Original Full Model Research Articles

Reducing the number of new constraints and variables in a linearised quadratic assignment problem

The quadratic assignment problem is a well known difficult discrete combinatorial optimization problem. The problem seeks to locate n facilities among n fixed locations in the most economical way. We propose a technique to reduce the number of new constraints and variables in a linearised quadratic assignment problem. It is computationally cheaper to solve a mathematical model with half the number of new constraints and variables than the original full model. The quadratic assignment problem is common in agricultural resource or facility location, economics, production, military operations or operations research in general.

A clumped-foliage canopy radiative transfer model for a Global Dynamic Terrestrial Ecosystem Model II: Comparison to measurements

In a previous paper, we developed an analytical clumped two-stream model (ACTS) of canopy radiative transfer from an analytical geometric-optical and radiative transfer (GORT) scheme ( Ni-Meister et al., 2010). The ACTS model accounts for clumping of foliage and the influence of trunks in vegetation canopies for modeling of photosynthesis, radiative fluxes and surface albedo in dynamic global vegetation models (DGVMs), and particularly for the Ent Dynamic Global Terrestrial Ecosystem Model (DGTEM). This study evaluates the gap probability and transmittance estimates from the ACTS model by comparing the modeled results with ground-based data, as well as with the original full GORT model and a layered Beer's law scheme. The ground data used in this study include vertical profile measurements of incident photosynthetically active radiation (PAR) in (1) mixed deciduous forests in Morgan-Monroe State Forest, IN, USA, (2) coniferous forests in central Canada, (3) mixed deciduous forests in Harvard Forest, MA, and (4) ground lidar measurements of the canopy gap fraction in woodland in Australia. The model comparisons with these measurements demonstrate that the ACTS model achieves better or similar performance compared to the full GORT and the layered Beer's law schemes with regard to agreements with field measurements and computational cost. The ACTS model has excellent accuracy and flexibility to model the canopy gap probability and transmittance for various forest scenarios. Also, it has advantages relative to the currently widely used two-stream scheme through better radiation estimation for photosynthesis by accounting for the impact of both vertical and horizontal structure heterogeneity of complex vegetation on radiative transfer. Currently the ACTS is being implemented in Ent and will be further tested for how it improves surface energy balance and carbon flux estimates.

OPTIMUM PLACEMENT OF NON-LINEAR DAMPERS IN HIGH-RISE BUILDINGS BY USING REDUCED LOAD AND STRUCTURE MODELS

A set of reduced models of structures and earthquake loads is proposed for a high-rise building under earthquake ground motions. A reduced structural model is constructed first based on an inverse problem formulation in terms of fundamental eigenfrequency and eigenmode. Then a reduced model of earthquake loads is proposed by requiring the equivalence of displacements at representative nodes in the frame model and the reduced model without inertial and damping terms. These reduced models are used in developing an optimum placement method of nonlinear dampers in high-rise buildings under earthquake ground motions. Numerical response sensitivity by the proposed reduced model is taken full advantage in the optimum placement method. The validity of the proposed method is investigated by the comparison with the results by the original full model.

REDUCED LOAD AND STRUCTURE MODELS VIA INVERSE FORMULATION FOR TIME-HISTORY WIND RESPONSE ANALYSIS OF HIGH-RISE BUILDINGS

A set of reduced models of structures and wind loads is proposed for a high-rise building under time-dependent wind loading. A reduced structural model is constructed first based on an inverse problem formulation in terms of fundamental eigenfrequency and eigenmode. Then a reduced model of time-dependent wind loads is proposed by requiring the equivalence of displacements at representative nodes in the frame model and the reduced model without inertial and damping terms. These reduced models are applied to both the bare frame and the frame with high hardness rubber dampers. The validity of the proposed reduced models is investigated by the comparison with the results by the time-history analysis for an original full model.

Is my model too complex? Evaluating model formulation using model reduction

While mechanistic models tend to be detailed, they are less detailed than the real systems they seek to describe, so judgements are being made about the appropriate level of detail within the process of model development. These judgements are difficult to test, consequently it is easy for models to become over-parameterised, potentially increasing uncertainty in predictions. The work we describe is a step towards addressing these difficulties. We propose and implement a method which explores a family of simpler models obtained by replacing model variables with constants (model reduction by variable replacement). The procedure iteratively searches the simpler model formulations and compares models in terms of their ability to predict observed data, evaluated within a Bayesian framework. The results can be summarised as posterior model probabilities and replacement probabilities for individual variables which lend themselves to mechanistic interpretation. This provides powerful diagnostic information to support model development, and can identify areas of model over-parameterisation with implications for interpretation of model results. We present the application of the method to 3 example models. In each case reduced models are identified which outperform the original full model in terms of comparisons to observations, suggesting some over-parameterisation has occurred during model development. We argue that the proposed approach is relevant to anyone involved in the development or use of process based mathematical models, especially those where understanding is encoded via empirically based relationships.

Model Reduction of Large-Scale Discrete Plants With Specified Frequency Domain Balanced Structure

A new model reduction technique for linear time-invariant systems is proposed. A new method that reduces the order of large-scale systems by integrating singular perturbation with specified frequency domain balanced structure is proposed. Considering a frequency range at which the system actually operates guarantees a good approximation of the original full order model. Simulation experiments for model reduction of several large-scale systems demonstrate the effectiveness of the proposed technique.

Efficient low-order auto regressive moving average (ARMA) models for speech signals

Using model reduction, an efficient low order (ARMA) modeling process for speech is presented. In this approach, the modeling process starts with a relatively high order (AR) model obtained by some classical methods. The AR model is then reduced using the SVD-based method. The model reduction yields a reduced order ARMA model which interestingly preserves the key properties of the original full order model such as stability. Line spectral frequencies LSF and signal-to-noise ratio (SNR) behavior are also investigated. To illustrate the performance and the effectiveness of the proposed approach, some simulations are conducted on some practical speech segments, such as phonemes and sentences.

Quasi-optimal case-selective neural network model for software effort estimation

A number of software effort estimations have attempted using statistical models, case based reasoning, and neural networks. The research results showed that the neural network models perform at least as well as the other approaches, so we selected the neural network model as the estimator. However, since the computing environment changes so rapidly in terms of programming languages, development tools, and methodologies, it is very difficult to maintain the performance of estimation models for the new breed of projects. Therefore, we propose a search method that finds the right level of relevant cases for the neural network model. For the selected case set, the scale of the neural network model can be reduced by eliminating the qualitative input factors with the same values. Since there exist a multitude of combinations of case sets, we need to search for the optimal reduced neural network model and corresponding case set. To find the quasi-optimal model from the hierarchy of reduced neural network models, we adopted the beam search technique and devised the case-set selection algorithm. We have shown that the resulting model significantly outperforms the original full model for the software effort estimation. This approach can be also used for building any case-selective neural network.

Some further results related to reduced singular linear models

Consider the linear model (y, Xβ, V}, where the model matrix X may not have a full column rank and V might be singular. Let the model matrix he partitioned as X = (X1 : X2) the corresponding vector of unknown parameters being (β′1β′2)′. In this paper we generalize some results obtained by Nurhonen and Puntanen (1992) and Puntanen (1996) which are related to the properties of the BLUE of X1β1 under some specific reduced models and under the original full model.

Some matrix results related to a partitioned singular linear model

Consider the linear model (y, Xβ V), where the model matrix X may not have a full column rank and V might be singular. In this paper we introduce a formula for the difference between the BLUES of Xβ under the full model and the model where one observation has been deleted. We also consider the partitioned linear regression model where the model matrix is (X1: X2) the corresponding vector of unknown parameters being (β′1 : β′2)′. We show that the BLUE of X1 β1 under a specific reduced model equals the corresponding BLUE under the original full model and consider some interesting consequences of this result.

Structural sensitivity analysis via reduced-order analytical model

In dynamic analyses of flexible structures, it is often required to reduce the order of analytical finite element models to achieve reliable and efficient eigensolutions as well as many other engineering applications which require the order of an analytical model to be reduced, such as optimal designs of feedback control of aerospace structures. However, when a structural finite element model is reduced for such applications, the effect of design variable changes, which is localized in the original full-order mass and stiffness matrices, generally becomes spread in the reduced-order mass and stiffness matrices. This makes the sensitivity analysis, which is required in almost all modern structural designs, very difficult to achieve. In this paper, a technique is developed which reduces the order of original analytical finite element model, yet enables design sensitivity analysis to be performed efficiently by suitable selection of master and slave coordinates. Also, a method for calculating eigenvalue and eigenvector derivatives via the reduced-order analytical model is presented and applied to structural design practice to predict the changes of eigenvalues and eigenvectors given structural modifications as well as to tailor the eigenvalues and eigenvectors by identifying the structural modifications required. A realistic structural model is used to demonstrate the concept developed and results are compared with those from the analysis of original full analytical model. Possible integration of the proposed techniques into commercial finite element analysis softwares is discussed.