Ranjan Ganguli

Survey of Recent Developments in Rotorcraft Design Optimization

OTORCRAFT engineering is highly interdisciplinary because the flexibility of the main rotor blades couples with the aerodynamics, dynamics, and control system. In addition, interaction between the rotor and fuselage further complicates helicopter system predictions. The multidisciplinary nature of the helicopter engineering problems has led researchers to investigate formal optimization methods for the design process. Applications of formal optimization methods for helicopter problems started in the early 1980s. Miura 1 provided a review of some of the early work on application of numerical optimization to helicopters. Friedmann, 2 Adelman and Mantay, 3 and Celi 4 provide further reviews of helicopter optimization. Sobieszczanski-Sobieski and Haftka 5 give a review of recent developments in multidisciplinary design optimization for aerospace problems and Gieseng and Barthelemy 6 provide an industrial perspective of multidisciplinary optimization research. Whereas considerable studies have been conducted on helicopter design optimization, several issues have prevented it from becoming as popular or successful as structural optimization. Many finite element-based design packages today have builtin optimization capacity. However, the predictive capacity of even the most sophisticated helicopter aeroelastic analysis codes remains quite poor, as evidenced in a recent study by Hansford and Vorwald, 7 where hub load predictions from several codes are compared with flight-test data. In addition, because of the nature of helicopter problems, comprehensive aeroelastic codes are highly multidisciplinary and very difficult to understand and alter except by domain experts. This is because of the complexity of the physical modeling. For example, as the blade moves over one revolution, it encounters transonic flow, reverse flow, stall, and unsteady effects including dynamic stall. Large azimuthal variations in lift result from changes in dynamic pressure

Structural damage detection in a helicopter rotor blade using radial basis function neural networks

A neural network approach is used for detection of structural damage in a helicopter rotor blade using rotating frequencies of the flap (transverse bending), lag (in-plane bending), elastic torsion and axial modes. A finite element method is used for modeling the helicopter blade. Radial basis function (RBF) neural networks are used and several combinations of modes are investigated for training and testing the neural network. Using the first 10 modes of the rotor blade for damage detection yields accurate results for the soft in-plane hingeless rotor considered in this study. Using a parametric study of the blade rotating frequency in conjunction with the neural network, it is found that a reduced measurement set consisting of five modes (the first two torsion modes, the second lag mode and the third and fourth flap modes) also gives good results for damage detection. Furthermore, taking only the first four flap modes also results in good damage detection accuracy. Three rotating frequency sets are therefore identified in this paper for structural damage detection in a helicopter rotor using RBF neural networks.

Identification of crack location and depth in a cantilever beam using a modular neural network approach

In this paper, the flexural vibration in a cantilever beam having a transverse surface crack is considered. The modal frequency parameters are analytically computed for various crack locations and depths using a fracture mechanics based crack model. These computed modal frequencies are used to train a neural network to identify both the crack location and depth. The sensitivity of the modal frequencies to a crack increases when the crack is near the root and decreases as the crack moves to the free end of the cantilever beam. Because of the sensitive nature of this problem, a modular neural network approach is used. First, the crack location is identified with computed modal frequency parameters. Next, the crack depth is identified with computed modal frequency parameters and the identified crack location. A comparative study is made using the modular neural network architecture with two widely used neural networks, namely the multi-layer perceptron network and the radial basis function network. The proposed modular neural network method with a radial basis function network is found to perform better than the multi-layer perceptron network. In addition, the radial basis function network takes less computational time to train the network than the multi-layer perceptron network. This modular neural network architecture can be used as a non-destructive procedure for health monitoring of structures.

A Fuzzy Logic System for Ground Based Structural Health Monitoring of a Helicopter Rotor Using Modal Data

A fuzzy logic system (FLS) is developed for ground based health monitoring of a helicopter rotor blade. Structural damage is modeled as a loss of stiffness at the damaged location that can result from delamination. Composite materials, which are widely used for fabricating rotor blades, are susceptible to such delaminations from barely visible impact damage. The rotor blade is modeled as an elastic beam undergoing transverse (flap) and in-plane (lag) bending, axial and torsion deformations. A finite element model of the rotor blade is used to calculate the change in blade frequencies (both rotating and nonrotating) because of structural damage. The measurements used for health monitoring are the first four flap (transverse bending) frequencies of the rotor blade. The measurement deviations due to damage are then fuzzified and mapped to a set of faults using a fuzzy logic system. The output faults of the fuzzy logic system are four levels of damage (undamaged, slight, moderate and severe) at five locations along the blade (root, inboard, center, outboard, tip). Numerical results with noisy data show that the FLS detects damage with an accuracy of 100% for noise levels below 15% when nonrotating frequencies are used. The FLS also correctly classifies the “undamaged” condition up to noise levels of 30% thereby reducing the possibility of false alarms, a key problem for diagnostics systems. The fuzzy logic approach is thus able to extract maximum information from very limited and uncertain data. Using rotating frequencies lowers the success rate for small damage because the centrifugal stiffening caused by rotation counters the stiffness reduction caused by structural damage. The fuzzy logic system in this study is proposed as an information-processing tool to help the maintenance engineer by locating the damage area roughly but accurately for further nondestructive inspections.

Structural damage detection using fuzzy cognitive maps and Hebbian learning

A new algorithmic approach for structural damage detection based on the fuzzy cognitive map (FCM) is developed in this paper. Structural damage is modeled using the continuum mechanics approach as a loss of stiffness at the damaged location. A finite element model of a cantilever beam is used to calculate the change in the first six beam frequencies because of structural damage. The measurement deviations due to damage are fuzzified and then mapped to a set of faults using FCM. The input concepts for the FCM are the frequency deviations and the output of the FCM is at five possible damage locations along the beam. The FCM works quite well for structural damage detection for ideal and noisy data. Further improvement in performance is obtained when an unsupervised neural network approach based on Hebbian learning is used to evolve the FCM. Numerical results clearly show that the use of FCM and Hebbian learning results in accurate damage detection and represents a powerful tool for structural health monitoring.

Filter design using radial basis function neural network and genetic algorithm for improved operational health monitoring

The problem of denoising damage indicator signals for improved operational health monitoring of systems is addressed by applying soft computing methods to design filters. Since measured data in operational settings is contaminated with noise and outliers, pattern recognition algorithms for fault detection and isolation can give false alarms. A direct approach to improving the fault detection and isolation is to remove noise and outliers from time series of measured data or damage indicators before performing fault detection and isolation. Many popular signal-processing approaches do not work well with damage indicator signals, which can contain sudden changes due to abrupt faults and non-Gaussian outliers. Signal-processing algorithms based on radial basis function (RBF) neural network and weighted recursive median (WRM) filters are explored for denoising simulated time series. The RBF neural network filter is developed using a K-means clustering algorithm and is much less computationally expensive to develop than feedforward neural networks trained using backpropagation. The nonlinear multimodal integer-programming problem of selecting optimal integer weights of the WRM filter is solved using genetic algorithm. Numerical results are obtained for helicopter rotor structural damage indicators based on simulated frequencies. Test signals consider low order polynomial growth of damage indicators with time to simulate gradual or incipient faults and step changes in the signal to simulate abrupt faults. Noise and outliers are added to the test signals. The WRM and RBF filters result in a noise reduction of 54-71 and 59-73% for the test signals considered in this study, respectively. Their performance is much better than the moving average FIR filter, which causes significant feature distortion and has poor outlier removal capabilities and shows the potential of soft computing methods for specific signal-processing applications.

Aeroelastic Stability Enhancement and Vibration Suppression in a Composite Helicopter Rotor

An optimization procedure to 1) reduce the 4/revolution oscillatory hub loads and 2) increase the lag mode damping of a four-bladed soft-in-plane hingeless helicopter rotor is developed using a two-level approach. At the upper level, response surface approximations to the objective function and constraints are used to find the optimal blade mass and stiffness properties for vibration minimization and stability enhancement. An aeroelastic analysis based on finite elements in space and time is used. The numerical sampling needed to obtain the response surfaces is done using the central composite design of the theory of design of experiments. The approximate optimization problem expressed in terms of quadratic response surfaces is solved using a gradient-based method. Optimization results for the vibration problem in forward flight with unsteady aerodynamic modeling show a vibration reduction of about 15%. The dominant loads are the vertical hub shear and the rolling and pitching moments, which are reduced by 22-26%. The results of stability enhancement problem show an increase of 6-125% in the lag mode damping. At the lower level, a composite box beam is designed to match the upper-level beam blade stiffness and mass using a genetic algorithm which permits the use of discrete ply angle design variables such as 0, +or-45, and 90 deg, which are easier to manufacture. Three different composite materials are used for designing the composite box beam, thus, showing the robustness of the genetic algorithm approach. Boron/epoxy composite gives the most compact box beam, whereas graphite/epoxy gives the lightest box beam

An automated hybrid genetic-conjugate gradient algorithm for multimodal optimization problems

The genetic algorithm (GA) have good global search characteristics and local optimizing algorithm (LOA) have good local search characteristics. In the present work, best characteristics of GA and LOA are combined to develop a hybrid genetic algorithm (HGA). A bank of GAs are used to get a good starting solution for a conjugate gradient algorithm. The number of GA banks is selected using an automated procedure based on Fibonacci numbers. This automated hybrid genetic algorithm (AHGA) is used for solving general multimodal optimization problems while assuring global optimality to a significant degree. The designed algorithm is also tested against a variety of standard test functions. Besides assuring global optimality to a significant extent AHGA is also found to be an efficient algorithm requiring only one tuning error parameter saving considerable time on the part of the user. The method also addresses the problem of selecting a good starting design for gradient based algorithm. Further in the few cases where the algorithm does not converge to a global minima, a local minima is assured because of the use of the gradient based local search in the final stage of the algorithm. Further, the algorithm assures one final solution to the optimization problem and addresses the problem of providing a deterministic output which inhibits the use of GA in engineering optimization software and engineering applications.

Aeroelastic Response of Composite Helicopter Rotor with Random Material Properties

This study investigates the effect of uncertainty in composite material properties on the cross-sectional stiffness properties, natural frequencies, and aeroelastic responses of a composite helicopter rotor blade. The elastic moduli and Poisson’s ratio of the composite material are considered as random variables with a coefficient of variation of around 4%, which was taken from published experimental work. An analytical box beam model is used for evaluating blade cross-sectional properties. Aeroelastic analysis based on finite elements in space and time is used to evaluate the helicopter rotor blade response in forward flight. The stochastic cross-sectional and aeroelastic analyses are carried out with Monte Carlo simulations. It is found that the blade cross-sectional stiffness matrix elements show a coefficient of variation of about 6%. The nonrotating rotor blade natural frequencies show a coefficient of variation of around 3%. The impact of material uncertainty on rotating natural frequencies varies from that on nonrotating blade frequencies because of centrifugal stiffening. The propagation of material uncertainty into aeroelastic response causes large deviations, particularly in the higher-harmonic components that are critical for the accurate prediction of helicopter blade loads and vibration. The numerical results clearly show the need to consider randomness of composite material properties in the helicopter aeroelastic analysis.

Matrix Crack Detection in Thin-walled Composite Beam using Genetic Fuzzy System

Since thin-walled composite structures are widely used in structural engineering, damage in such structures is an important issue of research. Matrix cracking is a principal cause of failure in composites. In the present study, a composite matrix cracking model is implemented in a thin-walled hollow circular cantilever beam using an effective stiffness approach. Such structures are used to model connecting shafts and helicopter tail boom, for example, because of their high stiffness-to-weight ratios and excellent crashworthiness characteristics. The effect of variation in crack density on the fundamental frequency, for various combinations of 1/2 m =90n s composite is studied. Using these change in frequencies due to matrix cracking, a genetic fuzzy system for crack density and crack location detection is generated. The genetic fuzzy system combines the uncertainty representation characteristics of fuzzy logic with the learning ability of genetic algorithm. It is observed that the success rate of the genetic fuzzy system in the presence of noise is dependent on crack density (level of damage), number of 90 plies, angle of constraining layer (), and noise level. It is found that the genetic fuzzy system shows excellent damage detection and isolation performance, and is robust to presence of noise in data.