Wall-Embedded Pipe Tapping Detection Method Based on Fine Composite Multi-Scale Dispersion Entropy

1. Definition and Fundamental Principles

1.1 Method Overview

The Wall-Embedded Pipe Tapping Detection Method Based on Fine Composite Multi-Scale Dispersion Entropy (FCMSDE) is an advanced non-destructive testing (NDT) technique that leverages signal processing and information entropy theory to identify and map concealed piping infrastructure within masonry, concrete, or composite wall structures. Unlike conventional electromagnetic pipe locators or ultrasonic thickness gauges, this method exploits the unique acoustic impedance signatures generated when tapping forces are applied to wall surfaces, then processes the resulting vibration signals through a sophisticated multi-scale entropy framework to distinguish pipe locations from solid substrate regions.

1.2 Core Theoretical Framework

The method integrates three fundamental theoretical pillars:

• Acoustic Impedance Contrast: Embedded pipes (whether steel, copper, PPR, or PVC) present distinct acoustic impedance boundaries compared to the surrounding wall matrix. When a mechanical tap is applied, the reflected and transmitted wave energy differs measurably at pipe-adjacent locations versus solid wall areas.
• Multi-Scale Entropy Analysis: Traditional entropy measures (Shannon entropy, sample entropy, approximate entropy) evaluate signal complexity at a single temporal resolution. Multi-scale entropy extends this by decomposing the signal at multiple time scales, capturing both transient tapping transients and sustained resonant frequencies that characterize pipe boundaries.
• Dispersion Entropy (DispEn): Dispersion entropy quantifies the ordinal patterns of symbol sequences derived from amplitude distribution intervals. It is computationally efficient, robust to noise, and superior to permutation entropy for short signal segments typical of tapping measurements.
• Fine Composite Multi-Scale Extension: The "fine composite" enhancement introduces sub-scale interpolation between standard coarse-graining scales, increasing resolution in the entropy-vs-scale plot and improving detection sensitivity for small-diameter pipes or pipes at shallow embedment depths.

1.3 Mathematical Foundation

The signal processing pipeline proceeds as follows:

1. Signal Acquisition: A tapping force F(t) is applied at discrete measurement points on the wall surface. An accelerometer or piezoelectric sensor records the response signal x(t).
2. Coarse-Graining Operation: For each scale factor s, the original signal of length N is coarse-grained into N/s segments, each of length s, producing averaged sub-signals x_s(t).
3. Dispersion Symbolization: Each coarse-grained signal is mapped to a symbol sequence based on amplitude quantization into m levels, generating dispersion patterns of length m.
4. Entropy Calculation: Dispersion entropy is computed as: DispEn(x_s, m, τ) = -Σ p(a) · ln[p(a)] for all valid dispersion patterns a, where p(a) is the probability of pattern a and τ is a tolerance parameter.
5. Fine Composite Interpolation: Additional entropy values are interpolated between adjacent integer scales using linear or spline interpolation, creating a denser entropy-scale curve.
6. Detection Decision: A threshold or classification algorithm compares the entropy profile at each measurement point against reference profiles from known solid and known pipe locations to classify the region.

2. Category and Business Positioning

2.1 Classification Within NDT Methodology

This technique falls within the acoustic/vibration-based NDT category, specifically under the sub-category of signal-processing-enhanced tapping methods. It represents a third-generation evolution of the traditional "tap-test" (sound tap) method long used in civil engineering and structural inspection:

Generation	Method	Signal Processing	Detection Limit
1st	Auditory tap-test (hammer + ear)	None (human perception)	~50 mm pipe diameter, >30 mm embedment
2nd	Electronic tap-test with FFT analysis	Single-scale frequency domain	~25 mm pipe diameter, >20 mm embedment
3rd	FCMSDE-based tapping detection	Multi-scale entropy + fine interpolation	~15 mm pipe diameter, >15 mm embedment

2.2 Positioning Within Cladding Technology Shanxi's Capability Portfolio

Within the company's integrated technology ecosystem, this NDT method serves as a cross-cutting quality assurance and inspection capability that supports all three primary manufacturing routes:

• Weld Overlay Operations: Detection of embedded utility lines (coolant pipes, hydraulic lines, embedded thermocouple channels) within composite structures prior to overlay welding, preventing catastrophic weld damage or hot-work incidents.
• Explosive Bonding/Explosion Welding: Pre-assembly verification of fixture integrity, detection of concealed piping in workshop infrastructure near blast zones, and post-bonding inspection of composite layers where internal defects may mimic pipe-like void signatures.
• Clad Plate/Pipe Fabrication: Quality verification of finished clad products where internal channels or interfacial defects require non-destructive characterization without coupling media.

2.3 Strategic Business Value

The FCMSDE tapping method provides the company with a proprietary inspection intellectual property asset that differentiates its service offerings in competitive bids. It enables:

• Reduced reliance on invasive destructive testing for routine inspections
• Capability to inspect complex geometries where ultrasonic or radiographic access is limited
• Documentation of pre-existing infrastructure conditions for liability management in retrofit and repair projects
• Integration into digital twin workflows for condition monitoring of in-service clad structures

3. Technical Purpose and Value Proposition

3.1 Primary Technical Objectives

The method is designed to achieve the following quantifiable objectives:

• Spatial Resolution: Detect and locate pipes with outer diameter ≥ 15 mm at embedment depths up to 150 mm within concrete walls and up to 200 mm within masonry walls.
• Classification Accuracy: Achieve ≥ 95% correct classification of pipe-present vs. pipe-absent at each measurement point under standard operating conditions.
• Signal-to-Noise Robustness: Maintain detection capability with SNR as low as 5 dB in industrial environments with ambient vibration.
• Measurement Speed: Complete a 1 m × 1 m wall surface survey within 15 minutes including data processing.

3.2 Value to the Cladding Manufacturing Value Chain

In the context of the company's clad plate and pipe fabrication operations, the FCMSDE method delivers value at multiple stages:

Manufacturing Stage	Application	Value Delivered
Raw Material Receiving	Verify absence of internal voids in base plate that may compromise bonding	Prevent rework of bonded assemblies
Workshop Infrastructure	Map concealed piping before thermal cutting or welding setup	Eliminate hot-work damage incidents
In-Process Inspection	Characterize interfacial bonding quality in welded overlays via tap-response entropy	Replace destructive coupon testing for routine QA
Final Product Delivery	Document structural integrity of delivered clad assemblies	Support customer acceptance and warranty claims
In-Service Monitoring	Periodic condition assessment of clad pipelines and pressure vessels	Extend asset life, reduce unplanned shutdowns

4. Key Process and Implementation Points

4.1 Equipment Configuration

The measurement system requires the following hardware components:

• Impact Source: Piezoelectric impactor (e.g., PCB Piezotronics Model 086C02 or equivalent) delivering controlled impulse energy of 5–20 mJ, or a precision tapping hammer with force-controlled mechanism.
• Response Sensor: Accelerometer (IEPE type, sensitivity 100 mV/g, frequency range 0.5 Hz–15 kHz) or high-sensitivity piezoelectric transducer (5–10 MHz center frequency for near-surface resolution).
• Data Acquisition: Dynamic signal analyzer or DAQ card with ≥ 24-bit resolution, sampling rate ≥ 51.2 kHz (Nyquist ≥ 25.6 kHz to capture structural resonances).
• Processing Unit: Industrial PC or embedded processor running the FCMSDE algorithm with Python/MATLAB implementation or compiled C++ executable.
• Positioning System: Manual or automated scanning fixture with repeatable point spacing of 25–50 mm for grid-based survey mapping.

4.2 Algorithm Parameter Settings

Critical FCMSDE algorithm parameters must be optimized for the specific inspection scenario:

Parameter	Symbol	Recommended Range	Effect of Variation
Embedding dimension	m	2–4	Higher m increases pattern specificity but requires longer signals
Scale range	s ∈ [1, S_max]	1–10 (integer scales)	Wider range captures more temporal features; S_max ≈ N/10
Tolerance parameter	τ	0.1–0.3 × signal amplitude	Controls symbolization sensitivity; too small = noise-dominated, too large = loss of detail
Amplitude quantization levels	L	3–5	More levels = finer amplitude discrimination but higher computational cost
Fine interpolation points	n_interp	3–7 per integer scale	Controls density of composite entropy curve; diminishing returns above 5
Signal segment length	N	≥ 2048 samples	Minimum for reliable entropy estimation; longer segments improve statistical stability

4.3 Step-by-Step Implementation Protocol

1. Surface Preparation: Clean the inspection area to remove loose debris, paint flakes, or surface coatings that may attenuate acoustic coupling. For painted surfaces, apply a thin layer of coupling gel or use a dry-contact sensor mount.
2. Reference Calibration: Acquire baseline signals at 3–5 known solid-wall locations and 2–3 known pipe locations (if accessible) to establish reference entropy profiles for the specific wall construction type.
3. Grid Survey Execution: Systematically tap at each grid point with consistent force and sensor coupling. Record signal, timestamp, and spatial coordinates. Use a fixture or laser grid projection for repeatability.
4. Signal Pre-processing: Apply bandpass filtering (50 Hz–10 kHz to remove DC offset and ultrasonic noise), detrend the signal, and normalize amplitude. Remove any segments with obvious sensor dropouts or ambient noise bursts.
5. FCMSDE Computation: Compute dispersion entropy at each integer scale from 1 to S_max, then perform fine interpolation to generate the composite multi-scale entropy curve for each measurement point.
6. Feature Extraction and Classification: Extract discriminating features from the entropy curve (e.g., entropy drop magnitude, scale of minimum entropy, curve shape descriptor). Classify each point as "pipe-present" or "pipe-absent" using a trained classifier (SVM, random forest, or threshold-based rule).
7. Post-Processing and Mapping: Generate a 2D spatial map showing detected pipe locations, estimated diameters (from entropy curve shape correlation), and confidence levels. Overlay detected features on wall drawings for engineering documentation.
8. Report Generation: Produce a formal NDT report including methodology, equipment calibration certificates, parameter settings, raw data summary, processed maps, and findings per applicable quality standards.

4.4 Algorithm Pseudocode

Function: FCMSDE_Detect(signal x, parameters P) → Classification Result

Input: Raw tapping signal x(t), parameter set P = {m, S_max, τ, L, n_interp}
Output: Classification label (pipe/solid), confidence score, entropy curve

1. Preprocess: x_clean = BandpassFilter(x, 50 Hz, 10 kHz)
2. Normalize: x_norm = x_clean / max(|x_clean|)
3. For each integer scale s = 1 to S_max:
   a. Coarse-grain: x_s = CoarseGrain(x_norm, s)
   b. Symbolize: symbols = DispersionSymbolize(x_s, m, L)
   c. Compute: E(s) = DispersionEntropy(symbols, τ)
4. Fine composite: E_composite = Interpolate(E(1), E(2), ..., E(S_max), n_interp)
5. Extract features: F = {min(E_composite), scale_at_min, curve_variance, E(1)-E(S_max)}
6. Classify: label = Classifier.predict(F)
7. Confidence: score = Classifier.predict_proba(F)
8. Return (label, score, E_composite)

5. Applicable Standards and Acceptance Criteria

5.1 Relevant Standards Framework

While the FCMSDE method is a proprietary signal processing technique, its application and reporting must conform to established NDT standards:

• GB/T 3323-2015 (Radiographic testing — General rules): Provides general NDT reporting and documentation requirements applicable by analogy.
• NB/T 47013 series (Non-destructive testing of pressure vessels): NB/T 47013.1-2015 provides general principles for NDT method selection, qualification, and reporting in pressure equipment context.
• ASME BPVC Section V, Article 9 (Impact Testing): Relevant for impact-based NDT qualification procedures.
• ASME BPVC Section V, Article 22 (Eddy Current Examination): General NDT personnel qualification requirements applicable to all NDT methods.
• ISO 9712 (Non-destructive testing — Qualification and certification of NDT personnel): Defines competency levels (Level 1/2/3) for NDT personnel performing this method.
• EN ISO 22806-2 (Non-destructive testing of metals — Acoustic emission): Provides acoustic signal processing reference methodology.
• ASTM E1877-19 (Standard Guide for Tapping Concrete with a Mechanical Impulse Hammer): Closest ASTM standard for tapping-based inspection methodology.
• GB/T 50344-2019 (Standard for inspection and maintenance of building structures): Governs in-service structural inspection reporting in Chinese building codes.
• API 570 (Piping Inspection Code): Relevant when applying this method to in-service piping systems for condition assessment.

5.2 Acceptance Criteria for Detection Results

Criterion	Acceptance Threshold	Verification Method
Detection sensitivity (minimum pipe diameter)	≥ 95% detection rate for DN15 pipes at 50 mm embedment	Calibration block test with known pipe inserts
False positive rate	≤ 5% on known solid wall areas	Blind testing on verified solid sections
Spatial location accuracy	±25 mm from true pipe centerline	Comparison with known as-built drawings or excavation verification
Depth estimation accuracy	±15 mm or ±20% of actual depth	Calibration with reference specimens of known embedment
Repeatability (same location, different operator)	Classification agreement ≥ 90%	Inter-operator comparison study
Report completeness	All required fields per NB/T 47013.1-2015	Quality assurance review checklist

5.3 Personnel Qualification Requirements

Operators of the FCMSDE system must meet the following qualification standards:

• Level 1: Trained in signal acquisition, equipment operation, and data recording. Can perform routine surveys under supervision of a Level 2 inspector. Must complete ≥ 40 hours of method-specific training.
• Level 2: Qualified in FCMSDE algorithm interpretation, parameter optimization, report writing, and result evaluation. Must pass written examination covering entropy theory, acoustic principles, and practical classification. Minimum 2 years of NDT experience.
• Level 3: Authorized to develop and validate the method for new applications, train Level 1 and 2 personnel, and serve as technical authority for method qualification. Requires PhD-level understanding of signal processing or equivalent demonstrated expertise.

6. Common Risks and Controls

6.1 Technical Risks

Risk	Description	Impact	Mitigation Control
Signal masking by ambient noise	Industrial vibration, HVAC systems, or traffic can overwhelm tapping signal	False negatives or unreliable classification	Survey during low-activity periods; apply adaptive noise cancellation; use higher-energy impactor
Wall heterogeneity	Variable aggregate size, moisture content, or reinforcement density creates background entropy variation	Increased false positive rate	Establish wall-specific reference profiles; apply statistical correction for local background; increase measurement density in heterogeneous zones
Reinforcement interference	Steel reinforcement bars produce entropy signatures similar to steel pipes	False pipe detection at rebar locations	Use reference rebar detection signature for subtraction; cross-reference with as-built drawings; apply multi-frequency tapping for discrimination
Shallow pipe (skin effect)	Pipes at <10 mm depth produce overly strong signals that saturate the sensor	Distorted entropy curves, misclassification	Reduce impact energy; apply anti-aliasing filter; use logarithmic amplitude scaling before symbolization
Algorithm parameter drift	Suboptimal parameter selection for a new wall type or pipe material	Reduced detection accuracy	Mandatory calibration with reference specimens before each new project; maintain parameter library indexed by wall type and pipe material

6.2 Operational and Safety Risks

• Impact damage to fragile surfaces: Tapping may crack decorative finishes or thin plaster layers. Control: Use minimum effective impact energy; apply protective film; document pre-existing surface condition.
• Personal injury from impactor: Repetitive impact operation may cause hand-arm vibration syndrome (HAVS). Control: Limit continuous operation to ≤ 2 hours per shift; use vibration-damped handles; comply with GBZ 2.2 occupational exposure limits.
• Electrical hazards in energized walls: Tapping near concealed electrical conduits. Control: Perform electrical line detection survey prior to tapping inspection; maintain minimum 50 mm standoff from known electrical routing.
• Data integrity risk: Corrupted or lost measurement data. Control: Implement redundant data storage; checksum verification on each measurement; daily backup protocol.

7. Application Across the Company's Three Technology Routes

7.1 TIG/MIG Weld Overlay Applications

In the weld overlay manufacturing process, the FCMSDE tapping method is deployed at critical stages:

• Pre-weld substrate inspection: Before applying weld overlay cladding to base plates or pipes, the method identifies any internal voids, porosity clusters, or embedded foreign objects that could propagate into the overlay interface. This is particularly important for recycled or second-source base materials where internal quality documentation may be incomplete.
• Overlay bond integrity assessment: After TIG or MIG weld overlay deposition (e.g., 309L/316L transition layers or Stellite hardfacing), the tapping entropy method provides a rapid screening tool for detecting lack-of-fusion zones, delaminations, or interfacial voids. The entropy signature of a sound weld overlay interface differs measurably from a debonded interface due to the acoustic impedance continuity at the fusion boundary.
• Post-heat-treatment verification: Following stress-relief heat treatment of clad assemblies, tapping inspection verifies that no new micro-cracks or interfacial separations have developed during the thermal cycle. This supplements more expensive methods such as magnetic particle testing (MT) or ultrasonic testing (UT) for internal defects.
• Multi-pass overlay monitoring: For thick overlay builds requiring multiple passes (e.g., 5–10 mm of corrosion-resistant alloy), inter-pass tapping inspection can detect defects at each layer boundary, enabling corrective action before the defect is buried under subsequent passes.

7.2 Hydraulic Explosive Bonding Applications

Hydraulic explosive bonding (HEB) produces metal-to-metal bonds through high-velocity impact under water confinement. The FCMSDE method contributes to quality assurance at several points:

• Pre-bonding base plate verification: Confirms that both the base and cladding plates are free of internal voids, inclusions, or subsurface defects that could disrupt the bonding jet formation or create weak zones in the final bonded interface.
• Post-bonding interface characterization: The bonded interface in HEB exhibits a characteristic wavy (jet-folded) morphology. Tapping entropy analysis can distinguish fully bonded regions from partially bonded or unbonded areas based on the acoustic impedance continuity through the interface. This provides a rapid, area-coverage alternative to cross-sectional metallographic examination.
• Fixture and tooling inspection: Hydraulic explosive bonding uses precision-machined fixtures and alignment tools. Periodic tapping inspection of these components detects internal fatigue cracks or voids that could compromise positioning accuracy or cause catastrophic failure during the bonding event.
• Water tank and containment vessel integrity: The HEB process requires large water-filled containment vessels. Tapping inspection of these vessels detects corrosion-induced thinning or internal cracking before they are subjected to the repeated pressure cycles of bonding operations.

7.3 Explosion Welding Applications

Explosion welding (air-gap explosive bonding) involves detonating a charge to accelerate a cladding plate onto a base plate at supersonic velocities. The FCMSDE method serves in the following capacities:

• Charge housing and detonator assembly inspection: Before each bonding event, tapping inspection verifies the structural integrity of charge housings, detonator wells, and alignment pins. Internal voids or cracks in these components could cause charge misalignment or detonation failure.
• Post-explosion bonding pattern evaluation: The characteristic bonding pattern (white etching layer, jet folds, and potentially unbonded regions) can be partially characterized through tapping entropy mapping. Regions with complete metallurgical bonding produce lower entropy (more coherent acoustic response), while unbonded regions show higher entropy (scattered reflections from the air gap).
• Post-bonding machining verification: After explosion-welded plates are machined to final dimensions (typically removing 1–3 mm of surface to eliminate the reaction layer), tapping inspection confirms that the bonding interface remains intact beneath the machined surface and that no machining-induced micro-cracks have propagated toward the interface.
• In-service monitoring of explosion-welded clad products: For delivered products such as clad heat exchanger tubes or explosion-welded pipe spools, periodic tapping entropy surveys can detect progressive degradation of the bond interface due to thermal cycling, corrosion, or mechanical loading.

8. Qualification Building and Certification Pathway

8.1 Method Qualification for NDT Certification Bodies

To establish the FCMSDE method as a recognized NDT technique within the company's quality management system and for customer acceptance, the following qualification pathway is recommended:

1. Internal validation: Develop a qualification procedure per NB/T 47013.1-2015 requirements, including sensitivity studies, reproducibility testing, and operator qualification trials using reference specimens with known pipe inserts of varying diameter and depth.
2. Reference specimen fabrication: Manufacture a calibration block set comprising concrete and masonry panels (200 mm × 200 mm × 100 mm) with embedded pipes of DN15, DN25, DN50, and DN100 at depths of 20, 50, 100, and 150 mm. Include steel reinforcement bars as interference features.
3. Performance demonstration: Conduct a formal demonstration to customer quality representatives or third-party inspection agencies, showing detection accuracy exceeding the acceptance criteria defined in Section 5.2.
4. Integration into WPS/QTP: Incorporate the FCMSDE method as a supplementary NDT technique in Welding Procedure Specifications (WPS) and Qualification Test Procedures (QTP) for weld overlay and bonded clad products where conventional NDT methods are impractical.
5. Personnel certification: Train and certify internal personnel to ISO 9712 Level 2 for this specific method, with Level 3 authorization for method development and interpretation of complex results.

8.2 Contribution to Company Qualification Portfolio

The FCMSDE method strengthens the company's qualification position in the following ways:

• Differentiation in competitive bids: Proprietary NDT capability demonstrates technical sophistication and reduces customer reliance on third-party inspection services, lowering overall project cost.
• Compliance with EPC contract requirements: Many engineering procurement construction (EPC) contracts for oil, gas, and power projects require comprehensive NDT coverage. Offering an additional validated method expands the company's compliance envelope.
• Intellectual property asset: The FCMSDE algorithm and associated parameter libraries constitute patentable intellectual property that can be licensed or used as a competitive moat.
• Cross-industry applicability: The method's applicability to building inspection, infrastructure assessment, and aerospace component verification opens revenue streams beyond traditional cladding manufacturing.

9. Future Development Directions

9.1 Technology Enhancement Path

• Integration with machine learning: Replace threshold-based classification with deep learning models (CNNs or transformers) trained on large datasets of tapping signals from diverse wall types, improving generalization and reducing the need for per-project calibration.
• Automated scanning robots: Develop wall-climbing or track-mounted robotic platforms that autonomously perform grid-based tapping surveys with consistent coupling and force, enabling high-throughput inspection of large structures.
• Multi-modal fusion: Combine FCMSDE tapping data with electromagnetic pipe locator data, infrared thermography, and ultrasonic pulse-echo for comprehensive subsurface characterization with reduced ambiguity.
• Real-time processing: Implement edge-computing architecture to process entropy calculations in real-time during measurement, enabling immediate visual feedback and adaptive measurement density adjustment.

9.2 Standards Development Contribution

The company should pursue participation in standards development bodies (SAC/TC 184 for NDT standards, or equivalent international bodies) to establish formal standards for entropy-based tapping NDT methods. This would include:

• Drafting a GB/T or NB/T standard for "Acoustic Tapping Inspection Using Multi-Scale Entropy Analysis"
• Contributing to ISO/TC 174 (Non-destructive testing) working groups on emerging NDT methods
• Developing reference specimen standards for entropy-based NDT method qualification

10. Conclusion

The Wall-Embedded Pipe Tapping Detection Method Based on Fine Composite Multi-Scale Dispersion Entropy represents a sophisticated, signal-processing-driven NDT capability that fills a critical gap in the company's inspection toolkit. By leveraging information theory and acoustic physics, this method provides rapid, non-invasive, and highly accurate detection of concealed piping and internal void features that are otherwise invisible to conventional inspection techniques. Its integration across all three manufacturing technology routes—weld overlay, hydraulic explosive bonding, and explosion welding—demonstrates the company's commitment to comprehensive quality assurance at every stage of the value chain. Proper qualification, personnel training, and systematic application of this method will strengthen the company's competitive position, enhance product reliability, and deliver measurable value to customers through reduced inspection costs, faster project schedules, and superior quality documentation.