Filter design using radial basis function neural network and genetic algorithm for improved operational health monitoring
Introduction
Health monitoring involves tracking damage in a system using measured data. A key problem in the operational health monitoring is the higher level of noise in the data than that which occurs in carefully controlled laboratory experiments. In general, the problem of health monitoring has a hierarchical structure [1]. At the highest level we want to know about the expected time to failure. At the lowest level the question is whether the damage or fault is present or not. This lower level problem, according to Worden et al. [1], is of a more fundamental nature. The lowest level damage detection problem depends on selecting an appropriate threshold for a measurement or the extracted feature to classify the damaged state as different from the undamaged state. The higher-level fault isolation problem involves solving the pattern recognition problem of finding a damage given a damage signature. Finally, the prognostic function involves suggesting possible maintenance action once damage has been isolated. All these functions of damage detection, isolation and prognostics depend on the quality of the measured data.
Raw measurement signals from an undamaged and damaged system are hard to distinguish. Therefore, a process of feature extraction often needs to be done to extract some relevant feature that magnifies the damage. For example, while time history of acceleration data may look very similar, modal properties such as frequencies, extracted from the time history data may show the presence of damage. These properties can be called damage indicators. In general, faults can be classified into three types [2] depending on the variation of the measurements or damage indicators: (1) intermittent faults, (2) incipient (gradually evolving) faults and (3) abrupt faults. Intermittent faults can often be due to problems in the electronic systems. Abrupt faults cause sudden changes in the damage indicator and can precede failure. If they are not detected and acted upon in timely manner, there may be catastrophic failure. Manders et al. [2] mention that the primary function of a diagnostic system is the extraction of magnitude and slope values from health signals and detection of abrupt changes. Therefore, in very general terms, damage diagnostics is a signal to symbol transformation problem. The objective of signal analysis for damage detection is therefore not necessarily to minimize all possible distortion, but also to preserve feature of interest.
It has been observed in structural damage detection by George et al. [3] that “virtually every damage indicator shows a near immediate increase at the onset of damage, followed by a sort of ‘saturation’ as the indicators change much less at higher damage levels”. In another area of gas turbine fault detection it has also been found that damage in jet engines is mostly preceded by sharp trend shift in one or more sensor measurements indicative of damage and the long-term damage behavior is well modeled as a low order polynomial, with a linear function being a good approximation [4]. Therefore, the presence of sharp trend shifts or edges is an important feature in damage indicator signals.
Various filtering technique have been developed to suppress noise in order to improve the quality of damage indicators. Linear filters such as moving average filter can be used to smooth noisy signals. However, when the signal contains sudden changes the linear filters tend to smooth out these sudden trend shifts. As we have discussed earlier, time series of damage indicators can show sudden change. In addition, linear filters are not good at removing outliers. Nonlinear filters have recently received increasing attention due to their capability of reducing noise and removing outliers while preserving the trend shifts in the signals.
Very few studies have highlighted the possibilities of applying nonlinear median type filters to fault detection and isolation problems. Nounou and Bakshi [5] used FIR median hybrid (FMH) filter [6] to de-noise chemical process control signals. Ganguli [4] used subfilter weighted FMH filters to de-noise gas turbine health signals. Manders et al. [2] used a median filter of length five to de-noise temperature data for monitoring the cooling system of an automobile engine having installed thermocouples and pressure sensors. Some researchers have also used wavelet based methods for noise removal [7].
The use of median filters is motivated by two intrinsic properties: edge preservation and efficient attenuation of impulse noise [8]. Weighted recursive median (WRM) filters are a modified version of median filters that can achieve much more noise suppression than a standard median filter in the same number of operations [9]. However, unless the weights of the WRM filters are suitably optimized to minimize some error measure, they tend to create blurring artifacts on the output.
Neural networks are a powerful soft computing tool, which can be used for signal processing. Neural networks like feed forward networks based on multi layer perceptron (MLP) are universal function approximators, which can be used for filtering. However, training MLP networks based on backpropagation learning is computationally expensive. Radial basis function (RBF) neural networks also share the universal approximation capability and take much less training time [10], [11]. The corrupting noise in measured data arises from a nonlinear low dimensional dynamical system. The design of RBF network is a curve-fitting (approximation) problem in a high dimensional space and the learning is equivalent to finding a surface in a multidimensional space that provides a best fit to the training data. The normalized Gaussian radial basis function network can be used to model the nonlinear noise [12]. RBF filtering is basically a nonlinear mapping to transform a difficult nonlinear filtering problem into an easier one that involves linear filtering.
In this paper, we develop WRM and RBF filters for noise removal in damage indicator time series consisting of frequency measurements on a helicopter rotor blade. It is shown that the application of genetic algorithm to develop the optimal WRM filter considerably improves its performance and removes the shortcoming associated with the un-weighted RM filter. In addition, the use of a radial basis neural network as a filter offers much better performance than traditional linear filters. The present study therefore applies soft computing methods to develop novel filters for use in operational health monitoring.
Section snippets
Health monitoring problem
A schematic of the damage detection process is shown in Fig. 1. Measurements are taken at regular intervals from the physical system using judiciously placed sensors. Typically, difference between the time series of the damaged and undamaged system is very difficult to detect by eye. In addition, a large amount of data is often measured and needs to be condensed to extract the features, which are useful for damage detection. Therefore, the measurements are often subjected to signal processing
Radial basis function neural network
The radial basis function network (RBFN) model consists of three layers: an input layer, a hidden (kernel) layer and an output layer, as shown in Fig. 3. The nodes within each layer are fully connected to the previous layer. The input variables are each assigned to a node in an input layer and pass directly to the hidden layer without weights. The hidden nodes or units contain the RBF, also called transfer functions.
An RBF is symmetrical about a given mean or center point in a multidimensional
Weighted recursive median filters
Standard median (SM) filters are a popular class of nonlinear filters and have been used for a long time for removing impulsive noise while preserving sharp edges in signals [8]. A N-point SM filter takes N points surrounding the central point and gives their median as the output, i.e., if xk denotes the input signal, then the output of the median filter isHere N = 2n + 1 is the window length of the filter. Since the median does not cause much blurring to
Genetic algorithm based weighted recursive median filter design
We use a five point weighted symmetric recursive median filter as a starting example in this study. Filter of greater length are studied later. Consider a five-point WRM filter with symmetric weightsThe above filter needs five points: the current point, two forward points and two backward points. Since it needs two forward points, it has a two-point time delay. Choosing longer filters may lead to greater noise reduction but the number of forward
Numerical results
The objective of this study is to develop and test a filter for damage detection applications and so an exact simulation of the damage growth is not required. Therefore, we assume different polynomial variations in the damage indicator such as frequency over time to show the effectiveness of the WRM and RBF filter. These range from stationary or constant signals to linear and quadratic variation and the highly nonlinear signal of a step edge. Three test signals are used in this study. Gaussian
Conclusions
Soft computing methods are used in this work to design filters for improved operational health monitoring. A weighted recursive median filter is developed in this study with optimal integer weights for a signal with linear variation embedded with Guassian noise. A genetic algorithm is used to solve the multimodal optimization problem for the integer design variables. A radial basis function neural network filter is developed using a clustering approach. The filters are illustrated for a
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