Equivalent linearization for Poisson white noise input

Methods are developed for calculating characteristic functions and mean upcrossing rates of the response of linear systems to α-stable input processes. The methods are based on the integral and series representations of these processes. The integral representation resembles the spectral representation of wide-sense stationary processes. The α-stable processes are non-Gaussian and have no moments of order two and higher. Therefore, classical methods of linear random vibration for calculating the mean and covariance functions of the response from the corresponding functions of the input do not apply. Applications are presented to illustrate the proposed methods of analysis.     

Analogy between magnetic recording media noise and shot noise

By comparing the analyses of magnetic recording media noise and shot noise, this paper shows that a very close analogy exists between the two. It demonstrates that all the well-known results for both kinds of noise are caused by random processes that have equal probabilities in equal volumes.     

A noise model for digitized data

The paper analyzes the overall conversion error of a noisy digitizer affected by Gaussian noise at its input or generated within the digitizer itself. It is shown that, under mild conditions concerning the ratio between the input noise standard deviation and the quantization step, the overall conversion error can be modeled by a Gaussian random variable uncorrelated with the input sequence. The power of the global conversion error is evaluated in closed formulae together with its degree of variability. Numerical simulations support the proposed analysis     

飞机噪声计算通用模型研究

为完善和规范现行的飞机噪声计算方法,根据飞行航线的几何特点,基于“直线段”和“曲线段”这两个基本的航线元素提出了航线分解的思想,阐述了其基本原理,建立了系统的飞机噪声计算通用模型,并实例验证了该模型的可行性和实用性。该模型解决了实际噪声环境影响评价工作中的相关技术问题,规范了噪声计算方法,使整个评价工作更直观、更智能、更科学。     

A non-homogeneous Poisson process predictive model for automobile warranty claims

Automobile warranties and thus lifetimes are characterized in the two-dimensional space of time and mileage. This paper presents a non-homogenous Poisson process (NHPP) predictive model for automobile warranty claims consisting of two components: a population size function and a failure or warranty claim rate. The population size function tracks the population in the time domain and accounts for mileage by removing vehicles from the population when they exceed the warranty mileage limitation. The model uses the intensity function of a NHPP—the instantaneous probability of failure—to model the occurrence of warranty claims. The approach was developed to support automobile manufacturers’ process of using claims observed during the early portion (first 7 months) of vehicle life to predict claims for the remainder of coverage, typically between 3 and 5 years. This paper uses manufacturer provided warranty data from a luxury car to demonstrate the NHPP model by predicting claims for three vehicle subsystems. Warranty predictions are then compared with the actual observed values and predictions made with a standard forecasting technique.     

A physical model for predicting the thermal conductivity of brine-wetted snow

Recent measurements by Crocker (1984) have shown that the snowcover overlying young sea ice contains large quantities of salt (concentrations as high as 100 ppt). The influence of the salt, which is incorporated into the snowpack in the form of brine, on the thermal conductivity of the snow is analysed using a modified form of the physical thermal conductivity model developed by Pitman and Zuckerman (1967). The new model indicates that at snow densities commonly encountered in young sea ice, the presence of the brine increases the thermal conductivity of the snow by up to 50%. When the thermal conductivities predicted by the model are input into an ice-growth model, better association between observed and predicted ice growth (on Resolute Passage, North West Territories, 1982) is obtained than with any of the empirical thermal conductivity formulae tested.     

一种模拟人耳实现噪声分类的方法

声品质主观评价方法中有基于成对比较的参考评分法,该方法在等级评分之前需要首先利用成对比较法对声音样本进行排序,设立参考噪声。该过程比较繁琐,劳动强度较大。提出通过建立人耳模型,对噪声样本按照声品质的不同属性实现粗略的分类排序,省去原方法中排序这一步骤,直接在每一类中设立参考噪声进行等级评分。选取燃料电池汽车8种行驶工况,24个噪声样本为例,介绍说明该方法的原理及有效性。     

A model for phase noise generation in amplifiers

In this paper, a model is presented for predicting the phase modulation (PM) and amplitude modulation (AM) noise in bipolar junction transistor (BJT) amplifiers. The model correctly predicts the dependence of phase noise on the signal frequency (at a particular carrier offset frequency), explains the noise shaping of the phase noise about the signal frequency, and shows the functional dependence on the transistor parameters and the circuit parameters. Experimental studies on common emitter (CE) amplifiers have been used to validate the PM noise model at carrier frequencies between 10 and 100 MHz     

A macroscale model for low density snow subjected to rapid loading

A Capped Drucker–Prager (CDP) model was used to simulate the deformation-load response of a low density (150–250 kg/m³) snow being loaded at high strain rates (i.e., strain rates associated with vehicle passage) in the temperature range of −1 to −10 °C. The range in the appropriate model parameters was determined from experimental data. The model parameters were refined by running finite-element models of a radially confined uniaxial compression test and a plate sinkage test and comparing these results with laboratory and field experiments of the same. This effort resulted in the development of two sets of model parameters for low density snow, one set that is applicable for weak or “soft” snow and a second set that is representative of stronger or “hard” (aged or sintered) snow. Together, these models provide a prediction of the upper and lower bound of the macroscale snow response in this density range. Furthermore, the modeled snow compaction density agrees well with measured data. These models were used to simulate a tire rolling through new fallen snow and showed good agreement with the available field data over the same depth and density range.     

The Wong-Zakai theorem for dynamical systems with parametric Poisson white noise excitation

The theorem of Wong and Zakai is applied to obtain a mathematical model for systems under random impulse excitation, in case that the excitation process tends to be delta-correlated. By means of the Wong-Zakai transformation, a class of reducible non-linear stochastic integro-differential equations is identified. Exact stationary probability density functions for reducible stochastic integro-differential equations are calculated.     

An alternative expression for stochastic dynamical systems with parametric Poisson white noise

Di Paola and Falsone's formula is widely used in expressing a correction term to the usual Ito integral in stochastic dynamical systems with parametric Poisson white noise. An alternative expression is presented here. Comparing with Di Paola and Falsone's original expression, the alternative one is applicable under more general conditions, and shows significantly improved performance in numerical implementation. The alternative expression turns out to be a special case of the Marcus integrals.     

A mathematical model for the prediction of temperature in a dry snow layer

A mathematical model for predicting the temperature in a homogeneous layer of dry snow is presented. The model, which is physically based, is capable of predicting diurnal temperature behaviour at the snow surface and at any depth within a snow layer given the variation in a limited set of meteorological parameters over that period. A sensitivity analysis is performed to determine the important parameters in the prediction of snow surface temperatures. These are found to be consistent with simple physical reasoning.     

Stochastic averaging of quasi-linear systems driven by Poisson white noise

The averaged generalized Itô and Fokker–Planck–Kolmogorov (FPK) equations for single-degree-of-freedom (SDOF) quasi-linear systems driven by Poisson white noise are derived and the approximate stationary solutions of the averaged generalized FPK equations are obtained by using the perturbation method for four typical quasi-linear systems, i.e., van der Pol oscillator, Rayleigh oscillator, system with energy-dependent damping, and system with power law damping. The effectiveness and accuracy of the perturbation solution are assessed by performing appropriate Monte Carlo simulations. It is found that analytical and numerical results agree well and the effect of non-Gaussianity of the excitation process is not negligible for predicting the probability densities of total energy and displacement of quasi-linear systems in most cases.     

A thermal activation model for noise in the dc SQUID

A thermal activation model is described for the dc SQUID. The equations of motion for the junction phase differences are shown to develop in time like the coordinates of a particle performing Brownian motion in a viscous medium in a two-dimensional potential field. Expressions are derived relating the average voltage, transfer function, and current and voltage noise spectral densities to the features of the potential determined by the device parameters. Comparison with a numerical simulation is presented. Calculations of the current noise as a function of loop inductance and critical current asymmetry are performed. An anomalously large current noise is predicted at certain values of the device characteristics. The correlation spectral density is also calculated as a function of loop inductance, and related to the optimal source resistance for a tuned SQUID amplifier. A theory of low-frequency noise sources in the SQUID is developed in a fashion compatible with the thermal activation model. Equilibrium temperature fluctuations as a possible source of 1/f noise in the SQUID are discussed. A scheme for optimizing the resolution at low frequencies is presented. Proper exploitation of low-capacitance Pb-PbOx-Pb junction technology is shown to increase the resolution at 1 Hz by at least a factor of 8, provided that the temperature fluctuations are the dominant source of noise.Work supported in part by ONR under contract #NR319-154.     

Estimating random errors due to shot noise in backscatter lidar observations

We discuss the estimation of random errors due to shot noise in backscatter lidar observations that use either photomultiplier tube (PMT) or avalanche photodiode (APD) detectors. The statistical characteristics of photodetection are reviewed, and photon count distributions of solar background signals and laser backscatter signals are examined using airborne lidar observations at 532 nm using a photon-counting mode APD. Both distributions appear to be Poisson, indicating that the arrival at the photodetector of photons for these signals is a Poisson stochastic process. For Poisson- distributed signals, a proportional, one-to-one relationship is known to exist between the mean of a distribution and its variance. Although the multiplied photocurrent no longer follows a strict Poisson distribution in analog-mode APD and PMT detectors, the proportionality still exists between the mean and the variance of the multiplied photocurrent. We make use of this relationship by introducing the noise scale factor (NSF), which quantifies the constant of proportionality that exists between the root mean square of the random noise in a measurement and the square root of the mean signal. Using the NSF to estimate random errors in lidar measurements due to shot noise provides a significant advantage over the conventional error estimation techniques, in that with the NSF, uncertainties can be reliably calculated from or for a single data sample. Methods for evaluating the NSF are presented. Algorithms to compute the NSF are developed for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations lidar and tested using data from the Lidar In-space Technology Experiment.     

A model for magnetic recording channels with signal dependent noise

This paper presents a model that includes both signal dependent and signal independent noises. A method for extracting statistics of the coefficients of the noise expansion from measured covariances is described. The paper also suggests how to take advantage of the signal dependence of the noise in the detection process     

A stress approach model for predictions of fatigue life by shot peening of EN45A spring steel

A lot of research has been done to improve fatigue strength of materials by creating compressive residual stress field in their surface layers through shot peening. In this paper, fatigue strength of shot peened leaf springs has been calculated from laboratory samples. The axial fatigue strength of EN45A spring steel specimen is evaluated experimentally as a function of shot peening in the conditions used for full-scale leaf springs testing in industries. Optimum shot peening condition for specimen is found and S/N curves of the specimens are correlated with leaf springs curve. A mathematical model has been developed which predicts the fatigue life of leaf springs for a given stress at varying shot peening conditions. Predictions from this model are compared with experimental data. The estimation of fatigue life and relaxation of compressive residual stress field are discussed.     

A bivariate zero-inflated Poisson regression model to analyze occupational injuries

The aim of many occupational safety interventions is to reduce the incidence of injury. However, when measuring intervention effectiveness within a period, population-based accident count data typically contain a large proportion of zero observations (no injury). This situation is compounded where injuries are categorized in a binary manner according to an outcome of interest. The distribution thus comprises a point mass at zero mixed with a non-degenerate parametric component, such as the bivariate Poisson. In this paper, a bivariate zero-inflated Poisson (BZIP) regression model is proposed to evaluate a participatory ergonomics team intervention conducted within the cleaning services department of a public teaching hospital. The findings highlight that the BZIP distribution provided a satisfactory fit to the data, and that the intervention was associated with a significant reduction in overall injury incidence and the mean number of musculoskeletal (MLTI) injuries, while the decline in injuries of a non-musculoskeletal (NMLTI) nature was marginal. In general, the method can be applied to assess the effectiveness of intervention trials on other populations at high risk of occupational injury.     

Stationary response of bilinear hysteretic system driven by Poisson white noise

Stationary response of single-degree-of-freedom (SDOF) bilinear hysteretic system driven by Poisson white noise is investigated via stochastic averaging of energy envelope in this paper. The averaged generalized Fokker–Planck–Kolmogorov (GFPK) equation for SDOF bilinear hysteretic system driven by Poisson white noise is derived and the approximate stationary solutions of the averaged GFPK equation are obtain by using a modified exponential polynomial closure method. The effectiveness and accuracy of the approximate solution are assessed by performing appropriate Monte Carlo simulations. It is found that analytical and numerical results agree well and the effect of non-Gaussianity of the excitation process on stationary probability densities of total energy and displacement of bilinear hysteretic system is predicted successfully via stochastic averaging of energy envelope.