Quadratic Response Surface Method Research Articles

Optimization design of hydro turbine support structure based on GA-FA-BP method

The rational design of the turbine support structure ensures the safe operation of the system, achieves significant economic benefits and improves the efficiency of the turbine. This paper presents a novel turbine support structure capable of vertical movement along the guide column. In addition, the GA-FA-BP method has been developed for the optimization design of the support structure, which combines genetic algorithm (GA), firefly algorithm (FA) and back-propagation neural network (BP). The use of quadratic response surface (RS) method along with NSGA-II for the result validation of the GA-FA-BP model ensures the robustness and reliability of the optimization results. A finite element model is set up to analyse the mechanical behaviour of the support structure under 10 different combined load conditions. The most critical load conditions in the static mechanical models are used to generate training data, and the mass, deformation and equivalent stress of the optimized and unoptimized support structures are analyzed and compared. The results show that the optimized support structure can maintain deformation and equivalent stress within a weight reduction of 21.83% compared to the original design. Compared to a single optimization model, the proposed GA-FA-BP model shows higher accuracy with a correlation coefficient up to 0.9989.

Optimal configuration of passive flow control devices to reduce the aerodynamics drag of a tractor-trailer model

Aerodynamic drag plays an important role in heavy vehicles, especially when traveling at high speeds. In this context, the application of passive flow control devices emerges as a potential approach to reduce the aerodynamic drag of vehicles, leading to improvements in fuel efficiency and environmental pollution. Consequently, this study focuses on using cab side extenders and rear flaps to reduce the aerodynamic drag of a 1:8 small-scale simplified tractor-trailer model. The main parameters of this device configuration, including the length LR and deflection angle θG of the cab side extenders, the length LR and deflection angle θR of the rear flaps, are optimized to minimize the model aerodynamic drag coefficient. Numerical studies are performed using the Computational Fluid Dynamics method, with the steady k-ω SST and the unsteady DES turbulence model. The optimal solution is implemented based on a 30-level Latin Hypercube design of the experiment and a full quadratic regression response surface method. The obtained results show that a maximum reduction in the aerodynamic drag coefficient of the simplified tractor-trailer model by 20.8 % is achieved with an optimized configuration of control devices. The mechanism of aerodynamic drag reduction is also evaluated based on the analysis of flow fields around the vehicle model.

Design and experiment of a soybean shaftless spiral seed discharge and seed delivery device

When the driven stubble-breaking and anti-blocking no-till planter operates in the Southwest China, the stubble-breaking blades will impact with the ground as they cut through the soil and straw stubble, causing the planter to vibrate. This results in poor performances of the seed discharge by seed discharger and the seed guide by the seed guide tube. Based on the principle of spiral conveying, a soybean shaftless spiral seed discharge and seed delivery device was designed. The optimum seed filling size and speed range of the spiral blade were obtained by analyzing the size, force, and motion of soybean seeds of "ZhongHuang 37". The quadratic regression orthogonal rotation test and response surface method were used to analyze the operating parameters of the shaftless spiral seed discharge and seed delivery device by joint EDEM (Discrete Element Method)-RecurDyn simulation. The optimum parameters were obtained: the spacing of spiral was 11.4 mm, spiral outer radius was 5.5 mm, spiral inner radius was 2.9 mm and rotation speed was 10.4 r·s−1. Based on simulation and optimization results, the device was trialed and its field performance was tested. The results showed that at a surface slope of 16.1°, an average surface flatness of 8.9 cm, an average planter vibration frequency of 75.2 Hz, and an average amplitude of 7.2 mm, the average seeding qualification index, multiple index, missing seeding index, and damage index of the shaftless spiral seed discharge and seed delivery device were 92.6%, 5.03%, 2.4% and 0.92%, respectively, which were in line with the local agronomic requirements. The designed soybean shaftless spiral seed discharge and seed delivery device meets the requirements of the quality of no-till seeding and can provide a reference for the design and improvement of seed discharger and seed guide tube under poor ground leveling and long-distance seed delivery conditions.

Non-Probabilistic Reliability Analysis of Slopes Based on a Multidimensional Parallelepiped Model

Aiming at the problem that the non-probabilistic reliability analysis method of slope engineering, which is based on an interval model, cannot consider the cross-correlation of geotechnical parameters, a non-probabilistic reliability analysis method of slopes based on a multidimensional parallelepiped model is proposed. This method can effectively alleviate the problem of difficult data survey in the field of geotechnical engineering. Using the limited sample data of soil parameters, the multidimensional parallelepiped model is constructed. The performance function of the slope is constructed based on Latin hypercube sampling and the quadratic response surface method. Then, the limit state equation of the slope can be standardized using the multidimensional parallelepiped model. The non-probabilistic reliability indexes of the slope are calculated based on the global optimal solution to judge the stability state of the slope. The example analysis verifies the feasibility of the proposed method. The results show that the correlation of shear strength parameters of soil has a great influence on the non-probabilistic reliability indexes of the slope. When the correlation coefficients of the shear strength parameters are between −1.0 and 0, the smaller the correlation coefficient is, the greater the non-probabilistic reliability index of the slope is; when the correlation coefficients of the shear strength parameters are between 0 and 1.0, the non-probabilistic reliability index of the slope does not change with the correlation coefficient. The non-probabilistic reliability indexes of the slope obtained using the multidimensional parallelepiped model are between the results obtained using an ellipsoid model and those obtained using an interval model, which are validated by Monte Carlo method and relatively more reasonable. In the absence of a large number of geotechnical sample data, this method provides a new way for slope stability analysis and expands the application field of calculation methods based on non-probabilistic theory.

Reliability analysis of composite laminate patch repaired structures based on response surface proxy model

In this paper, the reliability analysis of composite laminate patch repaired structures under unidirectional static load was studied by means of a probability model. First, a proxy model for the maximum static load carrying capacity of the repaired structure was established using quadratic polynomial response surface method (RSM) considering the repair material properties, repair patch design and adhesive layer thickness. Second, the probability distribution input of various basic random parameters including geometric characteristics and material properties were considered based on actual repair data. Finally, both the reliability and sensitivity analysis of the repaired structure were investigated by means of Monte Carlo simulation method. The results show that the reliability analysis model is of great significance for the subsequent design and properties evaluation of composite repaired structures.

Alkali-activated slag backfill grout materials optimization: statistical RSM modelling and NSGA-II performance control

Optimizing the performance of alkali-activated slag backfill grout (ASBG) is crucial for engineering applications. Fluidity and 28 d unconfined compressive strength (28 d UCS) are the two most important performances and multi-objective optimization is existed. In this research, the response surface method (RSM) for experiment design and model regression, non-dominated sorting genetic algorithm II (NSGA-II) for optimization, and entropy-based Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) for decision-making were implemented. The strength formation mechanism of the optimal ASBG was investigated via microstructure evolution. The results show that the quadratic RSM models for fluidity and 28 d UCS exhibit excellent predictive fitting capabilities, with the determination coefficients of 0.9713 and 0.9588 respectively. NSGA-II coupled with entropy-based TOPSIS determined the optimal mix proportion with water-binder ratio of 0.877, binder-sand ratio of 1.000 and alkali dosage of 4.138%. The porosities at 1–28 d decrease from 10.06% to 2.62%. And the mode of microstructure evolution can be divided into two stages according to the probability distribution index and fractal dimension. In early stage, probability distribution index and fractal dimension decreased from 0.9974 to 0.4833 and 1.2498 to 1.2022. This indicated that the number of the small pores decreased and the pore boundary transformed into the softer one as the irregular plate-like GGBS dissolved. In the later stage, probability distribution index and fractal dimension increased from 0.4833 to 1.4732 and 1.2022 to 1.3273, indicating a relatively denser microstructure with fewer large pores formed.

Horizontal Bearing Capacity and Reliability of Piles in Coastal Soft Soil Considering the Time-Varying Characteristics

In order to study the influence of the creep of soft soil and the corrosion damage of reinforced concrete on the horizontal bearing behavior of piles, the novel p-y curve model was established considering the time-varying characteristics of soil parameters. The attenuation law of the bending stiffness of reinforced concrete piles under chloride erosion was analyzed by introducing the bending stiffness reduction factor. The limit state function of pile reliability analysis was then established considering the time-varying characteristics. The reliability index of a pile under horizontal displacement failure mode was obtained using the quadratic response surface method. Finally, the sensitivity analysis of random variables (cohesion, internal friction angle, concrete cover, and chloride concentration) on the time-varying reliability of a pile under horizontal displacement failure mode was carried out. The influence of the distribution types of soil parameters on the time-varying reliability was considered. The results show that the load-bearing characteristics of the horizontally loaded pile are impacted significantly by the time-varying characteristics of the soil. The maximum horizontal displacement of the pile increases nonlinearly with the increase in service time. When the horizontal displacement failure mode occurs, the variability in the internal friction angle has a significant impact on the reliability of the pile. The reliability index decreases nonlinearly with an increase in service time. When the soil parameters obey the extreme value type I distribution, the corresponding reliability index is greater than that of log-normal distribution and normal distribution.

Design and optimization of a novel U-type vertical axis wind turbine with response surface and machine learning methodology

A novel U-type Darrieus Wind Turbine (UDWT) is proposed by this study. During the design and optimization of UDWT, Machine Learning (ML) method based on BPNN and three optimization algorithms, GA, PSO and SA, are adopted. Besides, the quadratic Response Surface (RS) method combined with NSGA - II serves as the comparison of ML method. Meanwhile, Fluid - Structure Interaction (FSI) model, simultaneously considering the aerodynamic and structural loads, is utilized to generate the training data and validate the optimization results of ML and RS method. Moreover, the rotor performance, aerodynamic forces, pressure differential on center of blade span, velocity deficit of near-field fluid as well as the deformation, equivalent stress of UDWT are analyzed and revealed extensively. Results show that optimal UDWT can operate effectively at broader range of tip speed ratio (TSR) and the power coefficient is improved by14.74% and 53.98% at TSR of 4.0 and 4.5, respectively. Meanwhile, the novel strut type can keep the deformation and equivalent stress of rotor within the allowable limits of material when it rotates under high angular velocity. UDWT is proven to improve aerodynamic and structural performances, compared with conventional two- and four-blade wind turbine.

Probabilistic analysis of maximum mode shape for mistuned blisk

Abstract The high-fidelity finite element model (HFFEM) and Monte Carlo (MC) simulation of the blisk involve large number of calculations, which leads to low computational efficiency. In this case, an improved quasi-static mode compensation method (IQSMCM) and quadratic function-extremum response surface method (QF-ERSM) are proposed to investigate the probability distribution of mistuned blisk based on its vibration characteristics. The number of nodes and elements of IQSMCM relative to HFFEM are, respectively, reduced by 79.66 and 80.03%. Thus, the degrees of freedoms (DOFs) of IQSMCM are obviously reduced compared with that of HFFEM, and its computational efficiency is obviously increased. The maximum displacement shape (MDS) is investigated via IQSMCM. The computational efficiency is enhanced in the condition of ensuring the computational accuracy. Based on the investigation of maximum mode shape, the probability analysis is performed via QF-ERSM. The computational accuracy of QF-ERSM is improved by 93.80% compared with that of MC. Furthermore, the computational efficiency of QF-ERSM is higher 57.06% than that of QF-RSM. The sample history, extremum response surface function, sample history and distribution histogram of MDS are obtained via QF-ERSM, which provides an important guidance for the reliability research of the mistuned blisk. This research can be applied not only to aeroengine’s blisk but also to other large and complex mechanical structures in practical engineering.

Numerical and Experimental Study of a Flexible Trailing Edge Driving by Pneumatic Muscle Actuators

A static aeroelastic analysis of the flexible trailing edge is conducted to calculate the deformed shape, aerodynamic coefficients and corresponding driving pressure. A physical flexible trailing edge model is manufactured using a honeycomb structure, which is measured based on binocular vision. The quadratic response surface method is adopted to establish the pneumatic artificial muscle actuator model. The wire-pulley transmission model is built to identify the existence of equivalent forces and produce the equivalent forces as the substitute of actuation force. A finite element model of the flexible trailing edge is established, which is validated by the test data. A nonlinear relationship is found between the driving pressure and deflection angle. The pressure needed to bear the structural stiffness is found to be much larger than that of the aerodynamic load. With the increase in pressure, the magnitude of the lift coefficient increases less. However, the magnitude of the drag coefficient increases more with the increase in pressure under 0.2 MPa. When the driving pressure exceeds 0.2 MPa, the relationship between them is nearly linear.

Statistical optimization of cellulases by Talaromyces thermophilus utilizing Saccharum spontaneum, a novel substrate

Abstract Background At present, cellulases are the most important enzymes worldwide, and their demand has been increasing in the industrial sector owing to their notable hydrolysis capability. Results In the present study, contrary to conventional techniques, three physical parameters were statistically optimized for the production of cellulase by thermophilic fungi by using response surface methodology (RSM). Among all the tested thermophilic strains, the best cellulase producing fungus was identified as Talaromyces thermophilus – both morphologically and molecularly through 5.8S/ITS rDNA sequencing. The central composite design (CCD) was used to evaluate the interactive effect of the significant factors. The CCD was applied by considering incubation period, pH, and temperature as the model factors for the present investigation. A second-order quadratic model and response surface method revealed that the independent variables including pH 6, temperature 50 °C, and incubation period 72 h significantly influenced the production of cellulases. The analysis of variance (ANOVA) indicated that the established model was significant (P ≤ 0.05) and showed the high adequacy of the model. The actual and predicted values of CMCase and FPase activity showed good agreement with each other and also confirmed the validity of the designed model. Conclusions We believe the present findings to be the first report on cellulase production by exploiting Kans grass (Saccharum spontaneum) as a substrate through response surface methodology by using thermophilic fungus, Talaromyces thermophilus. How to cite: Abdullah R, Tahseen M, Nisar K et al. Statistical optimization of cellulases by Talaromyces thermophilus utilizing Saccharum spontaneum, a novel substrate. Electron J Biotechnol 2021;51. https://doi.org/10.1016/j.ejbt.2021.03.007.

Analytic target cascading with fuzzy uncertainties based on global sensitivity analysis for overall design of launch vehicle powered by hybrid rocket motor

An analytic target cascading (ATC) method with fuzzy uncertainties based on global sensitivity analysis is proposed to solve the optimization problem of typical multilevel multidisciplinary nonlinear system. The overall design of launch vehicle (LV) powered by hybrid rocket motors (HRMs) involves multiply disciplines, and is decomposed into two levels using an ATC framework. The fuzzy theory is applied to describe the uncertain design factors caused by decisions and cognition insufficiency. The rank correlation coefficient method (RCCM) based on feasible optimization solutions and the quadratic response surface method (QRSM) based on Latin hypercube sampling (LHS) are used for global sensitivity analyses of input uncertainty and model uncertainty, respectively. The multi-island genetic algorithm (MIGA) is adopted in all examples, and the known two-phase optimization method is used to verify the LV design results. The results show that global sensitivity analysis can significantly filter the fuzzy uncertain factors which have little influence on the responses. The ATC decomposition is applicable in solving the calculation burden caused by uncertainties. The fuzzy-based design optimization with ATC is more efficient than that with MDF, and gives more reliable and robust results than the deterministic ATC method.

Multi-objective optimization of lubricant volume in an ELSD considering thermal effects

Lubricant filling into a closed fluid domain of a transmission component has always been a challenge, for it is limited by a number of factors, like structural characteristics of a transmission component, load characteristics, and oil temperature of during an operation. This paper proposes a lubricant volume optimization model that takes into account the effect of temperature and heat, with an electronically controlled limited slip differential (ELSD) for an automobile taken as the study object. In the paper, an ELSD simulation model was firstly constructed, based on a CFD numerical simulation method. After model simplification and assumption, the probes were established for fluid speed and temperature parameters during gear rotation. The influence law of lubricant volume in the ELSD on convective heat transfer was then determined by analyzing the working conditions, including different rotational speeds and different oil immersion depths. Finally, the optimization model was constructed, with the numerical values after the steady-state temperature fluctuation and the time required for the fluctuation taken as evaluation indexes. In the study, by taking specific parameters for examples and based on the proposed optimization model, quadratic response surface method was used for equation fitting of multiple results obtained from the simulation, and the lubricant volume of 37.21% of the total volume was found to be optimal, which verified the feasibility of the model. The method provides a new approach for determining the lubricant volume for a transmission component.

Optimization for maximum specific energy density of a lithium-ion battery using progressive quadratic response surface method and design of experiments

The demand for high-capacity lithium-ion batteries (LIB) in electric vehicles has increased. In this study, optimization to maximize the specific energy density of a cell is conducted using the LIB electrochemical model and sequential approximate optimization (SAO). First, the design of experiments is performed to analyze the sensitivity of design factors important to the specific energy density, such as electrode and separator thicknesses, porosity, and particle size. Then, the design variables of the cell are optimized for maximum specific energy density using the progressive quadratic response surface method (PQRSM), which is one of the SAO techniques. As a result of optimization, the thickness ratio of the electrode was optimized and the porosity was reduced to keep the specific energy density high, while still maintaining the specific power density performance. This led to an increase in the specific energy density of 56.8% and a reduction in the polarization phenomenon of 11.5%. The specific energy density effectively improved through minimum computation despite the nonlinearity of the electrochemical model in PQRSM optimization.

Multi-objective optimization of a permanent magnet synchronous motor based on an automated design and analysis procedure

Since traction motors for electric vehicles require a variety of features to be used simultaneously, research on the design optimization of permanent magnet synchronous motors (PMSMs) has been increasing. To apply design optimization in the industrial field, it must be accurate, simple, and the design time should be minimized. This study proposes an automated design and analysis procedure to optimize the shape of a PMSM. ANSYS Maxwell and PIAnO were combined to implement automation, which are finite element analysis and design optimization software programs, respectively. The average torque and total harmonic distortion of the back electromotive force were set as a multi-objective function. In addition, the efficiency and torque ripple were set as constraints with five design variables to satisfy them. To verify the superiority of the proposed design optimization procedure, three optimization algorithms were reviewed and compared with metamodel-based design optimization. These algorithms include parallel algorithm discovery and orchestration, a progressive quadratic response surface method, and sequential two-point diagonal quadratic approximate optimization Moreover, because it is a design optimization problem with a multi-objective function, the changes in the design optimization results according to the changes in the weighting ratio were examined. Finally, the validity of the design results was verified through experiments. The research results demonstrate that the proposed design optimization procedure is more accurate, faster, and better than the conventional method.

Multi-disciplinary design optimization with fuzzy uncertainties and its application in hybrid rocket motor powered launch vehicle

In this paper, an Uncertainty-based Multi-disciplinary Design Optimization (UMDO) method combining with fuzzy theory and Multi-Discipline Feasible (MDF) method is developed for the conceptual design of a Hybrid Rocket Motor (HRM) powered Launch Vehicle (LV). In the method proposed, membership functions are used to represent the uncertain factors, the fuzzy statistical experiment is introduced to analyze the propagation of uncertainties, and means, standard deviations and credibility measures are used to delineate uncertain responses. A geometric programming problem is solved to verify the feasibility of the Fuzzy-based Multi-Discipline Feasible (F-MDF) method. A multi-disciplinary analysis of a three-stage HRM powered LV involving the disciplines of propulsion, structure, aerodynamics and trajectory is implemented, and the mathematical models corresponding to the F-MDF method and the MDF method are established. A two-phase optimization method is proposed for multi-disciplinary design optimization of the LV, including the orbital capacity optimization phase based on the Ziolkowski formula, and the scheme trajectory verification phase based on the 3-degree-of-freedom point trajectory simulation. The correlation coefficients and the quadratic Response Surface Method (RSM) based on Latin Hypercube Sampling (LHS) are adopted for sensitive analysis of uncertain factors, and the Multi-Island Genetic Algorithm (MIGA) is adopted as the optimization algorithm. The results show that the F-MDF method is applicable in LV conceptual design, and the design with the F-MDF method is more reliable and robust than that with the MDF method.

Design study of impact performance of a DTH hammer using PQRSM and numerical simulation

This paper presents a simulation model to predict the percussive drilling performance of a down-the-hole (DTH) hammer. First, the pneumatic dynamic model of the DTH hammer is developed considering mass flow rate relations representing orifice opening areas of the air tube, the piston, and the bit flushing channels. Next, the performance of the DTH hammer is numerically simulated and evaluated by considering fluctuations of the upper and lower chamber pressure, impact frequency, and force. The simulation model is validated through a series of laboratory tests. Finally, design factors influencing the hammers impact performance are selected via screening design, and the progressive quadratic response surface method then optimizes the set of design factors to propose a design modification to increasing the impact performance of the DTH hammer.

An Innovative Methodology for Online Surrogate-Based Model Updating of Historic Buildings Using Monitoring Data

ABSTRACT Structural Health Monitoring (SHM) based on Automated Operational Modal Analysis (A-OMA) has gained increasing importance in the conservation of heritage structures over recent decades. In this context, finite element model updating techniques using modal data constitute a commonly used approach for damage identification. Nevertheless, the large number of simulations usually involved in the associated minimization problem hinders the application to real-time condition assessment. This is especially critical for historic buildings, where the modelling of complex geometries involves large computational burdens. Alternatively, surrogate models offer an efficient solution to replace computationally demanding numerical models and so perform continuous model updating. In this light, this paper presents a surrogate-based model updating approach for online assessment of historic buildings and its application to a medieval masonry tower, the Sciri Tower in Perugia (Italy). Using modal properties identified by A-OMA, the proposed approach allows the continuous fitting of certain damage-sensitive parameters of the structure. To do so, three different surrogate models are considered, including the quadratic response surface method, Kriging, and Random Sampling High-Dimensional Model Representation, and their effectiveness is compared from an SHM perspective. The reported results demonstrate the suitability of the proposed methodology for tracking the temperature-dependent intrinsic properties of the tower.

Nonlinear Optimization for Geometric Parameters of Reinforced Concrete Coupled Structural Walls

The coupling ratio (CR) has been widely used to quantitatively reflect the degree of coupling action between the component walls and link beams of a coupled wall. However, the CR index is very difficult to evaluate at early design stages. In order to develop alternative design parameters that can be easily utilized and ensure the dual lateral force resisting mechanism of coupled walls, nine prototype coupled walls were designed considering various aspect ratios of wall pier (αw) and span-to-depth ratios of coupling beams (αb). The incremental dynamic analyses on the seismic fragility was conducted to examine the influences of αw and αb on the fragility characteristics and the margin capacities corresponding to different performance limit states. The double-factorial quadratic response surface method was used to further reveal the interactive impact of αw and αb on the overall behavior of coupled walls. Then the combinations of αw and αb that can produce the optimal values of response variables were obtained. The curve-fitting technique was used to find the relationship between optimal αb and αw. It is indicated that αb and αw can effectively serve as the alternative parameters to CR and ensure optimal overall structural performance of RC coupled walls.

Non-probabilistic Integrated Reliability Analysis of Structures with Fuzzy Interval Uncertainties using the Adaptive GPR-RS Method

Due to its weak dependence on the quantity of variable samples, the non-probabilistic reliability analysis method based on the convex set model is applicable to practical problems in structural engineering with inherent uncertainties. However, when dealing with the black-box limit-state function issues in practical complex structural engineering, the traditional quadratic polynomial response surface (QP-RS) method has the problem of insufficient precision in approximating a highly nonlinear function. Meanwhile, fixing the limits of interval variables is trickier in case of scant samples and meager statistical information. To remedy the above deficiencies, this paper introduces a reasonable integrated reliability analysis approach. First, an adaptive Gaussian process regression response surface (GPR-RS) method that dynamically improves the fitted accuracy near the design point of the black-box limit-state function is formulated. Furthermore, the integrated reliability index with consideration of fuzzy interval uncertainties is presented. Three validation and two application examples are employed, which have justified the approach as a more reasonable assessor of practical complex structural reliability with safer results.