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Detection of the signal’s breakdown points is important for many science and engineering applications. Numerous signal processing methods have been used for this purpose. Of these, the adaptive prediction is simple and easy to implement, however; its simplicity and robustness are hindered by the required delay in the input signal. This paper introduces an efficient alternative to the adaptive prediction in the application of breakdown and inflection points’ detection. Unlike the adaptive predictor, the proposed filter doesn’t require a delay in the primary input to produce the filter’s reference input, which significantly improves the computation speed and overcome the problem of performance sensitivity to the delay value. The Normalized Least-Mean Squares algorithm was used to realize both the adaptive predictor and the proposed filter. The filters were implemented in LabVIEW system design software. The performances of the filters were studied using simulated signals and the simulation results were verified using an experimental signal. The simulation and experimental results showed that the proposed filter efficiently detects the signal breakdowns. Furthermore, the simplicity of the filter offered a significant improvement in the computation speed.

Abrupt changes in signals are characterized by the random time appearance and extremely short duration. Detection of these challenging signal events is crucial for many science and engineering applications such as in electrical systems.

The literature review reveals numerous signal processing methods that have been used for abrupt change detection such as control charts, filtered derivative algorithms, and the cumulative sum (CUSUM) algorithm [

Nevertheless, the adaptive prediction outperformed the wavelet transform methods by its simplicity in computations and implementation. In adaptive prediction, the future values of a signal are estimated based on the past values. The adaptive predictor has two inputs: the primary input; it is also known as the desired output, and a reference input, which is a delayed trace of the primary input. The adaptive predictor calculates the difference between the primary input and the filtered reference input to produce an error signal (

Based on adaptive prediction, the principle of adaptive line enhancer using the LMS and recursive LMS has been applied to the modeling of transient vibration signals in machinery operation. The success of the adaptive modeling method was demonstrated by monitoring the transient running-up process of healthy and faulty motors [

The adaptive predictor is a computational device that implements the delay by passing the values of the signal, from a previous iteration in a loop, through to the next iteration. This shift in the data points slows the computational speed. Moreover, the quality of the output is sensitive to the selection of the delay time. These limitations hinder the application of adaptive prediction in real-time measurements.

In this paper, a faster and simpler adaptive filter that doesn’t need a delayed input, to detect breakdown points is proposed.

The input signals and their configuration are crucial for determining the function and the application of the adaptive filters. To avoid the burden implied by the delayed input in the adaptive prediction, an intuitive realization of an adaptive filter is proposed, it takes the measured signal as the reference and primary inputs at the same time. This realization is explained as follows:

The measured signal can be modeled as:

where:

The subscript (e) in

If

where:

The coefficients

is minimized with respect to mean-square-error (MSE), where:

If the measured

The error signal between a signal with an event and a signal with no or smaller size event should have a large value (peak or valley) at the location of the event and ideally zero or close to zero elsewhere. The location of the event is determined by the onset of the peak or valley in the error signal. This intuitive approach of the proposed filter was named the Identical Inputs-Adaptive Filter (IAF). Using the measured signal as the reference and primary input at the same time will simplify the implementation of the filter, desensitizes the filter’s performance to the delay value selection, shorten the computation time and greatly supports the real-time application.

In this paper, the Normalized Least-Mean Squares (NLMS) algorithm is used to implement both the adaptive predictor and the IAF. The NLMS is an improved variant of the LMS algorithm, it enables a time-varying step size that results in an enhanced convergence speed and better handling of time-varying signals. The realization and mathematical formulation and of LMS and NLMS are well described in the literature, e.g. [

The NLMS update the filter coefficients as follows:

where

The adaptive predictor and the proposed IAF were implemented using LabVIEW system design software.

The first signal used in the simulation study was a sine wave with a breakdown point, shown in

The second signal was a simulation of a faulty power line, the fault starts at sample number 2052 and ends at 2053.

However, in both simulations, the amplitude of the valley in the error signal at the position of the detected points was larger when the adaptive prediction was used. The difference between the values before the breakdown point (past) and the values at the position of the breakdown (future) produces a large prediction error. On the other hand, the difference between the extremely short-duration event in the input signal, i.e. the breakdown point, and its smoothed counterpart

Signal | Filter length | Step-size |
---|---|---|

Sine | 2 | 0.013 |

Powerline | 2 | 0.1 |

in the output; produces a smaller value in the error signal of the proposed filter. This results in the lower amplitude of the peak or the valley, however; it is not a limitation since the amplitude is large enough to detect.

The robustness of the proposed method in a noisy environment was investigated. A Gaussian white noise of a 0.15 standard deviation was added to the sine wave used in the first simulation, the result is given in

onset of the breakdown point since the search starts from the valley.

The experimental signals were acquired from a system being investigated to develop a spatial velocimetry method. However, the system is still under development and the signals used in this paper were from the preliminary results. In the spatial velocimetry method, the velocity of moving particles is measured using two optical fibers, the detection of a particle passage produces two signals; one when the particle enters the field of the fiber, and the other one when the particle leaves. The system under investigation produces a signal with a rapid transition (inflection point) if the particle is larger than the distance between the two fibers. The inflection point occurs at the falling shoulder in the signal depicted in

The experimental results were in an agreement with the simulation results. The performances of adaptive predictor and the proposed filter were comparable. Simulation and experimental studies showed that the proposed filter can perform the function of the adaptive predictors, with the advantage of avoiding the delay in the reference input.

The delay in the input to produce the filter’s reference signal in the adaptive prediction introduces a delay in the computation speed of the filter. The proposed IAF proved a comparable efficiency to that of the adaptive prediction in the breakdown point detection. To demonstrate the advantage of the proposed filter, which used no delay, over the adaptive predictor; the computation times for both methods, which were implemented in a personal computer were calculated using a LabVIEW program. The results are shown in

These results show that the proposed filter is significantly faster than the adaptive predictor, it offered a substantial decrease in the computation speed by 96.8% and 97.4% in the simulation signals, and 97.3% in the experimental signal.

This significant improvement makes the proposed system more efficient in the real-time measurements and in the systems where speed and memory matter.

It was shown that the performance of the proposed Identical Inputs-Adaptive Filter in the detection of the breakdown points is comparable to that of the adaptive predictor. The proposed filter requires no delay in the input signal, which significantly improves the performance and the computation speed, and

Signal | Computation time (ms) | |
---|---|---|

Adaptive predictor | Proposed filter | |

Sine | 1.9 | 0.06 |

Powerline | 10.3 | 0.27 |

Experimental | 0.75 | 0.02 |

offers an efficient alternative for the time-consuming adaptive predictor in the real-time applications.

Mohammed, M.S.H. and Ki-Seong, K. (2017) An Identical Inputs-Adaptive Filter for the Detection of Signal’s Breakdown Points. World Journal of Engineering and Technology, 5, 232-240. https://doi.org/10.4236/wjet.2017.52018