Hand-considered hypotheses, 2601–2700

Misattribution
H2601. Backwall drop in a forged hub is routinely charged to a large inclusion, but when it appears at one refracted angle and vanishes at another the likelier cause is grain texture steering the beam. Forging reduction lines align the grain axes, and the velocity anisotropy that results bends the beam by a degree or two, enough to walk the reflection off a small backwall area. Scanning one spot at two refracted angles with a fixed zero-degree longitudinal probe separates them, because texture moves the echo and an inclusion dims it at every angle.

Hidden term
H2602. Attenuation obtained from the decay of successive backwall echoes always carries the beam-diffraction loss and the transmission loss at the two couplant films, and neither belongs to the metal. Diffraction grows with path length while absorption grows linearly with it, so a slope fitted over a short path is mostly geometry. Two probes of different aperture at the same nominal frequency, on one block, size the term: a material coefficient would not change with aperture.

Bound
H2603. For a fixed grain size and frequency there is a sound path beyond which a flat-bottom hole of specified size cannot be separated from grain noise, however much gain is applied, because gain lifts the signal and the scatter together. The limit sits where the power scattered per unit volume, integrated over the beam's volume, approaches the power the reflector returns. Two blocks of one alloy and one grain size but different thickness, run at a single frequency, locate it.

Conservation argument
H2604. In a scattering material the coherent backwall echo can lose only what the incoherent field gains, so a reported loss of backwall and a reported rise in grass are two views of one transfer of energy rather than two indications. Integrating the scattered intensity over angle and time and comparing it with the coherent deficit turns that into arithmetic. When the two do not balance, the missing energy has gone into a leak, a mode conversion, or a wedge reflection, and that imbalance is the finding.

Threshold
H2605. Amplitude sizing of a crack turns over below a certain height: while the crack is shorter than roughly a wavelength the echo is set by tip diffraction rather than by the faces, and for a tightly closed crack it can fall as the faces come into contact. The turnover sits between a quarter and a half wavelength of the incident shear wave, as an order of magnitude (estimate). A series of EDM slots of one width and increasing height, scanned at fixed gain from a single angle, marks where the curve bends.

Reversal
H2606. Tightening the focal spot raises the echo from a small flaw and is taken to improve sizing, yet a strongly focused probe has a short depth of field, so a flaw outside the focal zone is measured with an effective aperture smaller than the calibration assumed. Sizing can therefore degrade as focusing sharpens whenever depth is uncertain. One flaw at two depths, sized with a flat probe and with a tightly focused one at the same frequency, settles which penalty dominates.

Artefact mimics effect
H2607. What looks like a root indication in a thick weld is sometimes only the weld cap at work, the shear wave mode-converting on the cap's sloped face and returning along a path that a straight-ray assumption maps onto the root. What betrays it is that the apparent depth follows the cap profile rather than the weld preparation. Grinding one cap and re-scanning, with the root left untouched, settles whether the indication travels with the cap.

Scale argument
H2608. Surface finish is a wavelength-dependent problem and not a fixed one: a ground surface that reflects coherently at 5 MHz scatters diffusely at 20 MHz, because the roughness amplitude has crossed the Rayleigh criterion against the shorter wavelength. The crossing arrives sooner than the usual rule suggests for an angled beam, since the effective wavelength along the surface is shortened by the angle of incidence. One rough specimen inspected at three frequencies, with coherent and diffuse energy tracked separately, reveals the crossing in a single part.

Inversion of standard practice
H2609. Conventional practice sets scan index from beam width and treats anything finer as wasted effort, but in coarse-grained steel the binding constraint is the decorrelation distance of grain noise, so scanning finer and averaging along the scan both lowers the floor and changes which indications survive. The defensible index there is set by noise correlation, not by coverage. Scanning one region at three indices and asking which indications persist measures it without a reference flaw.

Selection effect
H2610. Probability-of-detection curves are nearly always fitted to flaws the technique already found, which selects reflectors tilted favourably to the beam and lying near the calibration depth, so the number describes that subpopulation rather than the fleet. A population of tight, tilted, near-surface cracks is then covered by a statistic that never sampled it. Seeding a block with flaws of randomized tilt and aspect, and computing detection within each orientation class, exposes how much of the quoted figure is selection.

Unit trap
H2611. Decibels per millimetre is a one-way figure in most tables and a round-trip figure in most instruments, so a sizing correction built with the wrong convention is out by a factor of two while looking entirely plausible; the neper-to-decibel factor of 8.686 lurks in the same arithmetic. Measuring a step wedge in one setup, applying the correction both ways, and comparing each against the known step heights identifies which convention the instrument is using.

Count
H2612. Within a plate thinner than the pulse, the number of resolvable backwall multiples is fixed by the pulse's time-bandwidth product and by the plate thickness, and no processing recovers more independent echoes than that. A claim of many-layer separation from a short pulse in a thin section exceeds the count the pulse can carry. Correlating the echo train against the known pulse at two bandwidths establishes how many multiples are real.

No-go claim
H2613. No correction applied after the fact makes dry-contact thickness gauging match immersion on a rough surface, because the coupling layer is an air gap whose thickness varies from point to point inside the footprint, and its transmission is not a function of any measurable average. The error is set by the distribution of gap thicknesses, not by their mean. Gauging one rough plate dry and by immersion, then comparing the scatter rather than the bias, isolates the part that cannot be removed.

Dimensional argument
H2614. Detectability of a tight crack is governed by the ratio of its opening displacement to the wavelength, not by its length, so a long closure-loaded crack can return less than a short open one at the same depth. The reflection from a thin scatterer depends on the impedance contrast across the gap, and face contact restores most of the contrast the void removed. Fatigue cracks grown to different lengths under different closure loads, examined at one angle and gain, put the two variables in opposition.

Degeneracy
H2615. Amplitude and time of flight from a single angle are degenerate, since a larger flaw deeper and a smaller flaw shallower give the same pair of numbers, and a sizing routine reading both from one A-scan is choosing a point on a curve without saying so. Two refracted angles break the degeneracy because the two curves cross at one depth. The same flaw measured from both angles, with the intersection checked against a known side-drilled hole, tells whether the routine was sizing or guessing.

Cancellation
H2616. A phased array focused with a velocity that is wrong by a percent can produce a steering-angle error and a focal-depth error that vary oppositely with depth, leaving a depth at which the two cancel and the array looks perfectly calibrated. That self-consistency is the hazard, because the check passes exactly where it is performed. Focal laws built with velocities one percent apart, compared over a range of depths against a side-drilled hole, show the crossing and where confidence in the array should end.

Sign error
H2617. The time-of-flight diffraction depth equation has two branches, and which one applies depends on whether the reflector lies above or below the mid-plane between the probes; taking the wrong branch mirrors the crack about that plane. The mirrored depth is usually plausible, sits inside the weld, and passes a check against the drawing. A reflector of known depth placed on both sides of the mid-plane discriminates at once, because only one branch puts each of them where it belongs.

Energy budget
H2618. Reverberation in a thin-walled component decays mainly by leakage at the boundaries and only secondarily by absorption, so a decay rate inverted as material damping returns a number that changes when the component is clamped differently. In thick sections the two terms trade places and the inversion becomes reasonable again. The same alloy as a thin plate and a thick block, with decay measured before and after a boundary is loaded, separates leakage from absorption.

Confound
H2619. When velocity is used to infer stress in a hot component, the temperature coefficient of velocity is of the same order as the acoustoelastic coefficient times the working stress, so an unstressed part at service temperature can read like a stressed one at ambient. A single velocity cannot separate the two contributions. Heating a stress-free coupon of the same alloy through the range gives the temperature term outright, and what remains in the component is then attributable to stress.

Bound
H2620. Time averaging improves signal-to-noise only against noise that is incoherent between acquisitions; grain noise from a fixed transducer position is coherent, so averaging at one position converges on a floor set by the material. The floor moves only when the beam or the part moves. Repeating a single A-scan a thousand times, then repeating a scan with small positional dithering about the same nominal location, reveals which average is accomplishing anything.

Misattribution
H2621. A baseline shift that follows a maintenance visit is usually read as damage, but re-torquing a nearby bolt or repainting a bracket alters the local boundary condition and rescales modal amplitudes with no new defect present. The signature is that the change appears in modes whose displacement peaks at the bracket and not in modes that are null there. Exciting a mode with a node at the bracket and another with an antinode, on the same path, separates the two causes.

Hidden term
H2622. Every guided-wave damage index contains a temperature term, because transducer coupling and material modulus both vary with temperature and they do not vary in step. Over a laboratory afternoon the term is negligible; over a diurnal swing it can exceed the damage signature it is supposed to reveal. Recording one path continuously for a week with no load applied gives the term's shape, which can then be subtracted instead of fitted.

Identity claim
H2623. Transmission measured from end A to end B and from B to A are the same quantity by reciprocity, so a path that appears damaged from one end and healthy from the other is reporting a transducer problem rather than a defect. The mechanism is simply that the Green's function is symmetric while a debonded sensor is not. Measuring every path in both directions, and flagging the asymmetric ones, converts a nuisance into a self-check.

Bound
H2624. Single-mode operation has a ceiling in frequency-thickness: above the cutoff of the first higher-order mode the clean pair is gone and the received signal is a superposition that no filter untangles. Resolution therefore cannot be bought by raising frequency indefinitely in a given wall. A frequency sweep on one plate, with the received packet's envelope shape tracked through the cutoff, marks where the usable band ends.

Threshold
H2625. Beneath a stiffener, a disbond escapes guided-wave detection below a size set by the ratio of the stiffener's mechanical impedance to the plate's, and that ratio, not the wavelength, fixes the threshold. The stiffener carries the wave around the disbond, so the shadow only forms once the bypass path is longer than the direct one by enough to matter. Bonded plates with stiffeners and inserts of graded size, tested in one setup, put the threshold where the impedance ratio predicts.

Reversal
H2626. Raising the excitation amplitude in a nonlinear guided-wave test increases the second harmonic at first and then reduces it, because the contact nonlinearity at a closed crack saturates once the faces are driven into full contact through the cycle. Sensitivity to a tight crack is therefore best at a moderate drive, not at the maximum the amplifier can produce. A drive sweep on one cracked specimen, with the harmonic measured at each level, locates the peak and the fall.

Artefact mimics effect
H2627. Thickness steps return packets that look like crack echoes in both amplitude and polarity, and in a structure with many steps the false calls can outnumber the true ones. The step's reflection is asymmetric with direction, stronger travelling from thin to thick than the reverse, while a crack reflects nearly equally both ways. Recording the same path in both directions and comparing the reflected amplitudes identifies the step without opening anything.

Scale argument
H2628. Group velocity measured over a short path is dominated by the excitation bandwidth, so the value obtained depends on the path length until the path exceeds the dispersion length of the mode. A velocity measured on a 200 mm path and applied to a 2 m path is then a different number, and the error looks like a material change. The same mode measured over three path lengths on one plate, plotted against length, marks where the value stops moving.

Inversion of standard practice
H2629. Uniform sensor spacing is the default because it is easy to defend, but for a structure whose likely damage sits in known hot spots the better arrangement is deliberate placement at antinodes of the modes that the damage would disturb, even if that leaves long stretches unwatched. Coverage maps drawn from spacing alone reward uniformity rather than sensitivity. Two arrays of equal channel count, one uniform and one placed by mode shape, compared on the same seeded damage, show which actually detects.

Selection effect
H2630. Laboratory validation of guided-wave monitoring usually employs saw cuts, drilled holes, and bonded masses, all of which reflect far more strongly than the disbonds and delaminations they stand in for, so the validated sensitivity belongs to the surrogate. Service damage that is closed, tapered, or partly bonded returns a fraction of that. Seeding one panel with both surrogates and with real impact damage of matched size, then comparing detection, measures the gap.

Unit trap
H2631. Tuning curves are drawn in frequency-thickness, and kHz·mm against MHz·mm is a factor of a thousand that silently moves the operating point into a different mode family. An entry in one unit read as the other produces a design that looks reasonable on the chart and excites the wrong mode in the part. Computing the same design point in both units, and checking the predicted phase velocity against a measured value, catches it before the hardware is built.

Count
H2632. At a given frequency-thickness only a fixed number of propagating modes exist, set by the plate's symmetry and its elastic constants, and any inversion claiming to resolve more independent damage parameters than there are modes is fitting the noise. The modes are the degrees of freedom, and no processing creates more. Exciting a band in which three modes propagate and attempting a four-parameter fit, with the residual examined against the mode count, demonstrates the overreach.

No-go claim
H2633. No baseline-free scheme removes a temperature effect that is nonlinear in temperature by stretching the time axis linearly, since the stretch is exact only for a pure and uniform velocity scaling. Real structures have adhesive layers and coatings whose modulus curves differ from the plate's, so the warp is not a stretch at all. Applying the optimal stretch to data taken at three temperatures and examining the residual's structure rather than its size exposes what remains.

Conservation argument
H2634. Energy arriving at a discontinuity is partitioned among reflection, transmission, and mode conversion, so a damage index built only on transmission loss will report a scatterer as an absorber. The three parts sum to the incident energy, and that sum is a stronger constraint than any one of them. Measuring reflection and transmission on the same path, and checking the sum against the undamaged case, distinguishes a scatterer from a genuine sink that turns wave energy into heat.

Derived quantity
H2635. The energy damage index is the square of the amplitude damage index, so a threshold transferred from one to the other is wrong by a square and a ten percent amplitude change becomes a twenty-one percent energy change. Both are called the index in the literature and neither carries its definition. Computing both from one recorded set and plotting them against each other yields the parabola, and a straight line through the origin would prove one of the two definitions wrong.

Confound
H2636. A kissing bond and a thick adhesive layer both attenuate the transmitted guided wave, and the two are hard to separate from transmission alone. The layer thickness changes the mode's phase velocity, while a kissing bond leaves velocity nearly intact and removes energy. Measuring phase as well as amplitude, on bonds of known thickness made with and without release agent, separates the two axes.

Mode conversion
H2637. At depth, a delamination sheds a mode-converted packet whose arrival time depends on where the interface sits through the thickness, and that timing carries the depth information amplitude does not. The conversion happens because a free interface admits both symmetric and antisymmetric families, and the coupling strength varies with the interface's position. Impact damage of graded depth, measured with a single transducer pair, orders itself by the converted packet's delay.

Reciprocity argument
H2638. When a transducer is poorly bonded, reciprocity between drive and sense breaks in a way that a simple amplitude check misses, because the same weak bond attenuates both directions similarly. What breaks is the phase relation between the two directions, which is sensitive to the bond's stiffness rather than its loss. Driving each transducer in turn and comparing the two transfer functions in phase, not just in magnitude, exposes a partial debond.

Limiting case
H2639. As an adhesive bond becomes perfectly rigid, the interface mode's frequency should approach the free-surface value, and watching that approach is a way to measure bond stiffness without a reference. A bond that is stiff but lossy will approach the frequency limit while keeping its attenuation, so the two properties separate along the approach. Bonds cured for different times, measured repeatedly through the cure, trace the approach and show where stiffness stops changing while loss does not.

Causality argument
H2640. Features in a differential guided-wave signal that drift as more averages accumulate are a property of the processing chain, not of the structure, because a physical scatterer's arrival time is fixed while an averaged artefact migrates toward the mean. The direction of migration is the tell: real damage moves the residual once and stops. Reconstructing the same residual at one, ten, and a hundred averages reveals whether the feature converges or continues to move.

Misattribution
H2641. Emission recorded during a proof test on a large frame is often dominated by the load train rather than the specimen, since every pin, shim, and hydraulic grip settles and frets under load and each of those events radiates. The events cluster at the load holds and at load reversals, which is also where real damage would be expected. Loading a dummy specimen of matched stiffness through the same schedule gives the load-train signature, and anything surviving subtraction is a candidate.

Hidden term
H2642. Recorded event energy is not a source property as recorded, because the sensor's own resonance shapes the spectrum and the coupling layer filters it again, so two sensors on one event return energies differing by more than the event's variance. (estimate) What is recorded is the source energy convolved with two transfer functions. Bonding two dissimilar sensors at one location and comparing their energy distributions over many events quantifies how much of the number is the sensor.

Identity claim
H2643. An event and a hit are the same physical occurrence only on a single channel; once several channels are used, the count of events becomes a function of the array's detection threshold and geometry rather than of the source. The number is then a property of the instrumentation. Recording one emission source with two array geometries at matched thresholds, and comparing event rates, measures how far the count has drifted from the source.

Bound
H2644. The measurable emission rate has a ceiling set by the system's dead time, and above it events overlap and are counted as one, so a rise in activity can produce a fall in the recorded rate. The peak of the recorded curve marks saturation, not the material's maximum. A controlled source pulsing at increasing rates, logged through the same acquisition chain, measures the dead time directly and locates that peak.

Threshold
H2645. Crack advance emits detectable emission only above an increment set by the grain size and the size of the plastic zone at the tip; below it, growth is aseismic and the silence is not evidence of arrest. The threshold is a property of the microstructure as much as of the loading. Fatigue tests at two stress-intensity ranges on one alloy, with emission per cycle compared against measured striation spacing, locate it.

Reversal
H2646. Faster loading raises the emission rate up to a point, after which it falls again, because at high rates the tip's plastic zone is constrained and the material responds by creep and distributed microplasticity rather than by discrete bursts. The fall is not a sign of healing. A rate sweep on one specimen, with emission counted per unit of crack advance, locates the maximum and the change of mechanism.

Artefact mimics effect
H2647. Electrical interference from a welding set or a pump start produces bursts that look like emission, but the artefact arrives at every channel with essentially zero time difference, while a real source's arrivals differ by the propagation delays. The two separate by the coherence of the arrival pattern, not by waveform shape alone. Logging plant electrical noise with the transducers on a nonloaded reference, and comparing arrival-time scatter, settles it in one shift.

Scale argument
H2648. The volume a sensor can monitor scales with the source amplitude raised to the reciprocal of the attenuation coefficient, so doubling the detection threshold shrinks the monitored volume by a large factor rather than a small one. (estimate) The monitored region is therefore a property of the threshold and the material's attenuation together. Moving a known source away from a sensor in steps, at two thresholds, maps the curve directly.

Inversion of standard practice
H2649. Standard practice holds the load during an emission test because that is when damage is thought to grow, yet in many structures the hold is dominated by friction and creep noise, and the informative part of the record is the unload and the reload. Unloading closes cracks and produces a distinctive signature, and reloading past the previous maximum produces the Felicity departure. Comparing emission accumulated during holds against that during the ramps, on one test, identifies which segment carries the information.

Selection effect
H2650. Emission databases are built from failures that emitted, and a crack that grew by a mechanism producing little emission leaves no record, so the apparent sensitivity of the method is a selection effect on the archive rather than a measured detection capability. The denominator is missing. Following a cohort of specimens to failure with continuous monitoring, and counting failures with and without recorded emission, supplies that denominator.

Unit trap
H2651. Absolute energy is reported in attojoules by one instrument family and in arbitrary units by another, and a threshold set in one is meaningless in the other because the arbitrary unit has no fixed reference to the input. A comparison across instruments then measures the instruments. Injecting a calibrated electrical pulse into both acquisition chains at a known energy fixes the conversion and settles whether the two scales differ by a constant or by a gain.

Count
H2652. The split between burst and continuous emission is set by the hit definition time and the lockout time, so shortening the definition time converts what was one long burst into a train of shorter ones and inflates the count with no change in the source. The classification is a property of the settings. Replaying one recorded continuous stream through three definition times moves the count and the burst fraction while the waveform stays put.

No-go claim
H2653. No frequency filter reliably separates friction from cracking when both radiate in the same band, which they do in most metals at frequencies where attenuation still permits detection, so a claim of friction rejection by spectral filtering alone is a claim about a coincidence. The overlap is physical, not a matter of filter design. A fretting couple and a growing fatigue crack, recorded with one wideband sensor, show how much of each spectrum lands in the other's band.

Conservation argument
H2654. Recorded emission energy is source energy minus attenuation and coupling losses along the path, so an energy comparison between two specimens at different source-to-sensor distances measures geometry more than damage. Only at matched distance does the number mean what it is usually taken to mean. Deliberately offsetting the sensor by a known distance on one specimen and fitting the decay supplies the correction rather than assuming it.

Geometry argument
H2655. Emission from a crack radiates preferentially in directions set by the crack's orientation and the local stress, so a sensor placed normal to the crack plane can sit near a null while a sensor much farther away receives more. Placement therefore matters more than distance in ways that amplitude-based location ignores. A known source rotated through a series of angles at fixed radius on a plate maps the radiation pattern and shows where the nulls fall.

Hysteresis
H2656. The Felicity ratio of a composite depends not only on the previous maximum load but on how long that load was held, because the matrix relaxes during the hold and the state at unloading is not the state at the peak. A ratio quoted without the hold time is therefore not comparable between tests. Two specimens taken to the same peak with holds of different duration, then reloaded, give different ratios and expose the dependence.

Misattribution
H2657. Dark spots on a weld radiograph are often charged to porosity, but static marks, roller scratches in the emulsion, and dust in the cassette all print dark and all survive a change of exposure. What distinguishes them is that they do not move when the source-to-film geometry changes, while a true internal void shifts with parallax. Re-exposing with the part rotated and comparing the two images separates a mark from a void.

Hidden term
H2658. The width of a crack measured on a radiograph is the crack's projected width convolved with the geometric unsharpness, so a tight crack can be reported wider than it is by an amount set by the focal spot and the distances. The term does not vanish at the magnification that maximises sharpness. Imaging one crack at two source-to-object distances, where the unsharpness differs by a known factor, and extrapolating to zero unsharpness recovers the true width.

Degeneracy
H2659. Dual-energy radiography returns a material thickness that is unique only for an object of two known materials, and any third material in the beam maps onto the same pair of measurements as some mixture of the first two. The ambiguity is not a calibration error and no reconstruction removes it. Inserting a third material of known thickness into a two-material phantom, and watching the retrieved values stay fixed while the object changes, demonstrates the degeneracy.

Bound
H2660. Contrast sensitivity has a floor set by quantum noise, falling as the square root of the exposure, so a factor of two improvement in thickness sensitivity costs roughly four times the dose. (estimate) No reconstruction or filtering recovers that, because the information was never in the beam. A dose series on a step wedge bearing a small thickness difference, with detection threshold plotted against dose, gives a slope approaching one half.

Threshold
H2661. Void detectability in a tomographic volume is not monotone in size near the voxel size, because partial volume averaging dilutes a small void's contrast below the noise while a slightly larger one crosses into visibility sharply. The threshold sits at roughly two to three voxels across. (estimate) A phantom with drilled voids of graded diameter, scanned at one voxel size, places the step.

Reversal
H2662. Geometric magnification improves the projection of a small feature up to a point, and beyond that the penumbra from the focal spot grows faster than the feature does, so there is an optimum magnification rather than a monotone gain. The optimum depends on the focal spot size, which is often quoted as a single number when it varies with power. Imaging one fine detail at five magnifications on the same tube, and measuring edge sharpness at each, locates the optimum for that tube.

Artefact mimics effect
H2663. Beam hardening produces cupping that reads as a density gradient toward the interior, and in a part with a concave section it can produce a band that looks like a crack running parallel to the surface. The artefact's position tracks the thickness map rather than the material. Reconstructing the same part with hardening correction on and off, and comparing where the band sits, indicates whether it follows the geometry.

Scale argument
H2664. The scattered fraction rises with the volume of material in the beam, so a contrast measurement made on a thin step wedge and applied to a thick section overestimates what the thick section will show. The scatter is what fills the shadows. Adding plates of the same alloy behind a step wedge, without changing the wedge, and measuring the contrast fall with each added plate, gives the correction as a function of thickness.

Inversion of standard practice
H2665. Raising kilovoltage to penetrate is the reflex, but for a low-contrast inclusion in a thin part the better move is often to lower it, since the attenuation difference between inclusion and matrix grows steeply as the spectrum softens while exposure time can be recovered by other means. The gain in contrast can exceed the loss in count rate. Exposing one thin part at two kilovoltages with exposure matched for equal density reveals which image resolves the inclusion.

Selection effect
H2666. Porosity detection limits quoted from machined-hole standards describe holes with sharp edges and clean walls, while real porosity is irregular, often partly bonded, and its effective contrast is lower than a hole of the same projected area. The published limit is therefore a hole-detection limit. Comparing a machined-hole phantom against a cast specimen with measured porosity of the same size class, radiographed together, measures the offset.

Unit trap
H2667. Radiographic density is an optical density and therefore a logarithm, so a density difference of 0.3 is a factor of two in transmitted intensity and not a difference of 0.3 in thickness; treating it as linear makes a thick step look proportionally thinner than it is. Film and digital displays both invite the misreading. Converting a step wedge's densities to intensities before fitting thickness, and checking the fit against the wedge's known steps, exposes the error.

Count
H2668. The number of distinguishable density levels in a tomographic volume is bounded by the detector's bit depth minus the noise in each voxel, so a classification claiming many material classes from a noisy scan is claiming more levels than the data hold. The bound is arithmetic, not a matter of clustering. Computing noise in a uniform region and comparing it with the spacing between the claimed classes sets how many classes the data can support.

No-go claim
H2669. No scatter correction calibrated on a uniform phantom transfers to a part whose thickness changes abruptly, because scatter is non-local and the correction must know the object's shape before the object has been reconstructed. The circularity is the obstacle, not the calibration's precision. Applying a phantom-derived correction to a stepped part, and comparing against a reconstruction from a narrow-beam geometry, exposes the residual at the steps.

Conservation argument
H2670. Reconstruction moves material between voxels but does not create it, so integrating the reconstructed density over a closed region returns the true mass even when local values are distorted by cupping and hardening. The integral is more trustworthy than the image. Weighing a part and comparing with the integral of its reconstruction, on a part thick enough to cup strongly, quantifies how much of the local error is redistribution rather than invention.

Dimensional argument
H2671. At fixed dose, signal-to-noise in a voxel scales with the square root of the voxel's volume, so halving the voxel size in all three directions demands roughly eight times the dose to hold the same noise. (estimate) A claim of finer resolution at unchanged dose is spending contrast, and contrast is what detects the flaw. Reconstructing one acquisition at two voxel sizes, and measuring noise and contrast in each, identifies where the cost was paid.

Confound
H2672. In single-energy radiography a thin dense region and a thick light one produce the same grey, so a density reading is really a line integral and cannot be inverted without an assumption about thickness. This is why a shim under a weld can mimic a void. Placing a known shim of a denser alloy beside a real void of matched projected density, and imaging both at two energies, breaks the tie.

Misattribution
H2673. Standoff between coil and surface changes the eddy-current signal in ways that look like a conductivity change, and in a hand-scanned inspection the standoff varies continuously. The two are nearly orthogonal in phase, though, because lift-off scales the coupling while conductivity rotates the impedance plane. Scanning a conductivity standard first at fixed lift-off and then at fixed conductivity with varying lift-off, and plotting both loci, demonstrates the separation the phase angle provides.

Hidden term
H2674. Coil resistance rises with coil temperature, and that rise enters the impedance measurement as an apparent change in the material, drifting over the first hour of use as the coil warms. The term is absent from the calibration certificate. Driving the coil at low power into a known standard and logging impedance through warm-up gives the drift curve, and repeating after thermal equilibration tells what part of a shift was ever the metal.

Identity claim
H2675. In magnetic flux leakage, depth and width both raise the peak amplitude, but the peak-to-peak spacing of the bipolar signal tracks length rather than depth, so the two features are not interchangeable measures of severity. The mapping is set by the field's divergence at the defect's edges. A machined series with depth and length varied independently, scanned at one magnetization, separates the two features, one tracking depth and the other length.

Bound
H2676. Pulsed eddy current reaches only as deep as the skin depth at the lowest frequency the coil can usefully drive, and no amount of time-domain averaging extends that, because the late-time signal is the decay of a current that never went deeper. The bound is set by diffusion, not by noise. Measuring a step wedge with the coil driven at three low frequencies, and plotting the depth at which the signal vanishes against frequency, confirms the bound moves as predicted.

Threshold
H2677. A crack is invisible to a surface coil when its opening is small compared with the lift-off and its length short compared with the coil's footprint, since the current is diverted around a region it cannot resolve. The threshold is geometric rather than electrical. Fatigue cracks of graded length and tightness, inspected with coils of two diameters at fixed frequency, place the threshold and expose the diameter dependence.

Reversal
H2678. Sensitivity to a small surface defect rises with frequency while penetration falls, so for a defect at fixed depth there is a frequency above which detectability decreases again, and the optimum is not the highest frequency the instrument offers. The peak depends on the defect's own depth. Sweeping frequency on one specimen with defects at three depths, and plotting signal against frequency for each, separates the peaks.

Artefact mimics effect
H2679. A warm patch in a flash thermograph is as likely to be a patch of high emissivity or a thin paint layer as a disbond, and in a single frame the two are indistinguishable. Emissivity differences exist before the flash and do not evolve with the thermal time constant, while a disbond appears after the flash and decays slowly. Comparing a pre-flash frame with frames at two delays separates them without touching the surface.

Scale argument
H2680. Thermal diffusion length grows as the square root of time, so the depth reached at a fixed delay depends on the material's diffusivity, and a detection depth quoted for steel does not transfer to a polymer composite of the same thickness. The square root compresses the difference but does not remove it. The same disbond simulated at equal depth in two materials, imaged with one flash and one delay, reveals how differently the contrast appears.

Inversion of standard practice
H2681. Coating a surface matte black to fix its emissivity is standard, but a thin coating of unknown thickness adds a thermal resistance in series with the defect and can hide the very feature being sought, so the better practice is often to measure the surface's emissivity in place and correct, rather than to paint. The coating's resistance scales with thickness over conductivity. Comparing a painted and an unpainted region of the same disbonded panel, with emissivity measured on each, settles which approach preserves contrast.

Selection effect
H2682. Thermographic validation leans on flat-bottomed holes in a plate, which have a well-defined air gap and a high thermal contrast, while a service disbond may be closed, partly conducting, or filled with corrosion product. The validated contrast therefore belongs to the reference. A panel containing both a flat-bottom hole and a closed disbond of the same footprint, imaged in one shot, exposes the contrast ratio the validation never sampled.

Unit trap
H2683. An infrared camera set to unit emissivity reports a temperature that is too low by an amount depending on the fourth power of absolute temperature, so a contrast computed from those readings and then corrected by subtracting a constant is wrong by a factor that changes with absolute temperature. The error is largest where the surface is coldest. Computing contrast both from raw radiance and from the camera's displayed temperature, on a target spanning a range, exposes the divergence.

Count
H2684. In lock-in thermography each modulation period contributes roughly one independent depth slice, so the number of separable depths is set by how many periods were recorded rather than by the frame rate or the pixel count. A claim of many depths from a short recording is claiming slices the data do not contain. Recording one defect at two modulation frequencies, and comparing the recovered depth against the known value, demonstrates how the count limits resolution.

No-go claim
H2685. No passive thermographic inspection finds a defect beneath a thick low-conductivity coating when the coating's thermal resistance exceeds that of the defect's own, because the coating dominates the surface temperature regardless of what lies under it. The limit is a ratio, not a matter of camera sensitivity. Imaging one defect under coatings of increasing thickness, at a steady heat load, makes the contrast vanish at a thickness predictable from the two resistances.

Confound
H2686. Moisture and a delamination both appear as cool areas in an afternoon roof thermograph, since wet insulation has a higher thermal inertia and a disbonded membrane a lower conductance. They diverge in time: moisture evaporates and cools further after sunset, while a delamination equilibrates. A dawn and an afternoon survey of the same roof, compared pixel by pixel, separates them without a core.

Misattribution
H2687. Rising damage index values on a permanently installed sensor are often read as accumulating damage, but a partially debonded sensor changes its own coupling and produces the same trend with no change in the structure. The ambiguity is built into the normalization, which divides by a baseline recorded when the bond was good. Comparing the index from a reference sensor bonded elsewhere on the same plate, or checking the sensor's own electromechanical impedance, distinguishes the two.

Hidden term
H2688. Every index formed by subtracting a baseline contains the baseline's own noise, so the index's repeatability is worse than the measurement's by the baseline's variance, and a control chart built on the index's apparent resolution will fire on noise. The term is invisible because the baseline is treated as exact. Recording a baseline twice on consecutive days with nothing changed gives the term directly, and it is usually larger than the drift being watched.

Threshold
H2689. Crossing a detection threshold requires the change to exceed the uncertainty of the baseline an index is compared against, so a sensor with excellent sensitivity and a noisy baseline performs worse than a mediocre sensor with a stable one. Sensitivity is the wrong figure of merit. Ranking several sensor types by the ratio of seeded-damage response to baseline variance, on one structure, reverses the ranking that sensitivity alone would give.

Identity claim
H2690. If a damage index is a linear projection of a measured vector, damage and temperature change are the same transformation unless the projection is orthogonal to the temperature direction, so no threshold on the index can distinguish them. The index has no information the projection discarded. Projecting the same data onto the temperature direction and onto its complement, and comparing damage response in each, tests whether the index was ever capable of separating them.

Reversal
H2691. Adding sensors to a monitoring network improves localization up to a point and then degrades it, because more channels bring more cabling capacitance, more connectors, and more opportunity for one bad bond to inject coherent noise into every path that uses it. The optimum is finite and depends on the structure's size. Building up a network one channel at a time on one structure, and measuring localization error at each count, finds where the curve turns.

Bound
H2692. Localization error cannot be smaller than the product of the timing resolution and the group velocity, so an algorithm reporting positions finer than that product is reporting interpolated smoothness rather than information. The bound holds for any triangulation, whatever the optimizer. Feeding the same arrival times, rounded to the system's real timing resolution, through the localization routine collapses the reported precision to the bound.

Inversion of standard practice
H2693. Inspection intervals are usually set by calendar or by regulation, but for a crack whose growth rate varies by an order of magnitude between nominally identical components, the interval that holds risk constant is set by the fastest credible growth rate rather than by the average. A fixed calendar therefore over-inspects the slow and under-inspects the fast. Measuring growth in a cohort of coupons and computing the interval at two confidence levels exposes the difference the fixed calendar hides.

Scale argument
H2694. Coupon-scale validation does not transfer to a structure because attenuation, mode density, and boundary reflections all grow with size, so a damage index calibrated at 300 mm behaves differently at 3 m with no change in the physics of the damage. The index is scale-dependent even when the damage is not. Instrumenting two geometrically similar panels at different scales, with matched relative damage, demonstrates the index's scale dependence.

Unit trap
H2695. Strain-based indices normalized by microstrain and by raw bridge voltage differ by the gauge factor and the bridge excitation, so a reported five percent change means different physical strains in the two conventions and thresholds do not transfer between laboratories. The normalization is rarely stated. Measuring one specimen with both a calibrated strain gauge and the raw bridge, and computing the index both ways, fixes the conversion.

Count
H2696. One baseline gives a differential index exactly one degree of freedom with which to absorb environmental variation, so a structure whose response depends on three independent environmental drivers cannot be corrected by it, and the residual will be dominated by whichever driver varies fastest. Correction requires as many independent references as there are drivers. Regressing the baseline's variation against measured temperature, load, and humidity, and counting how many coefficients are significant, establishes how many the index actually needs.

No-go claim
H2697. No index computed from a single guided-wave path can be independent of applied load, because load and damage both change that path's phase through the same elastic nonlinearity, and their effects differ only in how they distribute across paths. A single path has no distribution to inspect. Loading a damaged and an undamaged specimen through the same range, and comparing each path's phase response, demonstrates the overlap directly.

Conservation argument
H2698. Energy removed from a propagating mode by damage must reappear in another mode, in a reflection, or as heat, so an index reporting loss with no corresponding gain elsewhere is measuring a change in coupling rather than a change in the structure. The bookkeeping is the check. Measuring all propagating modes at the receiving end plus the reflection at the source end, and summing them, tests whether the missing energy has somewhere to be.

Self-reference
H2699. An index normalized by the current excitation amplitude reads healthy when the amplifier's output falls and the received signal falls with it, because the ratio is preserved while the measurement degrades. The failure is silent and looks like stability. Tapping the drive signal independently and comparing it with the commanded value over months exposes the amplifier's drift, which the normalization has been hiding.

Saturation
H2700. Remaining-life estimates from a damage index extrapolate the index's trend, but most indices saturate as damage grows, so the extrapolation flattens and the predicted life lengthens exactly when failure approaches. The error grows without bound near saturation. Fitting one index trajectory with a saturating model and with a linear one, and comparing both against run-to-failure data, indicates the direction in which each errs.