Optimum Design Research Articles

Potential use of piezoelectric laser-induced vibration energy harvesting in wireless power transmission: Theoretical modelling and simulation

Because of continuous trend in wireless microdevice technology, a novel model of a laser-induced piezoelectric microgenerator within the framework of the non-Fourier heat conduction and nonlocal elasticity theory is proposed in this research. A non-Gaussian profile is considered for the laser source. The Galerkin method and the Laplace transform are employed to discretize and solve the coupled electro-thermo-mechanical equations, respectively. The inverse Laplace transform is numerically calculated to investigate the influences of the resistance load, laser intensity, laser absorption depth, specific heat capacity and thickness of the piezoelectric layer on the voltage response and power output of the microharvester. The obtained results reveal that the performance of the microharvester is dramatically affected by changing these parameters. Also, some optimum design parameters are provided to ensure the best performance of the system. Therefore, the present study can be helpful in analysis, design and optimization of wireless power devices, light-induced actuators and sensors in the future.

Designing the geometry of compact tension specimens for easy fracture toughness measurement using reinforcement learning

Abstract For composite laminates, a rising R-curve is observed for their fracture toughness under Mode I stress, which is important for a comprehensive failure analysis of the materials. Since it is laborious to measure the R-curve due to its dependence on both the load and the crack extension, we put forward a novel compact tension specimen by modifying its geometry to eliminate the relation between fracture toughness and crack extension, so as to simplify the experimental process of the R-curve measurement by only recording the load history. Two machine learning models were developed for the optimum sample design based on the finite element analysis of the effect of sample geometries on the R-curve. A simple neural network model was built for designing tapered specimen and a reinforcement learning model was created for further finding the best design from a broader design space. The results showed that, in contrast to the specimens with a tapered shape, which only ensure the independence between the R-curve and crack extension in the case of a small extension, the design provided by the reinforcement learning provides such independence across a wider range of crack length and an improved accuracy.

Loss-Optimized Design of Magnetic Devices.

Maximizing efficiency, power density, and reliability stands as paramount objectives in the advancement of power electronic systems. Notably, the dimensions and losses of magnetic components emerge as primary constraints hindering the miniaturization of such systems. Researchers have increasingly focused on the design of loss minimization and size optimization of magnetic devices. In this paper, with the objective of minimizing the loss of magnetic devices, an optimal design method for the winding structure of devices is proposed based on the coupling relationship between the loss prediction model and the design variables. The method examines the decoupling conditions between the design variables and the loss model, deriving optimized design closure equations for the design variables. This approach furnishes a technical foundation for the miniaturized design of miniature apparatuses incorporating magnetic components, offering a straightforward and adaptable design methodology. The finite element method simulation results and experimental measurement data verify the accuracy of the prediction of the proposed method and the validity of the optimal design theory of device loss.

Tornado-induced instability assessment of super large hyperbolic reinforced concrete cooling towers

Cooling towers are typical high-rise thin-walled structures which are of hyperbolic rotating shell structure type and significantly sensitive to wind loads. Wind-related local instability is the key control factor in the design of structural geometric shape and tower shell thickness optimization. In fact, this kind of stability analysis has only conducted aiming at normal climate (such as monsoon, etc.) under the guideline of series of national Codes. In order to deal with the issues under disaster climate, physical and numerical investigation to evaluate local stability performance of a super large cooling tower (SLCT) under tornado environments based on Buckling Stress State (BSS) method is implemented. Besides, whole process elastic–plastic collapse simulation of the SLCT exposed to the tornados was also carried out to study the failure mechanism and re-evaluated the reasonability of the well-accepted BSS method for structural wind-resistant design. The results revealed that the tornados would have obvious adverse effects on the structural local stability when the SLCT is located at the tornado vortex core radius compared with those under traditional synoptic winds. The swirl ratios and the central distances between the SLCT and the tornado vortex core have significant effects on the local instability of the SLCT. The extended elastic–plastic collapse simulation discovered that the position of the first crack during SLCT collapse process is basically consistent with the critical position from the elastic local stability analysis of the SLCT, indicating that strengthening measures can be carried out in advance at the critical position for structural local stability improvement under tornado conditions. Besides, the extended elastic–plastic collapse numerical simulation of the SLCT could be as the effective supplement to the structural elastic stability assessment (such as BSS method) in the wind-resistant design of the SLCT.

Seismic design optimization of space steel frame buildings equipped with triple friction pendulum base isolators

To increase the seismic resilience of structures, it is necessary to utilize seismic isolation to increase structural periods and reduce story drifts. When seismic isolation is implemented, structures are capable of deforming by remaining within safe limits. Thus, more seismically resilient designs are achieved compared to conventional fixed-based structures since lighter structural design weights are attained. The principal aim of this study is to achieve the comparative design optimization of space steel frame buildings equipped with seismic base isolation and to examine the effect of seismic base isolation on optimum structural design weight by comparing the same structures with conventional rigid-based ones. For seismic base isolation, triple friction pendulums are implemented into steel frame buildings. For this aim, four different space steel frame buildings with 4-, 6-, 8-, and 10-story are treated as design examples. A novel design optimization algorithm is encoded, which includes nature-inspired metaheuristic artificial bee colony, crow search, and Archimedes optimization algorithms to achieve design optimizations of triple friction pendulums equipped with seismic-isolated space steel frame buildings. The practice code provisions of load and resistance factor design specification for structural steel buildings have been applied to control the structural design constraints of inter-story drift, top-story drift, strength, displacement, and connections geometry of beams and columns. Eventually, it has been remarked that seismic base isolation significantly reduces the structural optimal design weight of space steel frame buildings.

Symmetrical structure design of PLGA Biodegradable sinus stents and structure optimization based on surrogate models.

This study aims to enhance the degradation uniformity of PLGA sinus stents to minimize fracture risk caused by stress corrosion. Symmetric stent structures were introduced and compared to sinusoidal structure in terms of stress and degradation uniformity during implantation and degradation processes. Three surrogate models were employed to optimize the honeycomb-like structure. Results showed honeycomb-like structures exhibited the superior stress distribution and highest degradation uniformity. The kriging model achieved the smallest error and degradation uniformity of 83.24%. In conclusion, enhancing the symmetry of stent structures improves degradation uniformity, and the kriging model has potential for the optimization of stent structures.

An In-Depth Investigation of the Effects of Tungsten Inert Gas Welding Process Parameters on Hardness and Corrosion Resistance of 2205 DSS Weldments: New Design of Experiment Parametric Studies and Optimization

The aim of this work is to examine and analyze, using response surface methodology, how the TIG welding process parameters of welding current (WC), welding speed (WS), and N2 with argon as shielding gas affect the hardness and corrosion resistance of 2205 DSS weldments. Due to the equal amounts of ferrite and austenite phases and alloying elements, duplex stainless steel DSS offers good mechanical properties and corrosion resistance. The mechanical characteristics and resistance to corrosion of the weld zone, as well as the heat-affected zone of the DSS, are, however, disturbed as a result of the welding process since it changes the distribution of these two phases and also the alloy is thermally disturbed. Therefore, in this work, an in-depth investigation of the effects of the above-mentioned parameters on the DSS quality has been performed. Results showed that increasing welding current while decreasing welding speed, which corresponds to the highest heat input, led to lower critical pitting potential and weld zone hardness but higher heat-affected zone hardness. The same results were obtained for decreasing welding current while increasing welding speed, which correspond to the lowest heat input. However, the addition of a small percent (%) of N2 to argon shielding gas resulted in increasing the critical pitting potential and decreasing the hardness in welds and heat-affected zones. Numerically, the RSM planned experimental results showed that an optimum welding current of 175A, welding speed of 170 mm/min, and 10% N2 with argon as shielding gas maximized the critical pitting potential up to 318 mV and optimized the hardness of the weld and heat-affected zone to about base metal hardness of 288 and 286 HV, respectively.

Multi‐objective optimization of a Fibonacci phyllotaxis micro pin‐fin heat sink

AbstractThere are still significant technical challenges associated with thermal management of electronic devices such as microprocessors. To improve heat dissipation performance of integrated circuits, a new Fibonacci phyllotaxis design of circular micropin fin heat sinks has been developed. To minimize both chip temperature and pumping power, a multi‐objective optimization technique was employed. The effect of design parameters such as phyllotaxis coefficient, pin fin diameter, and pin fin height on response parameters was numerically investigated using the full factorial design of the experiment. Artificial neural network was coupled with MO‐Jaya, to arrive at a Pareto frontier of optimal compromise solutions. The optimal set of design variables were found to be a height of 300 μm, a diameter of 122.6 μm, and a phyllotaxis coefficient of 130 μm with an inlet velocity of coolant 2.263 m/s. The selected optimum design was then investigated numerically, and the outcomes were compared to those predicted by the MO‐Jaya algorithm. The final confirmed response variables were a maximum temperature of 51.6°C and a pumping power of 0.191 W. The results show that the Fibonacci phyllotaxis structure of the micro pin fin heat sink has better heat‐dissipating performance.

Analysis and Optimization of the Performances of the Tandem Blade Radial Compressor Using the CFD

Centrifugal compressors are frequently used in both military and commercial areas because they can be easily manufactured and reach high-pressure compression ratios. The factor that limits the performance and operating range of compressors is flow instability. Many ideas have been put forward for performance improvement, but tandem blade radial compressors, which do not require an extra air system, have attracted the most interest. In this study, computational fluid dynamics (CFD) analyses were carried out on various parameters of the tandem blade (TB) radial compressor, and an optimization study was carried out to find the best design using a genetic algorithm on a whole operating curve. It was investigated how these parameters affected the efficiency and total pressure ratio between the determined lower and upper limits. The numerical analyses of the optimum design obtained as a result of the iterations were carried out. As a result of the iterations, three optimum designs were obtained and numerical analysis was carried out according to one of them, and then they were compared with the results in the literature. The general agreement of computational fluid dynamics and the literature data served as a validation for the computational approach. The error rates between the numerical analysis results and the experimental results in the literature were calculated for different flow rates and were found to be 1.98% as the highest and 0.35 as the lowest. The work carried out in this article will provide a valuable reference for future advanced tandem blade compressor designs.

Enhancing transmission type frame structures: A BBO algorithm-based integrated design approach.

The stable and site-specific operation of transmission lines is a crucial safeguard for grid functionality. This study introduces a comprehensive optimization design method for transmission line crossing frame structures based on the Biogeography-Based Optimization (BBO) algorithm, which integrates size, shape, and topology optimization. By utilizing the BBO algorithm to optimize the truss structure's design variables, the method ensures the structure's economic and practical viability while enhancing its performance. The optimization process is validated through finite element analysis, confirming the optimized structure's compliance with strength, stiffness, and stability requirements. The results demonstrate that the integrated design of size, shape, and topology optimization, as opposed to individual optimizations of size or shape and topology, yields the lightest structure mass and a maximum stress of 151.4 MPa under construction conditions. These findings also satisfy the criteria for strength, stiffness, and stability, verifying the method's feasibility, effectiveness, and practicality. This approach surpasses traditional optimization methods, offering a more effective solution for complex structural optimization challenges, thereby enhancing the sustainable utilization of structures.

Integrative Probabilistic Design of River Jetties by 3D Numerical Models of Transport Phenomena: The Case Study of Kabakoz River Jetties

Various methods are employed to investigate the effects of coastal structures in coastal areas on marine environments and transport phenomena. These methods can be categorized into physical models and numerical simulations. Due to the lack of long-term wave height data in Türkiye, numerical models are utilized to estimate wave heights generated by wind based on long-term measured wind speeds. These wave heights generated in deep sea conditions can be transported to the coast by wave transformation and interactions between coastal structures and waves, turbulence, currents induced by wind and breaking waves, coastal sediment transport rates, and changes in the coastline can be successfully predicted with the assistance of numerical models. In the scope of this study, the new “Integrative Probabilistic Design Approach of River Jetties” was developed. 3D numerical models were used for the optimum design, considering the sediment transport near the jetties and aiming to protect the coastal environment in the long term. 3D numerical modeling has been conducted to investigate the transport phenomena occurring at the outlet of the Kabakoz River in the Şile District of İstanbul Province to acquire the optimum layout and design of the coastal structures. The study presents the “Integrative Probabilistic Design Approach” for coastal protection structures by wind and wave climate, wave transformation, coastal sediment transport, shoreline change, and coastal structure probabilistic design sub-models. Monte Carlo Simulation of Hudson Limit State function conducts probabilistic design for the jetties. The greatest advantage of probabilistic design (Monte Carlo Simulation) is the prediction of uncertainties, such as wave height changes under design conditions. Following the completion of the construction of groins, the effect of probabilistic design on both design and coastal morphology can be evaluated precisely. In conclusion, in the study area, 146,237.55 m3 of sediment is transported annually from west to east and 221,043.49 m3 from east to west. In the absence of coastal structures, sediment transport from east to west is approximately 1.5 times greater than from west to east. The annual net coastal sediment transport from east to west is approximately 74,805.94 m3, while the total transport is estimated to be 367,281.04 m3. The coastline is expected to reach sediment balance within approximately two years. In this study, the coastal structure of a jetty is designed from an innovative probabilistic design perspective. The aim is to ensure the reliability of the structure and, at the same time, protect the morphology of the coastline where the structure will be constructed. The region’s wind and wave climate were initially determined using Hydrotam 3D software. Following this procedure, the length of the jetty is predicted considering the closure depth. The model parameters were calibrated from coastline morphology using satellite images and Google Earth over the past twenty years. These parameters are defined to Hydrotam 3D as input data; a trial-and-error model application procedure calibrates the coastline’s accumulation and erosion. Finally, the probabilistic design is conducted with Monte Carlo Simulation using the Hudson Equation as the limit state function. Det Norske Veritas developed a design code for marine structures in 1992, where the target reliability is 10-3 for structures with less serious failure consequences. This reliability level validated the Level IV model presented in this paper. The class of failure depends on the possibility of timely warning, and these standards can be revised by the model presented to address the effects of climate change on the design of maritime structures.

Impact resistance behaviors of boride reinforced Ti-6Al-4 V functionally graded materials: Experimental and numerical analysis

The impact resistant behaviors of boride reinforced Ti-6Al-4 V functionally graded materials prepared by spark plasma sintering (SPS) with compositional gradients of 90°, 84°, 82°and 79° were investigated based on the experimental test and the finite element method. The material constitutive parameters of the boride reinforced Ti-6Al-4 V alloys with different TiB2 contents were determined, and the Johnson Holmquist Ceramics (JH-2) model and a cohesive contact model were established and developed to predict the crack propagation and the impact resistance behaviors of the materials. The calculated results agreed well with the split Hopkinson press bar (SHPB) experimental results. The optimum material composition gradient design scheme with a continuous transition property from a high-toughness end to a high-strength end along the thin-thickness direction was determined. The G84 (0, 0, 15, 30 wt% TiB2) had the best impact resistance, with Young's modulus of 55505±5 GPa, compressive strength of 2045±5 MPa, and microhardness ranging from 535±5HV to 1246±5HV, exhibiting high strength and hardness at a high-strength end that can prolong the interaction time between the impactor and the materials, while the elongation of 39 % at its high-toughness end can cause tensile deformation, consuming impact kinetic energy efficiently. Combined with the experimental and numerical analysis results, the impact resistance and the crack-alleviated mechanisms of boride reinforced Ti-6Al-4 V functionally graded materials were discussed. Reducing the compositional gradient can alleviate the difference in coefficients of thermal expansion between composites, which may lead to strengthen the reflected wave, lower the compression wave, and suppress high-strength end failure efficiently, meaning of relieving the stress concentration under extreme service conditions. Moreover, the effects of the presence of the borides, such as in situ-formed TiB, remained TiB2at al., the dislocation defects and the whisker-like TiB on the armour materials resist fracture and layer cracking were also analyzed. This work provided a method for designing high performance of boride reinforced Ti-6Al-4 V functionally graded materials with high impact resistance and thin thickness.

Comparison of multi-criteria decision-making methods for selection of optimum passive design strategy

In the pursuit of achieving high-performance building design, the selection of the most suitable passive design strategies often involves the use of multi-criteria decision-making (MCDM) methods to address multiple conflicting criteria simultaneously. However, identifying the appropriate MCDM method for a specific building design context poses a challenge, as methods commonly effective in other contexts may not yield equivalent results. This study evaluates five MCDM methods (AHP, COPRAS, TOPSIS, VIKOR, and WSM) to understand their sensitivity in recommending the best solution. The considered criteria are energy demand, thermal comfort and daylight availability. The sensitivity analysis involves the impact of the variability of assigned weights on the rank shifting given by the considered MCDM method and the sensitivity of each criterion to weights variability. The findings reveal that implementing a fair-weight allocation leads to similar top 5 solutions among all MCDM methods. However, when a negative shift is applied to each criterion weight, AHP demonstrates greater robustness to weight variability compared to the other methods evaluated, while VIKOR is the most sensitive to weight variation.

Time stability of soil volumetric water content and its optimal sampling design in contrasting forest catchments

Characterizing the temporal variation across a forest catchment soil volumetric water content (VWC) with different environmental conditions at different depths for different seasons requires a robust point-scale sampling strategy that balances monitoring cost with predicting accuracy. In the study, the most time-stable locations (MTSLs) using the time-stable concept and the minimum number of required samples (NRS) based on random selection method were studied to explore the optimal sampling design for catchment-mean VWC with an acceptable error (the relative bias (RBIAS) less than 10 %). VWC monitoring was conducted at approximately 25 plots throughout the year in five forest catchments with varying areas and VWC status. Results revealed that the number of MTSLs for mean-VWC estimation with RBIAS within 10 % was directly related to the spatial variability of VWC. Specifically, one MTSL was feasible for accurately estimating mean VWC at different depths in high-VWC catchments with area around or less than 100 ha; one MTSL was adequate for each depth in the catchment with moderate-level VWC; whereas more than one MTSL were necessary for each depth in low-VWC catchment with a larger are of 1800 ha. To identify the MTSL for each catchment, the location with mean VWC was typically situated at the mid-elevation or soil apparent electrical conductivity (ECa) at a certain spatial scale. The NRS for catchment-mean VWC could be determined based on the combination of VWC status, its temporal stability, and potential catchment size, and could be ranked based on the spatial variation of each catchment. If the MTSL cannot be guaranteed for a catchment, the NRS might be a better alternative for optimum sampling design. These finding could be useful in providing guidelines for optimizing VWC monitoring in forest catchments by sampling at a few selected locations representative of the catchment-scale behavior.

Mix Design and Field Detection of Large-Particle-Size Graded Crushed Stone Mixtures for Pavement Reconstruction

Large-particle-size graded crushed stone mixtures (LPS-GCSMs) can improve the shortcomings of conventional graded crushed stone, such as low strength, high deformation, and a low modulus of resilience. At present, there is no systematic research on the gradation design and field evaluation of the LPS-GCSMs. In this study, compaction and California bearing ratio (CBR) tests and field construction conditions were combined to design six kinds of gradation of LPS-GCSM, and the optimum gradation was revealed. In order to improve the mechanical properties of LPS-GCSM, 2.5% cement was added to the mixture to prepare a low-content cement-modified LPS-GCSM (LCC-LPS-GCSM) based on the suggested gradation. The mechanical properties of the LCC-LPS-GCSM were investigated through unconfined compression strength (UCS) and compression rebound modulus (CRM) tests. Moreover, the compaction and deflection properties of LPS-GCSM and LCC-LPS-GCSM were examined through the test battery. The results showed that the optimum gradation of LPS-GCSM can be achieved with a combination of aggregate sizes of 20–40 mm, 10–20 mm, 5–10 mm, and 0–5 mm at a ratio of 44:20:10:26. The passing rates of 19 mm and 4.75 mm should be approximately at the median value of the gradation in view of field construction uniformity and a coarse aggregate interlocking effect. The UCS and CRM values of LCC-LPS-GCSM increased rapidly from 0 day to 28 days while they slowed after 28 days, which was similar to those of cement-stabilized materials. The field detection suggested that LPS-GCSM exhibited favorable compaction and that the addition of cement improved the stability of the field compaction of the mixture. Adding a subbase course of LPS-GCSM between the old pavement and the LCC-LPS-GCSM base can lead to more uniform stress on the base. The results of this study provide a reference for the gradation design of LPS-GCSM and optimization of the design indicators.

Benchmark problems in optimum structural design of 3D reinforced concrete frames

Benchmarking goes hand in hand with the development and establishment of efficient and robust optimization methodologies in various scientific fields. Nevertheless, benchmark problems, with known global optima, are currently missing in the optimum structural design of reinforced concrete (RC) frames. In the present study, for first time, benchmark case studies in the optimum design of RC frames are presented. The aim is that these benchmarks are used for the calibration, tuning, improvement and development of optimization algorithms to address the efficient design of concrete frames. More particularly, six three-dimensional concrete building frames are optimally designed to Eurocodes. First, exhaustive search is conducted to identify the global optimum solutions and Pareto fronts. Useful conclusions are also made with respect to the properties of the optimal solutions. Moreover, all candidate designs results are provided in an supplementary file so that they can be used in future optimization studies. Next, the performance of several well-known, single- and multi-objective optimization algorithms is assessed against the global optima to examine their efficiency and applicability in this class of optimization problems. Closing, the need for further and larger in scale benchmark case studies in the optimum design of concrete frames is emphasized.

A generalized Benders decomposition approach for the optimal design of a local multi-energy system

A local multi-energy system (LMES) is a decentralized energy system producing energy under multiple forms to satisfy the energy demand of a set of buildings located in its neighborhood. We study the problem of optimally designing an LMES over a multi-phase horizon. This problem is formulated as a large-size mixed-integer linear program with a block-decomposable structure involving mixed-integer sub-problems. We propose a new way to adapt a recently published framework for generalized Benders decomposition to our problem. This is done by exploiting the fact that the constraint matrix appearing in front of the first-stage variables in the coupling constraints is non-negative. The obtained generalized Benders decomposition algorithm relies on the use of a new type of non-convex Benders cuts involving indicator functions. We first prove that, under the assumption that all first-stage decision variables are integer and bounded, the finite and optimal convergence of our algorithm is guaranteed in theory. We then investigate how to obtain a good numerical performance in practice. Finally, we report the results of a computational study carried out on a real-life case study. These results show that the proposed algorithm clearly outperforms both a mathematical programming solver directly solving the problem as a whole and a state-of-the art hierarchical decomposition algorithm.

Optimal design of chevron braced friction damper for mainshock–aftershock vulnerability control

This study proposes the optimum design of chevron braced friction dampers (CBFDs) for the vulnerability control of steel moment–resisting frames (SMRFs) under mainshock-aftershock (MS-AS) sequences. First, the optimum parameters of the CBFD systems installed in the stories of an inelastic SMRF are found through minimizing the maximum damage index of stories averaged over seven scaled earthquake excitations. The uniform distribution of the story damage along the height of the controlled SMRF is adopted as constraint in the optimization procedure. The damage index is calculated based on the Park-Ang damage model which is expressed based on a linear combination of deformation, moment, and absorbed hysteretic energy of structural elements imposed by an earthquake excitation. Results reveal that the optimized CBFDs-equipped SMRF exhibits better distribution of the story damage than that of the uncontrolled SMRF. Finally, the vulnerability assessment of the optimized CBFDs-equipped SMRF under MS and MS-AS ground motions is investigated by the fragility curves. The fragility assessment emphasize that the optimized CBFDs effectively mitigate the seismic vulnerability of the controlled SMRF under MS-AS sequences at different damage states.

Parametric Optimization of System Modes for Nozzle Turbine Vane by Means of Costimulated Artificial Immune System

One requirement posed by customers is to achieve adequate durability levels as described in technical requirement documents. Modal analysis is one of the design assessments aimed at identifying the risks of high cycle fatigue (HCF). This article presents a novel application of an artificial immune system (AIS) in the optimization of a nozzle guide vane’s modal characteristics. The aim is to optimize the system’s natural frequencies in the vibration vane and adjacent hardware (turbine casing). The geometrical characteristics accounted for in the optimization process include the shell thicknesses on the turbine casing side and the nozzle outer band features (hook thickness, leaning and position). The optimization process is based on a representative model established from FEM analysis results. The framework is robust because of the applied metamodel and does not require time-consuming FEM analysis in order to evaluate the fitness function. The aim is to minimize the model area (a derivative of the system weight) with constraints imposed on the frequency (a penalty function). The optimum design is given as the solution with an increased shell thickness in the turbine casing and leaning nozzle outer band hooks to obtain the maximum stiffness of the system. The results obtained by means of the artificial immune system (AIS) and a novel variant based on an additional costimulation procedure (CAIS) are compared with the solution obtained by means of a genetic algorithm implemented in the commercial CAE software (Ansys version 19.2).

Design of experiment (DOE) and process optimisation of palladium catalysed biphenyl synthesis

ABSTRACT The effects of time, temperature and catalyst concentration were investigated for an optimised condition of biphenyl synthesis by Suzuki-Miyaura cross-coupling reactions by Neolyst catalysts. The optimisation process was analysed using Box Behnken Face-Centred Experimental Design in Response Surface Methodology (RSM). The design was employed to derive a statistical model for the effect of parameters studied on the yield of biphenyl. The coefficient of determination, r 2 was 0.9883% after model reduction. With an optimum time of 6.63 h, a temperature of 73°C and with minimum catalyst concentration of 0.013 mol% gives the optimum conditions for the maximum yield of biphenyl.