Data measurement

Table 1 gives the measured data, estimates of the true values corresponding to the measurements, and deviations of the measured values from model predictions. Figure 1 shows the phase diagram corresponding to these parameters, together with the measured data. 

Figure 5.37 depicts the basic set up of a wireline logging operation. A sonde is lowered downhole after the drill string has been removed. The sonde is connected via an insulated and reinforced electrical cable to a winch unit at the surface. At a speed of about 600m per hour the cable Is spooled upward and the sonde continuously records formation properties like natural gamma ray radiation, formation resistivity or formation density. The measured data is sent through the cable and is recorded and processed in a sophisticated logging unita the surface. Offshore, this unit will be located in a cabin, while on land it is truck mounted. In either situation data can be transmitted in real time via satellite to company headquarters if required. 

Each of the input parameters has an uncertainty associated with it. This uncertainty arises from the inaccuracy in the measured data, plus the uncertainty as to what the values are for the parts of the field for which there are no measurements. Take for example a field with five appraisal wells, with the following values of average porosity for a particular sand ... 

When providing input for the STOMP calculation a range of values of porosity (and all of the other input parameters) should be provided, based on the measured data and estimates of how the parameters may vary away from the control points. The uncertainty associated with each parameter may be expressed in terms of a probability density function, and these may be combined to create a probability density function for STOMP. 

The starting point of this approach is that the 3D restoration is implemented by the solution of the variational problem for the trade-off functional M , which favors in a weighted manner measured data (functional A) and a priori knowledge (functional B) ... 

Often the a priori knowledge about the structure of the object under restoration consists of the knowledge that it contains two or more different materials or phases of one material. Then, the problem of phase division having measured data is quite actual. To explain the mathematical formulation of this information let us consider the matrix material with binary structure and consider the following potentials ... 

A novel optimization approach based on the Newton-Kantorovich iterative scheme applied to the Riccati equation describing the reflection from the inhomogeneous half-space was proposed recently [7]. The method works well with complicated highly contrasted dielectric profiles and retains stability with respect to the noise in the input data. However, this algorithm like others needs the measurement data to be given in a broad frequency band. In this work, the method is improved to be valid for the input data obtained in an essentially restricted frequency band, i.e. when both low and high frequency data are not available. This... 

The axial stress is the only stress component which can be determined directly from measurement data. Hence, we have the boundary-value problem with equations (27), (29)-(31) and the boundary conditions (34)-(36). 

The sampling precision of the measured data depends on the signal amplitude. The difference between simulated and experimental data can be mainly explained by the low numerical precision of the measured data. 

The comparison between measured data and simulated data are good for both real and imaginary parts. The measured signal has a low resolution due to the low interaction between the eddy current and the slot. 

The comparison between measured data and simulated data are good for the imaginary part, but differences appear for the real part. The ratio between simulated data and measured data is about 0.75 for TRIFOU calculation, and 1.33 for the specialised code. Those differences for the real part of the impedance signal can be explained because of the low magnitude of real part compared to imaginary part signal. 

The comparisons between measured and simulated data lead to the same conclusion as in case 2. The simulated data show more details on the curves, especially in the slot edges zones. This is linked most probably to the measured data resolution. 

The results obtained with the two methods confirm the measured data with a good precision, with less computational time for the specialised code than the general code. This validation on three representative test bloeks can lead to many applications of modelling of the thin-skin regime. 

At first, it is statistical standard of the undefective section. Such standard is created, introducing certain lower threshold and using measured data. Under the classical variant of the shadow USD method it is measured fluctuations of accepted signal on the undefective product and installed in each of 512 direction its threshold in proportion to corresponding dispersions of US signal in all 128 sections. After introducting of threshold signal is transformed in the binary form. Thereby, adaptive threshold is one of the particularities of the offered USCT IT. 

Chapter 4.3. discusses the explained theory for choosed examples. For several cracks the output is pre-calculated by using the impulse response and compared with measurement data. 

However the forms of the curves in fig. 5 are not fully symraetrieal. There are several causes for this nonlinear behaviour. For instance even small un-symmetrics in the coil construction or measurement errors caused by small differences in the position of the coil to the underground or the direction of coil movement influence the measured data and results in mistakes. 

At first a crack wider than the outer diameter of the coil winding is tested. The results of the superposition and the measured data are presented in fig. 8. 

A-scans with a visual evaluation by the tester to be of little significance. New measuring-data-evaluation-procedures were needed to place additional information at the testers disposal. 

If the signal features already have been chosen, another important problem is how to optimally combine these features in order to obtain the best estimate of the material property. The physical reasoning will give us ideas of how to combine the features but there will be no guarantee that we are using the chosen features in an optimal way. One reason for this is that we have to take into account the uncertainties that always are present in measurement data. 

As we have mentioned, the particular characterization task considered in this work is to determine attenuation in composite materials. At our hand we have a data acquisition system that can provide us with data from both PE and TT testing. The approach is to treat the attenuation problem as a multivariable regression problem where our target values, y , are the measured attenuation values (at different locations n) and where our input data are the (preprocessed) PE data vectors, u . The problem is to find a function iy = /(ii ), such that i), za jy, based on measured data, the so called training data. 

Ultrasonic techniques are an obvious choice for measuring the wall thickness. In the pulse-echo method times between echoes from the outer and inner surface of the tube can be measured and the wall thickness may be calculated, when the ultrasonic velocity of the material is known. In the prototype a computer should capture the measuring data as well as calculate and pre.sent the results. First some fundamental questions was considered and verified by experiments concerning ultrasonic technique (Table I), equipment, transducers and demands for guidance of the tube. 

As a fist attempt to see the influence of the tube drawing and the industrial environment on measured data, some experiments were performed for improving the measuring chamber and guidance as well optimizing the measuring condition. The main results were ... 

The Pascal code was updated to handle four channels. To follow the inspection speed all raw measuring data were captured and stored in the computer. All data for one coil could be stored in the computer memory (RAM) and transferred to the disk before inspection of the next coil. Evaluation of the data could be performed on-line or later using a special evaluation program. 

Figure B2.4.6. Results of an offset-saturation expermient for measuring the spin-spin relaxation time, T. In this experiment, the signal is irradiated at some offset from resonance until a steady state is achieved. The partially saturated z magnetization is then measured with a kH pulse. This figure shows a plot of the z magnetization as a fiinction of the offset of the saturating field from resonance. Circles represent measured data the line is a non-linear least-squares fit. The signal is nonnal when the saturation is far away, and dips to a minimum on resonance. The width of this dip gives T, independent of magnetic field inliomogeneity.

Statistical quaUty control charts of variables are plots of measurement data, preferably the average result of repHcate analyses, vs time (Fig. 2). Time is often represented by the sequence of batches or analyses. The average of all the data points and the upper and lower control limits are drawn on the chart. The control limits are closely approximated by the sum of the grand average plus for the upper control limit, or minus for the lower control limit, three times the standard deviation. 

The overall objective of research under way as of ca 1997 is to develop a system of sale by description for fine and medium wools whereby the buyer is presented only with measured data on the principal characteristics of the raw wool, as well as an assessment of the less important characteristics by an independent skilled appraiser (8). A scheme for assessing the risk of the presence of colored fiber content in greasy wool has been proposed which depends on production parameters and on the age and sex of the sheep (5). Instmmentation and computer algorithms for the measurement of style and handle... 

In Figure 2, a double-reciprocal plot is shown Figure 1 is a nonlinear plot of as a function of [S]. It can be seen how the least accurately measured data at low [S] make the deterrnination of the slope in the double-reciprocal plot difficult. The kinetic parameters obtained in this example by making linear regression on the double-reciprocal data ate =1.15 and = 0.25 (arbitrary units). The same kinetic parameters obtained by software using nonlinear regression are = 1.00 and = 0.20 (arbitrary units). 

Type of Data In general, statistics deals with two types of data counts and measurements. Counts represent the number of discrete outcomes, such as the number of defective parts in a shipment, the number of lost-time accidents, and so forth. Measurement data are treated as a continuum. For example, the tensile strength of a synthetic yarn theoretically could be measured to any degree of precision. A subtle aspect associated with count and measurement data is that some types of count data can be dealt with through the application of techniques which have been developed for measurement data alone. This abihty is due to the fact that some simphfied measurement statistics sei ve as an excellent approximation for the more tedious count statistics. 

For measurement data, probability is defined by the area under the curve between specified limits. A density function always must have a total area of 1. 

The sampling distribution of count data can be charac terized through probabihty distributions. In many cases, count data are appropriately interpreted through their corresponding distributions. However, in other situations analysis is greatly facilitated through distributions which have been developed for measurement data. Examples of each will be illustrated in the following subsections. 

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