condition-based-maintenance

name	condition-based-maintenance
description	Condition-based maintenance (CBM) — RUL estimation, PdM strategies, health index, vibration trending, oil analysis, thermography, degradation models, ISO 13373/17359, decision thresholds.
metadata	{"priority":7,"promptSignals":{"phrases":["condition based maintenance","CBM","predictive maintenance","remaining useful life","RUL","health index"],"minScore":3}}

Condition-Based Maintenance (CBM) — Complete Skill

CBM Framework

CBM: maintenance triggered by condition indicators exceeding thresholds; not time-based PdM (Predictive Maintenance): uses models to forecast failure before threshold crossed

CBM hierarchy:

1. Condition monitoring: collect data (vibration, temperature, oil, current)
2. Health assessment: compare to baselines; compute health index
3. Diagnostics: identify fault type and severity
4. Prognostics: estimate RUL (remaining useful life)
5. Decision: schedule maintenance at optimal time (RUL > 0; RUL < lead time)

Degradation Models

Linear Degradation

HI(t) = HI₀ - k × t [HI = health index; k = degradation rate; 0 = failed, 1 = healthy] Failure at HI = HI_threshold (typically 0.2–0.3 for alert; 0.0 = failed)

Exponential Degradation (most common for bearings, gears)

HI(t) = HI₀ × exp(-α × t) α = degradation parameter (fitted from historical data) RUL = ln(HI_current / HI_threshold) / α

Paris-Law Based (crack propagation)

da/dN = C × ΔK^m RUL = ∫ from a_current to a_critical: da / [C × (F × Δσ × √(πa))^m]

Wiener Process (stochastic)

X(t) = μ_d × t + σ_d × W(t) [X = degradation; W = Brownian motion] RUL distribution: Inverse Gaussian E[RUL] = (L - X_current) / μ_d [L = failure threshold] Var[RUL] = σ_d² × (L - X_current) / μ_d³

Hidden Markov Model (multi-state)

States: Good → Degraded → Failed Transition probabilities: P_ij per inspection interval Maintenance triggered when P(state ≥ Degraded) > threshold

Vibration-Based Monitoring

Key indicators:

Indicator	Fault type	Frequency
Overall RMS	Global severity	Broadband
1× synchronous	Unbalance, misalignment	1× RPM
Harmonics (2×, 3×)	Misalignment, looseness	n× RPM
BPFI, BPFO	Bearing defect	Bearing defect frequencies
GMF (gear mesh)	Gear wear	N_teeth × RPM
Kurtosis	Impulsive faults (early bearing)	—

Bearing defect frequencies (approximate): BPFO = (N_b/2) × f_rot × (1 - d_b/D_p × cos α) [ball pass frequency outer] BPFI = (N_b/2) × f_rot × (1 + d_b/D_p × cos α) BSF = (D_p / 2d_b) × f_rot × (1 - (d_b/D_p × cos α)²) [ball spin frequency] N_b = number of balls; d_b = ball diameter; D_p = pitch diameter; α = contact angle

Kurtosis: K = [Σ(x - x̄)⁴/N] / σ⁴ Healthy bearing: K ≈ 3.0; Early fault: K = 6–10; Severe fault: K > 10

ISO 10816-3 vibration severity:

RMS velocity [mm/s]	Class I	Class II	Class III	Condition
< 0.71	A	A	A	Good
0.71–1.8	B	B	A	Satisfactory
1.8–4.5	C	B	B	Unsatisfactory
4.5–11.2	D	C	C	Alarm
> 11.2	D	D	D	Danger

Oil Analysis

Parameters monitored:

Parameter	Indicates	Limit (example)
Particle count ISO 4406	Contamination/wear	ISO cleanliness ≥ 18/16/13 triggers action
Ferrography (ferrous)	Steel wear severity	DR > 200 = alarm
Viscosity change	Oil degradation	±15% from spec → change oil
Acid number (AN)	Oxidation	AN > 2 mg KOH/g → change
Water content	Contamination	> 0.1% by mass → dry
Wear metals (Fe, Cr, Cu)	Bearing/gear wear	Fe > 100 ppm → alarm

ASTM D4378: standard for in-service lubricant monitoring ISO 4406: contamination code (particles > 4, > 6, > 14 μm per mL)

Thermographic Inspection

Temperature rise ΔT as indicator:

ΔT above ambient	Condition
< 10°C	Normal
10–30°C	Monitor closely
30–60°C	Maintenance soon
> 60°C	Immediate action

Applications: electrical connections, motor windings, steam traps, heat exchangers, refractory

Emissivity: ε correction critical; for metals ε = 0.1–0.4 (shiny) vs. 0.9–0.98 (painted/oxide) T_apparent = T_true × ε^(1/4) [simplified for calibration check]

ASTM E1934: thermographic examination of electrical and mechanical equipment

Motor Current Signature Analysis (MCSA)

Fault frequencies in current spectrum: Bearing fault: f = f_line ± n × f_defect Eccentricity: f_ecc = f_line × (1 ± n × (1-s)/p) [s = slip; p = pole pairs; n = 1,2...] Broken rotor bar: f_brb = f_line × (1 ± 2ks) [k = 1,2...]

Broken rotor bar alarm: Amplitude at f_brb > -35 dB relative to fundamental → investigate

-20 dB → broken bar confirmed

Health Index Computation

Composite health index: HI = Σ (w_i × f_i(x_i)) [normalized 0–1; w_i = weight; f_i = feature mapping function] Example features: vibration RMS, kurtosis, oil Fe, temperature

Data normalization: f_i = (x_i - x_min) / (x_max - x_min) [0 = healthy limit; 1 = failure limit]

Machine learning approaches:

• Autoencoder reconstruction error → HI
• LSTM for RUL regression
• Random forest classification (healthy/degraded/critical)

Decision Thresholds

Optimal maintenance time: Schedule maintenance when: RUL < lead time for maintenance execution Cost model: C_pm (preventive) vs. C_cm (corrective) × P(failure before detection)

Risk-based threshold: Maintenance trigger at P(failure within interval T) > acceptable risk threshold (e.g., 5%) P(failure | HI) from conditional reliability

Standards

Standard	Scope
ISO 13373	Vibration condition monitoring of rotating machines
ISO 17359	Condition monitoring and diagnostics — general guidelines
ISO 10816	Mechanical vibration — evaluation of machine vibration
ISO 13381-1	Prognostics — general guidelines
ASTM D4378	In-service lubricant monitoring
ISO 4406	Fluid contamination classification

Output

Provide: degradation model type (linear/exponential/Wiener), current health index HI [0–1], degradation rate α or k, RUL estimate [days/hours] with uncertainty (±σ), condition indicators (vibration RMS [mm/s] vs. ISO 10816 severity, kurtosis, oil Fe [ppm], ΔT [°C]), fault type identified (bearing/gear/imbalance/electrical), bearing defect frequencies [Hz], maintenance trigger threshold and current status, maintenance type recommended (lubricate/replace/inspect), and applicable standard (ISO 13373, ISO 17359, ISO 13381-1).