperature of 24 °C. The recommended optimal HPLC conditions provided a 2.2-fold and 4.7-fold higher peak area for OTA when compared to the other two conditions. The recovery and LOD values of OTA under the recommended optimal conditions were 95.4% and 0.05 ng/g, respectively. The OTA contents of six different raw peanut brands were quantified using the newly optimized HPLC conditions, and the results demonstrated that all six brands were contaminated with OTA, with concentrations ranging from 2.82 to 7.41 ng/g.

Reliability Evaluation of the Design Space of the Granulation Process of Mefenamic Acid Tablets Using a Bootstrap Resampling Technique

The design space of the granulation process of mefenamic acid tablets, based on Box and Behnken design datasets, was described by a response surface method incorporating multivariate spline interpolation. The reliability of the optimal solutions and the acceptance ranges were evaluated by a bootstrap (BS) resampling technique. The distribution of the BS optimal solutions was almost symmetrical; however, several solutions, which were quite different from the original solution, were mixed. The reason for this problem was considered to be the mixing of the global and the local optima. Therefore, we applied self-organizing map (SOM) clustering for dividing data into several clusters and identified the cluster containing the global optima. The accuracy and reproducibility of the optimal solution in the cluster containing the optimal solution were quantitatively evaluated. In addition, the response surfaces modeled from all the BS datasets contained in the cluster were plotted into the same coordinates with the original response surface. The plots of BS optimal solutions were distributed around the original solution. Moreover, the average of all the BS response surfaces sufficiently corresponded with the original response surface. The conservative limits of the 95% confidence intervals of the acceptance ranges in three response variables could be calculated using the standard deviations of the BS response surfaces. Consequently, it was considered that a novel evaluation method based on BS resampling and SOM could be used for quantitatively evaluating the precision of the nonlinear response surface model.

Optimization of HPLC conditions for quantitative analysis of aflatoxins in contaminated peanut

The main objective of present study was to investigate the effect of HPLC conditions namely mobile phase composition (X 1), flow rate (X 2) and temperature (X 3) on peak area of four target aflatoxins (i.e. B 1 (Y 1), B 2 (Y 2), G 1 (Y 3) and G 2 (Y 4)) from the spiked peanut. The significant nonlinear response surface models with high coefficient of determinations ( R 2) ranging from 0.958 to 0.995 were fitted to evaluate the detection value of target aflatoxins as a function of HPLC variables. Flow rate had the most significant ( p < 0.05) effect on quantification value of target aflatoxins. The highest quantification value for target aflatoxins could be obtained under the following HPLC conditions: the mobile phase composition of ACN/H 2O/MeOH: 8/54/38, temperature of 24 °C and flow rate of 0.4 mL/min. The recommended optimum HPLC conditions provided higher peak area for all target aflatoxins by 1–2.5 fold compared to two other conditions (A: mobile phase (ACN/H 2O/MeOH: 23/54/23), ambient temperature (28–32 °C), flow rate 1 mL/min; B: mobile phase (ACN/H 2O/MeOH: 17/54/29), temperature 30 °C, flow rate 1 mL/min).

Evolutionary and swarm intelligence‐based approaches for optimization of lipase extraction from fermented broth

AbstractEvolutionary and swarm intelligence‐based optimization approaches, namely genetic algorithm (GA) and particle swarm optimization (PSO), were utilized to determine the optimal conditions for the lipase extraction process. The input space of the nonlinear response surface model of lipase extraction served as the objective function for both approaches. The optimization results indicate that the lipase activity was significantly improved, more than 20 U/g of dry substrate (U/gds), in both approaches. PSO (133.57 U/gds in the 27th generation) outperforms GA (132.24 U/gds in the 320th generation), slightly in terms of optimized lipase activity and highly in terms of convergence rate. The simple structure associated with the effective memory capability of PSO renders it superior over GA. The proposed GA and PSO approaches, based on a biological phenomenon, are considered as natural and thus may replace the traditional gradient‐based optimization approaches in the field of downstream processing of enzymes.

Statistical assessment of dissolution and drug release profile similarity using a model-dependent approach

A general multivariate procedure for assessing the similarity of dissolution and drug release profiles was developed. A mathematical model is fit to the data, and Hotelling's T 2 test is used to calculate the joint confidence region around the vector of differences between least-squares estimates of the parameters in the model. The method of Lagrange multipliers is used to determine if this confidence region is enclosed within a predetermined similarity region, and profile similarity is claimed if this is the case. The first-order, Gompertz, logistic, second-order, and Weibull models were fit to the in vitro extended-release profile of pseudoephedrine HCl from an asymmetric membrane (AM) film-coated osmotic tablet. The first-order model was selected because of its simplicity and because it was the best-fitting model according to a modified form of Akaike's Information Criterion. A nonlinear response surface model was also developed so that the formulator could calculate how much of the AM film coat should be applied in order to obtain the desired drug release profile. The usefulness of this model-dependent procedure was further demonstrated during an analytical method transfer exercise, where it was used to compare the drug release profiles obtained by two independent laboratories; additional research is required, however, before the appropriate acceptance criteria for demonstrating profile similarity can be recommended.

Concentration-Dependent Synergy and Antagonism within a Triple Antifungal Drug Combination againstAspergillusSpecies: Analysis by a New Response Surface Model

Triple antifungal combinations are used against refractory invasive aspergillosis without an adequate understanding of their pharmacodynamic interactions. We initially studied the in vitro triple combination of voriconazole, amphotericin B, and caspofungin against Aspergillus fumigatus, A. flavus, and A. terreus by a spectrophotometric microdilution broth method after 48 h of incubation. We then analyzed these results with a recently described nonlinear mixture response surface E(max)-based model modified to assess pharmacodynamic interactions at various growth levels. The new model allows flexibility in all four parameters of the E(max) model and is able to describe complex pharmacodynamic interactions. Concentration-dependent pharmacodynamic interactions were found within the triple antifungal combination. At the 50% growth level, synergy (median interaction indices of 0.43 to 0.82) was observed at low concentrations of voriconazole (<0.03 mg/liter) and amphotericin B (</=0.20 mg/liter) and at intermediate concentrations of caspofungin (0.95 to 14.88 mg/liter), whereas antagonism (median interaction indices of 1.17 to 1.80) was found at higher concentrations of voriconazole and amphotericin B. Ternary plot and interaction surface analysis further revealed the complexity of these concentration-dependent interactions. With increasing concentrations of amphotericin B, the synergistic interactions of voriconazole-caspofungin double combination decreased while the antagonistic interactions increased. A similar effect was observed when voriconazole was added to the double combination of amphotericin B and caspofungin. In conclusion, the new nonlinear mixture-amount response surface modeling of the triple antifungal combination demonstrated a net antagonism or synergy against Aspergillus species depending upon drug concentrations and species.

Asymptotic Probability Extraction for Nonnormal Performance Distributions

While process variations are becoming more significant with each new IC technology generation, they are often modeled via linear regression models so that the resulting performance variations can be captured via normal distributions. Nonlinear response surface models (e.g., quadratic polynomials) can be utilized to capture larger scale process variations; however, such models result in nonnormal distributions for circuit performance. These performance distributions are difficult to capture efficiently since the distribution model is unknown. In this paper, an asymptotic-probability-extraction (APEX) method for estimating the unknown random distribution when using a nonlinear response surface modeling is proposed. The APEX begins by efficiently computing the high-order moments of the unknown distribution and then applies moment matching to approximate the characteristic function of the random distribution by an efficient rational function. It is proven that such a moment-matching approach is asymptotically convergent when applied to quadratic response surface models. In addition, a number of novel algorithms and methods, including binomial moment evaluation, PDF/CDF shifting, nonlinear companding and reverse evaluation, are proposed to improve the computation efficiency and/or approximation accuracy. Several circuit examples from both digital and analog applications demonstrate that APEX can provide better accuracy than a Monte Carlo simulation with 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> samples and achieve up to 10times more efficiency. The error, incurred by the popular normal modeling assumption for several circuit examples designed in standard IC technologies, is also shown

A new study on optimisation under uncertainty for vehicle design

With continuous improvement of powerful computers, vehicle designs have been addressed using computational methods. This results in more efficient development of a new product. Most simulation-based optimisation generates deterministic optimal designs without considering variability effects. This paper presents a hybrid optimisation under uncertainty method for vehicle side impact design. Nonlinear response surface models are employed as the 'real' models for conducting this study. The main goal is to maintain or enhance the vehicle side impact performance while minimising the vehicle weight under uncertainty. The hybrid method alleviates the computational burden by estimating the objective and constraint functions during the optimisation process through a re-weighting approach. It also combines a genetic algorithm and sequential quadratic programming to achieve the global or near global optimal designs. The efficiency and accuracy of this method are demonstrated by solving a vehicle design problem.