Foldable compatibility matrix for the folding of programmable logic arrays

This paper describes a switching theoretic algorithm for the folding of programmable logic arrays (PLA). The algorithm is valid for both column and row folding, although it has been presented considering only the simple column folding. The pairwise compatibility relations among all the pairs of the columns of the PLA are mapped into a square matrix, called the compatibility matrix of the PLA. A foldable compatibility matrix (FCM), a new concept introduced by the author, is then derived from the compatibility matrix. A new theorem called the folding theorem is then proved. The theorem states that the existence of an m by 2m FCM is both necessary and sufficient to fold 2m columns of the n column PLA (2m ≤ n). Once an FCM is obtained, the ordered pairs of foldable columns and the re-ordering of the rows are readily determined.

Application of Mathematical Programming to the Plywood Design and Manufacturing Problem

Plywood manufacture includes two fundamental stages. The first is to peel or separate logs into veneer sheets of different thicknesses. The second is to assemble veneer sheets into finished plywood products. At the first stage a decision must be made as to the number of different veneer thicknesses to be peeled and what these thicknesses should be. At the second stage, choices must be made as to how these veneers will be assembled into final products to meet certain constraints while minimizing wood loss. These decisions present a fundamental management dilemma. Costs of peeling, drying, storage, handling, etc. can be reduced by decreasing the number of veneer thicknesses peeled. However, a reduced set of thickness options may make it infeasible to produce the variety of products demanded by the market or increase wood loss by requiring less efficient selection of thicknesses for assembly. In this paper the joint problem of veneer choice and plywood construction is formulated as a nonlinear integer programming problem. A relatively simple optimal solution procedure is developed that exploits special problem structure. This procedure is examined on data from a British Columbia plywood mill. Restricted to the existing set of veneer thicknesses and plywood designs used by that mill, the procedure generated a solution that reduced wood loss by 79 percent, thereby increasing net revenue by 6.86 percent. Additional experiments were performed that examined the consequences of changing the number of veneer thicknesses used. Extensions are discussed that permit the consideration of more than one wood species.

Functional programming systems revisited

Functional Programming (FP) systems are modified and extended to form Nondeterministic Functional Programming (NFP) systems in which nondeterministic programs can be specified and both deterministic and nondeterministic programs can be verified essentially within the system. It is shown that the algebra of NFP programs has simpler laws in comparison with the algebra of FP programs. "Regular" forms are introduced to put forward a disciplined way of reasoning about programs. Finally, an alternative definition of "linear" forms is proposed for reasoning about recursively defined programs. This definition, when used to test the linearity of forms, results in simpler verification conditions than those generated by the original definition of linear forms.

Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic

Uncertainties associated with the structural model and measured vibration data may lead to unreliable damage detection. In this paper, we show that geometric and measurement uncertainty cause considerable problem in damage assessment which can be alleviated by using a fuzzy logic-based approach for damage detection. Curvature damage factor (CDF) of a tapered cantilever beam are used as damage indicators. Monte Carlo simulation (MCS) is used to study the changes in the damage indicator due to uncertainty in the geometric properties of the beam. Variation in these CDF measures due to randomness in structural parameter, further contaminated with measurement noise, are used for developing and testing a fuzzy logic system (FLS). Results show that the method correctly identifies both single and multiple damages in the structure. For example, the FLS detects damage with an average accuracy of about 95 percent in a beam having geometric uncertainty of 1 percent COV and measurement noise of 10 percent in single damage scenario. For multiple damage case, the FLS identifies damages in the beam with an average accuracy of about 94 percent in the presence of above mentioned uncertainties. The paper brings together the disparate areas of probabilistic analysis and fuzzy logic to address uncertainty in structural damage detection.

On the bottleneck linear programming problem

In this paper, the results on primal methods for Bottleneck Linear Programming (BLP) problem are briefly surveyed, the primal method is presented and the degenerate case related to Bottleneck Transportation Problem (BTP) is explicitly considered. The algorithm is based on the idea of using auxiliary coefficients as is done by Garfinkel and Rao [6]. The modification presented for the BTP rectifies the defect in Hammer's method in the case of degenerate basic feasible solution. Illustrative numerical examples are also given.

Static RAM cell for ternary logic

A novel CMOS static RAM cell for ternary logic systems is described. This cell is based on the lambda diode. The operation of the cell has been simulated using the SPICE 2G program. The results of the simulation are given.

A Note on Easily Testable Realizations for Logic Functions

It is shown that at most, n + 3 tests are required to detect any single stuck-at fault in an AND gate or a single faulty EXCLUSIVE OR (EOR) gate in a Reed-Muller canonical form realization of a switching function.

Reed-Muller Canonical Forms in Multivalued Logic

Canonical forms for m-valued functions referred to as m-Reed-Muller canonical (m-RMC) forms that are a generalization of RMC forms of two-valued functions are proposed. m-RMC forms are based on the operations ?m (addition mod m) and .m (multiplication mod m) and do not, as in the cases of the generalizations proposed in the literature, require an m-valued function for m not a power of a prime, to be expressed by a canonical form for M-valued functions, where M > m is a power of a prime. Methods of obtaining the m-RMC forms from the truth vector or the sum of products representation of an m-valued function are discussed. Using a generalization of the Boolean difference to m-valued logic, series expansions for m-valued functions are derived.

Finite field computation technique for exact solution of systems of linear equations and interval linear programming problems

An error-free computational approach is employed for finding the integer solution to a system of linear equations, using finite-field arithmetic. This approach is also extended to find the optimum solution for linear inequalities such as those arising in interval linear programming probloms.

A Nonlinear Approach for Re-entry Guidance of Reusable Launch Vehicles Using Model Predictive Static Programming

A nonlinear suboptimal guidance scheme is developed for the reentry phase of the reusable launch vehicles. A recently developed methodology, named as model predictive static programming (MPSP), is implemented which combines the philosophies of nonlinear model predictive control theory and approximate dynamic programming. This technique provides a finite time nonlinear suboptimal guidance law which leads to a rapid solution of the guidance history update. It does not have to suffer from computational difficulties and can be implemented online. The system dynamics is propagated through the flight corridor to the end of the reentry phase considering energy as independent variable and angle of attack as the active control variable. All the terminal constraints are satisfied. Among the path constraints, the normal load is found to be very constrictive. Hence, an extra effort has been made to keep the normal load within a specified limit and monitoring its sensitivity to the perturbation.

Assessment of SET Logic Robustness Through Noise Margin Modeling

A compact model for noise margin (NM) of single-electron transistor (SET) logic is developed, which is a function of device capacitances and background charge (zeta). Noise margin is, then, used as a metric to evaluate the robustness of SET logic against background charge, temperature, and variation of SET gate and tunnel junction capacitances (CG and CT). It is shown that choosing alpha=CT/CG=1/3 maximizes the NM. An estimate of the maximum tolerable zeta is shown to be equal to plusmn0.03 e. Finally, the effect of mismatch in device parameters on the NM is studied through exhaustive simulations, which indicates that a isin [0.3, 0.4] provides maximum robustness. It is also observed that mismatch can have a significant impact on static power dissipation.

Fuzzy-logic-based health monitoring and residual-life prediction for composite helicopter rotor

A health-monitoring and life-estimation strategy for composite rotor blades is developed in this work. The cross-sectional stiffness reduction obtained by physics-based models is expressed as a function of the life of the structure using a recent phenomenological damage model. This stiffness reduction is further used to study the behavior of measurable system parameters such as blade deflections, loads, and strains of a composite rotor blade in static analysis and forward flight. The simulated measurements are obtained using an aeroelastic analysis of the composite rotor blade based on the finite element in space and time with physics-based damage modes that are then linked to the life consumption of the blade. The model-based measurements are contaminated with noise to simulate real data. Genetic fuzzy systems are developed for global online prediction of physical damage and life consumption using displacement- and force-based measurement deviations between damaged and undamaged conditions. Furthermore, local online prediction of physical damage and life consumption is done using strains measured along the blade length. It is observed that the life consumption in the matrix-cracking zone is about 12-15% and life consumption in debonding/delamination zone is about 45-55% of the total life of the blade. It is also observed that the success rate of the genetic fuzzy systems depends upon the number of measurements, type of measurements and training, and the testing noise level. The genetic fuzzy systems work quite well with noisy data and are recommended for online structural health monitoring of composite helicopter rotor blades.

Genetic programming metamodel for rotating beams

This paper investigates the use of Genetic Programming (GP) to create an approximate model for the non-linear relationship between flexural stiffness, length, mass per unit length and rotation speed associated with rotating beams and their natural frequencies. GP, a relatively new form of artificial intelligence, is derived from the Darwinian concept of evolution and genetics and it creates computer programs to solve problems by manipulating their tree structures. GP predicts the size and structural complexity of the empirical model by minimizing the mean square error at the specified points of input-output relationship dataset. This dataset is generated using a finite element model. The validity of the GP-generated model is tested by comparing the natural frequencies at training and at additional input data points. It is found that by using a non-dimensional stiffness, it is possible to get simple and accurate function approximation for the natural frequency. This function approximation model is then used to study the relationships between natural frequency and various influencing parameters for uniform and tapered beams. The relations obtained with GP model agree well with FEM results and can be used for preliminary design and structural optimization studies.

Modeling and Analysis of Noise Margin in SET Logic

In this paper the static noise margin for SET (single electron transistor) logic is defined and compact models for the noise margin are developed by making use of the MIB (Mahapatra-Ionescu-Banerjee) model. The variation of the noise margin with temperature and background charge is also studied. A chain of SET inverters is simulated to validate the definition of various logic levels (like VIH, VOH, etc.) and noise margin. Finally the noise immunity of SET logic is compared with current CMOS logic.