CC BY
52Electronic Journal «Technical Acoustics» http://www .ejta.org
2008, 1
S. Ramji*,f, G. Lathaf, S. Ramakrishnan*
INational Institute of Ocean Technology, NIOT Campus, Pallikaranai, Chennai - 601 302,
Tel: +91-44-66783399, Fax: +91-44-66783405, [email protected], [email protected] *Department of Instrumentation engineering, M.I.T Campus, Anna University, Chennai-44, Tel: +91-44-22516232, Fax: +91-44-22232403, [email protected]
Modeling and simulation of underwater high frequency noise spectrum using artificial neural networks
Received 07.09.2007, published 14.01.2008
In this work, estimation of high frequency underwater ambient noise spectrum carried out using neural network is reported. The periodic ambient noise data were measured at 5 m depth in Bay of Bengal using omni directional hydrophone. The data were acquired using portable, broadband high frequency data acquisition system. The noise level at high frequencies in the range of 5 kHz to 12 kHz was analyzed for the entire data set (N=100). The influence of wind speed covering a rage of 2.5 m/s to 9 m/s and wave height in the range of 0.2 m to 2 m were used for the analysis. Feed Forward Neural Network architecture using LevenbergMarquardt (LM) algorithm was employed and the network model obtained after training was used to estimate the noise level. Analysis of experimental data reveals that the noise level decreases with increase in frequency for the observed range of frequencies. The noise level increases with increase in wind speed and the variations were found to be non linear in nature. Similar observation was recorded for the considered range of wave height. Further it appears that the proposed method is useful in the estimation and interpolation of underwater Noise Spectrum Level (NSL) for the considered frequency range and it is observed through Mean Squared Error analysis. As the underwater measurements are often inhospitable due to the remote oceanic regions and conditions, these studies seems to be relevant. In this work, the objectives, experimental arrangement, data acquisition, neural network based modeling and analysis are presented in detail.
Keywords: Feed forward Neural Network (FNN); Ambient noise; Noise Spectrum Level (NSL); Bay of Bengal; Mean Squared Error (MSE).
INTRODUCTION
Ambient noise in the ocean spans at least five decades in the frequency domain and is the product of a plethora of sources, both natural and anthropological. It includes geological disturbances, non-linear wave-wave interaction, turbulent wind stress on the sea surface, shipping, distant storms, sonars and seismic prospecting, marine animals, breaking waves and spray, rain and hail impacts and turbulence [1]. The noise level is a measure of intensity and is calculated as the RMS pressure of a plane wave relative to a reference pressure of 1 ^Pa in 1 Hz frequency bands across the spectrum [2]. It is dominated by wind over a significant frequency band compared to other noise sources such as ship, rain, biological and human
activities [3] and hence noise received at a hydrophone is the spatial average of the distributed sources and consequently the spatial average of the effect of the wind speed [4].
There are many models obtained by different authors for wind dependency at various frequency ranges. From the earlier studies [5, 6, 7], it is shown that the relationship between the noise levels is assumed to be linear in the logarithm of the wind speed. It is also reported that the noise level difference dependence over various wind speeds was due to the change in the phenomena of noise generation at different wind speeds. While these studies explained the relation of noise level with wind speed and wave by expression, considerable variability was observed in the coefficients and hence in the estimation [8].
Feed forward Neural Networks (FNN) is an approximation model that can be trained by examples to implement a desired input-output mapping and interpolation [9]. Owing to its adaptive and parallel processing ability owned, it has been applied to many fields such as sonar signal processing [10] and automatic target recognition [11]. In order to carry the detection procedure, neural network needs to be trained. During training, samples are presented to the input layer that yield changes of the activation state of output processing elements. The calculated output value is compared to the required value or the target value given during the process. The network adjusts synaptic weights based on the difference between the required and calculated output values and this distribution constitutes the basis of the problem-solving algorithm. As neural network models are more robust than the regression models, a well-trained network is possible to minimize the error of the prediction values and can provide very accurate results by adjusting the weights [12].
In this work an attempt has been made to simulate the noise level for the frequency band from 5000 Hz to 12000 Hz using FNN by training the neural network with experimental data.
1. METHODOLOGY
1.1. Data Collection
Noise measurements were made using two calibrated omni directional hydrophones mounted in a vertical array at 5 m depth. The hydrophone was suspended from the measurement platform using the rope and mounting arrangement that links to the rope. The hydrophone has a receiving sensitivity of -170 dB over a wide frequency range 0.1 Hz to 120 kHz. The data were acquired at a rate of 200 kHz, filtered and digitized with portable data acquisition system with 12-bit resolution. During the period of data collection all machinery on the ship were switched off and the recording system was powered by battery. The wind speed was simultaneously measured during each sampling.
1.2. Implementation of FNN
The Feed forward Neural Network (FNN) with the architecture having three hidden layer and that operates on log sigmoid transfer function has been employed for the simulation of underwater Noise Spectrum Level (NSL) for the considered bandwidth. This network has number of simple neuron-like processing units organized in layers [13]. Each unit in a layer is connected with all the units in the previous layer. The weights on these connections encode the knowledge of a network. Data enters at the input and passes through the network, layer by
layer, until it arrives at the output [14]. The parameters of a network were adjusted by training the network on a set of reference data called training set with wind speed and wave height as input and Noise Spectrum Level (NSL) for the corresponding input as output. Training of the network was performed under back propagation of the error. The trained network were then be used to estimate the Noise Spectrum Level (NSL).
Figure 1 illustrates the architecture of one-hidden-layer feed forward neural network with
x1...xn as inputs and y as output. Each arrow in the figure symbolizes a parameter in the
network. The network is divided into input, hidden and output layers. The input layer consists of just the inputs to the network and is then followed by a hidden layer or hidden units placed in parallel. Each neuron performs a weighted summation of the inputs and then passes a nonlinear activation function (a). The hidden units in this network are free to construct their own representations of the input [13, 14].
Figure 1. Architectural representation of feed forward neural network
Mathematically the functionality of a hidden neuron is described by
( n \
a X wsxj + bj , (1)
V j=1 )
where the weights {w j, bj} are symbolized with the arrows feeding into the neuron.
The number of output neurons equals the number of outputs in the approximation problem. The output of this network is given by
nh ( n ^
7(0) = q(0, x) = £w]a X w^Xj + b), + j2 (2)
i=1 V j=1 y
where n is the number of inputs and nh is the number of neurons in the hidden layer.
The variables {w]J,b]1, wi2, j2} are the parameters of the network model and were
represented collectively by the parameter vector 0 The size of the input and output layers are defined by the number of inputs and outputs of the network and therefore only the number of hidden neurons has to be specified when the network is defined [14]. In training the network, its parameters are adjusted incrementally until the training data satisfy the desired mapping.
The nonlinear activation function of the network is usually a smooth step function. In the
present study log sigmoid function is used and is represented as [13, 14]:
Sigmoid (x) = 1 + g (x) (3)
The spectrum was calculated using Welch’s [15] method of averaging periodogram. The Noise Spectrum Level (NSL) thus obtained in dB was tabulated against the wind speed and wave height for the frequency band of 5000 Hz to 12000 Hz. The ANN used in this work were implemented using MATLAB® 6.5.1 neural network toolbox (version 4.0).
2. RESULTS AND DISCUSSIONS
For the present study, 100 sets of data, collected from the shallow waters in Bay of Bengal with wind speeds ranging from 2 m/s to 8.5 m/s and wave height ranging from 0.5 m to 1.5 m were considered. Recordings showing the evidence of noise from non-wind and wave dependent sources such as rain, dolphin and ship were not included in the study. The ambient noise spectrum plot, which depicts the variation of Noise Spectrum Level (NSL) for the different wind speeds, is shown in Figure. 2. It is seen that the noise level is higher for low frequency of the band and decreases with increasing frequencies. Also the variation in noise level is found to be higher for higher frequencies of the considered frequency range and the correlation between the noise level and wind speed decreases with increasing frequencies.
FNN is trained using the experimental data with wind speed and wave height as input and noise spectrum values for the corresponding input as output vector. Out of 100 experimental data sets, 80 sets were used for training and the remaining sets were used for validation. Simulation of noise spectrum was done after training the FNN and the simulation results were compared with the experimental values of noise spectrum. The simulated noise spectrum values are in good comparison with the actual values. The typical plot showing the comparison between Noise Spectrum Level (NSL) of test values and neural network simulated values for wind speed 4 m/s and 8.5 m/s are shown in Fig. 3 and Fig. 4 respectively. It is seen that the noise level deviation between the test values and neural network simulated values is less for the lower wind speeds where as the variation is found to be large for higher wind speeds. The deviation is observed to be less in the lower frequency region of the considered range for all wind speeds.
Mean Squared Error (MSE) was computed for different wind to analyze the performance of the simulation and the results are tabulated in Table1. It is seen that the simulation results are in close agreement with the experimental values with an MSE of 1.1 dB at 2.5 m/s wind speed. Also the difference between the noise level from simulation results and experimental values are found to be higher in the higher frequency range. The MSE was observed to be increasing with the increasing wind speed. It is evident from the result that the simulated values are in agreement with the test values for lower wind speeds. The variation increases with wind speed and it reaches 4.9 dB for the wind speed of 8.5 m/s.
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10000 Frequency (Hz)
12000
Fig. 2 Spectrum plot for different wind speeds
Frequency (Hz)
Fig. 3 Typical comparison plot of noise level form simulation and experiment at 4 m/s
Frequency (Hz)
Fig. 4 Typical comparison plot of noise level form simulation and experiment at 8.5 m/s
Table 1. Mean Squared Error (MSE)
Sl. No Input parameters MSE, dB
wind speed, m/s wave height, m
1 2.5 0.94 1.1
2 5.5 0.93 3.7
3 8.5 1.02 4.9
CONCLUSIONS
Detection of acoustic signals in the ocean is performed against noise background, which is more dominated by wind speed and wave height in the low frequency band, in the range 5000 Hz to 12000 Hz. It has been shown that the relationship between noise intensity and wind speed is of the form P = Un, where P is the sound pressure, U is the wind speed in m/s and n is constant. Earlier studies have reported that the noise level parameterized with wind speed using the relation gave irregular behavior and this was attributed to the wave height. In this work, the noise level for the frequency band from 5000 Hz to 12000 Hz is simulated using FNN by training the neural network using experimental data with wind speed and wave height as input and noise spectrum values for the corresponding input as output vector. Analysis of experimental data reveals that the noise level increases with wind speed and the variation of noise level is not linear with wind speed for every frequency. It is also shown that the noise level is higher for low frequency of the band and it decreases with the increasing frequency. Further comparison between simulated noise levels for different wind speed with the experimental data for the considered bandwidth shows close agreement for the lower wind speeds and the deviation increases with the wind speed. This is supported by analyzing the MSE values obtained for different wind speeds. The proposed method of simulation could thus be used to predict the noise level beforehand with the knowledge of the wind speed and wave height, using which the Signal-to-Noise Ratio of the underwater acoustic instruments can be enhanced dynamically. However, an efficient algorithm based simulation model with network trained with more possible input parameters could further be useful for accurate simulation of underwater ambient noise.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge the support extended by Naval Research Board, Government of India, in funding this research. The authors thank G. Raguraman, A. Thirunavukkarasu and G. Velu for their help in measuring the ambient noise. The authors thank the National Data Buoy Program of National Institute of Ocean Technology, for providing met-ocean data from data buoy in the region of interest.
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