【钠瞳 Sodium Pupil】三：模型与方法

三、模型与方法

3.1 仿真环境

仿真以 1 分钟为步长、1 天为时长（1440 步）。每步按能量守恒结算：

E(t+1) = E(t) + η·P_solar(t)/60 − (P_idle + P_action + P_selfdis + P_thermal)

用一句话说：上一分钟的电量，加上光伏这一分钟充进来的电，再减掉待机、动作、自放电与保温补偿四项开销。

其中光伏效率 η = 0.86，-10℃ 以下的保温补偿按约 2.5 Wh/日计入。温度、光照、触发与事件序列全部参数化生成，且对三种策略完全相同，以保证受控对照。

3.2 电池化学是显式变量

这是本模型与一般"能耗仿真"的关键差别：电池不是一块无差别的能量池，而带三项物理耦合。

耦合项	作用方式
低温容量保持率	直接缩放可用能量
低温可用功率	表现为"能否启动一次识别"的能量门槛
低温禁充阈值	决定光伏输入能否进入电池

三种化学（钠离子、磷酸铁锂、铅酸）的取值均采用公开文献与器件手册中的常见区间，并刻意取对钠电不利的一端，以保证结论保守。

3.3 决策器的三步判断

1. 能量门：单次"认+传"代价 × 3 须小于当前可用能量（可用能量 = 剩余电量 × 该温度下可用比例）；
2. 预留线：撑到日出的窗口内设定最低电量比例，低于此线只允许"看"不允许"认"；
3. 降级：能量不足时对高价值事件保留低分辨率证据，而不做完整识别，避免"全有或全无"的浪费。

3.4 评价口径

• 事件捕获率 = 被有效识别的事件权重 ÷ 设备存活期间的事件总权重。

注意分母是"存活期间"。否则一台早已断电的设备会被计入"漏检"，统计就不公平了。

III. Model and Method

3.1 Simulation environment

The simulation runs in one-minute steps over one day, that is 1440 steps. At each step the energy balance is settled as:

E(t+1) = E(t) + η·P_solar(t)/60 − (P_idle + P_action + P_selfdis + P_thermal)

In plain words: the charge of the previous minute, plus the solar energy charged during this minute, minus the four overheads of idle consumption, action consumption, self-discharge and thermal compensation.

Here the solar efficiency is η = 0.86, and the thermal compensation below -10℃ is accounted at about 2.5 Wh per day. The temperature, solar, trigger and event sequences are all generated parametrically and are exactly the same for the three strategies, which guarantees a controlled comparison.

3.2 Battery chemistry is an explicit variable

This is the key difference between this model and ordinary "energy-consumption simulations": the battery is not an undifferentiated energy pool, but carries three physical couplings.

Coupling	How it acts
Low-temperature capacity retention	Directly scales the usable energy
Low-temperature available power	Appears as the energy threshold for whether an identification can even start
Low-temperature charge cut-off	Determines whether solar input can enter the battery

The values for the three chemistries (sodium-ion, LFP and lead-acid) are all taken from common ranges reported in public literature and device datasheets, and we deliberately chose the end that is unfavourable to sodium-ion, so that the conclusions remain conservative.

3.3 The three checks of the decision engine

1. Energy gate: three times the cost of a single "identify plus transmit" must be smaller than the currently available energy (available energy = remaining charge × the usable ratio at that temperature);
2. Reserve line: within the window that must last until sunrise, a minimum charge ratio is set; below this line "look" is allowed but "identify" is not;
3. Degrade: when energy is insufficient, a low-resolution record is kept for high-value events instead of performing a full identification, avoiding the waste of "all or nothing".

3.4 Evaluation metrics

• Event capture rate = the weight of events effectively identified ÷ the total weight of events during the period the device is alive.

Note that the denominator is the "alive period". Otherwise a device that has long been dead would be counted as having "missed" events, and the statistics would not be fair.