"A failing bearing screams in four languages at once. My job is to be fluent before it stops talking."
A Multilingual AI Agent
The big picture
Section 35.2 gave you the plant's slow nervous system: setpoints, tags, and historian trends sampled every second or minute. That layer tells you what the machine is doing. It rarely tells you what the machine is becoming. Incipient faults live in fast, physical signals that the process-control layer never captures. This section covers the four modalities that dominate industrial condition monitoring: vibration, acoustic (audible and ultrasonic), thermal, and electrical. Each is a different physical window onto the same machine, each has a characteristic bandwidth and time constant, and each fails silently in a different way. Getting them into a leakage-safe, model-ready form is the bridge between raw physics and every predictive-maintenance model in Chapter 36. You are learning to read the same failure in four handwritings.
A drying-cylinder bearing in a paper mill does not fail at 3 a.m. without warning. Weeks earlier it changes how it vibrates; days earlier it emits ultrasound as its lubricant film breaks down; hours earlier it warms measurably above its neighbors; and its drive motor draws a slightly different current the whole time. Four signals, four physics, one failure. This section assumes you are comfortable with sampling and the Nyquist limit from Chapter 3 and with the spectral tools of Chapter 7; here we tie those tools to specific transducers and specific fault mechanisms. Where a signal's physics comes from per transducer, characterized as a response map \(x = h(s) + \eta\), is the subject of Chapter 2.
Vibration: the workhorse of rotating machinery
What it is. Vibration is the mechanical oscillation of a structure, sensed almost universally with a piezoelectric accelerometer (an IEPE / ICP transducer) bolted or magnet-mounted near a bearing housing. The output is acceleration in \(g\) or \(\mathrm{m/s^2}\), sampled fast: 10 to 50 kHz is routine, because bearing and gear faults live in the kilohertz range. Velocity (mm/s) and displacement follow by integration.
Why it dominates. Rotating machinery is periodic, so its faults are periodic too, and periodicity is exactly what spectral analysis exposes cleanly. A defect on a bearing's outer race strikes the rolling elements at a precise rate set by geometry and shaft speed. That ball-pass frequency of the outer race is
$$ f_{\mathrm{BPFO}} = \frac{n}{2}\, f_r \left(1 - \frac{d}{D}\cos\phi\right), $$where \(n\) is the number of rolling elements, \(f_r\) the shaft rotation frequency, \(d\) the ball diameter, \(D\) the pitch diameter, and \(\phi\) the contact angle. The point is not to memorize the formula; it is that each fault class (outer race, inner race, ball, cage) has its own signature frequency, so detecting a fault becomes detecting a peak at a known location. The catch: the impact energy is faint and buried under gear mesh and imbalance, so you rarely see it in the raw spectrum. You see it after envelope analysis, which demodulates the high-frequency structural resonance that the impacts excite. Band-pass around the resonance, take the amplitude envelope with a Hilbert transform, then take the spectrum of that envelope; the defect frequency pops out.
When speed varies. Constant-speed assumptions break on wind turbines and variable-frequency drives. There the fix is order tracking: resample the signal against shaft angle (from a tachometer or encoder) rather than against clock time, so a fault that smears across frequency in the time domain becomes a sharp line in the order domain. Vibration severity for trending against a limit follows ISO 20816 (the successor to ISO 10816), which specifies broadband RMS velocity bands per machine class.
Key insight
A rotating machine encodes its own health as periodicity. Every fault maps to a frequency you can compute from geometry and shaft speed before you ever collect data. That is why condition monitoring leans so hard on the frequency domain: you are not searching a haystack, you are checking a short list of addresses. The engineering work is getting the faint impact energy to those addresses (envelope demodulation, order tracking) so a peak-picker or a learned model can read them.
The right tool: envelope analysis in a handful of lines
Hand-rolling envelope analysis means designing a band-pass filter around a resonance you must first find, applying an analytic-signal transform, taking its magnitude, removing the DC term, and running an FFT with the right window and scaling: comfortably forty-plus lines with several places to get the scaling wrong. SciPy collapses the core to about eight lines because scipy.signal supplies the Butterworth design, the filtering, and the Hilbert-based analytic signal directly.
import numpy as np
from scipy.signal import butter, filtfilt, hilbert
def envelope_spectrum(x, fs, band=(2000, 6000)):
b, a = butter(4, np.array(band) / (fs / 2), btype="band")
xb = filtfilt(b, a, x) # isolate the resonance band
env = np.abs(hilbert(xb)) # amplitude envelope (demodulation)
env -= env.mean() # drop DC so it does not swamp the plot
spec = np.abs(np.fft.rfft(env * np.hanning(len(env))))
freqs = np.fft.rfftfreq(len(env), 1 / fs)
return freqs, spec # peak at f_BPFO reveals an outer-race faultAcoustic and ultrasonic: hearing what you cannot reach
What it is. Acoustic monitoring splits into two regimes. Airborne sound in the audible band (roughly 20 Hz to 20 kHz), captured by a microphone, is non-contact and covers a whole machine at once, which makes it ideal when you cannot mount a sensor on every part. Above that sits ultrasound (20 kHz to about 100 kHz) and, higher still, acoustic emission (AE), the elastic stress waves from 100 kHz into the megahertz range that crack growth, friction, and turbulent leaks radiate.
Why bother when vibration exists. Three reasons. Ultrasound catches events that are quiet in the audible band and slow to appear in vibration: pressurized-gas and vacuum leaks, compressed-air waste, electrical corona and arcing in switchgear, and the dry-friction onset when a bearing's lubricant film thins, often the earliest mechanical warning of all. Airborne microphones and microphone arrays scale cheaply and can localize a source by beamforming. And AE senses fracture directly, so it monitors structures (pressure vessels, welds, rotating blades) where the fault is a growing crack rather than a periodic impact. The cost is that acoustic signals are exposed to the plant's whole noise field, so denoising (Chapter 6) and robust features matter more than with a contact accelerometer.
In practice: a paper mill listens before it feels
On a tissue machine, a maintenance team instrumented the felt-roll bearings with both accelerometers and a 40 kHz ultrasonic sensor. For eight weeks the vibration RMS sat comfortably inside its ISO 20816 band, all green. The ultrasonic channel, meanwhile, climbed steadily: the lubricant film was breaking down and the metal-to-metal contact radiated ultrasound long before it radiated enough force to move the accelerometer. Only in the final week did the vibration envelope spectrum (the exact envelope_spectrum computation above) grow a clean peak at the computed \(f_{\mathrm{BPFO}}\), confirming an outer-race spall. The lesson the team drew: ultrasound gave the lead time to schedule the swap, vibration gave the diagnosis that told them which bearing and which race. Neither channel alone would have done both.
Thermal: the slow integrator of energy loss
What it is. Almost every failure mechanism dissipates energy as heat: friction, electrical resistance, a blocked coolant path, an overloaded winding. Thermal sensing reads that heat, either point-wise with thermocouples and RTDs wired into the historian, or spatially with infrared thermography from fixed IR cameras or handheld imagers. IR is non-contact and gives a whole 2D field, which is why it dominates electrical-panel, motor, and steam-trap inspection. The physics link is the Stefan-Boltzmann law: radiated power scales as \(T^4\), so hot spots stand out sharply, but the same law means you must know the surface emissivity to convert radiance to true temperature, and shiny metal (low, uncertain emissivity) is a classic trap.
Why and when. Heat is a low-pass integrator of fault energy, so temperature is a robust, slowly varying confirmatory signal rather than an early-warning one. A bearing that is failing will eventually run hot, but by then vibration and ultrasound have been shouting for weeks. Thermal earns its place where the fault is thermal (a loose, high-resistance electrical connection heats before it arcs) or where it aggregates a distributed problem (a motor's overall winding temperature reflects insulation stress you cannot localize). The long thermal time constant is both a virtue (it filters transient noise) and a limit (it cannot resolve a millisecond impact). The image side of thermal, radiometric calibration, spatial resolution, and IR-specific models, is developed in depth in Chapter 45; here it is one channel among four.
Electrical signatures: the motor as its own sensor
What it is. Roughly half of industrial motion runs through electric motors, and a motor's stator current is a remarkably rich diagnostic that needs no sensor on the machine itself, only a current clamp at the drive. Motor Current Signature Analysis (MCSA) reads mechanical faults reflected back into the electrical supply. A broken rotor bar in an induction motor modulates the current and produces sidebands around the line frequency \(f_1\) at
$$ f_{\mathrm{sb}} = (1 \pm 2s)\, f_1, $$where \(s\) is the per-unit slip. Static and dynamic eccentricity, and even bearing defects, imprint their own frequency combinations onto the current spectrum. Beyond MCSA, the raw voltage and current pair yields power quality, power factor, and, through the instantaneous power, a direct measure of mechanical load.
Why it is attractive, and when it struggles. The appeal is access: the sensor sits in the safe, dry motor control center, not on a hot or hazardous machine, so it is cheap to deploy and retrofit across a fleet. It also sees the whole drivetrain at once. The struggle is that the mechanical signature is a tiny modulation on a huge fundamental, so you need high spectral resolution (long records, careful windowing) and a stable-enough operating point to resolve a sideband a few tens of decibels below \(f_1\). Variable-frequency drives complicate the picture further by injecting their own switching harmonics, so MCSA on a VFD-fed motor demands drive-aware preprocessing. As with vibration, these four raw channels become model inputs only after the feature engineering of Chapter 8 turns each spectrum into compact, comparable descriptors.
Four windows, four bandwidths
Think of the four modalities as a bandwidth-versus-lead-time grid. Ultrasound and AE sit highest in frequency and earliest in lead time; vibration is the diagnostic workhorse in the mid-kilohertz range; electrical current is a whole-drivetrain view accessed remotely; thermal is the slow, robust confirmer. A mature monitoring program does not pick one. It fuses them, letting the early channels trigger attention and the diagnostic channels localize the fault, a fusion problem taken up in Chapter 37.
Exercise
Take a machine you can name (a rooftop HVAC fan, an EV traction motor, a pump). For each of the four modalities:
- State the transducer you would mount and the minimum sample rate the physics demands. Justify the rate from a fault frequency, not a round number.
- Name one fault the modality would catch early and one it would catch late or not at all.
- Rank the four by lead time for a lubrication-starvation fault, and explain the ordering from first principles.
Hint
Lead time tracks how directly the modality couples to the fault's earliest physical symptom. Lubricant breakdown first changes microscopic contact (ultrasound), then impact energy (vibration), then, much later, bulk temperature.
Self-check
- Why does a bearing outer-race defect usually stay invisible in the raw vibration spectrum yet appear clearly after envelope analysis? What does the Hilbert step actually do?
- Give one fault that ultrasound catches earlier than vibration, and explain the physics of why it is earlier.
- In MCSA, broken-rotor-bar sidebands sit at \((1 \pm 2s)f_1\). Why does resolving them demand a long record and a stable operating point?
What's Next
In Section 35.4, we confront a fact that quietly undermines every signature we just computed: a machine is never in one state. It idles, ramps, runs loaded, coasts, and each regime has its own baseline vibration, current, and temperature. Comparing a loaded reading against an idle baseline manufactures false alarms. We turn to operating-regime segmentation, the discipline of slicing a stream into comparable conditions so that anomaly detection compares like with like.