Search results for: statistical inverse analysis

Authors: Y. T. Tsai, Jin H. Huang

Abstract:

The sound pressure level (SPL) of the moving-coil loudspeaker (MCL) is often simulated and analyzed using the lumped parameter model. However, the SPL of a MCL cannot be simulated precisely in the high frequency region, because the value of cone effective area is changed due to the geometry variation in different mode shapes, it is also related to affect the acoustic radiation mass and resistance. Herein, the paper presents the inverse method which has a high ability to measure the value of cone effective area in various frequency points, also can estimate the MCL electroacoustic parameters simultaneously. The proposed inverse method comprises the direct problem, adjoint problem, and sensitivity problem in collaboration with nonlinear conjugate gradient method. Estimated values from the inverse method are validated experimentally which compared with the measured SPL curve result. Results presented in this paper not only improve the accuracy of lumped parameter model but also provide the valuable information on loudspeaker cone design.

Keywords: inverse problem, cone effective area, loudspeaker, nonlinear conjugate gradient method

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Authors: Phuoc Si Nguyen

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Infinite impulse response (IIR) filters can be designed from an analogue low pass prototype by using frequency transformation in the s-domain and bilinear z-transformation with pre-warping frequency; this method is known as frequency transformation from the s-domain to the z-domain. This paper will introduce a new method to transform an IIR digital filter to another type of IIR digital filter (low pass, high pass, band pass, band stop or narrow band) using a technique based on inverse bilinear z-transformation and inverse matrices. First, a matrix equation is derived from inverse bilinear z-transformation and Pascal’s triangle. This Low Pass Digital to Digital Filter Pascal Matrix Equation is used to transform a low pass digital filter to other digital filter types. From this equation and the inverse matrix, a Digital to Digital Filter Pascal Matrix Equation can be derived that is able to transform any IIR digital filter. This paper will also introduce some specific matrices to replace the inverse matrix, which is difficult to determine due to the larger size of the matrix in the current method. This will make computing and hand calculation easier when transforming from one IIR digital filter to another in the digital domain.

Keywords: bilinear z-transformation, frequency transformation, inverse bilinear z-transformation, IIR digital filters

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Authors: Jihye Jeon

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This paper analyzes the conceptual framework of three statistical methods, multiple regression, path analysis, and structural equation models. When establishing research model of the statistical modeling of complex social phenomenon, it is important to know the strengths and limitations of three statistical models. This study explored the character, strength, and limitation of each modeling and suggested some strategies for accurate explaining or predicting the causal relationships among variables. Especially, on the studying of depression or mental health, the common mistakes of research modeling were discussed.

Keywords: multiple regression, path analysis, structural equation models, statistical modeling, social and psychological phenomenon

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Authors: Yakin Hajlaoui, Richard Labib, Jean-François Plante, Michel Gamache

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This study introduces the Multi-Layer Inverse Distance Weighting Model (ML-IDW), inspired by the mathematical formulation of both multi-layer neural networks (ML-NNs) and Inverse Distance Weighting model (IDW). ML-IDW leverages ML-NNs' processing capabilities, characterized by compositions of learnable non-linear functions applied to input features, and incorporates IDW's ability to learn anisotropic spatial dependencies, presenting a promising solution for nonlinear spatial interpolation and learning from complex spatial data. it employ gradient descent and backpropagation to train ML-IDW, comparing its performance against conventional spatial interpolation models such as Kriging and standard IDW on regression and classification tasks using simulated spatial datasets of varying complexity. the results highlight the efficacy of ML-IDW, particularly in handling complex spatial datasets, exhibiting lower mean square error in regression and higher F1 score in classification.

Keywords: deep learning, multi-layer neural networks, gradient descent, spatial interpolation, inverse distance weighting

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Authors: D. S. Nagesh, G. L. Datta

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In the field of welding, various studies had been made by some of the previous investigators to predict as well as optimize weld bead geometric descriptors. Modeling of weld bead shape is important for predicting the quality of welds. In most of the cases, design of experiments technique to postulate multiple linear regression equations have been used. Nowadays, Genetic Algorithm (GA) an intelligent information treatment system with the characteristics of treating complex relationships as seen in welding processes used as a tool for inverse mapping/optimization of the process is attempted.

Keywords: smaw, genetic algorithm, bead geometry, optimization/inverse mapping

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Authors: D. S. Nagesh, G. L. Datta

Abstract:

In the field of welding, various studies had been made by some of the previous investigators to predict as well as optimize weld bead geometric descriptors. Modeling of weld bead shape is important for predicting the quality of welds. In most of the cases design of experiments technique to postulate multiple linear regression equations have been used. Nowadays Genetic Algorithm (GA) an intelligent information treatment system with the characteristics of treating complex relationships as seen in welding processes used as a tool for inverse mapping/optimization of the process is attempted.

Keywords: SMAW, genetic algorithm, bead geometry, optimization/inverse mapping

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Authors: Somruay Apichatibutarapong, Chookiat Pudprommart

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The purpose of this study was to develop of statistical analysis by using R programming via internet applied for agriculture experimental design. Data were collected from 65 items in completely randomized design, randomized block design, Latin square design, split plot design, factorial design and nested design. The quantitative approach was used to investigate the quality of learning media on statistical analysis by using R programming via Internet by six experts and the opinions of 100 students who interested in experimental design and applied statistics. It was revealed that the experts’ opinions were good in all contents except a usage of web board and the students’ opinions were good in overall and all items.

Keywords: experimental design, r programming, applied statistics, statistical analysis

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Authors: Minho Kwon, Seonghyeok Lee, Wooyoung Jung

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In recent years, with increase of construction of skyscraper structures, the study of concrete materials to improve their weight and performance has been emerging as a key of research area. Typically, the concrete structures has disadvantage of increasing the weight due to its mass in comparison to the strength of the materials. Therefore, in order to improve such problems, the light-weight aggregate concrete and high strength concrete materials have been studied during the past decades. On the other hand, the study of light-weight aggregate concrete materials has lack of data in comparison to the concrete structure using high strength materials, relatively. Consequently, this study presents the performance characteristics of light-weight aggregate concrete materials due to the material properties and strength. Also, this study conducted the experimental tests with respect to normal and lightweight aggregate materials, in order to indentify the tensile crack failure of the concrete structures. As a result, the Crack Mouth Opening Displacement (CMOD) from the experimental tests was constructed and the fracture energy using inverse problem analysis was developed from the force-CMOD relationship in this study, respectively.

Keywords: lightweight aggregate concrete, crack mouth opening displacement, inverse analysis, fracture energy

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Authors: Ajay R, Rammohan B, Sridhar K S S, Gurusharan N

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The objective of the work is to develop a numerical method to solve the inverse mode shape problem by determining the cross-sectional area of a structure for the desired mode shape via the vibration response study of the humerus bone, which is in the form of a cantilever beam with anisotropic material properties. The humerus bone is the long bone in the arm that connects the shoulder to the elbow. The mode shape is assumed to be a higher-order polynomial satisfying a prescribed set of boundary conditions to converge the numerical algorithm. The natural frequency and the mode shapes are calculated for different boundary conditions to find the cross-sectional area of humerus bone from Eigenmode shape with the aid of the inverse mode shape algorithm. The cross-sectional area of humerus bone validates the mode shapes of specific boundary conditions. The numerical method to solve the inverse mode shape problem is validated in the biomedical application by finding the cross-sectional area of a humerus bone in the human arm.

Keywords: Cross-sectional area, Humerus bone, Inverse mode shape problem, Mode shape

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Authors: Apurva Patil, Maithilee Kulkarni, Ashay Aswale

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This paper proposes an algorithm to develop the kinematic model of a 5 DOF robot arm. The formulation of the problem is based on finding the D-H parameters of the arm. Brute Force iterative method is employed to solve the system of non linear equations. The focus of the paper is to obtain the accurate solutions by reducing the root mean square error. The result obtained will be implemented to grip the objects. The trajectories followed by the end effector for the required workspace coordinates are plotted. The methodology used here can be used in solving the problem for any other kinematic chain of up to six DOF.

Keywords: 5 DOF robot arm, D-H parameters, inverse kinematics, iterative method, trajectories

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Authors: Adnan A. Y. Mustafa

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Image matching is a fundamental problem that arises frequently in many aspects of robot and computer vision. It can become a time-consuming process when matching images to a database consisting of hundreds of images, especially if the images are big. One approach to reducing the time complexity of the matching process is to reduce the search space in a pre-matching stage, by simply removing dissimilar images quickly. The Probabilistic Matching Model for Binary Images (PMMBI) showed that dissimilarity detection between binary images can be accomplished quickly by random pixel mapping and is size invariant. The model is based on the gamma binary similarity distance that recognizes an image and its inverse as containing the same scene and hence considers them to be the same image. However, in many applications, an image and its inverse are not treated as being the same but rather dissimilar. In this paper, we present a comparative analysis of dissimilarity detection between PMMBI based on the gamma binary similarity distance and a modified PMMBI model based on a similarity distance that does distinguish between an image and its inverse as being dissimilar.

Keywords: binary image, dissimilarity detection, probabilistic matching model for binary images, image mapping

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Authors: Gülçin Tekin, Fethi Kadıoğlu

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In this study, the dynamic analysis of viscoelastic plates with variable thickness is examined. The solutions of dynamic response of viscoelastic thin plates with variable thickness have been obtained by using the functional analysis method in the conjunction with the Gâteaux differential. The four-node serendipity element with four degrees of freedom such as deflection, bending, and twisting moments at each node is used. Additionally, boundary condition terms are included in the functional by using a systematic way. In viscoelastic modeling, Three-parameter Kelvin solid model is employed. The solutions obtained in the Laplace-Carson domain are transformed to the real time domain by using MDOP, Dubner & Abate, and Durbin inverse transform techniques. To test the performance of the proposed mixed finite element formulation, numerical examples are treated.

Keywords: dynamic analysis, inverse laplace transform techniques, mixed finite element formulation, viscoelastic plate with variable thickness

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Authors: Jin-Wei Liang, Hung-Yi Chen, Lung Lin

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In this paper feedforward controller is designed to eliminate nonlinear hysteresis behaviors of a piezoelectric stack actuator (PSA) driven system. The control design is based on inverse Prandtl-Ishlinskii (P-I) hysteresis model identified using particle swarm optimization (PSO) technique. Based on the identified P-I model, both the inverse P-I hysteresis model and feedforward controller can be determined. Experimental results obtained using the inverse P-I feedforward control are compared with their counterparts using hysteresis estimates obtained from the identified Bouc-Wen model. Effectiveness of the proposed feedforward control scheme is demonstrated. To improve control performance feedback compensation using traditional PID scheme is adopted to integrate with the feedforward controller.

Keywords: the Bouc-Wen hysteresis model, particle swarm optimization, Prandtl-Ishlinskii model, automation engineering

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Authors: Djamel Remache, Marie Semaan, Cécile Baron, Martine Pithioux, Patrick Chabrand, Jean-Marie Rossi, Jean-Louis Milan

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Cortical bone is a complex multi-scale structure. Even though several works have contributed significantly to understanding its mechanical behavior, this behavior remains poorly understood. Nanoindentation testing is one of the primary testing techniques for the mechanical characterization of bone at small scales. The purpose of this study was to provide new nanoindentation data of cortical bovine bone in different directions and at different bone microstructures (osteonal, interstitial and laminar bone), and then to identify anisotropic properties of samples with FEM (finite element method) based inverse method. Experimentally and numerical results were compared. Experimental and numerical results were compared. The results compared were in good agreement.

Keywords: mechanical behavior of bone, nanoindentation, finite element analysis, inverse optimization approach

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Authors: Hamsasew Hankebo Lemago, Dóra Hessz, Tamás Igricz, Zoltán Erdélyi, , Imre Miklós Szilágyi

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Metal oxide inverse opals are a promising class of photocatalysts with a unique hierarchical structure. Atomic layer deposition (ALD) is a versatile technique for the synthesis of high-precision metal oxide thin films, including inverse opals. In this study, we report the synthesis of TiO₂, ZnO, and Al₂O₃ inverse opal and their composites photocatalysts using thermal or plasma-enhanced ALD. The synthesized photocatalysts were characterized using a variety of techniques, including scanning electron microscopy (SEM)-energy dispersive X-ray spectroscopy (EDX), X-ray diffraction (XRD), Raman spectroscopy, photoluminescence (PL), ellipsometry, and UV-visible spectroscopy. The results showed that the ALD-synthesized metal oxide inverse opals had a highly ordered structure and a tunable pore size. The PL spectroscopy results showed low recombination rates of photogenerated electron-hole pairs, while the ellipsometry and UV-visible spectroscopy results showed tunable optical properties and band gap energies. The photocatalytic activity of the samples was evaluated by the degradation of methylene blue under visible light irradiation. The results showed that the ALD-synthesized metal oxide inverse opals exhibited high photocatalytic activity, even under visible light irradiation. The composites photocatalysts showed even higher activity than the individual metal oxide inverse opals. The enhanced photocatalytic activity of the composites can be attributed to the synergistic effect between the different metal oxides. For example, Al₂O₃ can act as a charge carrier scavenger, which can reduce the recombination of photogenerated electron-hole pairs. The ALD-synthesized metal oxide inverse opals and their composites are promising photocatalysts for a variety of applications, such as wastewater treatment, air purification, and energy production. The ALD-synthesized metal oxide inverse opals and their composites are promising photocatalysts for a variety of applications, such as wastewater treatment, air purification, and energy production.

Keywords: ALD, metal oxide inverse opals, photocatalysis, composites

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Authors: Yoshio Kurosawa

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The applications of soundproof materials for reduction of high frequency automobile interior noise have been researched. This paper presents a sound pressure prediction technique including wind noise by Hybrid Statistical Energy Analysis (HSEA) in order to reduce weight of acoustic insulations. HSEA uses both analytical SEA and experimental SEA. As a result of chassis dynamo test and road test, the validity of SEA modeling was shown, and utility of the method was confirmed.

Keywords: vibration, noise, road noise, statistical energy analysis

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Authors: Okolie Chukwulozie Paul, Iwenofu Chinwe Onyedika, Sinebe Jude Ebieladoh, M. C. Nwosu

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The research work is based on the statistical analysis of the processing data. The essence is to analyze the data statistically and to generate a design model for the production mix of soap manufacturing products in Bejoy manufacturing company Nkpologwu, Aguata Local Government Area, Anambra state, Nigeria. The statistical analysis shows the statistical analysis and the correlation of the data. T test, Partial correlation and bi-variate correlation were used to understand what the data portrays. The design model developed was used to model the data production yield and the correlation of the variables show that the R2 is 98.7%. However, the results confirm that the data is fit for further analysis and modeling. This was proved by the correlation and the R-squared.

Keywords: General Linear Model, correlation, variables, pearson, significance, T-test, soap, production mix and statistic

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Authors: Khanh To Duc, Monica Chiogna, Gianfranco Adimari

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With three diagnostic categories, assessment of the performance of diagnostic tests is achieved by the analysis of the receiver operating characteristic (ROC) surface, which generalizes the ROC curve for binary diagnostic outcomes. The volume under the ROC surface (VUS) is a summary index usually employed for measuring the overall diagnostic accuracy. When the true disease status can be exactly assessed by means of a gold standard (GS) test, unbiased nonparametric estimators of the ROC surface and VUS are easily obtained. In practice, unfortunately, disease status verification via the GS test could be unavailable for all study subjects, due to the expensiveness or invasiveness of the GS test. Thus, often only a subset of patients undergoes disease verification. Statistical evaluations of diagnostic accuracy based only on data from subjects with verified disease status are typically biased. This bias is known as verification bias. Here, we consider the problem of correcting for verification bias when continuous diagnostic tests for three-class disease status are considered. We assume that selection for disease verification does not depend on disease status, given test results and other observed covariates, i.e., we assume that the true disease status, when missing, is missing at random. Under this assumption, we discuss several solutions for ROC surface analysis based on imputation and re-weighting methods. In particular, verification bias-corrected estimators of the ROC surface and of VUS are proposed, namely, full imputation, mean score imputation, inverse probability weighting and semiparametric efficient estimators. Consistency and asymptotic normality of the proposed estimators are established, and their finite sample behavior is investigated by means of Monte Carlo simulation studies. Two illustrations using real datasets are also given.

Keywords: imputation, missing at random, inverse probability weighting, ROC surface analysis

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Authors: A.R. Eskandari, M.R. Eskandari

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A 2D complete identification algorithm for dielectric and multiple objects immersed in air is presented. The employed technique consists of initially retrieving the shape and position of the scattering object using a linear sampling method and then determining the electric permittivity and conductivity of the scatterer using adjoint sensitivity analysis. This inversion algorithm results in high computational speed and efficiency, and it can be generalized for any scatterer structure. Also, this method is robust with respect to noise. The numerical results clearly show that this hybrid approach provides accurate reconstructions of various objects.

Keywords: inverse scattering, microwave imaging, two-dimensional objects, Linear Sampling Method (LSM)

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Authors: S. S. Sathiesh

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The aim of this project is to study the radiation mechanism synchrotron and Inverse Compton scattering. Theoretically, we discussed spectral energy distribution for both. Programming is done for plotting the graph of Power-law spectrum for synchrotron Radiation using fortran90. The importance of power law spectrum was discussed and studied to infer its physical parameters from the model fitting. We also discussed how to infer the physical parameters from the theoretically drawn graph, we have seen how one can infer B (magnetic field of the source), γ min, γ max, spectral indices (p1, p2) while fitting the curve to the observed data.

Keywords: blazars/quasars, beaming, synchrotron radiation, Synchrotron Self Compton, inverse Compton scattering, mrk421

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Authors: Daria Beziakina, Elena Bulgakova

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The paper deals with cross-gender and cross-linguistic comparison of pitch characteristics for Tuvinian with two other Turkic languages - Uzbek and Azerbaijani, based on the results of statistical analysis of pitch parameter values and intonation patterns used by male and female speakers. The main goal of our work is to obtain the ranges of pitch parameter values typical for Tuvinian speakers for the purpose of automatic language identification. We also propose a cross-gender analysis of declarative intonation in the poorly studied Tuvinian language. The ranges of pitch parameter values were obtained by means of specially developed software that deals with the distribution of pitch values and allows us to obtain statistical language-specific pitch intervals.

Keywords: speech analysis, statistical analysis, speaker recognition, identification of person

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Authors: Shishen Xie, Yingda L. Xie

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Tuberculosis (TB) is a potentially serious infectious disease that remains a health concern. The Interferon Gamma Release Assay (IGRA) is a blood test to find out if an individual is tuberculous positive or negative. This study applies statistical analysis to the clinical data of interferon-gamma levels of seventy-three subjects who diagnosed pulmonary TB in an anti-tuberculous treatment. Data analysis is performed to determine if there is a significant decline in interferon-gamma levels for the subjects during a period of six months, and to infer if the anti-tuberculous treatment is effective.

Keywords: data analysis, interferon gamma release assay, statistical methods, tuberculosis infection

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Authors: F. Berna Benli, Özgür Keskin

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Lately, many mathematicians have been studied the statistical convergence of a sequence of fuzzy numbers. We know that Lambda-statistically convergence is a kind of convergence between ordinary convergence and statistical convergence. In this paper, we will introduce the new kind of convergence such as λ-levelwise statistical convergence. Then, we will define the concept of the λ-levelwise statistical cluster and limit points of a sequence of fuzzy numbers. Also, we will discuss the relations between the sets of λ-levelwise statistical cluster points and λ-levelwise statistical limit points of sequences of fuzzy numbers. This work has been extended in this paper, where some relations have been considered such that when lambda-statistical limit inferior and lambda-statistical limit superior for lambda-statistically convergent sequences of fuzzy numbers are equal. Furthermore, lambda-statistical boundedness condition for different sequences of fuzzy numbers has been studied.

Keywords: fuzzy number, λ-levelwise statistical cluster points, λ-levelwise statistical convergence, λ-levelwise statistical limit points, λ-statistical cluster points, λ-statistical convergence, λ-statistical limit points

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Authors: Tatiana A. Dolenko, Sergey A. Burikov, Alexander O. Efitorov, Sergey A. Dolenko

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In this study, a comparative analysis of the approaches associated with the use of neural network algorithms for effective solution of a complex inverse problem – the problem of identifying and determining the individual concentrations of inorganic salts in multicomponent aqueous solutions by the spectra of Raman scattering of light – is performed. It is shown that application of artificial neural networks provides the average accuracy of determination of concentration of each salt no worse than 0.025 M. The results of comparative analysis of input data compression methods are presented. It is demonstrated that use of uniform aggregation of input features allows decreasing the error of determination of individual concentrations of components by 16-18% on the average.

Keywords: inverse problems, multi-component solutions, neural networks, Raman spectroscopy

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Authors: Ashis Mallick, Rajeev Ranjan

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The closed form solution for thermal stresses in an annular fin with hyperbolic profile is derived using Adomian decomposition method (ADM). The conductive-convective fin with variable thermal conductivity is considered in the analysis. The nonlinear heat transfer equation is efficiently solved by ADM considering insulated convective boundary conditions at the tip of fin. The constant of integration in the solution is to be estimated using minimum decomposition error method. The solution of temperature field is represented in a polynomial form for convenience to use in thermo-elasticity equation. The non-dimensional thermal stress fields are obtained using the ADM solution of temperature field coupled with the thermo-elasticity solution. The influence of the various thermal parameters in temperature field and stress fields are presented. In order to show the accuracy of the ADM solution, the present results are compared with the results available in literature. The stress fields in fin with hyperbolic profile are compared with those of uniform thickness profile. Result shows that hyperbolic fin profile is better choice for enhancing heat transfer. Moreover, less thermal stresses are developed in hyperbolic profile as compared to rectangular profile. Next, Nelder-Mead based simplex search method is employed for the inverse estimation of unknown non-dimensional thermal parameters in a given stress fields. Owing to the correlated nature of the unknowns, the best combinations of the model parameters which are satisfying the predefined stress field are to be estimated. The stress fields calculated using the inverse parameters give a very good agreement with the stress fields obtained from the forward solution. The estimated parameters are suitable to use for efficient and cost effective fin designing.

Keywords: Adomian decomposition, inverse analysis, hyperbolic fin, variable thermal conductivity

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Authors: Queen Suraajini Rajendran, Sai Hung Cheung

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Statistical down scaling models are required to connect the global climate model outputs and the local weather variables for climate change impact prediction. For reliable climate change impact studies, the uncertainty associated with the model including natural variability, uncertainty in the climate model(s), down scaling model, model inadequacy and in the predicted results should be quantified appropriately. In this work, a new approach is developed by the authors for statistical classification, statistical down scaling and uncertainty assessment and is applied to Singapore rainfall. It is a robust Bayesian uncertainty analysis methodology and tools based on coupling dependent modeling error with classification and statistical down scaling models in a way that the dependency among modeling errors will impact the results of both classification and statistical down scaling model calibration and uncertainty analysis for future prediction. Singapore data are considered here and the uncertainty and prediction results are obtained. From the results obtained, directions of research for improvement are briefly presented.

Keywords: statistical downscaling, global climate model, climate change, uncertainty

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Authors: Fadi Awawdeh

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In this work, we highlight the key concepts in using semigroup theory as a methodology used to construct efficient formulas for solving inverse problems. The proposed method depends on some results concerning integral equations. The experimental results show the potential and limitations of the method and imply directions for future work.

Keywords: identification problems, semigroup theory, methods for inverse problems, scientific computing

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Authors: Da-Ming Huang, Ya-Ting Tsai, Shyh-Hau Wang

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Ultrasound signals backscattered from the soft tissues are mainly depending on the size, density, distribution, and other elastic properties of scatterers in the interrogated sample volume. The quantitative analysis of ultrasonic backscattering is frequently implemented using the statistical approach due to that of backscattering signals tends to be with the nature of the random variable. Thus, the statistical analysis, such as Nakagami statistics, has been applied to characterize the density and distribution of scatterers of a sample. Yet, the accuracy of statistical analysis could be readily affected by the receiving signals associated with the nature of incident ultrasound wave and acoustical properties of samples. Thus, in the present study, efforts were made to explore such effects as the ultrasound operational modes and attenuation of biological tissue on the estimation of corresponding Nakagami statistical parameter (m parameter). In vitro measurements were performed from healthy and pathological fibrosis porcine livers using different single-element ultrasound transducers and duty cycles of incident tone burst ranging respectively from 3.5 to 7.5 MHz and 10 to 50%. Results demonstrated that the estimated m parameter tends to be sensitively affected by the use of ultrasound operational modes as well as the tissue attenuation. The healthy and pathological tissues may be characterized quantitatively by m parameter under fixed measurement conditions and proper calibration.

Keywords: ultrasound backscattering, statistical analysis, operational mode, attenuation

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Authors: Avelino Marques, Diamantino Freitas

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Some important electroacoustic systems, like loudspeaker systems, exhibit a nonminimum phase behavior that poses considerable effort when applying advanced digital signal processing techniques, such as linear equalization. In this paper, the position and the number of zeros and poles of the inverse filter, FIR type or IIR type, designed using time domain techniques, are studied, compared and related to the nonminimum phase zeros of system to be equalized. Conclusions about the impact of the position of the system non-minimum phase zeros, on the length/order of the inverse filter and on the delay of the equalized system are outlined as a guide to previously decide which type of filter will be more adequate.

Keywords: loudspeaker systems, nonminimum phase system, FIR and IIR filter, delay

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Authors: Ali Anwar, Hu Qinglei, Li Bo, Muhammad Taha Ali

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In this paper a generic model of perturbed nonlinear systems is considered which is affected by hard backlash nonlinearity at the input. The nonlinearity is modelled by a dynamic differential equation which presents a more precise shape as compared to the existing linear models and is compatible with nonlinear design technique such as backstepping. Moreover, a novel backstepping based nonlinear control law is designed which explicitly incorporates a continuous-time adaptive backlash inverse model. It provides a significant flexibility to control engineers, whereby they can use the estimated backlash spacing value specified on actuators such as gears etc. in the adaptive Backlash Inverse model during the control design. It ensures not only global stability but also stringent transient performance with desired precision. It is also robust to external disturbances upon which the bounds are taken as unknown and traverses the backlash spacing efficiently with underestimated information about the actual value. The continuous-time backlash inverse model is distinguished in the sense that other models are either discrete-time or involve complex computations. Furthermore, numerical simulations are presented which not only illustrate the effectiveness of proposed control law but also its comparison with PID and other backstepping controllers.

Keywords: adaptive control, hysteresis, backlash inverse, nonlinear system, robust control, backstepping

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