This article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. Also an efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet.The energy values of the Wavelet transform are compared with the power spectrum of the Fourier transform. Useful definitions for power spectra are given.The focus of the work is on simple measures to evaluate the transform with the Morlet wavelet in an efficient way. The use of the transform and the defined values is shown in some examples.

This work addresses the response functions for infinite beams and plates with af orce excitation at the origin of the coordinate system and its application to time reversal and time frequencya nalysis. The response function for Euler-Bernoulli beams is derivedand for plates revisited. Interpretation concerning energy conservation and mobility are given. An possible alternative method to measure the coupling loss factors in SEA is sketched. The impulse response of afi nite beam is measured in an experiment and compared with that predicted theoretically.T he experimental data before the first reflection of the pulse showed good agreement with the theory. The response function is used to simulate at ime reversed pulse. This numerical simulation is verified with an experiment.

The work addresses the definition of a wavelet that is adapted to analyze a flexural impulse response of a beam or plate that can be modeled with the Euler-Bernoulli bending theory. The wavelet gives the opportunity to directly analyze the dispersion characteristics of a pulse. The aim is to localize a source or to measure material parameters. An overview of the mathematical properties of the wavelet is presented. An algorithm for the optimal extraction of the dispersion characteristics with the use of genetic algorithms is outlined. The application of the wavelet is shown in an example and experiment.

Objective and Scope Analysis of operational plant data needs experts in order to interpret detected anomalies which are defined as unusual operation points. The next step on the digital transformation journey is to provide actionable insights into the data. Prescriptive Maintenance defines in advance which kind of detailed maintenance and spare parts will be required. This paper details requirements to improve these predictions for rotating equipment and show potential to integrate the outcome into an operational workflow. Methods, Procedures, Process First principle or physics-based modelling provides additional insights into the data, since the results are directly interpretable. However, such approaches are typically assumed to be expensive to build and not scalable. Identification of and focus on the relevant equipment to be modeled in a hybrid model using a combination of first principle physics and machine learning is a successful strategy. The model is trained using a machine learning approach with historic or current real plant data, to predict conditions which have not occurred before. The better the Artificial Intelligence is trained, the better the prediction will be. Results, Observations, Conclusions The general aim when operating a plant is the actual usage of operational data for process and maintenance optimization by advanced analytics. Typically a data-driven central oversight function supports operations and maintenance staff. A major lesson-learned is that the results of a rather simple statistical approach to detect anomalies fall behind the expectations and are too labor intensive. It is a widely spread misinterpretation that being able to deal with big data is sufficient to come up with good prediction quality for Prescriptive Maintenance. What big data companies are normally missing is domain knowledge, especially on plant critical rotating equipment. Without having domain knowledge the relevant input into the model will have shortcomings and hence the same will apply to its predictions. This paper gives an example of a refinery where the described hybrid model has been used. Novel and Additive Information First principle models are typically expensive to build and not scalable. This hybrid model approach, combining first principle physics based models with artificial intelligence and integration into an operational workflow shows a new way forward.

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