Earl J. Kletsky

Diagnosis of Equipment Failures

This paper introduces several new concepts which are applicable to the problem of diagnosis of equipment failures. Following the definitions of an equipment, an element of the equipment, and the model of a test, a general diagram of a testing procedure is developed. The testing diagram is constructed in such a way that the various tests needed and the probability of failure of the elements are readily incorporated. While it is found that a completely general testing diagram becomes quite complicated even when the equipment under consideration is not intricate, a major simplification is obtained by introducing a simplified diagram with suitably restricted tests. This simplified testing diagram may be used repeatedly in order to find all the faulty elements of the equipment. With reference to the testing diagram, it is possible to compute the minimum average cost of diagnosing the equipment. This appears to be the most useful measure of the efficiency of a test procedure. The order of magnitude of this optimization problem is discussed and solutions for two special cases are obtained by analogy with an optimum coding problem.

Micromechanics in the theory of cochlear mechanics

Abstract The consensus of empirical data suggests that the shear motion between the tectorial membrane and the reticular lamina, which is believed to control the stimulation of the hair cells, is more sharply tuned than the transversal vibration of the basilar membrane. Interaction between the length of basilar-membrane waves and the longitudinal coupling within the tectorial membrane may contribute to the required sharpening. However, such a mechanism is unlikely to be sufficient, acting alone. Simple calculations indicate that damping of the tectorial membrane coupled viscoelastically to the organ of Corti is low enough to allow the system to exhibit local radial responses above about 150 Hz. Some effects of such resonances are illustrated by means of simple mechanical models. In particular, it is demonstrated that radial vibration of the tectorial membrane nearly at right angles to the transversal vibration of the basilar membrane constitutes an inherently nonlinear system. The radial vibration can produce strong loading of the basilar membrane, affecting its tuning and introducing nonlinearities. Nonlinear longitudinal coupling within the tectorial membrane, if present, can produce quadratic and cubic distortion products and strong two-tone suppression by second tones at frequencies above and below the resonance frequency. Such a coupling is suggested by the finding that, in the alligator lizard, the part of auditory papilla endowed with a tectorial membrane produces both effects, but the part not so endowed does not.

What basilar-membrane tuning says about cochlear micromechanics

Experiments performed within the last 15 years on cochleas of live animals indicate that the cochlear sound analysis is much sharper than was expected from Békésys experiments on postmortem preparations. The mechanism underlying the sharp analysis has not yet been ascertained experimentally. However, details of mechanical tuning curves defined by the amplitude of basilar-membrane vibration as a function of sound frequency ofr a constant amplitude of stapes displacement, together with structural and physical properties of he basilar and tectorial membranes and of the organ of Corti, strongly suggest a mechanism. The mechanism is assumed to result from a resonance of the tectorial membrane produced by interaction of the membranes mass with its viscoelastic attachments to the organ of Corti and the spiral limbus. The resonance would produce a strong vibration of the tectorial membrane in the radial plane and enhance the shear motion between the membrane and the reticular lamina. Mechanical and computer models of the mechanism have allowed the authors to reproduce in detail the empirical basilar membrane as well as corresponding neural tuning curves and to account for associated cochlear nonlinearities.

CM tuning can be compatible with sharply tuned receptor potentials

There is convincing evidence that cochlear microphonics (CM) arise primarily from outer hair cells and have a frequency distribution that is much broader than that measured in inner hair cells by Russel and Sellick [6,7]. The broad tuning results from the fact that CM generated at each location decays exponentially along the cochlear duct. This implies that the sources of CM (the outer hair cells) must be more sharply tuned than the CM itself. We modeled approximately the tuning of outer hairs on the assumption that it is proportional to the shear motion between the tectorial membrane and the reticular lamina. At each frequency the spatial distribution of CM is computed by convolving the shear distribution with an exponential decay function. The frequency dependence of CM at a given location can then be found by making a cut through a family of such frequency curves. The resulting CM tuning is much flatter than that of the modeled outer hair-cell receptor potentials and roughly parallels basilar-membrane tuning below the best frequency. Above the best frequency, the theoretical curves show a frequency-dependent plateau similar to that found in physiological CM measurements.

An Application of the Information Theory Approach to Failure Diagnosis

Brule, Johnson, and Kletsky1 have developed a technique based on information theory which leads to highly efficient procedures for diagnosing equipment failures. This paper demonstrates by means of a practical example the validity of this technique. In addition, the feasibility of the approach is shown and the procedure to be used in its implementation is outlined in detail. The paper concludes with a general discussion including comments on the generality of the technique, the possibility of machine computation, and possible areas of application.

A six-channel PDP-8 interface for nerve impulse data

An interface operating on the I/O bus of the LINC-8 has been built which accepts up to six channels of nerve impulse data simultaneously at rates up to 4,000 pps/channel. By means of a 100-KHz clock and a 17-bit counter, the time of occurrence of each nerve impulse is strobed into one of six 17-bit buffer registers. The strobe causes a program interrupt to occur. Two I/O instructions are used to read the buffers into the PDP-8 accumulator. Additional instructions for skipping on data or overflow, enabling the counter, clearing the overflow flag, and clearing the counter are available.

Upper Bounds on Mean Life of Self-Repairing Systems

Upper bounds on mean life of self-repairing systems are established on the basis of a very general system model. Expressions for system mean-life are obtained by formulating the problem as a two-dimensional difference equation in time and the number of nonfailed spare elements. Results indicate that mean life of an isolated system cannot be expected to exceed roughly three times the mean life of the elements which make it up, regardless of how standby elements are employed. If the element failure rate in standby is substantially less than the failure rate in operation, then system mean life is essentially linearly proportional to the number of available standby elements.

Cochlear tuning may reflect tectorial membrane resonance

Until recently it was not possible to account accurately for the basilar‐membrane amplitude and phase data of Rhode (1971). This may be so because the basilar membrane with its attachments was treated as a simple mechanical system consisting of stiffness, mass, and resistance distributed along the cochlea. When it is assumed instead that the mass of the tectorial membrane is attached elastically to the basilar membrane so that it can resonate in the radial mode at a frequency slightly above the measured best frequency, the resulting load on the basilar membrane leads to an amplitude and phase pattern in agreement with Rhodes. The effect was demonstrated on simple mechanical and network models. The latter yielded simultaneously a shear motion between the tectorial membrane and the reticular lamina, which paralleled neural tuning curves. The shear motion is generally regarded as the adequate stimulus for the hair cells. Construction of the tuning curves included a variable damping consistent with Rhodes r...

Outer Hair Cells: Sharpness of Tuning

According to Russell and Sellicks measurements. confirmed at our Institute, cochlear inner hair cells are more sharply tuned than the basilar membrane and as sharply as the cochlear-nerve fibers. Some measurements, including measurements of cochlear microphonics, have been interpreted as evidence that the outer hair cells are tuned more broadly. Straightforward calculations based on the approximately known tuning of the basilar membrane and the known electrical space constant of the cochlea reveal that outer hair cells must be approximately as sharply tuned as the inner hair cells to produce the known frequency distribution of cochlear microphonics.

Intensity Characteristics of Mechanoreceptors

According to recent detailed recordings of neural firing rates, the intensity characteristics of auditory and other mechanoreceptors closely approximate the input‐output function of an rms detector. This becomes particularly clearly evident when the stimulus consists of a sinusoid added to random noise. The characteristic remains the same for both extrinsic and intrinsic noise. It can be expressed by means of a simple equation that contains no free constants. The rms properties of auditory receptors appear to be reflected in psychophysical experiments that deal with monaural and central masking, signal detection as a function of duration, and loudness. In spite of great similarities, the mechanoreceptors should not be considered as true rms detectors, since they show some phase sensitivity. The difference can be ignored, however, under many experimental conditions.