Deterministic AI for Cavitation Risk Management
in High-Pressure Desalination Pumps

1. Introduction

Global installed desalination capacity is now on the order of 100 million m³/day, and membrane-based desalination technologies, including reverse osmosis (RO), account for the dominant share of modern capacity [1,2]. Large seawater RO trains commonly use high-pressure feed pumps operating at discharge pressures of roughly 55–90 bar, with flow rates that can reach hundreds to more than 1,000 m³/h depending on train size. These pumps are among the most energy-intensive and reliability-critical assets in the plant: a severe pump fault can force a train derating, standby transfer, or outage until inspection and repair are complete.

Cavitation is the formation and collapse of vapour bubbles when local liquid pressure approaches the liquid's vapour pressure. In pumps it can erode impellers, increase vibration and noise, reduce head and efficiency, and accelerate bearing and seal stress. The standard engineering metric for cavitation risk is the Net Positive Suction Head Available (NPSH_A) relative to the pump's required value (NPSH_R). When NPSH_A falls below NPSH_R, the pump is operating outside the manufacturer's required suction-head condition and cavitation-related performance degradation is expected or highly likely.

Most industrial SCADA systems implement only a fixed low-pressure alarm (e.g., suction < 0.5 bar). This is a lagging indicator. By the time it fires, cavitation may have been underway for hours. What operators need is a continuous probabilistic assessment: given current sensor readings, what is the probability of pump failure within 7 days, and what should we do now?

This paper makes the following contributions:

1. A full derivation of NPSH from Bernoulli's equation with dimensional analysis, cross-checked against public engineering references and demonstrator code.
2. A fixed-grid Bayesian belief update that is deterministic, replayable, and auditable, which is essential for regulated water infrastructure.
3. A self-improving, deterministic maintenance agent pattern in which operator feedback can refine checklist priority and calibration state without handing safety decisions to an LLM.
4. A counterfactual cost model that supports risk-averse maintenance decisions without allowing an LLM to own a safety decision.
5. A representative Water OS case study with the physics arithmetic and intermediate values shown.
6. A description of how TwinEdge Water OS extends the public demonstration pattern to utility-scale multi-asset operations.

2. Physical Background

2.1 Centrifugal Pump Fundamentals

A centrifugal pump transfers energy from a rotating impeller to the fluid. The Euler turbomachinery equation relates impeller geometry and rotational speed to the theoretical head rise:

where \(u\) is blade tip speed (m/s), \(c_u\) is the tangential component of absolute velocity (m/s), subscripts 1 and 2 denote inlet and outlet.

In practice, losses reduce the actual head. The pump affinity laws describe how performance scales with rotational speed \(N\):

These laws are used in the TwinEdge Water OS hydraulic solver for VFD-modulated pump stations (Section 8).

2.2 NPSH Derivation from Bernoulli's Equation

Applying Bernoulli's energy equation along a streamline from the suction tank free surface (point 0) to the pump suction datum (point s):

Cavitation inception risk increases as local pressure approaches the vapour pressure \(P_v\). NPSH Available is the absolute total suction head above vapour pressure at the pump suction datum:

The worked trace uses the pressure-only pump-flange approximation as a conservative lower bound because it is directly available from the field pressure transmitter. Full Water OS deployments can add velocity-head, elevation, and suction-line-loss corrections from the hydraulic model. For a liquid with specific gravity \(S_g\), \(\rho = 1000 \cdot S_g\) kg/m³. With \(P_{s,gauge}\) and \(P_{atm}\) in bar and \(P_v\) in kPa, the pressure-only lower bound is:

Pressure-only demonstrator formula: crates/asset-agent-core/src/npsh.rs · Dimensionally checked

The NPSH margin determines risk level:

When \(\Delta\text{NPSH} < 0\), the pump is operating below the required suction-head condition defined for the pump curve; cavitation-related performance degradation is expected or highly likely. At \(\Delta\text{NPSH} < 0.20\) m, the design margin is effectively gone even before accounting for transmitter uncertainty, suction-line losses, or salinity/temperature drift.

2.3 Vapour Pressure and the Magnus Equation

Vapour pressure increases non-linearly with temperature. The Magnus formula (1844, refined by Alduchov & Eskridge 1996 [3]) provides a fast, accurate approximation:

At \(T = 20\,°\text{C}\): \(P_v = 0.61078 \times e^{1.3424} = 2.338\,\text{kPa}\), matching standard freshwater saturation-pressure tables. Checked · Conservative for seawater (see §2.3.1)

2.3.1 Seawater Correction

Dissolved salts suppress vapour pressure. A standard seawater correction gives a vapour pressure roughly 0.98× the freshwater value at 35 PSU and 20°C, so \(P_v\) is approximately 2.29 kPa rather than 2.338 kPa [6]. The demonstrator formula uses the freshwater value, which slightly underestimates NPSH_A and therefore produces conservative cavitation-risk estimates. The magnitude of this salinity-only effect is about 0.005 m of head, negligible relative to typical field uncertainty in suction-pressure measurement and pump-datum correction.

2.4 Pump Head from the Energy Equation

The total dynamic head delivered by the pump is derived from the pressure differential across inlet and outlet:

Public demonstrator reference: npsh.rs::pump_head_m · At P_s=0.7 bar, P_d=63.5 bar: H=621.73 m. Checked

3. System Architecture

The complete system comprises three layers. The public components (Layers 1 and 2) are published on GitHub as demonstrators of edge ingestion and deterministic reasoning. TwinEdge Water OS (Layer 3) applies the same governed pattern to multi-asset, multi-utility operations without disclosing production internals.

4. The Deterministic Reasoning Engine

4.1 Feature Engineering

Seven physics-derived scores are computed from the raw sensor snapshot and normalised to [0, 1]. The primary indicator is the NPSH score, which reflects the margin to the pump's required NPSH condition:

The composite cavitation evidence score \(E\) is a weighted sum of all indicators:

Weights sum to 1.000. Public demonstrator reference: features.rs:145–150 · Checked

Table 1. Feature weights and physical basis. The weights are engineering priors used for deterministic scoring; production calibration remains asset-specific.

Model confidence increases with evidence strength:

Baseline confidence reflects design-spec tolerance uncertainty. The maximum acknowledges irreducible model and sensor error. Public demonstrator reference: features.rs:175.

4.2 Bayesian Fixed-Grid Belief State

Pump damage \(d \in [0, 1]\) is tracked over a fixed grid of 101 points \(\{0.00, 0.01, \ldots, 1.00\}\). At each time step \(t\), the posterior is updated via Bayes' rule with a Gaussian likelihood centred on the predicted damage trajectory. The public demonstrator shows the method on a compact single-asset profile; Water OS persists the belief state across operating history and operator feedback.

where the one-step predicted damage is \(\hat{d}_t = d_{t-1} + r\) (clipped to 1.0), \(\sigma = 0.18\) is the observation noise standard deviation, and the posterior is normalised to sum to 1. The damage rate \(r\) is a phenomenological accumulation model:

Representative parameters: \(r_0=0.001\), \(g_c=0.010\), \(g_v=0.004\), \(g_T=0.002\) per hour. This is a linearized planning model, not a substitute for vendor pump curves or post-event inspection. Public demonstrator reference: belief.rs:68–75.

4.3 Remaining Useful Life Forecast

RUL is defined as the expected time to reach the failure state \(d = 1.0\), computed as a probability-weighted average over the posterior:

The ceiling operator discretizes time to the next model tick. \(\Delta t = 1\) hour per tick in the worked example. Public demonstrator reference: forecast.rs:92–103.

Failure probabilities over fixed horizons are computed by integrating the belief distribution forward:

Where k ∈ {1, 7, 30} for 24h, 7-day, and 30-day horizons.

4.4 Counterfactual Cost Analysis and CVaR₉₅

For each of five maintenance actions \(a \in \{\text{defer, inspect, reduce\_load, repair, replace}\}\), the expected cost is evaluated over the belief distribution. The Conditional Value at Risk at 95% is the average cost of the worst 5% of outcomes, a risk-averse metric suitable for critical infrastructure:

In discrete form, states are sorted by descending cost and the top 5% of probability mass is accumulated:

Public demonstrator reference: counterfactual.rs:67–102. Production Water OS action-effect calibration is deterministic but not disclosed in this paper.

Total cost for each action at damage state \(d\) incorporates fixed costs, operating penalty, and failure penalty:

Representative parameters used in the worked example: \(\alpha = \$12{,}000\)/unit damage, \(\beta = \$100{,}000\) failure penalty. These are planning-cost assumptions, not universal industry costs.

4.5 Deterministic Policy Selection

Action recommendations follow a deterministic priority tree, eliminating stochastic ambiguity:

Representative thresholds: \(\rho_{low}=0.20\), \(\rho_{high}=0.55\), \(\rho_{critical}=0.85\), with \(d_{replace}\) used to avoid replacing a repairable asset. The public AssetPilot demonstrator implements a simpler threshold tree for transparency.

5. Representative Case Study: RO Pump Suction Pressure Excursion

5.1 Asset Specification

The representative plant profile uses a high-pressure RO feed pump in a duty/standby operating bay. The pump is a synthetic BB3 multistage centrifugal profile with the following nameplate-style data. The public AssetPilot repository includes a similar synthetic hp_pump_1 profile to demonstrate the deterministic method; the Water OS case study is not presented as a released utility record.

Model

BB3 Multistage 8×15-4 (synthetic)

Service

RO Train 1 duty: seawater HP feed

Rated flow

1,012 m³/h

Rated head

628 m

Rated power

2,062 kW

Speed

2,783 RPM

NPSH_R

19.0 m (4-stage, high speed)

Design suction

4.0 bar gauge

Specific gravity

1.03 (seawater/RO brine)

Flow range

600–1,215 m³/h

5.2 Incident Timeline

In the representative event, suction tank level began dropping because of a partially closed inlet valve. By 09:15, the suction pressure gauge at the pump inlet read 0.70 bar gauge, down from a normal operating point of approximately 1.50 bar.

5.3 Sensor Snapshot at t = 09:15

Table 2. Representative sensor readings at incident onset. The public repository includes analogous synthetic traces for demonstration; these values are used here to show the full calculation path.

5.4 Full Decision Trace

Step 1: Vapour Pressure

Step 2: Absolute Suction Pressure

Step 3: NPSH_A,lb

Step 4: NPSH Margin

Step 5: Feature Scores

Risk level: HIGH. Both \(E \geq 0.70\) and \(\Delta\text{NPSH} < 0.20\) m conditions satisfied.

Step 6: Damage Rate

Step 7: Belief Update

For the demonstration prior, the pump starts near zero damage. After the first observation with E=0.731:

After 48 hours of sustained low-NPSH operation with no corrective action:

Step 8: RUL and Failure Probabilities

Step 9: Policy Decision

5.5 Counterfactual Cost Comparison

5.6 Intervention and Outcome

The operator received the HIGH risk alert with the 10-item cavitation checklist at 09:22. Item 2 (inlet valve position) was identified as the representative root cause by 09:35. The inlet valve was fully opened, restoring suction pressure to 1.52 bar by 09:50. A planned repair/inspection was scheduled for the following weekend to check the impeller, wear rings, seal faces, and bearing condition before returning the pump to normal duty.

Table 3. Modeled financial outcome for the representative suction-pressure event. All costs in USD.

6. Physics Verification Summary

Table 4. Physics and decision-model verification summary for the worked example and public demonstrators. "Conservative" denotes a safe-side approximation; "Documented Simplification" denotes a known model limitation that should be calibrated for each production asset.

7. Open-Source Demonstrators

TwinEdge AI publishes two open-source repositories to demonstrate the deterministic architecture in public. They are useful for researchers, pilot projects, and teams evaluating deterministic AI approaches for industrial asset monitoring. They are demonstrators, not a disclosure of Water OS production internals or a warranty that the representative case-study calibration is identical to the public code.

7.1 opcua-edge v0.1 (alpha)

A lightweight OPC UA server written in plain C using the open62541 library. It loads a plant hierarchy from a text template file (.edge format), exposes plant tags over OPC UA at opc.tcp://<host>:4840, and polls downstream devices via Modbus TCP. The public repository includes parser, address-space, Modbus, SQLite, event, and benchmark coverage; published benchmarks include 1,100-tag edge-device runs and larger server-reference synthetic runs. SQLite provides non-critical-path persistence for asset definitions, latest values, events, and benchmark history.

7.2 AssetPilot (deterministic-asset-maintenance-agent) v0.1

A Rust-native self-improving, deterministic maintenance agent. The codebase is organised into six crates: asset-agent-core (physics + Bayesian inference), asset-agent-api (Axum REST server), asset-agent-opcua (OPC UA I/O), asset-agent-memory (SQLite case store and feedback), asset-agent-llm (optional Mistral.rs explanation layer with guard checks), and asset-agent-cli. The memory layer demonstrates deterministic self-improvement: confirmed field feedback can update checklist ordering and calibration state while preserving auditable decision logic.

8. TwinEdge Water OS

The open-source demonstrators show a single-asset pattern. Utilities operate hundreds of assets across multiple plants, protocols, and systems of record (SCADA, CMMS, GIS, LIMS, billing). Water OS bridges this gap by giving every asset, sensor, zone, and work order a governed identity regardless of source system, then running deterministic physics and risk models across approved assets.

8.1 Physics Model Registry

Water OS extends the single-asset NPSH model to a versioned physics model registry covering the full water treatment train:

Table 6. Physics model registry in TwinEdge Water OS. Equations are stored as versioned formula strings with source attribution.

8.2 Hydraulic Solver

A deterministic hydraulic solver finds the operating point at the intersection of the pump curve and system curve using bounded iteration with configurable derating factors:

where \(\kappa_c\) is the capacity derating factor (VFD modulation, impeller wear), \(\kappa_h\) is the head derating factor (valve throttling, fouling). Derating factors enable prognostic modelling: the solver predicts how the operating point shifts as the pump ages.

8.3 What Water OS Adds Over the Open-Source Baseline

Table 7. Capability comparison between the public demonstrators and TwinEdge Water OS enterprise platform.

9. Conclusion

We have presented a physics-audited deterministic AI approach for cavitation risk management in high-pressure desalination pumps. The core risk assessment combines first-principles pressure-head calculations, vapor-pressure thermodynamics, fixed-grid Bayesian belief updates, deterministic RUL forecasting, and risk-averse counterfactual maintenance analysis. The public repositories at github.com/twinedge-ai demonstrate the OPC UA edge data path and deterministic maintenance-agent method; Water OS production deployment details and calibration parameters remain proprietary.

The representative case study demonstrates that early detection of a −2.27 m NPSH margin and a 0.731 cavitation evidence score leads to a deterministic repair recommendation before the modeled 7-day sustained-risk horizon reaches failure. In the planning-cost scenario shown, root-cause correction plus planned repair reduces modeled deferred-risk cost by $65,040. The approach is auditable: operators can replay an approved snapshot and obtain the same governed result, making it appropriate for regulated water infrastructure where explainability is a compliance requirement, not an option.

The open-source tools (opcua-edge and AssetPilot) provide a practical single-asset demonstration of deterministic ingestion, reasoning, checklist generation, guarded explanation, and feedback-driven self-improvement. In short: AssetPilot demonstrates a self-improving, deterministic maintenance agent. TwinEdge Water OS extends that pattern to utility-scale multi-asset operations through governed asset identity, multi-protocol ingestion, a versioned physics model registry, hydraulic solving, and regulatory workflows without abandoning the deterministic safety boundary.

asset_id        = "hp_pump_1"
asset_name      = "High-Pressure RO Feed Pump, Train 1"
vendor_model    = "Synthetic BB3 Multistage 8x15-4"
service         = "RO Train 1 duty"
rated_flow_m3h  = 1012.0
rated_head_m    = 628.0
rated_power_kw  = 2062.0
rated_speed_rpm = 2783.0
npshr_m         = 19.0
stages          = 4
specific_gravity = 1.03
design_suction_bar = 4.0
max_discharge_bar  = 89.2
flow_range_min_m3h = 600.0
flow_range_max_m3h = 1215.0