Kazutatsu Hatakeyama

A unified study on the output probability distribution of arbitrary linear vibratory systems with arbitrary random excitation

Abstract New theoretical expressions of probability density and cumulative distribution functions for the output response are exactly derived without any simplification of the problem and any approximation of analysis in the case when a general random signal with arbitrary probability distribution and correlation functions is passed through an arbitrary linear vibratory system with finite order. The result is given as an explicit solution of expansion series in a functional form of input statistics and vibratory system parameters, and not given as a mere numerical solution by use of a recurrence algorithm. An effect of random input and system characteristics is concretely reflected in the expansion coefficients. The experimental results obtained by digital simulation are in good agreement with the theory. Thus, the above theory is experimentally confirmed for some typical examples by the method of digital simulation.

A state estimation with less information loss and a hierarchical digital filter in the acoustic environment

Abstract In the situation of evaluating an environmental sound phenomenon, there is often the necessity of estimating statistical quantities such as the mean, variance and the other higher order moments, owing to the arbitrariness of the phenomena and the complexity of human response to them. Furthermore, the measured data is usually contaminated by background noise of an arbitrary distribution type. In this paper, a unified methodology for detecting the unknown sound state in the presence of such background noise is proposed. An hierarchical expansion expression for the probability density function is developed, based on a successive differential procedure. This digital filter in a wide sense corresponds exactly with the well-known Kalman filter in the ideal case when the stochastic sound system is linear and Gaussian. The validity of the proposed wide sense digital filter has been experimentally confirmed by several applications to observed data. Three cases are presented, namely: (i) estimating the unknown reverberation time of a room; (ii) estimating the parameters of a sound insulation system between two reverberant rooms; (iii) estimating the waveform of traffic noise strongly contaminated by background noise.

A unified study of the multivariate joint probability function of the state variables with quantized levels for a stochastic environmental system with discrete data: Theory and experiment

Abstract All the information on statistical properties of the state variables of a stochastic system can be derived by first finding the multivariate joint probability function of their variables. Furthermore, random data are often obtained in digital form at discrete time intervals. Accordingly, theoretical consideration is given, first, to the joint probability function with quantized levels and its joint factorial moments, which are suited to an actual situation where real experimental data are taken in quantized form: i.e., as finite sets of discrete numbers. As a special case when the level width tends to 0, the above theory includes the well-known expansion series distribution in continuous form. Second, the validity of the theory is confirmed both by means of digital simulation and by application to experimentally observed road traffic noise and environmental noise data.

A dynamical identification method based on conditioned observations for a sound insulation system with the order determined by a new criterion index

Abstract This paper describes a new approach to the identification of arbitrary sound insulation systems with random excitations, for practical situations in which the observations of input and transmitted (output) signals are strongly contaminated by external additive noise in the reception and transmission rooms. First, the sound insulation system is modelled by a time series representation of the relationship among the output, signal input and contaminating noise acoustic powers, with discrete time sampling, rather than by using the usual respective spectral densities in the frequency domain. An hypothetical pre-experiment with a test input of white noise is analyzed to determine the order of this time series model. From the results of this analysis, it is shown that a criterion function can be found for use in actual observations when both an arbitrary input signal and an arbitrary contaminating noise are present, and that by using this function the time series model order can be determined from the actually observed data, so that in practice such a pre-experiment is not necessary. Second, the system model parameters are successively estimated by a wide sense digital filter based on Bayes theorem with input level conditioning. Third, these estimated parameters are then used to predict the probability distribution of the output power fluctuations for the system under arbitrary random excitations. Finally, the effectiveness of the proposed identification method is experimentally confirmed by applying it to a number of actual sound insulation systems.

A new method for parameter identification based on a new measure of statistical independence

This paper describes a new method for parameter identification for stochastic systems based on a new evaluation measure of the statistical independence between an input signal and extraneous noise. The error criterion used here enables an assessment to be made of the extremities of the distribution function of the random process as well as of the neighborhood of the mean value. Specifically, the joint probability density function (PDF) for an input signal and an extraneous noise of arbitrary distribution type is expanded into an infinite series, with the product of each marginal PDF included in the first expansion term. The expansion coefficients defined by the linear and nonlinear mutual correlations then display with precision and hierarchically the deviation from statistical independence. Several types of estimation methods are derived for evaluating and then decreasing this deviation. The validity and the effectiveness of the proposed methods are experimentally confirmed by applying them to identifying sound insulation parameters in room acoustics.

A prediction theory of random level distribution based on a generalized difference type of Fokker-Planck equation and its application to environmental noise and vibration, II: Experimental study

Abstract In a companion paper [1], a procedure for solving the short time prediction problem in terms of the transition probability distribution has been theoretically derived, for discrete time-sampled data. Explicit algorithms for estimating the non-stationary moment statistics of arbitrary order also have been derived, based on a generalized difference equation of Fokker-Planck type for the conditional probability distributed function, which is central to the theory. In this paper, evidence for the validity and effectiveness of the proposed method is presented, as obtained not only by means of digital simulation but also by using road traffic noise data obtained experimentally in Hiroshima. For several non-stationary random processes simulated by means of random numbers, the theoretical and experimental conditional probability functions are compared. For non-stationary road traffic noise data the theoretically predicted and experimentally determined confidence intervals are compared; in these comparisons several types of conditional probability function and various values of weighting parameter are used in the algorithm. All of the theoretical results show good agreement with the experimental results.

An Optimal Traffic Control Strategy to Regulate the Street Noise Over a City-Wide Area from the Two Methodological Viewpoints of D.P. and M.P

Abstract Generally speaking, the resultant fluctuation patterns of the environmental road traffic noise can be principally described by the physical factors of circumstances. Based on that fact, in this paper, the representative evaluation index based on the dB observation for the street noise over the city-wide area has been initially introduced in an analytical functional form with the physical parameters of the traffic flow. Then, the optimal traffic control strategies, in order to regulate the street noise from many vehicles over the area, can be generally determined by the methods proposed from the two different methodological viewpoints of dynamic programming and maximum principle. Finally, we have confirmed the validity and effectiveness of our theory by means of digital simulation.

A New Trial to Estimate the Noise Propagation Characteristics of a Traffic Noise System and its Application

Summary Generally speaking, a level-fluctuation of road-traffic noise is brought on by various causes. It is obvious that the ultimate causes are due to a variety of noise sources, i.e., uncertain behavior of individual cars, and to some effect of the noise-propagation characteristics affected by reflections and/or absorptions owing to surrounding buildings and their topographical locations. By dividing the road into a suitable number of blocks, and paying close attention to the mean value of noise intensity in each block, the mean value can be proportional to the number of cars in the block. In this paper, on the basis of the additive property of sound energy, the unified method has been proposed to estimate the inherent characteristics of noise-propagation in each block in the form of a synthetical evaluation with the number of cars for each car-type, also considering the entire back-ground noise. We have confirmed the validity of our theoretical results, not only by means of digital simulation, but also by road-traffic noise-data experimentally observed near Hiroshima City. The experimental results clearly show a good agreement with the values recently reported by other official groups 1) .