Indoor Air Quality, Occupancy & Health Risk

A.3 Indoor Air Quality, Occupancy & Health Risk

Indoor air quality (IAQ) and ventilation are increasingly recognized as critical to health, cognitive performance, and resilience to airborne disease. Most commercial buildings already have a wealth of signals (CO₂ sensors, temperature, humidity, HVAC control points), but they are typically used only for crude comfort bands. There is rarely a unified, spatially aware representation of:

• how occupancy and ventilation interact across zones,
• when a space is under-ventilated relative to its load,
• how often high-risk episodes occur and how long they last.

Spaxiom can act as a ventilation and health cortex for buildings, fusing IAQ sensors, occupancy estimates, and HVAC state into intelligible INTENT events like StaleAirEpisode, VentilationDebt, and HighRiskGathering.

Sensors and deployment

For a zone z (e.g., conference room, open office bay, classroom), typical signals include:

• CO₂ concentration C_z(t) (ppm);
• Temperature and humidity T_z(t), H_z(t);
• Fresh air / outdoor air fraction F^OA_z(t) (from damper positions or airflow sensors);
• Supply airflow V̇^sup_z(t) (m³/s or CFM);
• Occupancy proxies N_z(t) from:
  • PIR or time-of-flight sensors,
  • desk/seat occupancy sensors,
  • access-control patterns, or
  • Spaxiom-integrated floor/area sensing where present.

We assume each Zone in Spaxiom is wired to one or more of these signals and that zones can be grouped into higher-level areas for policy and analytics.

INTENT events and risk indices

We define several IAQ- and health-related INTENT events:

• StaleAirEpisode: CO₂ sustained above a threshold (e.g., 1000 ppm) for more than a minimum duration;
• VentilationDebt: integrated shortfall of outdoor air per person relative to recommended rates;
• HighRiskGathering: high occupancy combined with poor ventilation and adverse IAQ (CO₂, PM, humidity).

Let us formalize some of these.

Ventilation per person. For zone z, at time t, the outdoor airflow per person can be approximated as:

where F^OA_z(t) is the fraction of supply air that is outdoor air, and V̇^sup_z(t) is the total supply airflow.

Given a recommended per-person outdoor airflow q^rec (e.g., from a standard), we define a ventilation deficit rate:

Over a monitoring window [t₀, t₁] of length Δt, the ventilation debt is:

CO₂ excursion and stale air. Let C^stale be a CO₂ threshold (e.g., 1000 ppm). Define an indicator:

and the duration of stale air in the window:

Composite health risk score. A simple IAQ/health risk score for zone z over [t₀, t₁] can be defined as:

where:

• E^PM_z is a particulate matter excursion integral;
• E^RH_z is an excursion of relative humidity into high-risk bands (e.g., too dry or too humid);
• α, β, γ, δ are weights reflecting the relative importance of ventilation, CO₂, particulates, and humidity.

Normalization (e.g., dividing by window length or baseline values) can map R^IAQ_z into a dimensionless score in [0,1].

Spaxiom-style implementation sketch

In the Spaxiom DSL, a zone-level IAQ tracker can encapsulate sensor histories and risk computation:

from spaxiom import Zone, Condition
from spaxiom.temporal import within
from spaxiom.logic import on

class IaqZone:
    def __init__(self, name, co2, temp, rh, oa_frac, sup_flow, occupancy):
        self.zone = Zone.named(name)
        self.co2 = co2              # ppm sensor
        self.temp = temp            # degC
        self.rh = rh                # %RH
        self.oa_frac = oa_frac      # 0..1
        self.sup_flow = sup_flow    # m^3/s
        self.occupancy = occupancy  # persons

        # Configurable thresholds / recommendations
        self.q_rec = 10.0 / 3600.0  # 10 m^3/h/person -> m^3/s/person
        self.co2_stale = 1000.0     # ppm
        self.pm_threshold = 25.0    # ug/m^3 (example)
        self.rh_low = 30.0          # %
        self.rh_high = 60.0         # %

    def history(self, sensor, window_s: float):
        return sensor.history(window_s=window_s)  # [(dt, value), ...]

    def ventilation_debt(self, window_s: float) -> float:
        series_oa = self.history(self.oa_frac, window_s)
        series_flow = self.history(self.sup_flow, window_s)
        series_occ = self.history(self.occupancy, window_s)

        # Assume aligned histories or interpolate in real implementation
        total_debt = 0.0
        for ((dt, oa), (_, flow), (_, occ)) in zip(series_oa, series_flow, series_occ):
            q = oa * flow / max(occ, 1.0)
            d = max(0.0, self.q_rec - q)
            total_debt += d * dt
        return total_debt

    def stale_air_duration(self, window_s: float) -> float:
        series = self.history(self.co2, window_s)
        total = 0.0
        for dt, c in series:
            if c > self.co2_stale:
                total += dt
        return total

    def rh_excursion(self, window_s: float) -> float:
        series = self.history(self.rh, window_s)
        total = 0.0
        for dt, r in series:
            if r < self.rh_low or r > self.rh_high:
                total += dt
        return total

    def risk_score(self, window_s: float) -> float:
        D = self.ventilation_debt(window_s)
        S = self.stale_air_duration(window_s)
        RH = self.rh_excursion(window_s)

        alpha, beta, gamma, delta = 1.0, 0.5, 0.0, 0.2  # PM omitted here
        score = alpha * D + beta * S + delta * RH
        # Example squashing to [0,1]
        return 1.0 - (1.0 / (1.0 + score * 1e-4))

# Wire a specific conference room
conf_A = IaqZone(
    name="Conf_Room_A",
    co2=co2_conf_A,
    temp=temp_conf_A,
    rh=rh_conf_A,
    oa_frac=oa_conf_A,
    sup_flow=flow_conf_A,
    occupancy=occ_conf_A,
)

# Condition: high risk over the last 2 hours
high_risk_iaq = Condition(lambda: conf_A.risk_score(window_s=2 * 3600) > 0.7)

@on(within(300, high_risk_iaq))  # check every 5 minutes
def iaq_agent():
    snapshot = {
        "zone": conf_A.zone.name,
        "risk": conf_A.risk_score(window_s=2 * 3600),
        "vent_debt": conf_A.ventilation_debt(2 * 3600),
        "stale_air_s": conf_A.stale_air_duration(2 * 3600),
        "rh_excursion_s": conf_A.rh_excursion(2 * 3600),
    }
    # An LLM or rules engine can:
    # - suggest schedule changes,
    # - recommend window opening where applicable,
    # - adjust ventilation setpoints if allowed.
    propose_iaq_actions(snapshot)

This example shows how Spaxiom:

• computes physically meaningful quantities (ventilation per person) over time windows;
• aggregates multiple risk factors into a scalar risk_score;
• exposes a clean event hook (high_risk_iaq) for agents to react on.