Application of Genetic Algorithm for Fault Detection in Cracked Composite Structure

Purpose Modelling methods can be helpful for understanding vibrations of beam structures including cracks, as well as for early detection of crack. This study aims to provide an analytical modelling approach for a cantilever beam considering a slant vertical crack along its height. However, previous uniform crack methods cannot be used for describing this case. The results from the analytical, finite element (FE) and experimental methods are compared to verify the vibration problem. Design/methodology/approach A massless rotational spring model is adopted to describe the crack. An extended method based on the calculation method for a uniform vertical edge crack is proposed to obtain the stiffness of the slant case. The beam is divided into a series of independent thin slices along the beam height. An Euler–Bernoulli beam model is applied to formulate each slice. The crack in each slice is considered as a uniform one. The transfer matrix method in the literature is used to obtain the beam vibration frequencies and mode shapes. Influences of crack location and sizes on the natural frequencies for the cantilever beam, as well as the mode shapes, are analysed. An established FE model and test results in the listed references are used to validate the developed method. Findings The numerical results show that the rotational stiffness at the cracked section and the natural frequencies of the beam decrease by increasing the crack sizes; the natural frequencies for the beam are greatly influenced by the crack sizes and location; the first natural frequency decreases with the distance from the beam fixed end to the crack location; the value of the first natural frequency reaches a minimum value when the crack is at the beam fixed end; the value of the second natural frequency is a minimum value when the crack is at the beam middle; and the value of the third natural frequency is a minimum value when the crack is at the beam free end. Saltation is observed in some mode shapes at the crack location, especially for larger crack depths; but, the mode shapes of the beam are slightly influenced by the vertical crack. Originality/value This study gives a useful analytical modelling method for free vibration analysis for the cantilever beam with a vertical crack, which can overcome the disadvantages of the previous uniform crack methods.

A new genetic algorithm (GA), called intelligent GA, is proposed by the inclusion of a fractional factorial design in the crossover operator to determine the best combination of design variables. That is, in the proposed GA, the chromosomes of children are generated via an intelligent crossover process with factorial experiments after completing the selection of GA operators. This gene mating process differs from the traditional GA, where the child chromosome is generally generated via randomization. Accordingly, the traditional GA incorporating the technique of fractional factorial design into the crossover operator markedly enhances the performance in terms of evolutionary efficiency. Another GA, called Taguchi-GA, that incorporates the Taguchi orthogonal arrays into the crossover operator is also developed to compare the performance of the presented intelligent GA. Four representative test cases, including two multimodal functions, a nonlinear dynamic control function, and a profile fitting of a high lift airfoil are performed via the traditional GA, micro-GA, Taguchi-GA, and present GA to assess the capacity and efficiency of the proposed GA. The computational solutions of the convergence history and optimal objective function for the test cases demonstrate that the proposed intelligent GA outperforms the other three GAs. Moreover, the presented new intelligent GA and the other three GAs are applied to the aerodynamic optimization of two airplanes, namely, an advanced defense airplane and an F-16A fighter. The redesigned wing planform is obtained by computations made with an aerodynamic flow solver, and the present GA depicts the optimal swept angle, aspect ratio, and taper ratio. The drag distribution and convergence history show that the proposed intelligent GA has a high evolutionary efficiency when applied to practical engineering problems.

In this paper, the dynamic behavior of a cantilever beam without and with crack is observed. An elastic Aluminum cantilever beams having surface crack at various crack positions are considered to analyze dynamically. Crack depth, crack length and crack location are the foremost parameters for describing the health condition of beam in terms of modal parameters such as natural frequency, mode shape and damping ratio. It is crucial to study the influence of crack depth and crack location on modal parameters of the beam for the decent performance and its safety. Crack or damage of structure causes a reduction in stiffness, an intrinsic reduction in resonant frequencies, variation of damping ratios and mode shapes. The broad examination of cantilever beam without crack and with crack has been done using Numerical analysis (Ansys18.0) and experimental modal analysis. To observe the exact higher modes of beam, discretize the beam into small elements. An experimental set up was established for cantilever beam having crack and it was excited by an impact hammer and finally the response was obtained using PCB accelerometer with the help sound and vibration toolkit of NI Lab-view. After obtaining the Frequency response functions (FRFs), the natural frequencies of beam are estimated using peak search method. The effectiveness of experimental modal analysis in terms of natural frequency is validated with numerical analysis results. This paper contains the study of free vibration analysis under the influence of crack at different points along the length of the beam.

The present study outlines a sequentially integrated finite-element method (FEM)–response surface method (RSM)–genetic algorithm (GA) framework and implements this to predict the crack parameters, namely, crack location and crack depth ratio. A central composite face centered response surface design of the RSM technique is used to establish the direct relationships between the input parameters (crack location and crack depth ratio) and responses (natural frequencies) to build the response surface function (RSF). Multiple edge cracks are considered, which exist on the top flange of a thin-walled channel section cantilever beam and modeled as line spring elements. In order to obtain RSFs of the first five natural frequencies in terms of process factors such as crack position and crack depth ratio, a number of numerical experiments based on FEM are conducted by using the design-of-experiment approach. An objective function obtained as the square of the difference between RSF and experimentally measured natural frequency has been minimized using GA to find out the optimum crack parameters. Twenty-four steel channel beam specimens have been tested in the laboratory to extract the crack parameters from measured natural frequencies using the proposed approach. The results of the study indicate that the proposed approach performs remarkably, yielding crack parameters with great precision. Copyright © 2015 John Wiley & Sons, Ltd.

Most of the rotating machines used in process industries or in manufacturing plant need maintenance and repair. However, failure of just one of these machines can disturb an entire process with losses in terms of production, manpower, and equipment repair or replacement. Also failure of a single machine component in process industries like petrochemicals or power stations can result in the loss of millions of rupees per down time hour. These facts together with higher costs for new equipment have placed increased demand on plant maintenance to keep existing equipment operating efficiently with higher availability. A number of non-destructive crack detection techniques have been developed, such as ultrasonic testing, X-ray technique, magnetic particle method etc. Every method has some advantages and disadvantages. In recent years, ultrasonic testing has gained greater attention for monitoring the cracks in structures and machine components. Most of these methods are very laborious and time consuming, in the case of larger components like bridges, long pipe lines, railway tracks etc. These inconveniences can be avoided by the use of vibration monitoring technique such as model analysis. Therefore the development of vibration monitoring techniques has received increasing attention in recent years. Damage in structure alters its dynamic characteristics. The change is characterized by a change in model parameters i.e. model frequencies, model damping values and mode shapes associated with each model frequencies. Changes also occur in some of the structural parameters like mass, damping, stiffness and flexibility matrices of structure. Thus a vibration technique can be suitably used as a nondestructive test for crack detection of components to be tested. In this paper, theoretical and experimental analysis of a vibrating cantilever beam with a crack is carried out. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structure. The method is based on measurement of natural frequencies, which are global parameter and can be easily measured from any point on the structure. In theoretical analysis the crack is simulated by an equivalent spring, connecting the two segments of the beam. Analysis of this approximate model results in algebraic equation, which relates the natural frequencies of the beam, and crack location. Also the relationship between the natural frequencies, crack location and crack size has also been developed. For identification of crack location and crack size, it was shown that data on the variation of the first two natural frequencies are sufficient. The computation of natural frequencies of uncracked and cracked beam is facilitated by a finite element method package. This database is to be utilized in an analytical method to address the inverse problem to identify the crack location and crack size.

In engineering domains, modal analysis is a field that is studied extensively with the goal of better characterizingcomponents or structures. Themodal analysis produces modal parameters, which are essential properties of a system that can be employed for damage identification, vibration analysis, and structural health monitoring. Plated element’s relevance in variousapplications makes it an intriguing vibration study subject. In thisresearch, modal analysis was performed on a square steel plate in free ends condition. This work aimedto provide a complete anatomical description of this complex boundary condition and its implications on modal parameters. Before comparing modal parameters with experimental data, a primary modal analysis was performed using finite element (FE)method. Then experimental analysis was conducted under the operational modal analysis setup (OMA).As the results, six natural frequencies are retrieved and compared amongst the two methods, recording the maximum of 6% percentage difference from the readings. This implied a close values estimated between the methods used. For mode shapes, ninemodes are identified from FE method and discussed according to established free plate vibration studies, while threesimilarly identified modes successfully recognized by using OMA.

Modeling and analysis of a cracked composite cantilever beam vibrating in coupled bending and torsion

Modal analysis has developed into a major technology for the study of structural dynamics in the past several decades. Through it, complex structural dynamics phenomena can be represented in terms of structural invariants, i.e., the modal parameters: natural frequencies, damping ratios and mode shapes. Operational Modal Analysis (OMA) deals with the estimation of modal parameters on vibration data measured for operational conditions, when the excitation on the structure is not measured. In this work, OMA is performed on a wind turbine blade undergoing wind tunnel testing. These tests included different wind speeds, pitch angles and also different health conditions of the blade, where masses of different magnitude were fixed to the blade on different locations to emulate damage conditions. In order to monitor the modal parameters across multiple days of varied tests in the wind tunnel, the Polymax modal parameter estimator was implemented, coupled with an Automated Modal Analysis methodology. This methodology included an automatic modal parameter selection technique, using a Machine Learning (ML) clustering algorithm, coupled with a modal tracking procedure which applied statistical thresholds on the modal parameters’ values. The tracking procedure searches for modes similar to the ones calculated for healthy conditions. The results show how the modal parameters of the wind turbine blade vary with the different measured conditions in the wind tunnel. Moreover, a damage detection methodology is implemented to differentiate between the healthy and damaged conditions on the blade, by leveraging an anomaly detection algorithm using the Multivariate Gaussian Distribution (MGD). This algorithm takes as input the modal parameters calculated by the previous Automated Modal Analysis methodology and detects statistical deviations among them which could indicate the presence of damage. All steps of this work contribute to developing an automatic framework able to detect damages on a wind turbine blade, and therefore perform Structural Health Monitoring (SHM) for different operational conditions.

Generation Scheduling problem by Intelligent Genetic Algorithm

Non-uniform beam structures are widely applied in various engineering fields, and the accurate estimation of modal parameters is significant to the design and optimization of non-uniform beams. This work aims to investigate the transverse free vibration of non-uniform beams with exponentially varying rectangular and circular cross-sections. When solving the governing equations for non-uniform beams in transverse free vibration, utilizing the Adomian Decomposition Method (ADM) can achieve semi-analytical expressions for natural frequencies and modal shape functions. To verify the efficiency of ADM, comparisons are made among the results obtained by the present proposed method, previous studies, the Finite-Element-Method (FEM) model and the experimental modal testing. Variations of natural frequencies and modal shapes under representative constraint boundary conditions are illustrated considering the effects of exponential factors. The results indicate that the modal parameters of non-uniform beams depend on the exponential factors significantly. Especially, for non-uniform beams with varying rectangular cross-sections, the exponential factor of the thickness direction has a greater impact on the modal parameters compared to the width direction. In addition, the positions of modal nodes and antinodes in non-uniform beams will shift compared to uniform beams due to the exponential non-uniformity.

In case of a low pressure steam turbine the crack like flaws due to low cycle fatigue (LCF) is one of the main reasons for its premature failure as reported by various researchers. Non destructive testing (NDT) methods like dye penetrate, magnetic particle induction, acoustic, ultrasonic etc. are used for detection of crack which are very costly and time consuming task. Also vicinity of the fault has to be known beforehand and area has to be readily accessible. Since last two decades lot of research has been done in using vibration analysis to detect crack in beams by using modal parameters like natural frequency, mode shape, damping etc. In this research work an attempt is made to extend vibration characteristic based method for detection of crack in turbine blade. The finite element method is used with development of stiffness matrix for cracked element from the theory of linear elastic fracture mechanics.

A beam structure in presence of crack subjected to both bending and axial load has been investigated for damage diagnosis to predict crack location and crack depth based on an optimized intelligent technique using genetic algorithms approach. Numerical with experimental investigations have been conducted in a free-free beam model to calculate natural frequencies. In this work, genetic algorithm as an optimized artificial intelligent technique has been used which employs first three relative modal parameters like natural frequencies as input data taken from numerical and experimental results to obtain optimized crack locations and crack depths as output parameters. This methodology has been found to be quite reliable for fault diagnosis by monitoring the possible variations in the relative natural frequencies of a free-free beam element in presence of crack. This paper also gives an insight into the deviation of the results of the proposed methodology from the experimental result.

In this study, Genetic Algorithms (GAs) combined with the proposed neural networks were implemented to the free vibration analysis of an adhesively bonded double containment cantilever joint with a functionally graded plate. The proposed neural networks were trained and tested based on a limited number of data including the natural frequencies and modal strain energies calculated using the finite element method. GA evaluates a value generated iteratively by an objective function and this value is calculated by the finite element method. The iteration process restricts us apparently to use directly the finite element method in our multi-objective optimisation problem in which the natural frequency is maximised and the corresponding modal strain energy is minimised. The proposed neural networks were used accurately to predict the natural frequencies and modal strain energies instead of calculating directly them by using the finite element method. Consequently, the computation time and efforts were reduced considerably. The adhesive joint was observed to tend vertical bending modes and torsional modes. Therefore, the multi-objective optimisation problem was limited to only the first mode which appeared as a bending mode. The effects of the geometrical dimensions and the material composition variation through the plate thickness were investigated. As the material composition of the horizontal plate becomes ceramic rich, both natural frequency and modal strain energy of the adhesive joint increased regularly. The plate length and plate thickness were more effective geometrical design parameters whereas the support length and thickness were less effective. However, the adhesive thickness had a small effect on the optimal design of the adhesive joint as far as the natural frequencies and modal strain energies are concerned. The distributions of optimal solutions were also presented for the adhesive joints with fundamental joint lengths and material compositions in reference to their natural frequencies and corresponding modal strain energies.

In this present study, natural frequencies of the first two modes of bending vibration for the cracked simply supported Euler–Bernoulli beam is determined using finite element analysis (FEA). FEA natural frequencies for the cracked beam are used to investigate the behavior of the cracked beam and also used in the inverse problem of crack depth detection. Dynamic behavior of the cracked simply supported beam is observed, and it is found that normalized mode shape at crack location has great effect on amount of decreasing of natural frequencies. When normalized mode shape at crack location is increased, then natural frequencies decrease. In this study, pattern of mode shape played a vital role in decreasing or increasing natural frequencies. At the midpoint of the beam, there is largest bending moment in first bending mode and there is nodal point in second bending mode. Harmonic analysis for the cracked simply supported beam is carried out to find von Mises stress responses and appearance of peaks at frequency of first bending mode is noticed in graphs of von Mises stress response, expressing high values of von Mises stress at crack tip. Inverse problem of assessing the crack depth is performed using results of FEA first mode frequency ratio and published experimental results and the method showed good results in case of high crack depth ratios.

Damage analysis in composite materials using a hybrid artificial immune system