Search results for: Strongly convex function.

Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

Abstract:

In this paper, the problem of stability criteria for Markovian jumping BAM neural networks with leakage and discrete delays has been investigated. Some new sufficient condition are derived based on a novel Lyapunov-Krasovskii functional approach. These new criteria based on delay partitioning idea are proved to be less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, one numerical example is given to illustrate the the usefulness and feasibility of the proposed main results.

Keywords: Stability, Markovian jumping neural networks, Timevarying delays, Linear matrix inequality.

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Authors: Wajdi Bellil, Chokri Ben Amar, Adel M. Alimi

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An application of Beta wavelet networks to synthesize pass-high and pass-low wavelet filters is investigated in this work. A Beta wavelet network is constructed using a parametric function called Beta function in order to resolve some nonlinear approximation problem. We combine the filter design theory with wavelet network approximation to synthesize perfect filter reconstruction. The order filter is given by the number of neurons in the hidden layer of the neural network. In this paper we use only the first derivative of Beta function to illustrate the proposed design procedures and exhibit its performance.

Keywords: Beta wavelets, Wavenet, multiresolution analysis, perfect filter reconstruction, salient point detect, repeatability.

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Authors: C. Ardil

Abstract:

Using the aid of Hausdorff distance function and Minkowski distance function, this study proposes a novel method for selecting combat aircraft for Air Force. In order to do this, the proximity measure method was developed with determinate fuzzy degrees based on the relationship between attributes and combat aircraft alternatives. The combat aircraft selection attributes were identified as payloadability, maneuverability, speedability, stealthability, and survivability. Determinate fuzzy data from the combat aircraft attributes was then aggregated using the determinate fuzzy weighted arithmetic average operator. For the selection of combat aircraft, correlation analysis of the ranking order patterns of options was also examined. A numerical example from military aviation is used to demonstrate the applicability and effectiveness of the proposed method.

Keywords: Combat aircraft selection, multiple criteria decision making, fuzzy sets, determinate fuzzy sets, intuitionistic fuzzy sets, proximity measure method, Hausdorff distance function, Minkowski distance function, PMM, MCDM

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Authors: Veronica Sri Lestari, Djoni Prawira Rahardja, Tanrigiling Rasyid, Aslina Asnawi, Ikrar Muhammad Saleh, Ilham Rasyid

Abstract:

Urea Mineral Molasses Block is very important for beef cattle, because it can increase beef production. The purpose of this research was to know beef cattle farmers’ perception towards Urea Mineral Molasses Block (UMMB). This research was conducted in Gowa Regency, South Sulawesi, Indonesia in 2016. The population of this research were all beef cattle farmers. Sample was chosen through purposive sampling. Data were collected through observation and face to face with deep interview using questionnaire. Variables of perception consisted of relative advantage, compatibility, complexity, observability and triability. There were 10 questions. The answer for each question was scored by 1, 2, 3 which refer to disagree, agree enough, strongly agree. The data were analyzed descriptively using frequency distribution. The research revealed that beef cattle farmers’ perception towards UMMB was categorized as strongly agree.

Keywords: Beef cattle, farmers, perception, urea mineral molasses block.

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Authors: Mário A. R. Talaia

Abstract:

As it is known, buoyancy and drag forces rule bubble's rise velocity in a liquid column. These forces are strongly dependent on fluid properties, gravity as well as equivalent's diameter. This study reports a set of bubble rising velocity experiments in a liquid column using water or glycerol. Several records of terminal velocity were obtained. The results show that bubble's rise terminal velocity is strongly dependent on dynamic viscosity effect. The data set allowed to have some terminal velocities data interval of 8.0 ? 32.9 cm/s with Reynolds number interval 1.3 -7490. The bubble's movement was recorded with a video camera. The main goal is to present an original set data and results that will be discussed based on two-phase flow's theory. It will also discussed, the prediction of terminal velocity of a single bubble in liquid, as well as the range of its applicability. In conclusion, this study presents general expressions for the determination of the terminal velocity of isolated gas bubbles of a Reynolds number range, when the fluid proprieties are known.

Keywords: Bubbles, terminal velocity, two phase-flow, vertical column.

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Authors: Adil AL-Rammahi

Abstract:

When we prefer to make the data secure from various attacks and fore integrity of data, we must encrypt the data before it is transmitted or stored. This paper introduces a new effective and lossless image encryption algorithm using a natural logarithmic function. The new algorithm encrypts an image through a three stage process. In the first stage, a reference natural logarithmic function is generated as the foundation for the encryption image. The image numeral matrix is then analyzed to five integer numbers, and then the numbers’ positions are transformed to matrices. The advantages of this method is useful for efficiently encrypting a variety of digital images, such as binary images, gray images, and RGB images without any quality loss. The principles of the presented scheme could be applied to provide complexity and then security for a variety of data systems such as image and others.

Keywords: Linear Systems, Image Encryption, Calculus.

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Authors: S. R. Nikhashemi, L. Haj Paim, Ali Khatibi

Abstract:

Structural Equation Modeling (SEM) was used to test a hypothesized model explaining Malaysian hypermarket customers’ perceptions of brand trust (BT), customer perceived value (CPV) and perceived service quality (PSQ) on building their brand loyalty (CBL) and generating positive word-of-mouth communication (WOM). Self-administered questionnaires were used to collect data from 374 Malaysian hypermarket customers from Mydin, Tesco, Aeon Big and Giant in Kuala Lumpur, a metropolitan city of Malaysia. The data strongly supported the model exhibiting that BT, CPV and PSQ are prerequisite factors in building customer brand loyalty, while PSQ has the strongest effect on prediction of customer brand loyalty compared to other factors. Besides, the present study suggests the effect of the aforementioned factors via customer brand loyalty strongly contributes to generate positive word of mouth communication.

Keywords: Brand trust, perceived value, perceived service quality, brand loyalty, positive word of mouth communication.

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Authors: Arturo Aquino, Manuel Emilio Gegundez, Jose Manuel Bravo, Diego Marin

Abstract:

Retinal vascularity assessment plays an important role in diagnosis of ophthalmic pathologies. The employment of digital images for this purpose makes possible a computerized approach and has motivated development of many methods for automated vascular tree segmentation. Metrics based on contingency tables for binary classification have been widely used for evaluating performance of these algorithms and, concretely, the accuracy has been mostly used as measure of global performance in this topic. However, this metric shows very poor matching with human perception as well as other notable deficiencies. Here, a new similarity function for measuring quality of retinal vessel segmentations is proposed. This similarity function is based on characterizing the vascular tree as a connected structure with a measurable area and length. Tests made indicate that this new approach shows better behaviour than the current one does. Generalizing, this concept of measuring descriptive properties may be used for designing functions for measuring more successfully segmentation quality of other complex structures.

Keywords: Retinal vessel segmentation, quality assessment, performanceevaluation, similarity function.

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Authors: Lianglin Xiong, Shouming Zhong, Mao Ye

Abstract:

This paper addresses the stabilization issues for a class of uncertain switched neutral systems with nonlinear perturbations. Based on new classes of piecewise Lyapunov functionals, the stability assumption on all the main operators or the convex combination of coefficient matrices is avoid, and a new switching rule is introduced to stabilize the neutral systems. The switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. Finally, three simulation examples are given to demonstrate the significant improvements over the existing results.

Keywords: Switched neutral system, piecewise Lyapunov functional, nonlinear perturbation, Lyapunov-Metzler linear matrix inequality.

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Authors: Jeffrey L. Duffany

Abstract:

The equivalence class subset algorithm is a powerful tool for solving a wide variety of constraint satisfaction problems and is based on the use of a decision function which has a very high but not perfect accuracy. Perfect accuracy is not required in the decision function as even a suboptimal solution contains valuable information that can be used to help find an optimal solution. In the hardest problems, the decision function can break down leading to a suboptimal solution where there are more equivalence classes than are necessary and which can be viewed as a mixture of good decision and bad decisions. By choosing a subset of the decisions made in reaching a suboptimal solution an iterative technique can lead to an optimal solution, using series of steadily improved suboptimal solutions. The goal is to reach an optimal solution as quickly as possible. Various techniques for choosing the decision subset are evaluated.

Keywords: np-complete, complexity, algorithm.

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Authors: Sukhwinder Singh Billing, Sushma Gupta, Sukhjit Singh Dhaliwal

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In the present paper, we obtain a sandwich-type theorem. As applications of our main result, we discuss the univalence and starlikeness of analytic functions in terms of certain differential subordinations and differential inequalities.

Keywords: Univalent function, Starlike function, Differential subordination, Differential superordination.

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Authors: R. Uporn, P. Luangpaiboon

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This paper presents a comparative study of statistical methods for the multi-response surface optimization of a cryogenic freezing process. Taguchi design and analysis and steepest ascent methods based on the desirability function were conducted to ascertain the influential factors of a cryogenic freezing process and their optimal levels. The more preferable levels of the set point, exhaust fan speed, retention time and flow direction are set at -90oC, 20 Hz, 18 minutes and Counter Current, respectively. The overall desirability level is 0.7044.

Keywords: Cryogenic Freezing Process, Taguchi Design and Analysis, Response Surface Method, Steepest Ascent Method and Desirability Function Approach.

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Authors: P. Sanzo

Abstract:

Ten percent of the population will develop plantar fasciitis (PF) during their lifetime. Two million people are treated yearly accounting for 11-15% of visits to medical professionals. Treatment ranges from conservative to surgical intervention. The purpose of this study was to assess the effects of extracorporeal shockwave therapy (ECSWT) on heel pain, function, range of motion (ROM), and strength in patients with PF. One hundred subjects were treated with ECSWT and measures were taken before and three months after treatment. There was significant differences in visual analog scale scores for pain at rest (p=0.0001); after activity (p= 0.0001) and; overall improvement (p=0.0001). There was also significant improvement in Lower Extremity Functional Scale scores (p=0.0001); ankle plantarflexion (p=0.0001), dorsiflexion (p=0.001), and eversion (p=0.017),and first metatarsophalangeal joint flexion (p=0.002) and extension (p=0.003) ROM. ECSWT is an effective treatment improving heel pain, function and ROM in patients with PF.

Keywords: Extracorporeal shockwave therapy, shockwave therapy, plantar fasciitis, heel pain, function, range of motion, strength.

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Authors: John R. Rose, James P. Cleveland, Alvin Fox

Abstract:

Tandem mass spectrometry (MS/MS) is the engine driving high-throughput protein identification. Protein mixtures possibly representing thousands of proteins from multiple species are treated with proteolytic enzymes, cutting the proteins into smaller peptides that are then analyzed generating MS/MS spectra. The task of determining the identity of the peptide from its spectrum is currently the weak point in the process. Current approaches to de novo sequencing are able to compute candidate peptides efficiently. The problem lies in the limitations of current scoring functions. In this paper we introduce the concept of proteome signature. By examining proteins and compiling proteome signatures (amino acid usage) it is possible to characterize likely combinations of amino acids and better distinguish between candidate peptides. Our results strongly support the hypothesis that a scoring function that considers amino acid usage patterns is better able to distinguish between candidate peptides. This in turn leads to higher accuracy in peptide prediction.

Keywords: Tandem mass spectrometry, proteomics, scoring, peptide, de novo, mutual information

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Authors: Sanjay Kanade, Danielle Camara, Dijana Petrovska-Delacretaz, Bernadette Dorizzi

Abstract:

In this paper, a two factor scheme is proposed to generate cryptographic keys directly from biometric data, which unlike passwords, are strongly bound to the user. Hash value of the reference iris code is used as a cryptographic key and its length depends only on the hash function, being independent of any other parameter. The entropy of such keys is 94 bits, which is much higher than any other comparable system. The most important and distinct feature of this scheme is that it regenerates the reference iris code by providing a genuine iris sample and the correct user password. Since iris codes obtained from two images of the same eye are not exactly the same, error correcting codes (Hadamard code and Reed-Solomon code) are used to deal with the variability. The scheme proposed here can be used to provide keys for a cryptographic system and/or for user authentication. The performance of this system is evaluated on two publicly available databases for iris biometrics namely CBS and ICE databases. The operating point of the system (values of False Acceptance Rate (FAR) and False Rejection Rate (FRR)) can be set by properly selecting the error correction capacity (ts) of the Reed- Solomon codes, e.g., on the ICE database, at ts = 15, FAR is 0.096% and FRR is 0.76%.

Keywords:

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Authors: Muhammad Rizwan Azhar, Emadadeen Ali

Abstract:

In this paper, periodic force operation of a wastewater treatment process has been studied for the improved process performance. A previously developed dynamic model for the process is used to conduct the performance analysis. The static version of the model was utilized first to determine the optimal productivity conditions for the process. Then, feed flow rate in terms of dilution rate i.e. (D) is transformed into sinusoidal function. Nonlinear model predictive control algorithm is utilized to regulate the amplitude and period of the sinusoidal function. The parameters of the feed cyclic functions are determined which resulted in improved productivity than the optimal productivity under steady state conditions. The improvement in productivity is found to be marginal and is satisfactory in substrate conversion compared to that of the optimal condition and to the steady state condition, which corresponds to the average value of the periodic function. Successful results were also obtained in the presence of modeling errors and external disturbances.

Keywords: Dilution rate, nonlinear model predictive control, sinusoidal function, wastewater treatment.

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Authors: Kenichiro Hida, Shin-Ichi Kuribayashi

Abstract:

In a conventional network, most network devices, such as routers, are dedicated devices that do not have much variation in capacity. In recent years, a new concept of network functions virtualisation (NFV) has come into use. The intention is to implement a variety of network functions with software on general-purpose servers and this allows the network operator to select their capacities and locations without any constraints. This paper focuses on the allocation of NFV-based routing functions which are one of critical network functions, and presents the virtual routing function allocation algorithm that minimizes the total power consumption. In addition, this study presents the useful allocation policy of virtual routing functions, based on an evaluation with a ladder-shaped network model. This policy takes the ratio of the power consumption of a routing function to that of a circuit and traffic distribution between areas into consideration. Furthermore, the present paper shows that there are cases where the use of NFV-based routing functions makes it possible to reduce the total power consumption dramatically, in comparison to a conventional network, in which it is not economically viable to distribute small-capacity routing functions.

Keywords: Virtual routing function, NFV, resource allocation, minimum power consumption.

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Authors: V.K. Mukhomorov

Abstract:

The solvated electron is self-trapped (polaron) owing to strong interaction with the quantum polarization field. If the electron and quantum field are strongly coupled then the collective localized state of the field and quasi-particle is formed. In such a formation the electron motion is rather intricate. On the one hand the electron oscillated within a rather deep polarization potential well and undergoes the optical transitions, and on the other, it moves together with the center of inertia of the system and participates in the thermal random walk. The problem is to separate these motions correctly, rigorously taking into account the conservation laws. This can be conveniently done using Bogolyubov-Tyablikov method of canonical transformation to the collective coordinates. This transformation removes the translational degeneracy and allows one to develop the successive approximation algorithm for the energy and wave function while simultaneously fulfilling the law of conservation of total momentum of the system. The resulting equations determine the electron transitions and depend explicitly on the translational velocity of the quasi-particle as whole. The frequency of optical transition is calculated for the solvated electron in ammonia, and an estimate is made for the thermal-induced spectral bandwidth.

Keywords: Canonical transformations, solvated electron, width of the optical spectrum.

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Authors: E. Praynlin, P. Latha

Abstract:

Software Effort Estimation is the process of estimating the effort required to develop software. By estimating the effort, the cost and schedule required to estimate the software can be determined. Accurate Estimate helps the developer to allocate the resource accordingly in order to avoid cost overrun and schedule overrun. Several methods are available in order to estimate the effort among which soft computing based method plays a prominent role. Software cost estimation deals with lot of uncertainty among all soft computing methods neural network is good in handling uncertainty. In this paper Radial Basis Function Network is compared with the back propagation network and the results are validated using six data sets and it is found that RBFN is best suitable to estimate the effort. The Results are validated using two tests the error test and the statistical test.

Keywords: Software cost estimation, Radial Basis Function Network (RBFN), Back propagation function network, Mean Magnitude of Relative Error (MMRE).

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Authors: V. K. Ananthashayana, Jyothirmayi M.

Abstract:

This paper addresses the problem of source separation in images. We propose a FastICA algorithm employing a modified Gaussian contrast function for the Blind Source Separation. Experimental result shows that the proposed Modified Gaussian FastICA is effectively used for Blind Source Separation to obtain better quality images. In this paper, a comparative study has been made with other popular existing algorithms. The peak signal to noise ratio (PSNR) and improved signal to noise ratio (ISNR) are used as metrics for evaluating the quality of images. The ICA metric Amari error is also used to measure the quality of separation.

Keywords: Amari error, Blind Source Separation, Contrast function, Gaussian function, Independent Component Analysis.

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Authors: Simon B. Cooper, Stephan Bandelow, Maria L. Nute, John G. Morris, Mary E. Nevill

Abstract:

Previous research has indicated a variable effect of exercise on adolescents’ cognitive function. However, comparisons between studies are difficult to make due to differences in: the mode, intensity and duration of exercise employed; the components of cognitive function measured (and the tests used to assess them); and the timing of the cognitive function tests in relation to the exercise. Therefore, the aim of the present study was to assess the time course (10 and 60min post-exercise) of the effects of 15min intermittent exercise on cognitive function in adolescents. 45 adolescents were recruited to participate in the study and completed two main trials (exercise and resting) in a counterbalanced crossover design. Participants completed 15min of intermittent exercise (in cycles of 1 min exercise, 30s rest). A battery of computer based cognitive function tests (Stroop test, Sternberg paradigm and visual search test) were completed 30 min pre- and 10 and 60min post-exercise (to assess attention, working memory and perception respectively).The findings of the present study indicate that on the baseline level of the Stroop test, 10min following exercise response times were slower than at any other time point on either trial (trial by session time interaction, p = 0.0308). However, this slowing of responses also tended to produce enhanced accuracy 10min post-exercise on the baseline level of the Stroop test (trial by session time interaction, p = 0.0780). Similarly, on the complex level of the visual search test there was a slowing of response times 10 min post-exercise (trial by session time interaction, p = 0.0199). However, this was not coupled with an improvement in accuracy (trial by session time interaction, p = 0.2349). The mid-morning bout of exercise did not affect response times or accuracy across the morning on the Sternberg paradigm. In conclusion, the findings of the present study suggest an equivocal effect of exercise on adolescents' cognitive function. The mid-morning bout of exercise appears to cause a speed-accuracy trade off immediately following exercise on the Stroop test (participants become slower but more accurate), whilst slowing response times on the visual search test and having no effect on performance on the Sternberg paradigm. Furthermore, this work highlights the importance of the timing of the cognitive function tests relative to the exercise and the components of cognitive function examined in future studies. 

Keywords: Adolescents, cognitive function, exercise.

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Authors: Safeer Hussain Khan

Abstract:

In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.

Keywords: One-step iteration scheme, asymptotically quasi non expansive mapping, common fixed point, condition (a'), weak and strong convergence.

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Authors: Roman V. Yampolskiy, Venu Govindaraju

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Functioning of a biometric system in large part depends on the performance of the similarity measure function. Frequently a generalized similarity distance measure function such as Euclidian distance or Mahalanobis distance is applied to the task of matching biometric feature vectors. However, often accuracy of a biometric system can be greatly improved by designing a customized matching algorithm optimized for a particular biometric application. In this paper we propose a tailored similarity measure function for behavioral biometric systems based on the expert knowledge of the feature level data in the domain. We compare performance of a proposed matching algorithm to that of other well known similarity distance functions and demonstrate its superiority with respect to the chosen domain.

Keywords: Behavioral Biometrics, Euclidian Distance, Matching, Similarity Measure.

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Authors: V. Swarnalatha, A. V. Narasimha Rao, P. Pal

Abstract:

The present research reports the investigation of fast etching of silicon for the fabrication of microelectromechanical systems (MEMS) structures using silicon wet bulk micromachining. Low concentration tetramethyl-ammonium hydroxide (TMAH) and hydroxylamine (NH₂OH) are used as main etchant and additive, respectively. The concentration of NH₂OH is varied to optimize the composition to achieve best etching characteristics such as high etch rate, significantly high undercutting at convex corner for the fast release of the microstructures from the substrate, and improved etched surface morphology. These etching characteristics are studied on Si{100} and Si{110} wafers as they are most widely used in the fabrication of MEMS structures as wells diode, transistors and integrated circuits.

Keywords: KOH, MEMS, micromachining, silicon, TMAH, wet anisotropic etching.

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Authors: Artion Kashuri, Rozana Liko

Abstract:

In this paper, some generalization integral inequalities of Hermite–Hadamard type for functions whose derivatives are s–convex in modulus are given by using k–fractional integrals. Some applications to special means are obtained as well. Some known versions are recovered as special cases from our results. We note that our inequalities can be viewed as new refinements of the previous results. Finally, our results have a deep connection with various fractional integral operators and interested readers can find new interesting results using our idea and technique as well.

Keywords: Hermite–Hadamard’s inequalities, k–Riemann–Liouville fractional integral, H¨older’s inequality, Special means.

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Authors: Thandar Aung, Tun Lin Naing

Abstract:

In this paper, the DC-link voltage control of DC-DC boost converter–inverter system is proposed. The mathematical model is developed from four different sub-circuits that depended on the switch positions. The developed differential equations are combined to develop the dynamic model. Transfer function is generated from the switched function model. Fluctuation of DC-link voltage causes connected loads malfunction. For this problem, a kind of traditional controller, the PI controller is applied to achieve constant DC-link voltage. The PI controller gains are obtained based on transfer function step response. The simulation work has been studied by using MATLAB/Simulink software and hardware prototype is implemented with a low-cost microcontroller Arduino Nano. Experimental results are collected by using ArduinoIO library package. Closed-loop DC-link voltage control system is tested with various line and load disturbances. It is found that the experimental results give equal responses with the simulation results.

Keywords: ArduinoIO library package, boost converter-inverter system, low cost microcontroller, PI controller, switched function model.

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Authors: Xiuyong Ding, Lan Shu

Abstract:

This paper addresses the stability of the switched systems with discrete and distributed time delays. By applying Lyapunov functional and function method, we show that, if the norm of system matrices Bi is small enough, the asymptotic stability is always achieved. Finally, a example is provided to verify technically feasibility and operability of the developed results.

Keywords: Switched system, stability, Lyapunov function, Lyapunov functional, delays.

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Authors: Leila Nasiri

Abstract:

In this paper, we present the concept of preinvex functions on the co-ordinates on an invex set and establish some triple integral inequalities of Hermite-Hadamard type for functions whose third order partial derivatives in absolute value are preinvex on the co-ordinates. The results presented here generalize the obtained results in earlier works for functions whose triple order partial derivatives in absolute value are convex on the co-ordinates on a rectangular box in R³.

Keywords: Co-ordinated preinvex functions, Hermite-Hadamard type inequalities, partial derivatives, triple integral.

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Authors: Chia-Ling Chang, Chung-Sheng Liao

Abstract:

The present study focuses on the discussion over the parameter of Artificial Neural Network (ANN). Sensitivity analysis is applied to assess the effect of the parameters of ANN on the prediction of turbidity of raw water in the water treatment plant. The result shows that transfer function of hidden layer is a critical parameter of ANN. When the transfer function changes, the reliability of prediction of water turbidity is greatly different. Moreover, the estimated water turbidity is less sensitive to training times and learning velocity than the number of neurons in the hidden layer. Therefore, it is important to select an appropriate transfer function and suitable number of neurons in the hidden layer in the process of parameter training and validation.

Keywords: Artificial Neural Network (ANN), sensitivity analysis, turbidity.

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Authors: Salah R. Al Zaidee, Ali S. Mahdi

Abstract:

Except for simple problems of statically determinate structures, optimum design problems in structural engineering have implicit objective functions where structural analysis and design are essential within each searching loop. With these implicit functions, the structural engineer is usually enforced to write his/her own computer code for analysis, design, and searching for optimum design among many feasible candidates and cannot take advantage of available software for structural analysis, design, and searching for the optimum solution. The meta-model is a regression model used to transform an implicit objective function into objective one and leads in turn to decouple the structural analysis and design processes from the optimum searching process. With the meta-model, well-known software for structural analysis and design can be used in sequence with optimum searching software. In this paper, the meta-model has been used to develop an explicit objective function for plane steel frames subjected to dead, live, and seismic forces. Frame topology is assumed as predefined based on architectural and functional requirements. Columns and beams sections and different connections details are the main design variables in this study. Columns and beams are grouped to reduce the number of design variables and to make the problem similar to that adopted in engineering practice. Data for the implicit objective function have been generated based on analysis and assessment for many design proposals with CSI SAP software. These data have been used later in SPSS software to develop a pure quadratic nonlinear regression model for the explicit objective function. Good correlations with a coefficient, R², in the range from 0.88 to 0.99 have been noted between the original implicit functions and the corresponding explicit functions generated with meta-model.

Keywords: Meta-modal, objective function, steel frames, seismic analysis, design.

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