Allows adjustment of the pdf probability density function. Generating nongaussian vibration for testing purposes. Statistical characterization of acceleration levels of random. Problems with using kurtosis in random vibration testing. Pdf a new practical and intuitive method for kurtosis. Random variables that have a negative kurtosis are called subgaussian, and those with positive kurtosis are called supergaussian.
Katsuhiko saito transport packaging laboratory, kobe university abstract random vibration tests for packaging are conducted to confirm safety during shipping by truck. The random vibration is stationary if these statistical properties remain constant with time. For these distributions, the pdf can be described as a continuous function of the amplitude, x, and plays a significant role in understanding random vibration analysis. Random vibration is desireable for package testing because this type of motion occurs in the real world. Key words kurtosis control, gaussian amplitude distribution, random vibration. A method for generating random vibration using acceleration kurtosis and velocity kurtosis daichi nakai sankyu inc. Random vibration testing with kurtosis control by ifft phase. The fourth moment is called the kurtosis and it measures the highg. Nongaussian random vibration testing with kurtosis control is considered in the paper as a way of introducing realistic high peaks into shaker drive signals, thereby increasing the excitation. The moment method is based on the definitions of kurtosis for distributions. Amplitude level rms need a third knob to adjust the kurtosis.
That third dimension is kurtosis control, which matches the amplitude distribution of the test to that of the environment. One reason for this difference is the shock caused by road roughness. A new practical and intuitive method for kurtosis control in random vibration testing jinyi zhang 1. Also, this is the typical maximum peak seen on a kurtosis 3 random test. Random vibration an overview by barry controls, hopkinton, ma abstract. Kurtosis control in vibration testing crystal instruments. A method is presented here for generating time histories that are realizations of a zero mean, nongaussian random process with a specified spectrum, skewness, and kurtosis. The pdf shown in figure 8 conveys the probability of the signal. It is a constantly changing vibration, and best described in a power spectral density psd curve. Calculation of kurtosis in the sliding window of a pulse signal advantages kurtosis can be assimilated with a shape factor.
Realworld random vibration environments, however, may have kurtosis value greater than 3. This would be the case if transient pulses or highsigma peaks appeared on the random time history data. Also, this is the typical maximum peak seen on a kurtosis3 random test. Starting from fundamental vibration and fatigue damage concepts, kurtosis control on an electrodynamic shaker is found to be an inefficient, poorly defined, and nonportable method for. Estech may 2006 what is missing on shaker controllers. Grms rootmeansquare is calculated by taking the square root of the area under the psd curve. For normally distributed random noise, the kurtosis will be 3. In the automotive world, this arises from changes in road surface quality and vehicle speed. Kurtosis in vibration analysis by tom irvine email.
A psd plot presents random vibration as an average intensity. The pdf of a random variable x can be transformed to the pdf of a different. In this study, a kurtosis response spectrum was proposed, which is an. Vibration research recently introduced random vibration control based on a variable kurtosis distribution. Nonstationary random vibration by tom irvine automobile example. Kurtosis control is widely touted as a way to increase the damage content of a random vibration test without changing the. When using software to compute the sample kurtosis, you need to be aware of which convention is being followed.
The goal is to simulate real life environments and test the product to make sure it will function properly and. Pdf a new practical and intuitive method for kurtosis control in. Vibration analysis for condition assessment and fault diagnostics. Join steve hanlys webinar to gain a better understanding of shock and vibration analysis. The kurtosis for a time seriesyi is kurtosis 4 n i 1 4 i n y. Review of vibration analysis methods for gearbox diagnostics and prognostics mitchell lebold, katherine mcclintic, robert campbell, carl byington, and kenneth maynard applied research laboratory the pennsylvania state university p.
Components, apparatus, and passengers of ground and flight vehicles in steady motion, which constitutes most inservice operations, are subjected to random vibration excitations. A random vibration controller sometimes called a shaker controller is a piece of equipment that produces random vibration as prescribed by the frequency domain levels the psd profile, for power spectral density. The effects of kurtosis are illustrated using a parametric family of distributions whose kurtosis can be adjusted while their lowerorder moments and cumulants remain constant. Random vibration analysis is usually performed over a large range of frequencies from 20 to 2,000 hz, for example. Random vibration tests for packaging are conducted to confirm safety during shipping by truck. Random testingthe most common and widely used probability distribution in statistical analysis is the normal or gaussian distribution function. Fft or fast fourier transformer vibration analysis uses a fft to pull data from the time waveform then inputs to a discrete fourier transform dft, a mathematical process or algorithm that transforms a waveform into the components to a frequency spectrum of the input signal from the time waveform. Pdf experimental simulations of random vibrations are important for automotive and aerospace component testing. On the meaning and use of kurtosis columbia university. Which definition of kurtosis is used is a matter of convention this handbook uses the original definition.
Kurtosis and density crossings figures 2 and 3 show a basic characteristic of dis. Such a study does not look at a specific frequency or amplitude at a specific moment in time but rather statistically looks at a structures response to a given random vibration. Because realworld vibrations are not sinusoidal, sine testing has a limited place. On the response of a nonlinear structure to high kurtosis. Normal distribution the first histogram is a sample from a normal distribution. Grms is used to define the overall energy or acceleration level of random vibration. The perceived advantages, disadvantages, and the role each of these techniques may play in the diagnosis of safety critical failure modes is discussed. It is common to apply random vibration excitation to a product with an electrodynamic or hydraulic shaker system. The following example shows histograms for 10,000 random numbers generated from a normal, a double exponential, a cauchy, and a weibull distribution. Random vibration kurtosis control vibration research. This work presents two novel algorithms to effectively control kurtosis in random. Kurtosis control algorithms include many more peak accelerations in the vibration test than are.
Vibration research corp increased kurtosis higher peaks crest factor. Kurtosis control, gaussian amplitude distribution, random vibration testing. Random forcing function and response vibrationdata. Shaker simulation of random vibration with a high kurtosis value. Jun 20, 2011 kurtosis topic in descriptive statistics the video is part of the eureka project a seniorsteachingjuniors learning project by jalnidh kaur, gaurav poddar and devika bhalla second year. Many sources use the term kurtosis when they are actually computing excess kurtosis, so it may not always be clear. The paper proposes a single mathematical model that. The resulting probability density function would then. Steinwolf 1997 shaker simulation of random vibration with a high kurtosis value. Hence, many studies have been conducted to improve random vibration testing. Free webinar on problems with using kurtosis in random. Kurtosis is a statistical indicator used to characterise the.
Shaker simulation of random vibration with a high kurtosis. I am able to visualise the distribution of a specific record using the code from the top answer in skew normal distribution in scipy but i am not sure how to apply a kurtosis value to a distribution. Sep 23, 2016 kurtosis the missing dashboard knob introduction vibration kurtosis the missing dashboard knob. These peaks could, for example, represent a transient event. Ofrequency content power spectral density psd oamplitude level rms need a third knob to adjust the kurtosis oallows adjustment of the pdf probability density function. Probability density function for a normal distribution.
Vibrationview syllabus 2014 background increasing the kurtosis of a random vibration test improves the realistic nature of random testing. Two methods for random shaker testing with low kurtosis. Key words kurtosis control, gaussian amplitude distribution, random vibration testing, reliability. There is some confusion about the various tests available to the vibration testing engineer.
Index terms random vibrations, rms distribution, weibull distribution. For most but not quite all nongaussian random variables, kurtosis is nonzero. If excess is selected, then the value of the kurtosis is computed by the moment method and a value of 3 will be subtracted. Random vibration controllers have 2 basicrandom vibration controllers have 2 basic knobsknobs. The classic ifft technique for simulating random vibrations on shakers does not take into account any other characteristics of random signals except the psd. Shock and vibration response spectra course unit 5. Another class of high kurtosis random signals is made of nonstationary processes. Sep 16, 2008 thus, there is a need for a system and method for simultaneously controlling both the frequency spectrum and the kurtosis of a random vibration such that each can be controlled independently of the other, and where the amplitude and phase of the psd retains the full randomness typical of current gaussian random vibration control methods.
In probability theory and statistics, kurtosis from greek. Synthesis of vibration signals with prescribed power spectral. The principal characters describing nongaussian pdf fea tures are skewness l and kurtosis g. Random vibration tests are an efficient way to simulate the mechanical vibratory. The spectrum is defined and fully controlled just like in traditional random tests with no change as a result of adjusting the kurtosis. System and method for simultaneously controlling spectrum and.
On the response of a nonlinear structure to high kurtosis non. As john van baren, the company president, stated, a newly developed kurtosis control distributes the random data at higher kurtosis levels while maintaining the same testing profile and spectrum attributes. Thus, kurtosis is zero for a gaussian random variable. On the other hand, they may simply represent random vibration which has a probability density function which departs from the gaussian ideal. The fatigue damage spectrum shows the increasing fatigue damage across all frequencies that accompany the increased kurtosis levels that. A method for generating random vibration using acceleration.
The corresponding time history usually has a normal distribution, with a kurtosis of 3. Starting from fundamental vibration and fatigue damage concepts, kurtosis control on an electrodynamic shaker is found to be an inefficient, poorly defined, and nonportable method for delivering and describing fatigue damage. Random vibration testing with crest factor limiting by kurtosis manipulation article in experimental techniques 345. Probability density function for measured field data compared with that produced by random vibration testing with and without matching kurtosis. The relevance of this work to high kurtosis random vibration testing is additionally discussed. However, there is a difference between the traditional random vibration tests and the real vibrations on the truck bed. However, there is a difference between the traditional random. Fourth moment of the probability density function pdf. Gaussian random vibrations, and therefore, it is necessary to carry out antivibration packaging design, taking into consideration the non.
Like skewness, kurtosis describes the shape of a probability distribution and there are different ways of quantifying it for a theoretical distribution and corresponding ways of. By controlling both the rms and kurtosis of the random waveform, you get more control over the probability distribution, allowing a closer match between the real world and your test lab. Kurtosis is a measure of the frequency of occurrences of large peaks in a waveform. Gaussianity characteristics and acceleration rms of the transport vibrations. Although vibration is generally of random form, it is often nonstationary. Random vibration is a well developed technology on its own and is readily available and reasonably easy to use. Deriving a random vibration maximum expected level. As noted earlier, many realworld vibrations are nongaussian, that is, have peak accelerations greater than 3x the average vibration accelerations.
Consider the pearson type vii family, which is a special case of the pearson type iv family restricted to symmetric densities. In the field of random vibration testing, a test specification is typically given in the form of a that is processed by the shaker controller via the ifft technique to construct a time history. Random vibration testing with kurtosis control by ifft. In these studies, the root mean square, power spectral density, kurtosis, and probability density of. Sinusoidal and random vibration testing primer delserro. Thus, there is a need for a system and method for simultaneously controlling both the frequency spectrum and the kurtosis of a random vibration such that each can be controlled independently of the other, and where the amplitude and phase of the psd retains the full randomness typical of current gaussian random vibration control methods. Furthermore, in contrast to kurtosis, no strict theoretical value can be defined for the crest factor of a gaussian signal because the magnitude of the largest peak depends on the length nongaussian random vibration testing with kurtosis control has been known as a way of increasing the excitation crest fac. The normal distribution is a symmetric distribution with wellbehaved tails. Kurtosis control allows the user to specify the target kurtosis of the random control signal, and the controller will adjust the amplitude distribution of the vibration to match the target. Deriving a random vibration maximum expected level revision c. A model for the statistical distribution of road vehicle. Nonetheless, kurtosis control is still currently widely employed by engineers in the nongaussian random vibration test due to its easy implementation, although there is no uniform standard to. Many test personnel have recognized that random testing, while good, has shortcomings when it comes.
For simplicity, consider that random vibration can be characterized in terms of its statistical properties, such as mean value, standard deviation, and kurtosis. Random vibration testing as used today is largely unchanged in technique since. Difficulties encountered usually center on the differences between sinusoidal vibration sine testing and random vibration testing. Development and validation of kurtosis response spectrum. Kurtosis is a statistical indicator used to characterise the pulse character of a signal. Random vibration testing with crest factor limiting by. A new practical and intuitive method for kurtosis control in random vibration testing. Kurtosis and crest factor parameters are some of these missing characteristics and it is discussed below in section 2 why it would be useful to add the kurtosis to vibration testing. Psd is not always adequate as the sole descriptor of road vehicle vibrations as the process generally tends to be. Free webinar problems with using kurtosis in random vibration testing watch a recording of the webinar now. Kurtosis control is a more effective method than traditional random vibration tests because it brings products to failure more quickly.
655 170 1309 1419 906 1019 619 1455 1047 825 946 971 353 1185 184 303 37 755 356 822 367 311 473 267 11 1435 416 630 269 655 865 539 481 56 1138 977 884 708 184 131 62 1067 511 379 592 1336 365