System Model Validation Research Articles

Squared and absolute errors in optimal approximation of nonlinear systems

Optimal squared error and absolute error-based approximation problems for static polynomial models of nonlinear, discrete-time, systems are studied in detail. These problems have many similarities with other linear-in-the-parameters approximation problems, such as with optimal approximation problems for linear time-invariant models of linear and nonlinear systems. Nonprobabilistic signal analysis is used. Close connections between the studied approximation problems and certain classical topics in approximation theory, such as optimal L 2(−1,1) and L 1(−1,1) approximation, are established by analysing conditions under which sample averages of static nonlinear functions of the input converge to appropriate Riemann integrals of the static functions. These results should play a significant role in the analysis of corresponding system identification and model validation problems. Furthermore, these results demonstrate that optimal modelling based on the absolute error can offer advantages over squared error-based modelling. Especially, modelling problems in which some signals possess heavy tails can benefit from absolute value-based signal and error analysis.

Using Statistical Learning Theory to Rationalize System Model Identification and Validation Part I: Mathematical Foundations

Existing procedures for model validation have been deemed inadequate for many engineering systems. The reason of this inadequacy is due to the high degree of complexity of the physical mechanisms that govern these systems. It is proposed in this paper to shift the attention from modeling the engineering system itself to modeling the uncertainty that underlies its behavior. A mathematical framework for modeling the uncertainty in complex engineering systems is developed. This framework uses the results of computational learning theory. It is based on the premise that a system model is a learning machine.

Erratum

The Turkey Lakes Watershed Study (TLWS) was initiated in 1980 to assess the effects of anthropogenic perturbation on Shield ecosystems. The goal of the study was to obtain a whole-ecosystem analysis of the biogeochemical processes that control pollutant–ecosystem interactions and thence to promote the development and validation of system models. It is a cooperative effort that includes investigators from Environment Canada (National Water Research Institute, Meteorological Service of Canada, and Canadian Wildlife Service), Natural Resources Canada (Great Lakes Forestry Centre), and Fisheries and Oceans Canada (Great Lakes Laboratory for Fisheries and Aquatic Science), as well as several universities. The initial impetus for research in the TLW arose from the desire to assess and understand the aquatic and terrestrial effects of acidic deposition. The TLW (Figure 1) is located 50 km north of Sault Ste. Marie, Ontario, on the Canadian Shield near the northern margin of the Great Lakes–St. Lawrence forest region. The basin, which is 10.5 km in area, is situated predominantly on metamorphic silicate bedrock (greenstone) overlain by thin to absent glacial tills. These geological conditions make the basin moderately sensitive to acidic deposition. The terrestrial and aquatic resources within the basin are representative of the surrounding Algoma district, although for an Ontario site, the TLW has relatively high relief (290 m) and precipitation (mean, more than 1200 mm y ). The forest is an uneven-aged, mature-toovermature, old-growth hardwood system dominated by sugar maple (Acer saccharum Marsh.) and yellow birch (Betula alleghaniensis Britton). The drainage system is composed of many intermittent and perennial first-order streams draining into and through a chain of four dimictic lakes that range in size from 5.8 to 52.0 ha and in mean depth from 2.2 to 12.2 m. There is a chemical gradient in the aquatic system such that higherelevation waters are more dilute (that is, they have lower Ca and alkalinity concentrations) than lower-elevation waters. The TLW ultimately drains into the Batchawana River and thence to Lake Superior. For greater detail on basin characteristics, see Jeffries and others (1988). From time to time, study participants have conducted workshops to present, discuss, and integrate the findings from the scientific investigation now being done in the TLW (for example, see the Canadian Journal of Fisheries and Aquatic Sciences, 1988, vol. 45, Suppl. 1, pages 1–178,). This issue of Ecosystems presents six papers from a 1999 workshop that summarize the results from either long-term monitoring of conditions in the TLW or specific research projects. According to Sirois and others (2001), mean annual wet SO4 2 deposition declined from 31 mmol m 2 during 1981–1984 to 18 mmol m 2 during 1994–97. Two of the following papers address trends or responses in precipitation or surface-water chemistry that were contemporaneous with this change in acid input. Three other papers consider some of the physical and chemical processes that regulate watershed biogeochemistry, and another describes the development and application of a predictive soil acidification model that was designed to assess whether the reduced acid Received 19 September 2000; accepted 19 September 2000. *Corresponding author; e-mail: dean.jeffries@cciw.ca Ecosystems (2001) 4: 501–502 DOI: 10.1007/s10021-001-0023-2 ECOSYSTEMS

Modelling rainfall interception by vegetation of variable density using an adapted analytical model. Part 2. Model validation for a tropical upland mixed cropping system

To improve the description of rainfall partitioning by a vegetation canopy that changes in time a number of adaptations to the revised analytical model for rainfall interception by sparse canopies [J. Hydrol., 170 (1995) 79] was proposed in the first of two papers. The current paper presents an application of this adapted analytical model to simulate throughfall, stemflow and interception as measured in a mixed agricultural cropping system involving cassava, maize and rice during two seasons of growth and serial harvesting in upland West Java, Indonesia. Measured interception losses were 18 and 8% during the two measuring periods, while stemflow fractions were estimated at 2 and 4%, respectively. The main reasons for these discrepancies were differences in vegetation density and composition, as well as differences in the exposure of the two sites used in the two respective years. Functions describing the development of the leaf area index of each of the component crops in time were developed. Leaf area index (ranging between 0.7 and 3.8) was related to canopy cover fraction (0.41–0.94). Using average values and time series of the respective parameters, interception losses were modelled using both the revised analytical model and the presently adapted version. The results indicate that the proposed model adaptations substantially improve the performance of the analytical model and provide a more solid base for parameterisation of the analytical model in vegetation of variable density.

Neurovascular coupling in terms of a control system: validation of a second-order linear system model

Neurovascular coupling (NC) adapts cerebral blood flow to cortical activity. Functional transcranial Doppler (f-TCD) investigations revealed a typical time course of evoked blood flow responses with an initial overshoot and a stabilization at a lower, but stable, level. This blood flow reaction can be described in terms of a control-system model. We tested reliability and validity of this new approach using different stimulation paradigms. The P2 segment of the posterior cerebral artery was insonated in 14 healthy volunteers and, subsequently, NC was stimulated using two tests, a checkerboard stimulus of 1 s with different repetition rates and a reading test. Data were analyzed according to algorithms of control-system theory. The reading test was used to measure test reliability and side differences. A second-order linear system can describe blood flow regulation of NC. Different stimulation protocols of the checkerboard test and the related evoked blood flow curves could be described by the same control-system model. Further, there were no differences between the checkerboard and reading test nor between right and left side or test and retest of the reading test. NC can be described in a much more detailed manner using control-system analysis. We were able to show that blood flow response due to different visual stimuli follow one common control-system model. Unlike quantification of NC using overshoot, parameters of the control system have smaller SDs, increasing the statistical power and, thereby, usefulness of f-TCD as a diagnostic instrument. (E-mail:Manfred.Kaps@Neuro.med.uni-Giessen.de)

Modelling of a thermosyphon solar water heating system and simple model validation

A thermosyphon solar water heater consisting of two flat plate collectors of total aperture area of 2.7 m 2 and 150 l storage tank is modelled using TRNSYS. Simple experiments were conducted in order to validate the model. During the experiments weather conditions were measured every 10 min and integrated over an hour. The temperature of the water in the storage tank was also measured at the beginning and at the end of the day. The storage tank temperature rise was used to validate the model by using the actual weather data as input to the program. Validation tests were performed for 25 days spread over 6 months and the mean deviation between the predicted and the actual values of water temperature rise is 4.7% which is very satisfactory. Subsequently, long term system performance is estimated by using TRNSYS model run with the weather values of TMY file for Nicosia, Cyprus. The annual solar fraction obtained was 79% and the system could cover all the hot water needs of a house of four people during the three summer months. The maximum auxiliary energy was needed during the months of December and January (about 280 MJ/month). In addition, an economic analysis of the system was carried out. The pay-back time of the system was found to be 8 years and the present worth of life cycle savings was found equal to C£ 161.

Modelling and Vibration Analysis of Misaligned Rotor-Ball Bearing Systems

A dynamic model is derived for misaligned rotor-ball bearing systems driven through a flexible coupling by treating the reaction loads and deformations at the bearing and coupling elements as the misalignment effect. In order to verify the validity of the misaligned rotor system model, experiments are extensively carried out with a laboratory test rig. Both the experimental and simulation results agree well in that, as the angular misalignment increases, the whirling orbits tend to collapse toward a straight line and the natural frequency of the misaligned rotor system associated with the misalignment direction increases largely. It is found that the increase in natural frequency is mostly due to the increase in effective bearing moment stiffness associated with the misalignment direction.

A High Performance Pneumatic Force Actuator System: Part I—Nonlinear Mathematical Model

In this paper, we developed a detailed mathematical model of dual action pneumatic actuators controlled with proportional spool valves. Effects of nonlinear flow through the valve, air compressibility in cylinder chambers, leakage between chambers, end of stroke inactive volume, and time delay and attenuation in the pneumatic lines were carefully considered. We performed system identification, numerical simulation, and model validation experiments for two types of air cylinders and different connecting tubes length. The mathematical model of the present article is used in a sequel article to develop high performance nonlinear pneumatic force controllers. [S0022-0434(00)00503-7]

Model Validation for LFT Described System in the Time Domain

Linear fractional transformation is one of the most general model forms utilised in robust control theory. The purpose of this paper is to investigate the problem of model validation for system described by linear fractional transformation model, on the basis of time domain input output data. By means of Parrott's theorem, a necessary condition for a system model to be not invalidated by the given input output data is obtained, which finally leads to a convex optimization problem.

Enhanced environments for the development and validation of dynamic system models

Many modern continuous system simulation tools provide good facilities for the efficient implementation of simulation models and for interactive experimentation using a simulation model. In most cases, however, the environment lacks some important features which can greatly assist the user in tackling efficiently some of the broader issues which arise in the model development process, such as model testing and validation. This paper reviews the problems which arise in the validation of dynamic system models and discusses the implications in terms of the type of computing environment within which model development can be carried out efficiently.

Poisson wavelets applied to model identification

Abstract A novel wavelet transform is introduced based on the backward difference of the Poisson probability density function. This family of wavelets is a function of one discrete and two continuous variables. The Poisson wavelet transform is useful for system identification, parameter estimation and model validation. In particular, it is well-suited for linear time-invariant systems that are modelled as combinations of decaying exponentials with a single time delay. A fast computational algorithm for computing the Poisson wavelet transform is developed using cascaded first-order filters. The concepts are demonstrated on a three-tank process and a simplified heat exchanger.

Poisson Wavelets Applied to Model Identification

A novel wavelet transform is introduced based on the backward difference of the Poisson probability density function. This family of wavelets is a function of one discrete and two continuous variables. The Poisson wavelet transform is useful for system identification, parameter estimation and model validation. It is particularly well-suited for linear time-invariant systems that are modelled as combinations of decaying exponentials with a single time delay. This is demonstrated on a three-tank system modelled as a first-order plus deadtime functional form.

Analytical development of an equivalent system mismatch function

A mismatch function is used to check the validity of a low-order equivalent system model that has been derived from a high-order system representation. If the difference between the low- and high-order models is greater than allowed by the mismatch function, the flying qualities predictions obtained from parameters of the low-order equivalent system may not be representative of the ratings a pilot would give the actual aircraft. A methodology is developed in this paper to derive equivalent system mismatch functions analytically. The methodology is used to analytically determine a mismatch function for the longitudinal axis of a class IV fighter aircraft in the category A, nonterminal flight phase.

Time-varying system identification and model validation using wavelets

Parametric identification of time-varying (TV) systems is possible if each TV coefficient can be expanded onto a finite set of basis sequences. The problem then becomes time invariant with respect to the parameters of the expansion. The authors address the question of selecting this set of basis sequences. They advocate the use of a wavelet basis because of its flexibility in capturing the signal's characteristics at different scales, and discuss how to choose the optimal wavelet basis for a given system trajectory. They also develop statistical tests to keep only the basis sequences that significantly contribute to the description of the system's time-variation. By formulating the problem as a regressor selection problem, they apply an P-test and an AIC based approach for multiresolution analysis of TV systems. The resulting algorithm can estimate TV AR or ARMAX models and determine their orders. They apply this algorithm to both synthetic and real speech data and compare it with the Kalman filtering TV parameter estimator. >

Air pressure transient propagation in building drainage vent systems, an application of unsteady flow analysis

Air pressure variations within building drainage systems as a result of appliance discharge may result in the loss of trap seal protection by induced syphonage and/or overpressure. Air pressure transient propagation may be described by the quasilinear hyperbolic partial differential equations of continuity and momentum, solvable numerically by the method of characteristics. This paper develops these governing equations and illustrates the numerical model validation for a drainage system and vent network, including a wide range of commonly found boundary conditions. Trap seal response and retention are modelled and the technique shown to be applicable to both code and standard preparation and systems design.

An architecture for the development of real-time fault diagnosis systems using model-based reasoning

This article presents an architecture for implementing real-time telemetry-based diagnostic systems using model-based reasoning. First, we describe Paragon, a knowledge acquisition tool for off-line entry and validation of physical system models. Paragon provides domain experts with a structured editing capability to capture the physical component's structure, behavior, and causal relationships. We next describe the architecture of the run-time diagnostic system. The diagnostic system, written entirely in Ada, uses the behavioral model developed off-line by Paragon to simulate expected component states as reflected in the telemetry stream. The diagnostic algorithm traces causal relationships contained within the model to isolate system faults. Since the diagnostic process relies exclusively on the behavioral model and is implemented without the use of heuristic rules, it can be used to isolate unpredicted faults in a wide variety of systems. Finally, we discuss the implementation of a prototype system constructed using this technique for diagnosing faults in a science instrument. The prototype demonstrates the use of model-based reasoning to develop maintainable systems with greater diagnostic capabilities at a lower cost.

Development and validation of a soil-based geographic information system model of habitat of Fossaria bulimoides, a snail intermediate host of Fasciola hepatica

Soil maps were investigated for their potential to indicate the spatial distribution of habitat of the amphibious snail, Fossaria bulimoides, the intermediate host of Fasciola hepatica in Louisiana. On a 760 ha farm adjacent to the Gulf of Mexico, most snail habitats clustered along interfaces of cheniers (relict beaches with sandy soils) with marsh (heavy, gleyed clays). A few small foci occurred on the cheniers above interfaces. Virtually no habitats occupied marsh away from these interfaces, on this or several other farms previously examined. Habitat and soil map overlays were analyzed in a raster-based geographic information system (GIS) with a 10 m pixel size; a model of habitat was generated as bands 50–90 m wide at chenier-marsh interfaces. The model was extrapolated to a 29 000 ha study area and tested on 12 additional farms not adjacent to the Gulf. On these farms, snail surveys were carried out as transects on three strata: waveface (WF, former beachfront) and backslope (BS) chenier-marsh interfaces, and chenier. The perimeters of all habitats encountered were outlined. The interface of marsh with chenier backslopes occupied 5.25% of the area of the farms, but held 21.69% of snail habitat area. Additionally, chenier soils of the Hackberry-Mermentau complex (HM) occupied 12.32% of farm area, but held 61.39% of habitat. Habitat area was related by regression analysis to the proportion of farm consisting of HM soils ( r 2 = 0.41, P < 0.05).

On the design and simulation-based validation of an active compliance law for multi-arm robots

A special active compliance law is presented as the feedback element in a non-master/slave (i.e. symmetric) coordination strategy with explicit force distribution for robots with multiple cooperating arms. The method used to design the compliance controller comprise a structural design phase and dynamics design phase. The proposed controller structure simplifies the design problem as it maps the multivariate system onto two decoupled SISO loops with PI controllers describing internal and external compliance behavior. The conditions for the validity of this conceptual system model are discussed and the significance of task parameters such as grasp configuration, force distribution law and mechanical compliance values for the controller structure is explored. The dynamic behavior of internal and external compliance is determined in the second design phase by the choice of gain and integral action time of the respective controllers. An example shows the applicability of classical SISO control system design tools such as the root locus technique. The validity of the design method has been verified by means of the multi-arm robot simulation program MAROSIM, which is also presented in the paper.

The Relationship Between System Identification and Model Validation In a Clinical Model of Renal Dialysis

A mathematical model of the human renal and related subsystems, part of a systems approach to the management of renal dialysis patients, is described. The results of identifiability and parameter estimation procedures are presented - conducted to determine unknown parameters in patients and as part of an extensive validation exercise. The link between identification and model validation that emerged is analysed as well as difficulties caused by conflicting objectives required of the model for clinical application.

Validity of an arterial system model: a quantitative evaluation.

The purpose of this investigation was to validate an arterial system model in a quantitative fashion. The model is based on a finite difference solution to the Navier-Stokes equations and retains certain nonlinear features of the system. Rather than apply standard error measures that test waveform correlation, the validation method used relies on the quantification of differences between the model and animals over a wide range of parametric changes. A series of functions was used to define the difference between the dependent variables of the model and corresponding hemodynamic variables of the animals. These functions were displayed as a family of three-dimensional difference surfaces which related the function value to parametric changes of the independent variables. Experimental data from three dogs were compared with model predictions. Regions of validity for the independent variables were then assessed by examining the difference surfaces.