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Frequency domain stability criteria for dynamical systems with random parameters, considering open loop stability, stochastic gain element rms value and linear element effective bandwidth
The problem of designing optimal inputs in the identification of linear systems with unknown random parameters is considered using a Bayesian approach. The information matrix, which is positive definite for the class of systems analyzed, gives a measure of performance for the system inputs. The computation of the optimal closed-loop input mappings is shown to be a nontrivial exercise in adaptive control. Deterministic optimal inputs are shown to be easily computable. Numerical examples are given. A Kalman filter is used to estimate the parameters. A necessary condition for the Kalman filter not to diverge when applying linear feedback is also given.
Studies are summarized on the application of advanced analytical and computational methods to the development of mathematical models of human controllers in multiaxis manual control systems. Specific accomplishments include the following: (1) The development of analytical and computer methods for the measurement of random parameters in linear models of human operators. (2) Discrete models of human operator behavior in a multiple display situation were developed. (3) Sensitivity techniques were developed which make possible the identification of unknown sampling intervals in linear systems. (4) The adaptive behavior of human operators following particular classes of vehicle failures was studied and a model structure proposed.
The Extended Kalman-Bucy Filter is a powerful technique for estimating non-stationary random parameters in situations where the received signal is a noisy non-linear function of those parameters. A practical causal filter for retrieving atmospheric temperature profiles from radiances observed at a single scan angle by the Scanning Microwave Spectrometer (SCAMS) carried on the Nimbus 6 satellite typically shows approximately a 10-30% reduction in rms error about the mean at almost all levels below 70 mb when compared with a regression inversion.
This paper presents an analytical approach for assessing the effect of pulsed RFI on the error probability of a coherent phase-shift keyed signal through a nonlinear satellite repeater. The RFI is assumed to affect the uplink channel and to consist of CW pulses with random power levels and arriving randomly in time with a Poisson distribution. A model to approximate the effect of intermodulation products is introduced and the error probability conditioned on the output of the satellite repeater is computed. The classical moment technique is then used as an efficient method of averaging the conditional error probability over the numerous random parameters associated with the uplink signal.
This paper is a 1-D analysis of the degradation caused by image sampling and interpolative reconstruction. The analysis includes the sample-scene phase as an explicit random parameter and provides a complete characterization of this image degradation as the sum of two terms: one term accounts for the mean effect of undersampling (aliasing) and nonideal reconstruction averaged over all sample-scene phases; the other term accounts for variations about this mean. The results of this paper have application to the design and performance analysis of image scanning, sampling, and reconstruction systems.
The probability distributions of the spatial distribution of precipitation from storms of different types were studied. The occurrence of wetted rainstorm area within a catchment was modeled as a Poisson arrival process in which each storm is composed of stationary, nonoverlapping, independent random cell clusters whose centers are Poisson-distributed as through fractals. The portion of a catchment covered by a stationary rainstorm was modeled by the common area of two overlapping circles. The first two moments of the distribution of the common area were derived from purely geometrical considerations. The spatial structure of the depth of rainfall from a stationary rainstorm was investigated using point process techniques. Total storm rainfall at the center of each cell is a random variable, and rainfall is distributed around the center specified by a spread function that may incorporate random parameters.
The spatial structure of the depth of rainfall from a stationary storm event is investigated by using point process techniques. Cells are assumed to be stationary and to be distributed in space either independently according to a Poisson process, or with clustering according to a Neyman-Scott scheme. Total storm rainfall at the centre of each cell is a random variable and rainfall is distributed around the centre in a way specified by a spread function that may incorporate random parameters. The mean, variance and covariance structure of the precipitation depth at a point are obtained for different spread functions. For exponentially distributed centre depth and a spread function having quadratically exponential decay, the total storm depth at any point in the field is shown to have a gamma distribution. The probability of zero rainfall at a point is investigated, as is the stochastic variability of model parameters from storm to storm. Data from the Upper Rio Guaire basin in Venezuela are used in illustration.
Various papers on recent advances in engineering science are presented. Some individual topics addressed include: advances in adaptive methods in computational fluid mechanics, mixtures of two medicomorphic materials, computer tests of rubber elasticity, shear bands in isotropic micropolar elastic materials, nonlinear surface wave and resonator effects in magnetostrictive crystals, simulation of electrically enhanced fibrous filtration, plasticity theory of granular materials, dynamics of viscoelastic media with internal oscillators, postcritical behavior of a cantilever bar, boundary value problems in nonlocal elasticity, stability of flexible structures with random parameters, electromagnetic tornadoes in earth's ionosphere and magnetosphere, helicity fluctuations and the energy cascade in turbulence, mechanics of interfacial zones in bonded materials, propagation of a normal shock in a varying area duct, analytical mechanics of fracture and fatigue.
A reliability-based optimization methodology has been developed to design the raked wing tip of the Boeing 767-400 extended range airliner made of composite and metallic materials. Design is formulated for an accepted level of risk or reliability. The design variables, weight and the constraints became functions of reliability. Uncertainties in the load, strength and the material properties, as well as the design variables, were modeled as random parameters with specified distributions, like normal, Weibull or Gumbel functions. The objective function and constraint, or a failure mode, became derived functions of the risk-level. Solution to the problem produced the optimum design with weight, variables and constraints as a function of the risk-level. Optimum weight versus reliability traced out an inverted-S shaped graph. The center of the graph corresponded to a 50 percent probability of success, or one failure in two samples. Under some assumptions, this design would be quite close to the deterministic optimum solution. The weight increased when reliability exceeded 50 percent, and decreased when the reliability was compromised. A design could be selected depending on the level of risk acceptable to a situation. The optimization process achieved up to a 20-percent reduction in weight over traditional design.
Information about the spatiotemporal variability of soil moisture is critical for many purposes, including monitoring of hydrologic extremes, irrigation scheduling, and prediction of agricultural yields. We evaluated the temporal dynamics of 18 state-of-the-art (quasi-)global near-surface soil moisture products, including six based on satellite retrievals, six based on models without satellite data assimilation (referred to hereafter as “open-loop” models), and six based on models that assimilate satellite soil moisture or brightness temperature data. Seven of the products are introduced for the first time in this study: one multi-sensor merged satellite product called MeMo (Merged soil Moisture) and six estimates from the HBV (Hydrologiska Byråns Vattenbalansavdelning) model with three precipitation inputs (ERA5, IMERG, and MSWEP) with and without assimilation of SMAPL3E satellite retrievals, respectively. As reference, we used in situ soil moisture measurements between 2015 and 2019 at 5 cm depth from 826 sensors, located primarily in the USA and Europe. The 3-hourly Pearson correlation (R) was chosen as the primary performance metric. We found that application of the Soil Wetness Index (SWI) smoothing filter resulted in improved performance for all satellite products. The best-to-worst performance ranking of the four single-sensor satellite products was SMAPL3E SWI , SMOS SWI , AMSR2 SWI , and ASCAT SWI , with the L-band-based SMAPL3E SWI (median R of 0.72) outperforming the others at 50 % of the sites. Among the two multi-sensor satellite products (MeMo and ESA-CCI SWI ), MeMo performed better on average (median R of 0.72 versus 0.67), probably due to the inclusion of SMAPL3E SWI . The best-to-worst performance ranking of the six open-loop models was HBV-MSWEP, HBV-ERA5, ERA5-Land, HBV-IMERG, VIC-PGF, and GLDAS-Noah. This ranking largely reflects the quality of the precipitation forcing. HBV-MSWEP (median R of 0.78) performed best not just among the open-loop models but among all products. The calibration of HBV improved the median R by +0.12 on average compared to random parameters, highlighting the importance of model calibration. The best-to-worst performance ranking of the six models with satellite data assimilation was HBV-MSWEP+SMAPL3E, HBV-ERA5+SMAPL3E, GLEAM, SMAPL4, HBV-IMERG+SMAPL3E, and ERA5. The assimilation of SMAPL3E retrievals into HBV-IMERG improved the median R by +0.06, suggesting that data assimilation yields significant benefits at the global scale.
Optimal control of plants with random slowly varying parameters
A unified design philosophy is presented for limited state feedback control problems with parameter uncertainty for both deterministic and stochastic problems. Two approaches are considered: linear compensator for the deterministic problem with parameter uncertainty, and for the single input-single output system with parameter uncertainty, a model on order equal to that of the system less the number of zeroes. The limitations of these approaches are discussed along with suggestions for further research.
The critical parameters of subsonic jet aircraft response in a random atmospheric environment are determined. Equations of motion are presented for semirigid aircraft with a flexible primary airfoil. However, the analysis is easily extendable to include additional appendage flexibility. The analysis establishes the mechanical admittance values for pitching, plunging, and the first mode effects from wing elastic bending and torsion. Nondimensional parameters are established which allow the representation of all subsonic jet transport aircraft with one nondimensional model. The critical parameters for random forcing are found to be aircraft relative mass, reduced natural and forcing frequencies, and Mach number. Turbulence scale lengths are found to be directly related to the critical values of reduced forcing frequency. Results are given for subsonic craft traveling at constant altitude. Specific values of admittance functions are tabulated at Mach numbers of 0.2, 0.5, and 0.7. The relative mass range covers all aircraft currently in operation.
This paper is concerned with the parameter adaptive least squares estimation of random processes. The main result is a general representation theorem for the conditional expectation of a random variable on a product probability space. Using this theorem along with the general likelihood ratio expression, the least squares estimate of the process is found in terms of the parameter conditioned estimates. The stochastic differential for the a posteriori probability and the stochastic differential equation for the a posteriori density are found by using simple stochastic calculus on the representations obtained. The results are specialized to the case when the parameter has a discrete distribution. The results can be used to construct an implementable recursive estimator for certain types of nonlinear filtering problems. This is illustrated by some simple examples.
Analog computer method for approximating stationary Gaussian random process depending only on position parameter
The design procedure of feedback controllers was described and the considerations for the selection of the design parameters were given. The frequency domain properties of single-input single-output systems using state feedback controllers are analyzed, and desirable phase and gain margin properties are demonstrated. Special consideration is given to the design of controllers for tracking systems, especially those designed to track polynomial commands. As an example, a controller was designed for a tracking telescope with a polynomial tracking requirement and some special features such as actuator saturation and multiple measurements, one of which is sampled. The resulting system has a tracking performance comparing favorably with a much more complicated digital aided tracker. The parameter sensitivity reduction was treated by considering the variable parameters as random variables. A performance index is defined as a weighted sum of the state and control convariances that sum from both the random system disturbances and the parameter uncertainties, and is minimized numerically by adjusting a set of free parameters.
Concepts of information theory are applied to examine various proteins in terms of their redundancy in natural originators such as animals and plants. The Monte Carlo method is used to derive information parameters for random protein sequences. Real protein sequence parameters are compared with the standard parameters of protein sequences having a specific length. The tendency of a chain to contain some amino acids more frequently than others and the tendency of a chain to contain certain amino acid pairs more frequently than other pairs are used as randomness measures of individual protein sequences. Non-periodic proteins are generally found to have random Shannon redundancies except in cases of constraints due to short chain length and genetic codes. Redundant characteristics of highly periodic proteins are discussed. A degree of periodicity parameter is derived.