Optimal post-experiment estimation of poorly modeled dynamic systems

Recently, a novel strategy for post-experiment state estimation of discretely-measured dynamic systems has been developed. The method accounts for errors in the system dynamic model equations in a more general and rigorous manner than do filter-smoother algorithms. The dynamic model error terms do not require the usual process noise assumptions of zero-mean, symmetrically distributed random disturbances. Instead, the model error terms require no prior assumptions other than piecewise continuity. The resulting state estimates are more accurate than filters for applications in which the dynamic model error clearly violates the typical process noise assumptions, and the available measurements are sparse and/or noisy. Estimates of the dynamic model error, in addition to the states, are obtained as part of the solution of a two-point boundary value problem, and may be exploited for numerous reasons. In this paper, the basic technique is explained, and several example applications are given. Included among the examples are both state estimation and exploitation of the model error estimates

Time domain modal identification/estimation of the mini-mast testbed

The Mini-Mast is a 20 meter long 3-dimensional, deployable/retractable truss structure designed to imitate future trusses in space. Presented here are results from a robust (with respect to measurement noise sensitivity), time domain, modal identification technique for identifying the modal properties of the Mini-Mast structure even in the face of noisy environments. Three testing/analysis procedures are considered: sinusoidal excitation near resonant frequencies of the Mini-Mast, frequency response function averaging of several modal tests, and random input excitation with a free response period

Correlation techniques to determine model form in robust nonlinear system realization/identification

The fundamental challenge in identification of nonlinear dynamic systems is determining the appropriate form of the model. A robust technique is presented which essentially eliminates this problem for many applications. The technique is based on the Minimum Model Error (MME) optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature is the ability to identify nonlinear dynamic systems without prior assumption regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. Model form is determined via statistical correlation of the MME optimal state estimates with the MME optimal model error estimates. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length

An experimental study of nonlinear dynamic system identification

A technique based on the Minimum Model Error optimal estimation approach is employed for robust identification of a nonlinear dynamic system. A simple harmonic oscillator with quadratic position feedback was simulated on an analog computer. With the aid of analog measurements and an assumed linear model, the Minimum Model Error Algorithm accurately identifies the quadratic nonlinearity. The tests demonstrate that the method is robust with respect to prior ignorance of the nonlinear system model and with respect to measurement record length, regardless of initial conditions

An experimental study of nonlinear dynamic system identification

A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length

Scalar gain interpretation of large order filters

A technique is developed which demonstrates how to interpret a large fully-populated filter gain matrix as a set of scalar gains. The inverse problem is also solved, namely, how to develop a large-order filter gain matrix from a specified set of scalar gains. Examples are given to illustrate the method

Theoretical constraints in the design of multivariable control systems

The research being performed under NASA Grant NAG1-1361 involves a more clear understanding and definition of the constraints involved in the pole-zero placement or assignment process for multiple input, multiple output systems. Complete state feedback to more than a single controller under conditions of complete controllability and observability is redundant if pole placement alone is the design objective. The additional feedback gains, above and beyond those required for pole placement can be used for eignevalue assignment or zero placement of individual closed loop transfer functions. Because both poles and zeros of individual closed loop transfer functions strongly affect the dynamic response to a pilot command input, the pole-zero placement problem is important. When fewer controllers than degrees of freedom of motion are available, complete design freedom is not possible, the transmission zeros constrain the regions of possible pole-zero placement. The effect of transmission zero constraints on the design possibilities, selection of transmission zeros and the avoidance of producing non-minimum phase transfer functions is the subject of the research being performed under this grant

An automated method of tuning an attitude estimator

Attitude determination is a major element of the operation and maintenance of a spacecraft. There are several existing methods of determining the attitude of a spacecraft. One of the most commonly used methods utilizes the Kalman filter to estimate the attitude of the spacecraft. Given an accurate model of a system and adequate observations, a Kalman filter can produce accurate estimates of the attitude. If the system model, filter parameters, or observations are inaccurate, the attitude estimates may be degraded. Therefore, it is advantageous to develop a method of automatically tuning the Kalman filter to produce the accurate estimates. In this paper, a three-axis attitude determination Kalman filter, which uses only magnetometer measurements, is developed and tested using real data. The appropriate filter parameters are found via the Process Noise Covariance Estimator (PNCE). The PNCE provides an optimal criterion for determining the best filter parameters

MME-based attitude dynamics identification and estimation for SAMPEX

A method is described for obtaining optimal attitude estimation algorithms for spacecraft lacking attitude rate measurement devices (rate gyros), and then demonstrated using actual flight data from the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) spacecraft. SAMPEX does not have on-board rate sensing, and relies on sun sensors and a three-axis magnetometer for attitude determination. Problems arise since typical attitude estimation is accomplished by filtering measurements of both attitude and attitude rates. Rates are nearly always sampled much more densely than are attitudes. Thus, the absence/loss of rate data normally reduces both the total amount of data available and the sampling density (in time) by a substantial fraction. As a result, the sensitivity of the estimates to model uncertainty and to measurement noise increases. In order to maintain accuracy in the attitude estimates, there is increased need for accurate models of the rotational dynamics. The proposed approach is based on the minimum model error (MME) optimal estimation strategy, which has been successfully applied to estimation of poorly modeled dynamic systems which are relatively sparsely and/or noisily measured. The MME estimates may be used to construct accurate models of the system dynamics (i.e. perform system model identification). Thus, an MME-based approach directly addresses the problems created by absence of attitude rate measurements

Projecting ocean acidification impacts for the Gulf of Maine to 2050: new tools and expectations

© The Author(s), 2021. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Siedlecki, S. A., Salisbury, J., Gledhill, D. K., Bastidas, C., Meseck, S., McGarry, K., Hunt, C. W., Alexander, M., Lavoie, D., Wang, Z. A., Scott, J., Brady, D. C., Mlsna, I., Azetsu-Scott, K., Liberti, C. M., Melrose, D. C., White, M. M., Pershing, A., Vandemark, D., Townsend, D. W., Chen, C,. Mook, W., Morrison, R. Projecting ocean acidification impacts for the Gulf of Maine to 2050: new tools and expectations. Elementa: Science of the Anthropocene, 9(1), (2021): 00062, https://doi.org/10.1525/elementa.2020.00062.Ocean acidification (OA) is increasing predictably in the global ocean as rising levels of atmospheric carbon dioxide lead to higher oceanic concentrations of inorganic carbon. The Gulf of Maine (GOM) is a seasonally varying region of confluence for many processes that further affect the carbonate system including freshwater influences and high productivity, particularly near the coast where local processes impart a strong influence. Two main regions within the GOM currently experience carbonate conditions that are suboptimal for many organisms—the nearshore and subsurface deep shelf. OA trends over the past 15 years have been masked in the GOM by recent warming and changes to the regional circulation that locally supply more Gulf Stream waters. The region is home to many commercially important shellfish that are vulnerable to OA conditions, as well as to the human populations whose dependence on shellfish species in the fishery has continued to increase over the past decade. Through a review of the sensitivity of the regional marine ecosystem inhabitants, we identified a critical threshold of 1.5 for the aragonite saturation state (Ωa). A combination of regional high-resolution simulations that include coastal processes were used to project OA conditions for the GOM into 2050. By 2050, the Ωa declines everywhere in the GOM with most pronounced impacts near the coast, in subsurface waters, and associated with freshening. Under the RCP 8.5 projected climate scenario, the entire GOM will experience conditions below the critical Ωa threshold of 1.5 for most of the year by 2050. Despite these declines, the projected warming in the GOM imparts a partial compensatory effect to Ωa by elevating saturation states considerably above what would result from acidification alone and preserving some important fisheries locations, including much of Georges Bank, above the critical threshold.This research was financially supported by the Major Special Projects of the Ministry of Science and Technology of China (2016YFC020600), the Young Scholars Science Foundation of Lanzhou Jiaotong University (2018033), and the Talent Innovation and Entrepreneurship Projects of Lanzhou (2018-RC-84)