NEWMOD®, developed by R.C. Reynolds, Jr., has been an important tool for evaluating quantitatively X-ray diffraction (XRD) patterns from interstratified clay minerals for more than 20 years. However, a significant drawback to the NEWMOD® approach is that analyses are done by forward simulation, making results sensitive to user input and starting-model assumptions. In the present study, a reverse-fitting procedure was implemented in a new program, FITMOD, which automatically minimizes the differences between experimental and simulated XRD patterns. The differences are minimized by varying model parameters (such as Reichweite, crystal-size distribution, cation content, type of disorder, etc.) using the downhill simplex method. The downhill simplex method is a non-linear optimization technique for determining minima of functions. This method does not require calculation of the derivatives of the functions being minimized, an important consideration with many of the parameters in NEWMOD- type simulations. Instead, the downhill simplex method calculates pseudo-derivatives by evaluating sufficient points to define a derivative for each independent variable. The performance of FITMOD was evaluated by fitting a series of synthetic XRD patterns generated by NEWMOD+, yielding agreement factors, Rwp, of <0.3%. As long as the correct interstratified system was specified (e.g. illite-smectite), excellent fits were obtained irrespective of the starting parameters for the simulations. FITMOD was also tested using experimental XRD patterns, which gave very good fits, in agreement with previously published results. The optimization routine yields good fits for both synthetic and experimental XRD profiles in a reasonable time, with the possibility of varying all important structural parameters. FITMOD automatically provides optimum fits to experimental XRD data without operator bias, and fitting efficiency and accuracy were, therefore, significantly improved.

In the era of Unmanned Aerial Systems (UAS), an onboard autopilot occupies a prominent place and is inevitable for many of their modern applications. The efficacy of autopilot heavily relies upon the accuracy of the sensors employed and the capability of the onboard flight controller. In general, aerodynamic behaviour and flight dynamic capabilities of Unmanned Aerial Vehicles (UAVs) govern the selection and the design of flight controllers. Precise modeling of linear aerodynamic characteristics from flight data can be achieved using many of the existing classical parameter estimation techniques such as Output Error Method (OEM), Equation Error Method (EEM), and Filter Error Method (FEM). However, all the classical methods may not be readily applicable for aerodynamic modeling in nonlinear flight envelopes. The current manuscript is an attempt to exploit the capabilities of the Artificial Intelligence (AI) technique, named Particle Swarm Optimisation (PSO), in combination with Least Squares (LS) cost function to perform linear as well as nonlinear aerodynamic parameter estimation. The aforementioned task is accomplished by considering flight data from manoeuvers pertaining to linear angles of attack, moderate and near stall flight envelopes of two different UAVs with cropped delta planform geometry. Parameters estimated using the proposed LS-PSO method are consistent with minimum standard deviation and are on a par with OEM estimates. The proposed LS-PSO method enhances the capabilities of LS-based EEM while estimating stall characteristic parameters, which was not possible with LS alone. The longitudinal and lateral-directional static parameters estimated from the full-scale wind tunnel testing of the two UAVs were also used to corroborate the results obtained from the flight data using the LS-PSO method.

This paper contributes by presenting a parameter identification procedure for n-degrees-of-freedom flexible joint robot manipulators. An advantage of the given procedure is the obtaining of robot parameters in a single experiment. Guidelines are provided for the computing of the joint position filtering and velocity estimation. The method relies in the filtered robot model, for which no acceleration measurements are required. The filtered model is expressed in regressor form, which allows applying a parameter identification procedure based on the least squares algorithm. In order to assess the performance of the proposed parameter identification scheme, an implementation of a least squares with forgetting factor (LSFF) parameter identification method is carried out. In order to assess the reliability of the tested identification schemes, a model-based trajectory tracking controller has been implemented twice in different conditions: one control experiment using the estimated parameters provided by the proposed scheme, and another experiment using the parameters given by the LSFF method. These real-time control experiments are compared with respect to numerical simulations using the estimated parameters for each identification method. For the proposed scheme, the comparison between experiments and numerical simulations indicates better accuracy in the torque and position prediction.

In this paper, we consider a least squares nonconforming finite element of low order for solving the transport equations. We give a detailed overview on the stability and the convergence properties of our considered methods in the stability norm. Moreover, we derive residual type a posteriori error estimates for the least squares nonconforming finite element methods under H–1-norm, which can be used as the error indicators to guide the mesh refinement procedure in the adaptive finite element method. The theoretical results are supported by a series of numerical experiments.

A new approach in meshless methods has been introduced for stress assessment around a crack in two-dimensional elastic solids. This method with the name VDLSM (Voronoi Based Discrete Least Squares Meshless) is a pure meshless method which does not implement nodal mesh for trial and test functions. Rather, it uses a collection of the scattered nodal points and implements the discrete least squares approach to discretize the strong form of the governing differential equations on the domain of interest. This can reduce considerably the pre-processing cost of the analysis. Meshless methods generally are faced with some difficulty to accommodate the stress analysis in the vicinity of sharply concave surfaces such as cracks. Some techniques have been used to fix that problem such as visibility, transparency and diffraction, but these methods require some additional back corrective analyses for those parts of the domain located near the crack, which lengthen the time consumed for the solution and, moreover, do not provide the desired accuracy for the unknowns in these regions. VDLSM as a new, straightforward and easy applicable method has been suggested here for overcoming such deficiency using the algorithm of the Voronoi tessellation for constructing the Moving Least Squares (MLS) shape functions.

Research on estimation of a psychometric function Ψ has usually focused on comparing alternative algorithms to apply to the data, rarely addressing how best to gather the data themselves (i.e., what sampling plan best deploys the affordable number of trials). Simulation methods were used here to assess the performance of several sampling plans in yes–no and forced-choice tasks, including the QUEST method and several variants of up–down staircases and of the method of constant stimuli (MOCS). We also assessed the efficacy of four parameter estimation methods. Performance comparisons were based on analyses of usability (i.e., the percentage of times that a plan yields usable data for the estimation of all the parameters of Ψ) and of the resultant distributions of parameter estimates. Maximum likelihood turned out to be the best parameter estimation method. As for sampling plans, QUEST never exceeded 80% usability even when 1000 trials were administered and rendered accurate estimates of threshold but misestimated the remaining parameters. MOCS and up–down staircases yielded similar and acceptable usability (above 95% with 400–500 trials) and, although neither type of plan allowed estimating all parameters with optimal precision, each type appeared well suited to estimating a distinct subset of parameters. An analysis of the causes of this differential suitability allowed designing alternative sampling plans (all based on up–down staircases) for yes–no and forced-choice tasks. These alternative plans rendered near optimal distributions of estimates for all parameters. The results just described apply when the fitted Ψ has the same mathematical form as the actual Ψ generating the data; in case of form mismatch, all parameters except threshold were generally misestimated but the relative performance of all the sampling plans remained identical. Detailed practical recommendations are given.

The subject of the paper is the old and well-known linear least squares method for determining the lattice dimension of a crystalline phase from the peak locations of a powder diffraction pattern. Approximations, limits, and extensions of the method are discussed with reference to the assignment of hkl indices to an experimental multiphase pattern.

The main difficulty in the quantitative mineral analysis of rocks is connected with the variable nature of the mineral species. In the present paper a combined method (and a corresponding computer program) is proposed, which practically overcomes this difficulty. This method is based on linear equations, which are a combination of the chemical mass-balance equations with those of the quantitative X-ray diffractometry, and can perform (completely or partly) both the quantification and the chemical characterization of the minerals on several rock samples simultaneously, demanding only easily accessible initial information, such as: (i) major element (oxide) compositions for the samples; (ii) qualitative mineral composition of the samples; (iii) X-ray intensities for one or few nonoverlapped reflections of the crystalline minerals (not necessarily of all): (iv) some characteristic data for the phases (i.e., chemical composition data), if these are accurately known. Where it is possible the minerals may be expressed via end members. The samples may contain amorphous phases and/or phases without X-ray data. From the general case some very simple partial cases are derived, demanding less initial information. This method has the following advantages over the previous ones of similar philosophy: (i) drastic reduction of the number of required samples; (ii) sufficiency of equations for any analytical problem; (iii) possibility of performing partial analysis when a complete one is impossible; (iv) possibility of using the same end member in more than one solid solution. Analysis examples are given.

The constant elasticity of variance (CEV) diffusion process can be used to model heteroscedasticity in returns of common stocks. In this diffusion process, the volatility is a function of the stock price and involves two parameters. Similar to the Black-Scholes analysis, the equilibrium price of a call option can be obtained for the CEV model. The purpose of this paper is to propose a new estimation procedure for the CEV model. A merit of our method is that no constraints are imposed on the elasticity parameter of the model. In addition, frequent adjustments of the parameter estimates are not required. Simulation studies indicate that the proposed method is suitable for practical use. As an illustration, real examples on the Hong Kong stock option market are carried out. Various aspects of the method are also discussed.

This paper discusses possible approaches to the construction of gilt yield indices published by the Financial Times. The existing method, described by Dobbie & Wilkie (1978) splits bonds into high, medium and low-coupon bands and fits separate yield curves to each. This method has been identified as susceptible to ‘catastrophic’ jumps when the least-squares fit jumps from one set of parameters to another set of quite different values. This problem is a result of non-linearities in the least-squares formula which can give rise to more than one local minimum. A desire to remove the risk of catastrophic changes prompted this research, which is being carried out as part of the work of the Fixed Interest Working Group.

Recent changes in the taxation of bonds has, further, prompted the need for a review of the yield indices. Significantly, since the announcement of the new tax regime, the old coupon effect has been removed. This has made the use of a single forward-rate curve appropriate for the first time.

A particular form of forward-rate curve is proposed as the basis for a revision of the gilt yield indices. This curve appears to give a significantly better fit than the present yield–curve model. It is also argued that the risk of catastrophic jumps has been reduced significantly.

In the last decades, robust estimation has been widely applied to overcome the presence of gross errors in observations. Recently it has been shown that robust estimation, if computed appropriately, is able to cope with a larger amount of gross errors and also capable of providing reliable estimations in situations where systematic errors are present. It is the purpose of this paper to propose the use of global robust estimation for computing baselines strongly affected by multipath effects.

In this paper we report on the results of a recent dissection experiment in The Netherlands where prediction formulae for the percentage lean meat in pig carcasses with the Hennessy Grading Probe (HGP) and a vision system (from now on referred to as Vision) were determined. Predictions with the HGP were based on one fat and one muscle depth measurement only, while predictions with Vision were based on as many as 115 direct and derived measurements. The data from this dissection experiment were used to illustrate the statistical calculations involved in relation to the number of carcass measurements. Prediction with instruments that gather a large number of measurements per carcass is not covered by the present European Community (EC) regulations. Therefore the calculations were conducted according to new regulations for statistical methodology in pig carcass grading that are expected to be adopted by the EC in the near future. The calculations included consideration of 3 subpopulations (females, entire males and castrated males). The Vision data were also used to show that ordinary regression after selection of a subset of carcass measurements severely under estimates the accuracy of prediction: instruments and associated prediction formulae are seemingly much more accurate than they truly are. When standard regression methods are used for instruments that gather a large number of measurements, there is a considerable risk that measurement instruments will be selected for the wrong reasons. Accuracy of approved instruments may not even comply with the EC-regulations, with poor consequences for harmonization within the EC.