Multi-Scale Fluctuation Dispersion Entropy for Hydraulic Pump Fault Diagnosis in Hydraulic Explosive Cladding Systems

1. Definition and Fundamental Principles

Multi-Scale Fluctuation Dispersion Entropy (MSFDE) is an advanced nonlinear signal processing technique that quantifies the complexity, randomness, and structural disorder of time-series data across multiple temporal scales. In the context of hydraulic pump fault diagnosis within hydraulic explosive bonding (HEB) systems, MSFDE serves as a robust feature extraction method capable of characterizing the dynamic behavior of hydraulic pumps under normal and degraded operating conditions.

The foundational principles of MSFDE build upon three successive mathematical frameworks:

• Dispersion Entropy (DE): Originally proposed by Yentes et al., dispersion entropy maps time-series data into a discrete symbol space using z-score normalization followed by uniform binning into a symbol alphabet of dimension M. The entropy is then computed as the Shannon entropy of the resulting symbol probability distribution. DE offers computational efficiency and noise robustness compared to traditional sample entropy and permutation entropy.
• Fluctuation Dispersion Entropy (FDE): By incorporating a coarse-graining (fluctuation) operation prior to dispersion encoding, FDE captures both the fine-scale irregularities and the coarse-scale trends in the signal. This dual-resolution capability makes FDE particularly suitable for detecting incipient faults in rotating machinery where early-stage degradation manifests as subtle changes in both high-frequency noise and low-frequency periodicity.
• Multi-Scale Extension (MSFDE): The multi-scale framework applies progressive coarse-graining at multiple time scales (typically τ = 1 to 10 or higher), generating a trajectory of entropy values. The divergence behavior of the MSFDE trajectory across scales provides a diagnostic fingerprint that distinguishes between healthy operation, cavitation, seal wear, bearing degradation, and other failure modes.

2. Category and Business Positioning

Within the capability architecture of Cladding Technology Shanxi Co., Ltd., MSFDE-based hydraulic pump fault diagnosis occupies a strategic position at the intersection of process equipment reliability engineering and quality assurance infrastructure. It is not a cladding fabrication technology per se, but rather a critical enabling competency that ensures the integrity of the hydraulic explosive bonding production line.

The company's three primary technology routes—TIG/MIG weld overlay, hydraulic explosive bonding, and explosion welding—each depend on different energy delivery systems. Hydraulic explosive bonding, in particular, relies on high-pressure hydraulic pumps (typically 200–600 MPa rated) to store and release the mechanical energy that drives the cladding sheet into collision with the base substrate. Any degradation in hydraulic pump performance directly translates to:

• Insufficient collision velocity, resulting in incomplete metallurgical bonding
• Uncontrolled pressure spikes causing substrate deformation or damage
• Batch-to-batch inconsistency in cladding quality
• Unplanned equipment downtime and production schedule disruption

Therefore, MSFDE-based condition monitoring is positioned as a quality infrastructure competency that underpins the company's ability to deliver consistent, certified cladding products across all three technology routes.

3. Technical Purpose and Value

3.1 Primary Technical Objectives

1. Early Fault Detection: Identify incipient hydraulic pump degradation (bearing wear, seal leakage, cavitation onset) before catastrophic failure occurs, enabling planned maintenance rather than emergency shutdown.
2. Fault Classification and Severity Assessment: Distinguish between multiple fault types and quantify degradation severity levels, supporting prioritized maintenance decisions.
3. Process Quality Correlation: Establish quantitative relationships between hydraulic pump health indicators and cladding quality outcomes (bond strength, interface morphology, microstructure), creating a traceable quality chain.
4. Predictive Maintenance Scheduling: Estimate remaining useful life (RUL) of hydraulic pump components to optimize spare parts inventory and maintenance resource allocation.

3.2 Business Value

The implementation of MSFDE-based diagnosis delivers measurable business value through:

• Reduced unplanned downtime: Target reduction of 40–60% in unexpected hydraulic system failures
• Improved first-pass yield: By ensuring hydraulic pump parameters remain within specification, cladding quality consistency improves, reducing NDT rejection rates
• Extended equipment service life: Condition-based maintenance extends hydraulic pump operational life by 20–35% compared to time-based replacement schedules
• Enhanced customer confidence: Demonstrable process control through equipment health monitoring supports qualification audits and customer quality assurance reviews

4. Key Process and Implementation Points

4.1 Sensor Configuration and Data Acquisition

Effective MSFDE analysis requires appropriate sensor placement and acquisition parameters tailored to the hydraulic pump architecture used in explosive bonding systems.

Parameter	Recommended Specification	Rationale
Acceleration Sensor Type	IEPE piezoelectric, frequency range 10 Hz–20 kHz	Captures both low-frequency periodic components and high-frequency impact signatures
Pressure Transducer	Dynamic pressure sensor, 0–100 MPa range, response time <1 ms	Monitors pressure fluctuations indicative of cavitation and seal degradation
Sampling Rate	≥25.6 kHz (minimum 10× highest fault frequency)	Adequate resolution for bearing defect frequencies in medium-speed hydraulic pumps
Signal Duration	1024–4096 data points per analysis window	Balances statistical significance with computational efficiency
Sensor Mounting Location	Pump housing bearing seat, inlet/outlet flange, motor coupling	Optimal proximity to fault generation sources
Multi-Channel Configuration	Minimum 3 channels (vibration + pressure + temperature)	Multi-modal fusion improves diagnostic reliability

4.2 MSFDE Computation Workflow

1. Signal Preprocessing: Apply band-pass filtering (0.5–10 kHz) to remove electrical noise and DC offset; perform detrending to eliminate slow drift components.
2. Coarse-Graining: For each scale τ, construct a coarse-grained time series by averaging non-overlapping windows of length τ: y_i^(τ) = (1/τ) Σ x_j for j = (i-1)τ+1 to iτ.
3. Dispersion Encoding: Normalize the coarse-grained series using z-score transformation, then map each value to a symbol from the alphabet {1, 2, ..., M} using uniform quantization into M bins.
4. Pattern Extraction: Construct M-dimensional patterns from consecutive symbol sequences (embedding dimension M, typically M = 3 to 6).
5. Entropy Calculation: Compute Shannon entropy over the probability distribution of all observed patterns: DE = -Σ p_μ log p_μ.
6. Multi-Scale Trajectory: Repeat steps 2–5 for τ = 1 to T (typically T = 10 or 20) to generate the complete MSFDE trajectory.
7. Feature Vector Construction: Extract diagnostic features from the trajectory: mean value, variance, slope at specific scales, and divergence rate.

4.3 Fault Classification Model

The MSFDE feature vectors are typically fed into a classification model. The following comparison outlines suitable approaches:

Classification Method	Advantages	Limitations	Recommended Use Case
Support Vector Machine (SVM)	Effective with small datasets; good generalization	Performance degrades with high-dimensional features	Initial deployment with limited fault samples
Random Forest	Robust to overfitting; provides feature importance	Less effective with very small training sets	Multi-fault classification with moderate data
Convolutional Neural Network (1D-CNN)	Automated feature extraction; handles raw MSFDE trajectories	Requires larger training datasets	Long-term deployment with accumulated data
One-Class SVM / Isolation Forest	Only requires normal operation data	Cannot classify specific fault types	Early-stage anomaly detection

4.4 Typical Fault Signatures in Hydraulic Pump MSFDE

Fault Condition	MSFDE Trajectory Characteristics	Physical Mechanism
Healthy Operation	Stable, low-variance trajectory; moderate entropy values	Periodic, deterministic flow pattern with minimal noise
Bearing Inner Race Wear	Progressive increase in entropy across all scales; accelerated divergence at fine scales	Impact-induced vibration adds randomness to signal
Seal Leakage	Entropy decrease at coarse scales; increase at fine scales	Loss of pressure pulsation periodicity with increased turbulence noise
Cavitation	Sharp entropy spike at fine scales (τ=1-3); relatively stable at coarse scales	Bubble collapse generates broadband high-frequency noise
Impeller Erosion	Gradual entropy increase across all scales; trajectory slope becomes steeper	Asymmetric flow patterns introduce increasing complexity

5. Applicable Standards and Acceptance Criteria

5.1 Equipment and Process Standards

• GB/T 25341-2010 — Hydraulic systems — Condition monitoring and diagnostics — General principles
• ISO 13373-1:2002 — Condition monitoring and diagnostics of machines — General guidelines
• ISO 13373-2:2002 — Condition monitoring and diagnostics of machines — Vibration analysis
• ISO 10816-21:2009 — Mechanical vibration — Evaluation of machine vibration by measurements on non-rotating parts
• API 676 — Petrochemical pumps — Condition monitoring and diagnostics (reference for pump health criteria)
• GB/T 11348 series — Mechanical vibration — Evaluation of machine vibration by measurements on non-rotating parts

5.2 Cladding-Specific Quality Standards (Linked via Equipment Health)

• ASTM A240 / ASTM A270 — Specifications for clad plate and clad pipe materials (quality assurance through equipment reliability)
• ASME SA-270 / SA-358 — Specification for clad pipe (process consistency requirements)
• NB/T 47012 — Technical conditions for explosion-welded steel clad plate (bond quality depends on hydraulic system integrity)
• GB/T 17748 — Test methods for explosion-welded clad plates
• ASTM A780 — Standard practice for qualification and approval of weld overlay procedures

5.3 Acceptance Criteria for Diagnostic System Performance

Performance Metric	Acceptance Threshold	Verification Method
Fault detection sensitivity	≥95% for faults exceeding ISO 10816 Zone B threshold	Simulated fault injection testing
Fault classification accuracy	≥90% for top-3 fault categories	Cross-validation on labeled dataset
False alarm rate	≤2% per 1000 hours of normal operation	Extended normal operation monitoring period
Detection lead time	≥72 hours before critical failure threshold	Accelerated degradation testing
System response latency	≤5 seconds from data acquisition to diagnostic output	Real-time performance benchmarking

6. Common Risks and Controls

6.1 Technical Risks

Risk	Description	Mitigation Strategy
Overfitting to specific operating conditions	Model trained on one load regime fails under different process parameters	Train with multi-condition data; implement adaptive baseline updating
Sensor degradation or drift	Accelerometer sensitivity changes over time, corrupting MSFDE values	Implement sensor health self-check; periodic calibration per ISO 13373-2
Environmental electromagnetic interference	Hydraulic explosion operation generates significant EM noise	Shielded sensor cables; differential measurement; signal preprocessing filters
Insufficient fault training data	New fault modes not represented in training dataset	Implement semi-supervised learning; maintain fault knowledge base; conduct periodic fault injection tests
False negatives during rapid degradation	Fault progresses too quickly for MSFDE trajectory to show gradual change	Supplement with threshold-based hard limits; real-time pressure monitoring as safety backup

6.2 Process and Quality Risks

• Undetected pump degradation leading to substandard cladding: If hydraulic pump cavitation is not detected early, collision velocity falls below the minimum required for metallurgical bonding, producing cladding with incomplete or weak interfaces. Control: Establish minimum MSFDE-based health index as a release criterion before each cladding batch.
• Pressure surge from undiagnosed seal failure: A failing hydraulic seal can cause pressure spikes that deform thin cladding sheets or damage the workpiece. Control: Implement real-time pressure monitoring with automated shutdown at 110% of design pressure, supplemented by MSFDE trend analysis for early warning.
• Batch traceability gaps: Without documented equipment health records, it becomes impossible to trace quality issues back to equipment condition. Control: Integrate MSFDE health indices into the batch quality record system, linking each cladding batch to the hydraulic pump condition at time of manufacture.

7. Application Across the Three Technology Routes

7.1 TIG/MIG Weld Overlay Applications

In TIG and MIG weld overlay operations, hydraulic pumps are used for:

• Automatic wire feed systems (hydraulic-driven feed mechanisms for high-deposition-rate applications)
• Clamping and positioning systems for large-diameter pipe overlay
• Coolant circulation systems for high-heat-input overlay processes

MSFDE diagnosis ensures that wire feed consistency is maintained, which directly impacts overlay layer thickness uniformity—a critical parameter per ASTM A780 qualification requirements. Variations in feed rate due to hydraulic pump degradation can cause porosity, incomplete fusion, or excessive dilution in the overlay weld, leading to WPS non-conformance.

7.2 Hydraulic Explosive Bonding Applications

This is the primary application domain where MSFDE diagnosis delivers maximum value. In hydraulic explosive bonding:

• The hydraulic pump system must deliver precise, repeatable pressure pulses to accelerate the cladding sheet to collision velocities of 300–700 m/s
• Pressure uniformity across the bonding area is critical for consistent metallurgical bonding
• System response time and energy delivery consistency directly determine bond quality

MSFDE monitoring of the hydraulic pump enables:

1. Pre-shoot health verification: Confirm pump is within optimal operating envelope before each bonding cycle
2. In-process monitoring: Detect real-time degradation during multi-shot bonding sequences
3. Post-shoot assessment: Verify that pump performance did not drift during the bonding operation

7.3 Explosion Welding Applications

In explosive welding (using propellant detonation), hydraulic pumps serve auxiliary but critical functions:

• Hydraulic clamping of the workpiece assembly during detonation
• Hydraulic positioning of the explosive charge at precise standoff distances
• Post-weld hydraulic straightening and flattening of clad plates

MSFDE diagnosis ensures that clamping force is adequate to resist detonation shock loads, preventing workpiece displacement that would compromise bond quality and dimensional accuracy per NB/T 47012 requirements.

8. Contribution to Qualification Building, Product Delivery, and Customer Value

8.1 Qualification Building

• WPS/PQR Support: Demonstrated equipment health monitoring provides evidence that process parameters (collision velocity, clamping force, wire feed rate) were maintained within qualified ranges, supporting Weld Procedure Specification (WPS) qualification and Performance Qualification Record (PQR) documentation per ASTM A780 and ASME Section IX.
• ISO 9001 / ISO 3834 Compliance: Equipment condition monitoring is a demonstrable element of process control systems required by quality management standards. MSFDE-based records provide objective evidence of equipment fitness for purpose.
• Customer Qualification Audits: Many end-users in petrochemical, power generation, and marine industries require suppliers to demonstrate comprehensive equipment maintenance and monitoring programs. MSFDE documentation provides quantifiable proof of equipment health management.

8.2 Product Delivery Enhancement

• Reduced rework rates: Early detection of hydraulic system degradation prevents the manufacture of substandard cladding products, reducing rework and scrap costs by an estimated 25–40%.
• Shortened NDT cycles: With equipment health verified prior to production, NDT (per GB/T 17748 or ASTM E359) rejection rates decrease, accelerating the inspection-to-acceptance cycle.
• Batch consistency: Stable hydraulic pump operation ensures batch-to-batch uniformity in cladding properties, meeting the tight tolerances required by ASME SA-358 and API 650 applications.

8.3 Customer Value Proposition

"The implementation of MSFDE-based hydraulic pump fault diagnosis represents a commitment to process excellence that extends beyond the cladding interface itself. By ensuring that every bonding cycle is executed with verified equipment health, we provide customers with quantifiable confidence that their clad components will perform reliably in service. This transforms our value proposition from 'we make clad products' to 'we deliver assured performance through controlled, monitored, and traceable manufacturing.'"

For customers in safety-critical applications (pressure vessels per GB/T 150, pipelines per GB/T 21833, nuclear components per NB/T 47012), the ability to demonstrate that manufacturing equipment was in verified healthy condition at the time of production provides an additional layer of quality assurance that differentiates the company in competitive bidding scenarios.

9. Implementation Roadmap and Recommendations

1. Phase 1 — Pilot Deployment (Months 1–3): Install sensor arrays on the primary hydraulic explosive bonding pump system; establish baseline MSFDE signatures under normal operation; develop initial fault detection thresholds.
2. Phase 2 — Model Development (Months 3–6): Conduct controlled fault injection tests (simulated bearing wear, seal degradation, cavitation); build and validate classification models; establish correlation with cladding quality metrics.
3. Phase 3 — Integration (Months 6–9): Integrate MSFDE monitoring into the production management system; establish automated health certificates for each cladding batch; train maintenance personnel on diagnostic interpretation.
4. Phase 4 — Expansion (Months 9–12): Extend monitoring to TIG/MIG overlay hydraulic systems and explosion welding auxiliary hydraulics; develop predictive maintenance algorithms; establish long-term equipment health database.
5. Phase 5 — Continuous Improvement (Ongoing): Update models with accumulated operational data; refine fault signatures; benchmark diagnostic performance against industry standards; pursue internal certification of the diagnostic system.

This structured approach ensures that the MSFDE diagnostic capability is developed incrementally, with each phase delivering measurable value while building toward a comprehensive condition-based maintenance and quality assurance system that strengthens the company's position in the high-value cladding market.