Response Surface Modeling Approach Research Articles

Tailoring the formulation of sugar-snap cookies to lower in vitro starch digestibility: A response surface modelling approach

An I-optimal response surface experimental design revealed impacts of dough moisture content (DMC, 14–22%) and level of wheat flour substitution (10–50%) by wheat gluten and one of six different native starches [wheat, (waxy) maize, rice, potato, pea] on sugar-snap cookie starch thermal properties, in vitro starch digestion, dough and cookie hardness and spread ratio. Increasing DMCs from 14 to 22% increased the cookie starch digestion rate constants of each starch source used. A linear increase of the constant by 25–30% across the 14 to 22% DMC range for all starches was predicted and validated. That cookie spread and hardness were related to the water retention capacity of the native starches used suggested that they underwent limited changes during baking. For each starch examined, formulations were optimized to lower in vitro starch digestion rate and extent, and cookie hardness, while maximizing dough spread ratio.

Response surface modeling and optimization scheme of an internally cooled liquid desiccant air conditioning system

Applying an internally cooled liquid desiccant air conditioning system (LDAC) is a promising energy-saving and emission-reduction scheme for hot and humid areas. This research investigates the application of an internally cooled LDAC for performance enhancement in hot and humid areas like Hong Kong. The combined system integrates liquid desiccant dehumidification (LDD) and regenerative indirect evaporative cooling (RIEC) without a power-intensive compressor. The internally cooled LDD removes latent heat from the hot and humid air before the RIEC cools it. To ensure efficient energy utilization, the LDD captures the exhaust air to assist in the dehumidification and initial cooling of the fresh air, which alleviates the efficiency deterioration of the desiccant. An all-fresh air system is used for better indoor air quality. To optimize the performance of a system with many influencing parameters, the response surface method (RSM) and multi-objective optimization are used to optimize and assess the potential and performance of the system. The system cooling capacity (C), latent heat removal rate (Qd), and dehumidification efficiency (ηd) are used as the optimization objectives. The response surface model and desirability function approach optimize six critical parameters, achieving a 7.6% improvement in dehumidification performance with low airspeed (1.5 m/s) and high desiccant concentration (40%) during high-humidity months. Increasing the extraction ratio of the RIEC by 20% in warmer months enhances the peak cooling capacity by 23.6%. This research contributes to implementing internally cooled LDAC systems and provides insights into optimizing monthly operation patterns in hot and humid regions.

Predictive performance and costing model for Membrane Capacitive Deionization (MCDI) at operational scale

A model that can be used to predict the performance of Membrane Capacitive Deionization (MCDI), including current efficiency, flowrate of the product water, water recovery and energy consumption is established in this work. The model was developed using a Response Surface Model approach that considers the influence of influent conductivity, flowrate passing by the electrodes and applied current on MCDI system performance rather than relying on electrochemical principles or the description of the intrinsic properties of the carbon electrodes and ion exchange membranes. In the scenarios tested here, flowrate contributes the most towards MCDI performance. The appropriateness of using NaCl for an MCDI performance model is confirmed. The model can be applied to extensive applications with two examples detailed here including a small town potable application of 100 m3/day with influent water of 2000 μS/cm and an industrial wastewater application of 1000 m3/day with influent water of 4000 μS/cm. A costing model is developed and applied to the two scenarios with the optimised levelized cost of water (LCOW) found to be US$0.74/m3 for the small town and US$1.08/m3 to US$1.41/m3 for the industrial wastewater (product water quality dependent). By maximising the production rate, the LCOW can be minimised. The model presented here can be applied to a wide range of applications or used as a framework for efficient performance modelling of other MCDI configurations.

Crashworthiness optimization of crash box with 3D-printed lattice structures

Crash boxes are important energy-absorbing components to ensure the passive safety of automobile vehicles during crashworthiness. The current study presents an investigation of a novel crash box, which consists of Al shell and 3D-printed lattice core. In view of obtaining a good lightweight and energy absorption, the lattice structures are fabricated by fused filament fabrication (FFF) technology using carbon fiber reinforced polyamide 6 (PA6/CF) composites. First, the correlations between fiber content and elastic modulus, maximum tensile stress are established by a least squares method. Four different lattice structures including hexagonal, kagome, re-entrant and triangular honeycombs are additive-manufactured. The results reveal that the experimental data from compression test is in good agreement with the simulation analysis, and the kagome achieves the maximum specific energy absorption (SEA) values through numerical analysis. Then, an integrated “material-structure” model is constructed in an Isight environment to analyze the sensitivity of the material property (elastic modulus (E), tensile strength (σ) and fracture strain (ε)) and geometric parameters (thickness (t) and unit size (r) on the crashworthiness performance. A multi-objective optimization strategy with maximum SEA and minimum mass as objectives for the novel crash box is established using response surface model approach and optimal Latin hypercube. Simulation results show that the crash box optimized by non-dominated sorting genetic algorithm (NSGA-II) algorithm can improve the energy absorption with mass reduction, which provides some reference for the structural design and optimization of the crash box.

Artificial neural network modeling on trichloroethylene biodegradation in a packed-bed biofilm reactor and its comparison with response surface modeling approach

An artificial neural network (ANN) model was developed for predicting trichloroethylene (TCE) biodegradation via co-metabolism in a packed-bed biofilm reactor using Pseudomonas putida F1 as the bio-catalyst and toluene as the primary substrate. The model uses an architecture with three hidden layers (3–2–1) and resilient back-propagation algorithm to obtain optimal weights for the associated neurons. ANN model predictions of TCE degradation efficiency have not only successfully validated those obtained from a Response Surface Model (RSM), but the model also outperformed RSM with a better predicting power that the ANN showed a lower root mean square error (RMSE) 9.07 and a higher determination of coefficient (R2) 80.32 % than those of RSM (RMSE=9.93, 10.88 after corrected for model degree of freedom; R2 = 76.4 %). Further model analysis revealed that this ANN model correctly interpreted the experimental data with the underlying biological mechanisms and would be able to provide guidance on local operations to achieve optimal TCE degradation. Sensitivity analysis showed that the ANN model was still a robust model when an extreme TCE data point was added during the model development. A simulation study also indicated that on average, ANN models had better fit to the experimental data than the RSM.

The role of hydrothermal treatment (steaming and tempering) parameters on oat groat, flake and flour properties

The role of hydrothermal treatment (steaming and tempering) parameters on oat groat, flake, and flour properties was studied by using experimental design and response surface modelling approach. The modelled properties were oat groat hardness, oat flake hardness, and oat flour particle size milled from oat groats and oat flakes. In the design of experiments, the studied factors were moisture content, temperature, and duration of the hydrothermal treatment using the central composite face-centred design (CCF). Three untreated oat groat cultivar samples with varying native groat hardness were studied. Among the studied factors, tempering temperature influenced both groat hardness and flour particle size in all samples. High temperature led to fragile groats and fine flours, while low temperature resulted in hard groats and coarse flours. The treatment parameters affected groat and flour properties in a generally similar way, but sample-specific differences remained in groat hardness and flour particle size after identical treatments. In the sample with the softest native groats, also the moisture content influenced groat hardness and flour particle size. Our results suggest that with a proper selection of the native groats and by adjusting the hydrothermal treatment parameters, the milling properties of oat could be optimised for specific uses.

Photocatalytic Activity of TiO2 for the Degradation of Anticancer Drugs.

To prevent water pollution, photocatalysis is often used to remove small molecules such as drugs by generating reactive species. This study aimed to determine the photocatalytic activity of two anticancer drugs, imatinib and crizotinib, and to investigate various influences that may alter the kinetic degradation rate and ultimately the efficacy of the process. In order to obtain optimal parameters for the removal of drugs with immobilized TiO2, the mutual influence of the initial concentration of the contaminant at environmentally relevant pH values was investigated using the response surface modeling approach. The faster kinetic rate of photocatalysis was obtained at pH 5 and at the smallest applied concentration of both drugs. The photocatalytic efficiency was mostly decreased by adding various inorganic salts and organic compounds to the drug mixture. Regarding the degradation mechanism of imatinib and crizotinib, hydroxyl radicals and singlet oxygen showed a major role in photochemical reactions. The formation of seven degradation products for imatinib and fifteen for crizotinib during the optimal photocatalytic process was monitored by high-resolution mass spectrometry (HPLC-QqTOF). Since the newly formed products may pose a hazard to the environment, their toxicity was studied using Vibrio fischeri, where the significant luminescence inhibition was assessed for the mixture of crizotinib degradants during the photocatalysis from 90 to 120 min.

Nutrigonometry II: Experimental strategies to maximize nutritional information in multidimensional performance landscapes.

Animals regulate their nutrient consumption to maximize the expression of fitness traits with competing nutritional needs (“nutritional trade‐offs”). Nutritional trade‐offs have been studied using a response surface modeling approach known as the Geometric Framework for nutrition (GF). Current experimental design in GF studies does not explore the entire area of the nutritional space resulting in performance landscapes that may be incomplete. This hampers our ability to understand the properties of the performance landscape (e.g., peak shape) from which meaningful biological insights can be obtained. Here, I tested alternative experimental designs to explore the full range of the performance landscape in GF studies. I compared the performance of the standard GF design strategy with three alternatives: hexagonal, square, and random points grid strategies with respect to their accuracy in reconstructing baseline performance landscapes from a landmark GF dataset. I showed that standard GF design did not reconstruct the properties of baseline performance landscape appropriately particularly for traits that respond strongly to the interaction between nutrients. Moreover, the peak estimates in the reconstructed performance landscape using standard GF design were accurate in terms of the nutrient ratio but incomplete in terms of peak shape. All other grid designs provided more accurate reconstructions of the baseline performance landscape while also providing accurate estimates of nutrient ratio and peak shape. Thus, alternative experimental designs can maximize information from performance landscapes in GF studies, enabling reliable biological insights into nutritional trade‐offs and physiological limits within and across species.

Response surface model based emission source contribution and meteorological pattern analysis in ozone polluted days

Urban and regional ozone (O3) pollution is a public health concern and causes damage to ecosystems. Due to the diverse emission sources of O3 precursors and the complex interactions of air dispersion and chemistry, identifying the contributing sources of O3 pollution requires integrated analysis to guide emission reduction plans. In this study, the meteorological characteristics leading to O3 polluted days (in which the maximum daily 8–h average O3 concentration is higher than the China Class II National O3 Standard (160 μg/m3)) in Guangzhou (GZ, China) were analyzed based on data from 2019. The O3 formation regimes and source apportionments under various prevailing wind directions were evaluated using a Response Surface Modeling (RSM) approach. The results showed that O3 polluted days in 2019 could be classified into four types of synoptic patterns (i.e., cyclone, anticyclone, trough, and high pressure approaching to sea) and were strongly correlated with high ambient temperature, low relative humidity, low wind speed, variable prevailing wind directions. Additionally, the cyclone pattern strongly promoted O3 formation due to its peripheral subsidence. The O3 formation was nitrogen oxides (NOx)-limited under the northerly wind, while volatile organic compounds (VOC)-limited under other prevailing wind directions. Anthropogenic emissions contributed largely to the O3 formation (54–78%) under the westerly, southwesterly, easterly, southeasterly, or southerly wind, but only moderately (35–47%) under the northerly or northeasterly wind. Furthermore, as for anthropogenic contributions, local emission contributions were the largest (39–60%) regardless of prevailing wind directions, especially the local NOx contributions (19–43%); the dominant upwind regional emissions contributed 12–46% (e.g., contributions from Dongguan were 12–20% under the southeasterly wind). The emission control strategies for O3 polluted days should focus on local emission sources in conjunction with the emission reduction of upwind regional sources.

Effect of frying oil stability over repeated reuse cycles on the quality and safety of deep-fried Nile tilapia fish (Oreochromis niloticus): a response surface modeling approach

ABSTRACT Fresh water fish is considered a source of good quality proteins and essential fats. Frying is among widely used fish preparation techniques globally. Deep-frying oil quality with repeated uses, has been a concern. This research investigated the influence of frying oil stability (expressed as levels of peroxide values (0.2, 1.2 meq/kg) and free fatty acids (0.05, 0.13% palmitic acid)) over repeated uses (1,6 cycles) on the oxidative stability and essential nutrients of fried fish using a response surface approach, with the objectives of generating information relevant for the improvement of community health outcomes, with a special focus of this particular research was on trends, but not optimization. The frying oil and fried fish quality were adequately explained by response surface model and supported by principal component analysis. The result showed that the oxidative stability of both the frying oil and fried fish were deteriorating over the reuse cycles of the frying oil (with increasing trends of unhealthy fats, saturated and trans) corresponding to decreasing trends in the healthy fat components and vitamin A). It was also indicated that the essential fats (omega 3, omega 6, cis, vitamin A), were decreased while the risky fats (saturated, trans) were increased along with the frying cycles. The result revealed the urgent need for regulating frying oil and fried food qualities, particularly in developing countries.

Simultaneous Determination of Droplet Size, pH Value and Concentration to Evaluate the Aging Behavior of Metalworking Fluids.

Metalworking fluids (MWFs) are widely used to cool and lubricate metal workpieces during processing to reduce heat and friction. Extending a MWF’s service life is of importance from both economical and ecological points of view. Knowledge about the effects of processing conditions on the aging behavior and reliable analytical procedures are required to properly characterize the aging phenomena. While so far no quantitative estimations of ageing effects on MWFs have been described in the literature other than univariate ones based on single parameter measurements, in the present study we present a simple spectroscopy-based set-up for the simultaneous monitoring of three quality parameters of MWF and a mathematical model relating them to the most influential process factors relevant during use. For this purpose, the effects of MWF concentration, pH and nitrite concentration on the droplet size during aging were investigated by means of a response surface modelling approach. Systematically varied model MWF fluids were characterized using simultaneous measurements of absorption coefficients µa and effective scattering coefficients µ’s. Droplet size was determined via dynamic light scattering (DLS) measurements. Droplet size showed non-linear dependence on MWF concentration and pH, but the nitrite concentration had no significant effect. pH and MWF concentration showed a strong synergistic effect, which indicates that MWF aging is a rather complex process. The observed effects were similar for the DLS and the µ’s values, which shows the comparability of the methodologies. The correlations of the methods were R2c = 0.928 and R2P = 0.927, as calculated by a partial least squares regression (PLS-R) model. Furthermore, using µa, it was possible to generate a predictive PLS-R model for MWF concentration (R2c = 0.890, R2P = 0.924). Simultaneous determination of the pH based on the µ’s is possible with good accuracy (R²c = 0.803, R²P = 0.732). With prior knowledge of the MWF concentration using the µa-PLS-R model, the predictive capability of the µ’s-PLS-R model for pH was refined (10 wt%: R²c = 0.998, R²p = 0.997). This highlights the relevance of the combined measurement of µa and µ’s. Recognizing the synergistic nature of the effects of MWF concentration and pH on the droplet size is an important prerequisite for extending the service life of an MWF in the metalworking industry. The presented method can be applied as an in-process analytical tool that allows one to compensate for ageing effects during use of the MWF by taking appropriate corrective measures, such as pH correction or adjustment of concentration.

A New Approach for Design Optimization and Parametric Analysis of Symmetric Compound Parabolic Concentrator for Photovoltaic Applications

A compound parabolic concentrator (CPC) is a non-imaging device generally used in PV, thermal, or PV/thermal hybrid systems for the concentration of solar radiation on the target surface. This paper presents the geometric design, statistical modeling, parametric analysis, and geometric optimization of a two-dimensional low concentration symmetric compound parabolic concentrator for potential use in building-integrated and rooftop photovoltaic applications. The CPC was initially designed for a concentration ratio of “2×” and an acceptance half-angle of 30°. A MATLAB code was developed in house to provoke the CPC reflector’s profile. The height, aperture width, and concentration ratios were computed for different acceptance half-angles and receiver widths. The interdependence of optical concentration ratio and acceptance half-angle was demonstrated for a wide span of acceptance half-angles. The impact of the truncation ratio on the geometric parameters was investigated to identify the optimum truncation position. The profile of truncated CPC for different truncation positions was compared with full CPC. A detailed statistical analysis was performed to analyze the synergistic effects of independent design parameters on the responses using the response surface modeling approach. A set of optimized design parameters was obtained by establishing specified optimization criteria. A 50% truncated CPC with an acceptance half-angle of 21.58° and receiver width of 193.98 mm resulted in optimum geometric dimensions.

Residues of herbal hemp leaf teas – How much of the cannabinoids remain?

Herbal teas of fiber-type hemp varieties (Cannabis sativa L.) rich in cannabidiolic acid (CBDA) and cannabidiol (CBD) and poor in Δ9-tetrahydrocannabinol acid (THCA) and Δ9-tetrahydrocannabinol (THC) are very popular today. The conditions for preparing herbal infusions are not well standardized and analysis of the lipophilic cannabinoids in infusions is difficult. Therefore, we analyzed the hemp leaf residues after tea preparation by using a response surface modelling approach to estimate the effects of variations in temperature, water volume and extraction time on the residual content of five cannabinoids (CBDA, CBD, THCA, THC, cannabinol (CBN)) in the hemp leaves after extraction. The quantity of remaining cannabinoids was mainly influenced by temperature in the first order. Volume and extraction time were only exerting minor influences under usual tea preparation processes. At elevated water temperatures CBD and THC values were even higher than in the original drug material presumably due to decarboxylation of CBDA and THCA. Rising temperatures increased extraction of CBDA and CBD, as opposed to THCA and THC. The degradation of THC to CBN was not significant at the conditions of infusion preparation.Analyzing herbal residues after tea brewing is just an approximation to the true values of valuable or unfavorable compounds in tea, overestimating the true values. However, that approach offers a good control for further improvements of herbal tea analysis and gives reliable indications for risk assessment.

Development of High-Efficient Centrifugal Pump Through Optimization of Its Volute Tongue and Expeller Vane

Abstract Centrifugal pumps are often used for pumping liquids from one priority area to another, which require working effectively in terms of performance and reliability. The objective of this study is to enhance the hydraulic performance and reliability of a centrifugal pump based on computational fluid dynamics (CFD) optimization. The shapes of the expeller vane and volute tongue were optimized based on the following six design parameters; outer diameter, exit angle, front and rear heights, back sidewall gap, and tongue angle. The hydraulic efficiency and axial thrust were chosen as the optimization objectives. In this sense, a design of experiment (DOE) technique was utilized to generate 45 design samples. A response surface modeling (RSM) approach was employed to investigate the interaction between the parameters and objectives. The accuracy of the numerical simulation was verified by the experimental data and showed a good agreement. The optimization was found to improve the hydraulic efficiency by 2.92%, whereas the axial thrust was decreased by 7.51%.

Hybrid multi-task learning-based response surface modeling in manufacturing

Response surface modeling is an essential technique for identifying the optimal input parameters in a process, especially when the physical knowledge about the process is limited. It explores the relationships between the process input variables and the response variables through a sequence of designed experiments. Conventional response surface models typically rely on a large number of experiments to achieve reliable modeling performance, which can be cost prohibitive and time-consuming. Furthermore, nonlinear input-output relationships in some processes may not be sufficiently accounted for by existing modeling methods. To address these challenges, this paper develops a new response surface modeling approach based on hybrid multi-task learning (H-MTL). This approach decomposes the variability in process responses into two components–a global trend and a residual term, which are estimated through self-learning and MTL of Gaussian process (GP), respectively. MTL leverages the similarities between multiple similar-but-not-identical GPs, thus achieving superior modeling performance without increasing experimental cost. The effectiveness of the proposed method is demonstrated by a case study using experimental data collected from real-world ultrasonic metal welding processes with different material combinations. In addition, the hyperparameter selection, the effects of the number of tasks, and the determination of the stopping criterion are discussed in detail.

Optimization of Congo red dye adsorption from wastewater by a modified commercial zeolite catalyst using response surface modeling approach.

In the present work, Zeolite A was modified by using hexadecyltrimethylammonium bromide (HDTMABr) for adsorption of the Congo red (CR) dye from synthetic aqueous solutions. The Modified Zeolite A (MZA) was characterized by XRD, SEM, and FTIR. The influence of solution pH (in the 4-12 range), ionic strength (0.1-1 M), contact time (180 min), initial CR concentration (20-60 mg/L), temperature (24-36 °C), and an adsorbent dose (1-3 g m/L) on the % dye removal and adsorbent capacity were studied. A combined effect of the initial CR concentration and temperature on the CR removal % by MZA was also studied by applying response surface methodology (RSM). Experimental values were in a good agreement with those predicated by a second-order quartic model. A maximum of 99.24% dye removal and adsorbent capacity of 21.11 mg/g was achieved under the following conditions: pH = 7, initial CR concentration = 60 mg/L, temperature = 24 °C, ionic strength = 0.1 M, adsorbent dose = 3 g/L and 90 min contact time. The equilibrium data were subjected to the Langmuir, Freundlich and Temkin isotherms, with the latter providing the best fit while kinetic adsorption studies were conducted by applying three models. The results indicated that the removal process was best described by the pseudo-second-order model. The present study demonstrates that modified MZA can be utilized for the highly efficient CR dye removal.

Response surface modeling of humic acid stimulation of the rice (Oryza sativa L.) root system

ABSTRACT This study aimed to apply statistical response surface models (RSMs) to evaluate morphological parameters of plant root system changes in response to humic acid (HA). The study was carried out in a growth chamber. Experimental treatments consisted of HA extracted using IHSS methodology at increasing doses: 0, 20, 40, 60, 80, 110, and 150 mg HA L−1. Seedlings were collected at 24, 48, 72, 96, 120 and 144 h, and the rice root system was analyzed with WinRHIZO software. Different parameters of the root systems were analyzed. The stimulation pattern of increasing doses of HA on the root morphology of rice seedlings showed a quadratic response surface, presenting with high statistical significance (p < 0.001). The rice root system during the early growth stage was highly stimulated by HA, especially the superfine and thick root diameter classes. The RSMs proved to be robust and useful in studying the bioactivity of HA, as they integrated dose and time variables, which are usually addressed separately, resulting in confusing interpretations. The response surface modeling approach showed that the effect of HA is cumulative during the initial period of formation of rice seedlings, which may result in more vigorous seedlings for crop planting.

Cloud Point Extraction in Presence of Multi-walled Carbon Nanotubes for Removal of Direct Green 26 from Aqueous Solutions: Optimization by Box-Behnken Design and Desirability Functions

The novel approach of cloud point extraction in the presence of multi-walled carbon nanotubes (CPE/MWCNTs) is presented for removal of Direct Green 26 (DG26) from aqueous solutions. The experiments were conducted based on the Box-Behnken experimental design and the removal process was optimized by the response surface modeling and desirability function (DF) approach. Effects of the experimental variables (MWCNTs amount, solution pH, clouding time and volume of Triton X-100 solution) on the process efficiency were modeled using a quadratic equation with the coefficient of determination (R2) value of 0.9944 and Fisher ratio of 177.07. Using the DF approach, optimum levels of the variables determined as MWCNTs amount of 0.7 mg, pH 3, clouding time of 40 min and Triton X-100 solution volume of 993 µL. Experimental checking of the conditions resulted in the dye removal efficiency of 95.86%. Results of the study proved the applicability of the proposed method for DG26 removal from real water samples.

Solar-active photocatalysts based on TiO2 and conductive polymer PEDOT for the removal of bisphenol A

The study explores the potential of novel composite photocatalyst made of TiO2 and conductive polymer poly(3,4-ethylenedioxythiophene) (TiO2-PEDOT) for the removal of bisphenol A (BPA), a water contaminant of emerging concern. TiO2-PEDOT with different PEDOT contents were prepared by oxidative chemical polymerization of (3,4-ethylenedioxythiophene) (EDOT) in the presence of TiO2, using either (NH4)2S2O8 or FeCl3 as oxidants, to study their role on photocatalytic properties. Composites were characterized for their composition and morphology, as well as surface, structural and optical properties. Composites have core-shell-like morphology, possessing homogeneous polymer distribution over TiO2 surface. Composites have specific surface area comparable to benchmark material (TiO2 P25), while band gaps and recombination rates are significantly lower. The photocatalytic activity was evaluated under simulated Solar irradiation for the removal of BPA. The observed effects were correlated with the changes of process parameters (PEDOT content, photocatalyst loading and initial pH) using response surface modeling approach. TiO2-PEDOT showed higher effectiveness than benchmark material TiO2 P25. The influence of various water matrix constituents (carbonates, nitrates, sulphates, chlorides, phosphates and natural organic matter) on BPA removal were studied as well, and were found to be detrimental to BPA removal through scavenging bulk and surface hydroxyl radicals.

Optimization and development of drug loading in hydroxyapatite–polyvinyl alcohol nanocomposites via response surface modeling approach

In the present study, parameters affecting the particle size and drug loading of curcumin-loaded hydroxyapatite–polyvinyl alcohol (HAp-PVA) nanocomposites were investigated and optimized. The nanocomposites were synthesized by using chemical precipitation technique, and curcumin was subsequently incorporated into the prepared nanocomposites through an impregnation methodology. Dynamic light scattering and scanning electron microscopy were applied for the evaluation of HAp-PVA nanocomposites. Besides, response surface methodology (carried out using Minitab 16) assessed the correlation between design parameters and experimental data. The independent variables selected in Box–Behnken design were time of milling (X1), polyvinyl alcohol (PVA), concentration (X2) and the concentration of drug (X3), while particle size and drug loading were considered as the responses. The size of nanoparticles ranged from 71 to 123 nm, and drug loading varied between 8.9 and 61.1%. Contour plots and surface plots were benefitted in order to realize the combined effects of different variables. Optimized formulation using response optimizer design demonstrated the particle size of 95 nm and drug loading of 61.24%. From the acquired results, it was concluded that the chemical precipitation method accompanied by the Box–Behnken experimental design approach could be successfully applied to optimize the nanoformulation of curcumin-encapsulated HAp-PVA nanocomposites.