Number Of Unknown Values Research Articles

X-Sand Filter: An X-Tolerant Response Compaction Technique for Faster-Than-At-Speed Testing

Faster-than-at-speed testing provides an effective way of detecting small delay defects but at the cost of increased number of unknown logic values on longer paths of the circuit under test. For efficient testing, these unknown logic values need to be filtered out of the circuit under test output. In past, different compaction hardware schemes were presented to minimize these unknown logic values, all these schemes were effective in handling a limited number of unknown values arising due to design imperfections, processing problems manufacturing problems material problems etc. but no effective compaction scheme is available to handle large number of these logic values arising due to faster-than-at-speed testing. This paper presents “X-sand filter”, a compaction technique, an extension of already presented idea of “X-tolerant signature analysis”. Here, the idea of “X-tolerant signature analysis” with modifications has been applied and has attained a considerable improvement in the X-tolerance. X-sand filter is a hierarchical structure that handles gradual X-density reduction in an efficient manner. Simulation results obtained show that we can achieve up to 90 % reduction in the X-density if we use X-sand filter. Extensions to the work of X-sand filter can be carried out in future to enhance its capabilities and make its configuration more flexible in terms of layer designing.

X-Sand Filter: An X-Tolerant Response Compaction Technique for Faster-Than-At-Speed Testing

Faster-than-at-speed testing provides an effective way of detecting small delay defects but at the cost of increased number of unknown logic values on longer paths of the circuit under test. For efficient testing, these unknown logic values need to be filtered out of the circuit under test output. In past, different compaction hardware schemes were presented to minimize these unknown logic values, all these schemes were effective in handling a limited number of unknown values arising due to design imperfections, processing problems manufacturing problems material problems etc. but no effective compaction scheme is available to handle large number of these logic values arising due to faster-than-at-speed testing. This paper presents “X-sand filter”, a compaction technique, an extension of already presented idea of “X-tolerant signature analysis”. Here, the idea of “X-tolerant signature analysis” with modifications has been applied and has attained a considerable improvement in the X-tolerance. X-sand filter is a hierarchical structure that handles gradual X-density reduction in an efficient manner. Simulation results obtained show that we can achieve up to 90 % reduction in the X-density if we use X-sand filter. Extensions to the work of X-sand filter can be carried out in future to enhance its capabilities and make its configuration more flexible in terms of layer designing.

Parametric Reconstruction of Diffuse Optical Tomography Using Gaussian Mixture Model and Genetic Algorithm

The inverse problem of diffused optical tomography is highly ill-posed as well as often nonunique and unstable. The ill-posedness can be reduced by reducing the number of unknown values (e.g., adding soft or hard-prior constraints). In this paper, this has been achieved by parameterization of the tissue optical properties. The optical parameters of the tissue have been modeled by a Gaussian mixture model (GMM) of eight components, and the image is reconstructed by estimating the parameters of the mixture model. Therefore, the number of unknowns is drastically reduced while maintaining some amount of generality by using an 8 component GMM. Unlike conventional GMM, the parameters are estimated using the Genetic algorithm in a multi-step predictor-corrector model. A new cost function is proposed using mean square error and asymmetry measurement of detected intensity. Object centroid error, structural similarity index, maximum error and normalized root mean squared error of reconstructed absorption coefficients are evaluated for performance assessment and comparison. Extensive numerical and experimental results have been illustrated to show the potential of the proposed method. Use of CW (continuous wave) measurement and single imaging modality make the system cost effective and portable.

Lipschitz Stability of an Inverse Boundary Value Problem for a Schrödinger-Type Equation

In this paper we study the inverse boundary value problem of determining the potential in the Schr\"{o}dinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that, under general settings, the optimal stability estimate is of logarithmic type. In this work, a Lipschitz type stability is established assuming a priori that the potential is piecewise constant with a bounded known number of unknown values.

Lipschitz Stability for the Electrical Impedance Tomography Problem: The Complex Case

In this article we investigate the boundary value problem where γ is a complex valued L ∞ coefficient, satisfying a strong ellipticity condition. In electrical impedance tomography, γ represents the admittance of a conducting body. An interesting issue is the one of determining γ uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map Λγ. Under the above general assumptions this problem is an open issue. In this article we prove that, if we assume a priori that γ is piecewise constant with a bounded known number of unknown values, then Lipschitz continuity of γ from Λγ holds.

Tomographic Reconstruction of Tracer Gas Concentration Profiles in a Room with the Use of a Single OP-FTIR and Two Iterative Algorithms: ART and PWLS

ABSTRACT Computed tomographic (CT) reconstructions of air contaminant concentration fields were conducted in a room-sized chamber employing a single open-path Fourier transform infrared (OP-FTIR) instrument and a combination of 52 flat mirrors and 4 retroreflectors. A total of 56 beam path data were repeatedly collected for around 1 hr while maintaining a stable concentration gradient. The plane of the room was divided into 195 pixels (13 × 15) for reconstruction. The algebraic reconstruction technique (ART) failed to reconstruct the original concentration gradient patterns for most cases. These poor results were caused by the “highly underdetermined condition” in which the number of unknown values (156 pixels) exceeds that of known data (56 path integral concentrations) in the experimental setting. A new CT algorithm, called the penalized weighted least-squares (PWLS), was applied to remedy this condition. The peak locations were correctly positioned in the PWLS-CT reconstructions. A notable feature of the PWLS-CT reconstructions was a significant reduction of highly irregular noise peaks found in the ART-CT reconstructions. However, the peak heights were slightly reduced in the PWLS-CT reconstructions due to the nature of the PWLS algorithm. PWLS could converge on the original concentration gradient even when a fairly high error was embedded into some experimentally measured path integral concentrations. It was also found in the simulation tests that the PWLS algorithm was very robust with respect to random errors in the path integral concentrations. This beam geometry and the use of a single OP-FTIR scanning system, in combination with the PWLS algorithm, is a system applicable to both environmental and industrial settings.

Control System of Substance and Energy Balances of Combined Heat-and-Power Plants Applying the Least Squares Adjustment Method

The set of substance and energy balance equations of water and steam collectors, together with the balance of boilers and turbines (including the regeneration system) is the base of the control system of the exploitation of a combined heat-and power plant. The initial values of this system are the results of measurements in the course of exploitation. Due to inevitable errors in the measurements the substance balances display discrepancies between the balance of steam and the balance of the feed water, and the calculated technical indices are uncertain. In order to increase the reliability of the results of the technical analysis of exploitation and to co-ordinate the balance equations we may use the least squares adjustment method. It may be applied on the condition that we have a sufficient surplus of measuring data. The number of balance equations must be higher than the number of unknown values. This makes it possible to apply the criterion of least squares warranting a maximum of the reliability function in an n dimensional. space of errors (n - number of measuring data). This method has been applied in the balance systems of the combined heat-and-power generating plant.