Algorithms for spectrum background estimation of non-stationary signals


Monitoring the health state of rotating machinery components is one fundamental way of enhancing their efficiency, operations and longevity and is a critical aspect of condition-based maintenance. Vibration signal analysis is one of the commonly used techniques to monitor the conditions of the rotating components. The vibration signals propagate through the transfer function that responsible for distorting the signal shape, hence complicating the diagnosis procedure. The spectrum background, henceforth referred to as the background, is often characterized by slow variations of the spectrum. The background resamples the transfer function magnitude because the background contains noise that propagate via the transfer function.

Accurate spectrum background estimation is an important step in the application of vibration-based condition-based maintenance. It can be applied in the pre-whitening process to benefit the mitigation of the effects of the transfer function on the vibration signal and also the identification of the critical machine structural variations. It emphasizes defect manifestation in the vibrations by separating the structure effects from discrete frequencies to reduce its related impact on the vibration analysis.

Despite the availability of several background estimation methods, most of them are suitable for estimating stationary signals and not non-stationary signals. Similarly, various techniques for background estimation of non-stationary signals like estimation of the background in the order domain have several drawbacks that comprise their practical applications. To this note, Mr. Omri Matania, Dr. Renata Klein led by Professor Jacob Bortman from Ben-Gurion University of the Negev developed a much more robust method for estimating the spectrum background of non-stationary signals. Their work is currently published in the journal, Mechanical Systems and Signal Processing.

In brief, the background was defined as the spectrum expectation without considering the contributions of the discrete frequencies of the rotating machine components. The research team started by exploring the abilities and limitations of the existing methods and addressing the to propose two new algorithms for improved performance. Lastly, the performance and feasibility of these algorithms were compressively studied using a large database containing about 2000 vibration signals. These signals comprised measured transfer functions on various rotating machines and simulated data of machine components rotating at different speeds and profiles that included exponential, linear and random fluctuations in the range 0.01 – 10 Hz/s representing different non-stationarity levels.

The authors demonstrated the feasibility of the two algorithms: time-frequency background estimation (TFBE) and cycle-order background estimation (COBE). TFBE used the time-frequency spectrogram to filter the discrete frequencies and was recommended for unknown rotational speeds. It used the 50% percentile in each slice of the spectrogram to estimate the background. On the other hand, COBE used Dephase to filter the synchronous signals and filtered the semi-synchronous signals by using separate segments in the cycle domain. The results were reconstructed back in the time domain while the background was estimated in the frequency domain with the help of other techniques like adaptive clutter separation. COBE was recommended for known rotation speeds. Rotation speed was the main factor influencing the accuracy of these algorithms in estimating the background of the vibration signals. Rotational speeds up to 10 Hz/s provided good background estimations. COBE and TFBE had errors up to 3 dB and 5 dB, respectively.

In summary, scientists of PHM-BGU laboratory of Ben-Gurion University developed two algorithms for improving the estimation of the spectrum background of non-stationary signals. Their performance was evaluated and compared to those of existing techniques. For the simulated signals, COBE outperformed TFBE and other existing methods for all the considered rotational speed profiles due to the benefits of the known rotational speeds. Furthermore, COBE and TFBE performed better than existing methods for all the tested non-stationary signals. In a statement to Advances in Engineering, Professor Jacob Bortman, the lead and corresponding author explained that the newly proposed algorithms are fundamental tools for improving the health monitoring of rotating components.

Algorithms for spectrum background estimation of non-stationary signals - Advances in Engineering

About the author

Jacob Bortman is currently full Professor in the Department of Mechanical Engineering and the Head of the PHM Lab in Ben- Gurion University of the Negev. Retired from the Israeli Air Force as Brigadier General after 30 years of service with the last position of the Head of Material Directorate. Chairman and member of several boards: Director of Business development of Scoutcam Ltd, Chairman of the board of directors, Selfly Ltd., Board member of Augmentum Ltd., Board member of Harel Finance Holdings Ltd., Chairman of the board of directors, Ilumigyn Ltd. Member of the committee for “The National Initiative for Secured Intelligent Systems to Empower the National Security and Techno-Scientific Resilience: A National Strategy for Israel”. Editorial Board member of: “Journal of Mechanical Science and Technology Advances (Springer, Quarterly issue)”. Member of: BINDT – The British Institute of Non-Destructive Testing, Head of the Israeli Organization for PHM, IACMM – Israel Association for Comp. Methods in Mechanics, ISIG – Israel Structural Integrity Group, ESIS – European Structural Integrity Society. Received the Israël National Defense prize for leading with IAI strategic development program, Outstanding lecturer in BGU, The Israeli Prime Minister National Prize for Excellency and Quality in the Public Service – First place in Israel. Over 80 refereed articles in scientific journals and in international conferences.

About the author

Omri Matania is currently a Ph.D. candidate in BGU-PHM LAB in the department of mechanical engineering in Ben- Gurion University of the Negev, under the supervision of Prof. Jacob Bortman. Omri Matania is a Talpiot graduate and served nine years in IDF in several roles including algorithm section leader. He completed with honors his bachelor’s degree in mathematics and physics in the Hebrew University of Jerusalem and completed his master’s degree with honors in mechanical engineering in Ben- Gurion University of the Negev.

About the author

Dr. Renata Klein received her B.Sc. in Physics and Ph.D. in the field of Signal Processing from the Technion, Israel Institute of Technology. In the first 17 years of her professional career, she worked in ADA-Rafael, the Israeli Armament Development Authority, where she managed the Vibration Analysis department. Since then, she focused on development of vibration based health management systems for machinery. She invented and managed the development of vibration based diagnostics and prognostics systems that are used successfully in combat helicopters of the Israeli Air Force, in UAVs and in commercial jet engines. Renata is a lecturer in the faculty of Aerospace Engineering of the Technion, and in the faculty of Mechanical Engineering in Ben Gurion University of the Negev. Renata is the CEO and owner of R.K. Diagnostics, providing R&D services and algorithms to companies who wish to integrate Machinery Health diagnostics and prognostics capabilities in their products. In the recent years, she has supervised MSc and PhD students and co-managed the PHM Lab in Ben Gurion University of the Negev, jointly with Prof. Jacob Bortman.


Matania, O., Klein, R., & Bortman, J. (2022). Algorithms for spectrum background estimation of non-stationary signalsMechanical Systems and Signal Processing, 167, 108551.

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