A new multi-gene genetic programming approach to nonlinear system modeling. Part I: materials and structural engineering problems

This paper presents a new approach for behavioral modeling of structural engineering systems using a promising variant of genetic programming (GP), namely multi-gene genetic programming (MGGP). MGGP effectively combines the model structure selection ability of the standard GP with the parameter estimation power of classical regression to capture the nonlinear interactions. The capabilities of MGGP are illustrated by applying it to the formulation of various complex structural engineering problems. The problems analyzed herein include estimation of: (1) compressive strength of high-performance concrete (2) ultimate pure bending of steel circular tubes, (3) surface roughness in end-milling, and (4) failure modes of beams subjected to patch loads. The derived straightforward equations are linear combinations of nonlinear transformations of the predictor variables. The validity of MGGP is confirmed by applying the derived models to the parts of the experimental results that are not included in the analyses. The MGGP-based equations can reliably be employed for pre-design purposes. The results of MSGP are found to be more accurate than those of solutions presented in the literature. MGGP does not require simplifying assumptions in developing the models.     

Revised multi-segment goal programming: Percentage goal programming

The multi-segment goal programming (MSGP) model is an extension model of GP wherein the core thinking is inherited from the multi-choice goal programming (MCGP) model. In this paper, we recommend certain points of the MSGP model and offer a Revised MSGP Model as an aid to burdened decision makers who cannot expect an either-or selection of coefficients in practice. The proposed model takes into account a scenario in which the selection of all possible coefficients pertaining to each decision variable in the MSGP model can be an in-between selection instead of an exclusive-or selection. We hope this study can fill in a possible gap that might exist when applying the MSGP model, and can offer an extension model for practitioners when they use this model to solve related decision problems.     

Revised multi-segment goal programming: Percentage goal programming

The multi-segment goal programming (MSGP) model is an extension model of GP wherein the core thinking is inherited from the multi-choice goal programming (MCGP) model. In this paper, we recommend certain points of the MSGP model and offer a Revised MSGP Model as an aid to burdened decision makers who cannot expect an either-or selection of coefficients in practice. The proposed model takes into account a scenario in which the selection of all possible coefficients pertaining to each decision variable in the MSGP model can be an in-between selection instead of an exclusive-or selection. We hope this study can fill in a possible gap that might exist when applying the MSGP model, and can offer an extension model for practitioners when they use this model to solve related decision problems.     

Efficient training of RBF neural networks for pattern recognition.

The problem of training a radial basis function (RBF) neural network for distinguishing two disjoint sets in R(n) is considered. The network parameters can be determined by minimizing an error function that measures the degree of success in the recognition of a given number of training patterns. In this paper, taking into account the specific feature of classification problems, where the goal is to obtain that the network outputs take values above or below a fixed threshold, we propose an approach alternative to the classical one that makes use of the least-squares error function. In particular, the problem is formulated in terms of a system of nonlinear inequalities, and a suitable error function, which depends only on the violated inequalities, is defined. Then, a training algorithm based on this formulation is presented. Finally, the results obtained by applying the algorithm to two test problems are compared with those derived by adopting the commonly used least-squares error function. The results show the effectiveness of the proposed approach in RBF network training for pattern recognition, mainly in terms of computational time saving.     

A new stability test for nonlinear nonautonomous systems

We consider a class of nonlinear nonautonomous systems, whose linear parts are slowly varying matrices. Stability conditions and estimates for the region of attraction of the zero solution are derived. These conditions are formulated in terms of the determinants of the variable matrices.     

Optimal Design of Object-Oriented Databases in Automatic Information-Control Systems. II. Models and Methods of Design of Optimal Logical Structures for Object-Oriented Databases

Part II is devoted to the formulation of the problem and models and methods of design of optimal logical structures for object-oriented databases used in designing automatic information control systems. The effectiveness criteria used for the problem design are defined by the minimal total time of utilization of databases and service of a given set of user inquires and transactions, minimal total time of implementation of a set of inquires and transactions over the database. Design problems are formulated as nonlinear integer programming problems and effective exact and heuristic algorithms are developed to solve them.     

Fuzzy analytical hierarchy process and multi-segment goal programming applied to new product segmented under price strategy

New product development (NPD) is becoming an important competitive advantage in the marketing strategies of current businesses. Developing a new product will incur fixed and variable costs, which then determine the product prices. Although this is a fundamental issue of marketing theory and practice, only a few papers on marketing models deal with price levels. The objective of this paper is proposing a model based on fuzzy analytical hierarchy process (AHP) and multi-segment goal programming (MSGP) to help decision makers to select the best pricing strategy for NPD. A case study of NPD under market selection strategy in multiple segment pricing levels for a Taiwan-based Watch Company is presented to illustrate the proposed methodology. The proposed method will guide the product development team to select the best market strategy by taking into account the price level and product/market segmentation.     

H∞ Static Output Feedback Control of 2‐D Discrete Systems in FM Second Model

The problem of H_∞ static output feedback (SOF) control of two‐dimensional (2‐D) discrete systems described by the Fornasini‐Marchesini (FM) second model is investigated in this paper. First, by applying the 2‐D Bounded Real Lemma, the 2‐D H_∞ SOF control problem is formulated in terms of a bilinear matrix inequality (BMI). Then, by combining the slack variable technique with two kinds of existing LMI methods, respectively, less conservative sufficient LMI conditions are proposed for the BMI formulation. The relation of these two kinds of LMI conditions are revealed by analyzing the choices of coordinate transformation matrices involved in the first kind of LMI conditions. Finally, a numerical example is provided to demonstrate the effectiveness and merits of the proposed methods.     

Nonlinear inverse optimization approach for determining the weights of objective function in standing reach tasks

This paper presents a nonlinear inverse optimization approach to determine the weights for the joint displacement function in standing reach tasks. This inverse optimization problem can be formulated as a bi-level highly nonlinear optimization problem. The design variables are the weights of a cost function. The cost function is the weighted summation of the differences between two sets of joint angles (predicted posture and the actual standing reach posture). Constraints include the normalized weights within limits and an inner optimization problem to solve for joint angles (predicted standing reach posture). The weight linear equality constraints, obtained through observations, are also implemented in the formulation to test the method. A 52 degree-of-freedom (DOF) human whole body model is used to study the formulation and visualize the prediction. An in-house motion capture system is used to obtain the actual standing reach posture. A total of 12 subjects (three subjects for each percentile in stature of 5th percentile female, 50th percentile female, 50th percentile male and 95th percentile male) are selected to run the experiment for 30 tasks. Among these subjects one is Turkish, two are Chinese, and the rest subjects are Americans. Three sets of weights for the general standing reach tasks are obtained for the three zones by averaging all weights in each zone for all subjects and all tasks. Based on the obtained sets of weights, the predicted standing reach postures found using the direct optimization-based approach have good correlation with the experimental results. Sensitivity of the formulation has also been investigated in this study. The presented formulation can be used to determine the weights of cost function within any multi-objective optimization (MOO) problems such as any types of posture prediction and motion prediction.     

Nonlinear inverse optimization approach for determining the weights of objective function in standing reach tasks

This paper presents a nonlinear inverse optimization approach to determine the weights for the joint displacement function in standing reach tasks. This inverse optimization problem can be formulated as a bi-level highly nonlinear optimization problem. The design variables are the weights of a cost function. The cost function is the weighted summation of the differences between two sets of joint angles (predicted posture and the actual standing reach posture). Constraints include the normalized weights within limits and an inner optimization problem to solve for joint angles (predicted standing reach posture). The weight linear equality constraints, obtained through observations, are also implemented in the formulation to test the method. A 52 degree-of-freedom (DOF) human whole body model is used to study the formulation and visualize the prediction. An in-house motion capture system is used to obtain the actual standing reach posture. A total of 12 subjects (three subjects for each percentile in stature of 5th percentile female, 50th percentile female, 50th percentile male and 95th percentile male) are selected to run the experiment for 30 tasks. Among these subjects one is Turkish, two are Chinese, and the rest subjects are Americans. Three sets of weights for the general standing reach tasks are obtained for the three zones by averaging all weights in each zone for all subjects and all tasks. Based on the obtained sets of weights, the predicted standing reach postures found using the direct optimization-based approach have good correlation with the experimental results. Sensitivity of the formulation has also been investigated in this study. The presented formulation can be used to determine the weights of cost function within any multi-objective optimization (MOO) problems such as any types of posture prediction and motion prediction.     

A second-order cone programming formulation for nonparallel hyperplane support vector machine

Expert systems often rely heavily on the performance of binary classification methods. The need for accurate predictions in artificial intelligence has led to a plethora of novel approaches that aim at correctly predicting new instances based on nonlinear classifiers. In this context, Support Vector Machine (SVM) formulations via two nonparallel hyperplanes have received increasing attention due to their superior performance. In this work, we propose a novel formulation for the method, Nonparallel Hyperplane SVM. Its main contribution is the use of robust optimization techniques in order to construct nonlinear models with superior performance and appealing geometrical properties. Experiments on benchmark datasets demonstrate the virtues in terms of predictive performance compared with various other SVM formulations. Managerial insights and the relevance for intelligent systems are discussed based on the experimental outcomes.     

A novel criterion for nonlinear time-delay systems using LMI fuzzy Lyapunov method

This study presents a kind of fuzzy robustness design for nonlinear time-delay systems based on the fuzzy Lyapunov method, which is defined in terms of fuzzy blending quadratic Lyapunov functions. The basic idea of the proposed approach is to construct a fuzzy controller for nonlinear dynamic systems with disturbances in which the delay-independent robust stability criterion is derived in terms of the fuzzy Lyapunov method. Based on the robustness design and parallel distributed compensation (PDC) scheme, the problems of modeling errors between nonlinear dynamic systems and Takagi–Sugeno (T–S) fuzzy models are solved. Furthermore, the presented delay-independent condition is transformed into linear matrix inequalities (LMIs) so that the fuzzy state feedback gain and common solutions are numerically feasible with swarm intelligence algorithms. The proposed method is illustrated on a nonlinear inverted pendulum system and the simulation results show that the robustness controller cannot only stabilize the nonlinear inverted pendulum system, but has the robustness against external disturbance.     

Identification of Objects by the Maximal Information Criterion

The design of predictive input-output models for linear and nonlinear systems with random signals is studied. Definitions are formulated and conditions for identifiability by information criteria are derived. A consistent method of identification of systems by the maximal information criterion is designed. The values of parameters of an object are used for identifying and designing unbiased models.     

An ILMI Approach to RFDF for Uncertain Linear Systems with Nonlinear Perturbations

The robust fault detection filter design for uncertain linear systems with nonlinear perturbations is formulated as a two-objective optimization problem. Solvable conditions for the existence of such a robust fault detection filter are given in terms of matrix inequalities (MIs), which can be solved by applying iterative linear matrix inequality (ILMI) techniques. Particularly, compared with two existing LMI methods, the developed algorithm is more generalized and less conservative. An illustrative example is given to show the effectiveness of the proposed method.     

非线性摄动系统的鲁棒故障诊断滤波器设计ILMI算法

The robust fault detection filter design for uncertain linear systems with nonlinear perturbations is formulated as a two-objective optimization problem. Solvable conditions for the exis- tence of such a robust fault detection filter are given in terms of matrix inequalities (MIs), which can be solved by applying iterative linear matrix inequality (ILMI) techniques. Particularly, compared with two existing LMI methods, the developed algorithm is more generalized and less conservative. An illustrative example is given to show the effectiveness of the proposed method.     

Parity Relation Based Fault Estimation for Nonlinear Systems： An LMI Approach

This paper proposes a parity relation based fault estimation for a class of nonlinear systems which can be modelled by Takagi-Sugeno （TS） fuzzy models. The design of a parity relation based residual generator is formulated in terms of a family of linear matrix inequalities （LMIs）. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.     

Nonlinear bending of beams using the finite element method

In this paper a finite element formulation for determining the finite deflection of thin bars is presented. The nonlinear stiffness equations are generated after simple approximate expressions involving the nodal parameters are used to replace the nonlinear terms in the energy functional. The procedure used results in a simplified set of nonlinear algebraic equations which are more amenable to solution than the equations usually presented. The applicability and accuracy of the method together with an evaluation of three incremental solution techniques, a step by step method, a one step Newton-Raphson procedure, and a variable interpolation technique is demonstrated by solving a cantilever beam with a point load acting on the end. Curves showing the sensitivity to increment size and to the number of elements are also presented. The results indicate that the formulation is accurate and inexpensive in terms of computational effort.     

Stochastic Control of Linear and Nonlinear Econometric Models: Some Computational Aspects

This paper considers the optimal control of small econometric models applying the OPTCON algorithm. OPTCON determines approximate numerical solutions to optimum control problems for nonlinear stochastic systems. These optimum control problems consist in minimizing a quadratic objective function for linear and nonlinear econometric models with additive and multiplicative (parameter) uncertainties. The algorithm was programmed in C# and in MATLAB and allows for stochastic control with open-loop and passive learning (open-loop feedback) information patterns. Here we compare the results of applying the OPTCON2 version of the algorithm to two macroeconomic models for Slovenia, the nonlinear model SLOVNL and the linear model SLOVL. The results for both models are similar, with open-loop feedback controls giving better results on average and less outliers than open-loop controls. The number of outliers is higher in the nonlinear case and especially under high parameter uncertainty.     

Control of a nonlinear liquid level system using a new artificial neural network based reinforcement learning approach

Most industrial processes exhibit inherent nonlinear characteristics. Hence, classical control strategies which use linearized models are not effective in achieving optimal control. In this paper an Artificial Neural Network (ANN) based reinforcement learning (RL) strategy is proposed for controlling a nonlinear interacting liquid level system. This ANN-RL control strategy takes advantage of the generalization, noise immunity and function approximation capabilities of the ANN and optimal decision making capabilities of the RL approach. Two different ANN-RL approaches for solving a generic nonlinear control problem are proposed and their performances are evaluated by applying them to two benchmark nonlinear liquid level control problems. Comparison of the ANN-RL approach is also made to a discretized state space based pure RL control strategy. Performance comparison on the benchmark nonlinear liquid level control problems indicate that the ANN-RL approach results in better control as evidenced by less oscillations, disturbance rejection and overshoot.