The Math of Random Signals, Fatigue Damage, Vibration Tests

سرفصل های دوره

The Math of Reliability Engineering, Fatigue Damage, and its Interesting Applications in the World of Vibration Tests.

1. The mathematics of Fatigue Damage

1.1 Pesaresi PhD dissertation.pdf

1. Introduction to the course

2. Joint Gaussian Distribution

3. Probability Distribution of the Envelope of a Gaussian Signal (Rayleigh distrib)

4. Mathematical Definition of Fatigue damage

5. Formula for the Expected number of Positive Peaks

6. Power Spectral Density, Standard Deviation of a Random Process & its Derivatives

7. Relating the Fatigue Damage Spectrum to the Power Spectral Density

8. Practical Explanation on How to Calculate the Fatigue Damage Spectrum

9. Maximum Response Spectrum

2. Applications of the theory of Fatigue Damage

1. Practical use of the theory of Fatigue Damage

2. Algorithms for the Calculation of the Power Spectral Density

3. How to Create Non-Gaussian Signals with a Prescribed Fatigue Damage Spectrum

4. Application Synthesis of Non-Gaussian Signals with a Prescribed Fatigue Damage

5. Application of the Maximum Response Spectrum

3. How the distribution of a Gaussian signal or sinusoidal signal occurs in nature

1. How the Central Limit Theorem Arises from Stochastic Processes

2. Integral of Even Powers of Sinusoids

3. Some Representations of the Bessel function of Order Zero

4. Probability Density of a Sinusoid

5. Distribution of a Sinusoid Derived Intuitively

6. Why a Random Signal with Uniformly Distributed Phases is Gaussian

4. Sine on Random Vibrations

1. Probability Density of the Envelope of Gaussian Noise + a Deterministic Sinusoid

2. Calculating the Damage caused by Sine on Random Signals

5. Appendix on Fourier series and Fourier Transforms

1. Introduction to Stochastic Processes

2. Derivation of the Properties of a Linear System

3. Properties of the Fourier Transform of a Real Time Signal

4. Fourier Series Representation of the Output of a Linear System

5. Another Useful Representation of the Fourier Series

6. Recalling the Relationship Between the Fourier Series and the Fourier Transform

6. Appendix on Ordinary Differential Equations

1. Solution to 2nd order ODE (ordinary differential equations)

7. Appendix on Random Variables and the Central Limit Theorem

1. Sterlings Formula

2. How the Binomial Distribution Converges to the Gaussian One

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تولید کننده: Udemy-Training