1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
#![no_std]
#![forbid(unsafe_code)]
#![deny(warnings, clippy::all)]
use micromath::F32Ext;
#[derive(Copy, Clone, Eq, PartialEq, Ord, PartialOrd, Hash, Debug)]
pub enum AlgorithmType {
Voc,
Nox,
}
#[derive(Debug)]
pub struct GasIndexAlgorithm {
state: GasIndexAlgorithmParams,
}
impl GasIndexAlgorithm {
pub const fn new_uninitialized(algorithm_type: AlgorithmType) -> Self {
Self {
state: GasIndexAlgorithmParams::new_uninit(algorithm_type),
}
}
pub fn new(algorithm_type: AlgorithmType, sampling_interval: f32) -> Self {
let mut s = Self::new_uninitialized(algorithm_type);
s.init_with_sampling_interval(algorithm_type, sampling_interval);
s
}
pub fn init_with_sampling_interval(
&mut self,
algorithm_type: AlgorithmType,
sampling_interval: f32,
) {
self.state
.init_with_sampling_interval(algorithm_type, sampling_interval);
}
pub fn process(&mut self, sraw: i32) -> i32 {
self.state.process(sraw)
}
}
#[derive(Copy, Clone, PartialEq, PartialOrd, Debug)]
pub struct GasIndexAlgorithmParams {
pub algorithm_type: AlgorithmType,
pub sampling_interval: f32,
pub index_offset: f32,
pub sraw_minimum: i32,
pub gating_max_duration_minutes: f32,
pub init_duration_mean: f32,
pub init_duration_variance: f32,
pub gating_threshold: f32,
pub index_gain: f32,
pub tau_mean_hours: f32,
pub tau_variance_hours: f32,
pub sraw_std_initial: f32,
pub uptime: f32,
pub sraw: f32,
pub gas_index: f32,
pub mean_variance_estimator_initialized: bool,
pub mean_variance_estimator_mean: f32,
pub mean_variance_estimator_sraw_offset: f32,
pub mean_variance_estimator_std: f32,
pub mean_variance_estimator_gamma_mean: f32,
pub mean_variance_estimator_gamma_variance: f32,
pub mean_variance_estimator_gamma_initial_mean: f32,
pub mean_variance_estimator_gamma_initial_variance: f32,
pub mean_variance_estimator_gamma_mean2: f32,
pub mean_variance_estimator_gamma_variance2: f32,
pub mean_variance_estimator_uptime_gamma: f32,
pub mean_variance_estimator_uptime_gating: f32,
pub mean_variance_estimator_gating_duration_minutes: f32,
pub mean_variance_estimator_sigmoid_k: f32,
pub mean_variance_estimator_sigmoid_x0: f32,
pub mox_model_sraw_std: f32,
pub mox_model_sraw_mean: f32,
pub sigmoid_scaled_k: f32,
pub sigmoid_scaled_x0: f32,
pub sigmoid_scaled_offset_default: f32,
pub adaptive_lowpass_a1: f32,
pub adaptive_lowpass_a2: f32,
pub adaptive_lowpass_initialized: bool,
pub adaptive_lowpass_x1: f32,
pub adaptive_lowpass_x2: f32,
pub adaptive_lowpass_x3: f32,
}
impl GasIndexAlgorithmParams {
const fn new_uninit(algorithm_type: AlgorithmType) -> Self {
GasIndexAlgorithmParams {
algorithm_type,
sampling_interval: 0.0,
index_offset: 0.0,
sraw_minimum: 0,
gating_max_duration_minutes: 0.0,
init_duration_mean: 0.0,
init_duration_variance: 0.0,
gating_threshold: 0.0,
index_gain: 0.0,
tau_mean_hours: 0.0,
tau_variance_hours: 0.0,
sraw_std_initial: 0.0,
uptime: 0.0,
sraw: 0.0,
gas_index: 0.0,
mean_variance_estimator_initialized: false,
mean_variance_estimator_mean: 0.0,
mean_variance_estimator_sraw_offset: 0.0,
mean_variance_estimator_std: 0.0,
mean_variance_estimator_gamma_mean: 0.0,
mean_variance_estimator_gamma_variance: 0.0,
mean_variance_estimator_gamma_initial_mean: 0.0,
mean_variance_estimator_gamma_initial_variance: 0.0,
mean_variance_estimator_gamma_mean2: 0.0,
mean_variance_estimator_gamma_variance2: 0.0,
mean_variance_estimator_uptime_gamma: 0.0,
mean_variance_estimator_uptime_gating: 0.0,
mean_variance_estimator_gating_duration_minutes: 0.0,
mean_variance_estimator_sigmoid_k: 0.0,
mean_variance_estimator_sigmoid_x0: 0.0,
mox_model_sraw_std: 0.0,
mox_model_sraw_mean: 0.0,
sigmoid_scaled_k: 0.0,
sigmoid_scaled_x0: 0.0,
sigmoid_scaled_offset_default: 0.0,
adaptive_lowpass_a1: 0.0,
adaptive_lowpass_a2: 0.0,
adaptive_lowpass_initialized: false,
adaptive_lowpass_x1: 0.0,
adaptive_lowpass_x2: 0.0,
adaptive_lowpass_x3: 0.0,
}
}
fn init_with_sampling_interval(
&mut self,
algorithm_type: AlgorithmType,
sampling_interval: f32,
) {
self.algorithm_type = algorithm_type;
self.sampling_interval = sampling_interval;
match self.algorithm_type {
AlgorithmType::Nox => {
self.index_offset = 1.0;
self.sraw_minimum = 10000;
self.gating_max_duration_minutes = 60.0 * 12.0;
self.init_duration_mean = 3600.0 * 4.75f32;
self.init_duration_variance = 3600.0 * 5.70;
self.gating_threshold = 30.0;
}
AlgorithmType::Voc => {
self.index_offset = 100.0;
self.sraw_minimum = 20000;
self.gating_max_duration_minutes = 60.0 * 3.0;
self.init_duration_mean = 3600.0 * 0.75f32;
self.init_duration_variance = 3600.0 * 1.45f32;
self.gating_threshold = 340.0;
}
}
self.index_gain = 230.0;
self.tau_mean_hours = 12.0;
self.tau_variance_hours = 12.0;
self.sraw_std_initial = 50.0;
self.reset();
}
fn reset(&mut self) {
self.uptime = 0.0;
self.sraw = 0.0;
self.gas_index = 0.0;
self.init_instances();
}
fn init_instances(&mut self) {
self.mean_variance_estimator_set_parameters();
let sraw_std = self.mean_variance_estimator_get_std();
let sraw_mean = self.mean_variance_estimator_get_mean();
self.mox_model_set_parameters(sraw_std, sraw_mean);
match self.algorithm_type {
AlgorithmType::Nox => {
self.sigmoid_scaled_set_parameters(614.0, -0.0101f32, 1.0);
}
AlgorithmType::Voc => {
self.sigmoid_scaled_set_parameters(213.0, -0.0065f32, 100.0);
}
}
self.adaptive_lowpass_set_parameters();
}
fn process(&mut self, mut sraw: i32) -> i32 {
if self.uptime <= 45.0 {
self.uptime += self.sampling_interval;
} else {
if sraw > 0 && sraw < 65000 {
if sraw < self.sraw_minimum + 1 {
sraw = self.sraw_minimum + 1;
} else if sraw > self.sraw_minimum + 32767 {
sraw = self.sraw_minimum + 32767;
}
self.sraw = (sraw - self.sraw_minimum) as f32;
}
if self.algorithm_type == AlgorithmType::Voc
|| self.mean_variance_estimator_is_initialized()
{
self.gas_index = self.mox_model_process(self.sraw);
self.gas_index = self.sigmoid_scaled_process(self.gas_index);
} else {
self.gas_index = self.index_offset;
}
self.gas_index = self.adaptive_lowpass_process(self.gas_index);
if self.gas_index < 0.5f32 {
self.gas_index = 0.5f32;
}
if self.sraw > 0.0 {
self.mean_variance_estimator_process(self.sraw);
let sraw_std = self.mean_variance_estimator_get_std();
let sraw_mean = self.mean_variance_estimator_get_mean();
self.mox_model_set_parameters(sraw_std, sraw_mean);
}
}
(self.gas_index + 0.5f32) as i32
}
fn mean_variance_estimator_set_parameters(&mut self) {
self.mean_variance_estimator_initialized = false;
self.mean_variance_estimator_mean = 0.0;
self.mean_variance_estimator_sraw_offset = 0.0;
self.mean_variance_estimator_std = self.sraw_std_initial;
self.mean_variance_estimator_gamma_mean = 8.0 * 64.0 * (self.sampling_interval / 3600.0)
/ (self.tau_mean_hours + self.sampling_interval / 3600.0);
self.mean_variance_estimator_gamma_variance = 64.0 * (self.sampling_interval / 3600.0)
/ (self.tau_variance_hours + self.sampling_interval / 3600.0);
match self.algorithm_type {
AlgorithmType::Nox => {
self.mean_variance_estimator_gamma_initial_mean =
8.0 * 64.0 * self.sampling_interval / (1200.0 + self.sampling_interval);
}
AlgorithmType::Voc => {
self.mean_variance_estimator_gamma_initial_mean =
8.0 * 64.0 * self.sampling_interval / (20.0 + self.sampling_interval);
}
}
self.mean_variance_estimator_gamma_initial_variance =
64.0 * self.sampling_interval / (2500.0 + self.sampling_interval);
self.mean_variance_estimator_gamma_mean2 = 0.0;
self.mean_variance_estimator_gamma_variance2 = 0.0;
self.mean_variance_estimator_uptime_gamma = 0.0;
self.mean_variance_estimator_uptime_gating = 0.0;
self.mean_variance_estimator_gating_duration_minutes = 0.0;
}
fn mean_variance_estimator_get_std(&mut self) -> f32 {
self.mean_variance_estimator_std
}
fn mean_variance_estimator_get_mean(&mut self) -> f32 {
self.mean_variance_estimator_mean + self.mean_variance_estimator_sraw_offset
}
fn mean_variance_estimator_is_initialized(&mut self) -> bool {
self.mean_variance_estimator_initialized
}
fn mean_variance_estimator_calculate_gamma(&mut self) {
let uptime_limit = 32767.0 - self.sampling_interval;
if self.mean_variance_estimator_uptime_gamma < uptime_limit {
self.mean_variance_estimator_uptime_gamma += self.sampling_interval;
}
if self.mean_variance_estimator_uptime_gating < uptime_limit {
self.mean_variance_estimator_uptime_gating += self.sampling_interval;
}
self.mean_variance_estimator_sigmoid_set_parameters(self.init_duration_mean, 0.01f32);
let sigmoid_gamma_mean =
self.mean_variance_estimator_sigmoid_process(self.mean_variance_estimator_uptime_gamma);
let gamma_mean = self.mean_variance_estimator_gamma_mean
+ (self.mean_variance_estimator_gamma_initial_mean
- self.mean_variance_estimator_gamma_mean)
* sigmoid_gamma_mean;
let gating_threshold_mean = self.gating_threshold
+ (510.0 - self.gating_threshold)
* self.mean_variance_estimator_sigmoid_process(
self.mean_variance_estimator_uptime_gating,
);
self.mean_variance_estimator_sigmoid_set_parameters(gating_threshold_mean, 0.09f32);
let sigmoid_gating_mean = self.mean_variance_estimator_sigmoid_process(self.gas_index);
self.mean_variance_estimator_gamma_mean2 = sigmoid_gating_mean * gamma_mean;
self.mean_variance_estimator_sigmoid_set_parameters(self.init_duration_variance, 0.01f32);
let sigmoid_gamma_variance =
self.mean_variance_estimator_sigmoid_process(self.mean_variance_estimator_uptime_gamma);
let gamma_variance = self.mean_variance_estimator_gamma_variance
+ (self.mean_variance_estimator_gamma_initial_variance
- self.mean_variance_estimator_gamma_variance)
* (sigmoid_gamma_variance - sigmoid_gamma_mean);
let gating_threshold_variance = self.gating_threshold
+ (510.0 - self.gating_threshold)
* self.mean_variance_estimator_sigmoid_process(
self.mean_variance_estimator_uptime_gating,
);
self.mean_variance_estimator_sigmoid_set_parameters(gating_threshold_variance, 0.09f32);
let sigmoid_gating_variance = self.mean_variance_estimator_sigmoid_process(self.gas_index);
self.mean_variance_estimator_gamma_variance2 = sigmoid_gating_variance * gamma_variance;
self.mean_variance_estimator_gating_duration_minutes +=
self.sampling_interval / 60.0 * ((1.0 - sigmoid_gating_mean) * (1.0 + 0.3f32) - 0.3f32);
if self.mean_variance_estimator_gating_duration_minutes < 0.0 {
self.mean_variance_estimator_gating_duration_minutes = 0.0;
}
if self.mean_variance_estimator_gating_duration_minutes > self.gating_max_duration_minutes {
self.mean_variance_estimator_uptime_gating = 0.0;
}
}
fn mean_variance_estimator_process(&mut self, mut sraw: f32) {
if !self.mean_variance_estimator_initialized {
self.mean_variance_estimator_initialized = true;
self.mean_variance_estimator_sraw_offset = sraw;
self.mean_variance_estimator_mean = 0.0;
} else {
if self.mean_variance_estimator_mean >= 100.0
|| self.mean_variance_estimator_mean <= -100.0
{
self.mean_variance_estimator_sraw_offset += self.mean_variance_estimator_mean;
self.mean_variance_estimator_mean = 0.0;
}
sraw -= self.mean_variance_estimator_sraw_offset;
self.mean_variance_estimator_calculate_gamma();
let delta_sgp = (sraw - self.mean_variance_estimator_mean) / 64.0;
let c = if delta_sgp < 0.0 {
self.mean_variance_estimator_std - delta_sgp
} else {
self.mean_variance_estimator_std + delta_sgp
};
let mut additional_scaling = 1.0;
if c > 1440.0 {
additional_scaling = c / 1440.0 * (c / 1440.0);
}
self.mean_variance_estimator_std =
sqrtf(additional_scaling * (64.0 - self.mean_variance_estimator_gamma_variance2))
* sqrtf(
self.mean_variance_estimator_std
* (self.mean_variance_estimator_std / (64.0 * additional_scaling))
+ self.mean_variance_estimator_gamma_variance2 * delta_sgp
/ additional_scaling
* delta_sgp,
);
self.mean_variance_estimator_mean +=
self.mean_variance_estimator_gamma_mean2 * delta_sgp / 8.0;
};
}
fn mean_variance_estimator_sigmoid_set_parameters(&mut self, x0: f32, k: f32) {
self.mean_variance_estimator_sigmoid_k = k;
self.mean_variance_estimator_sigmoid_x0 = x0;
}
fn mean_variance_estimator_sigmoid_process(&mut self, sample: f32) -> f32 {
let x: f32 = self.mean_variance_estimator_sigmoid_k
* (sample - self.mean_variance_estimator_sigmoid_x0);
if x < -50.0 {
1.0
} else if x > 50.0 {
0.0
} else {
1.0 / (1.0 + expf(x))
}
}
fn mox_model_set_parameters(&mut self, sraw_std: f32, sraw_mean: f32) {
self.mox_model_sraw_std = sraw_std;
self.mox_model_sraw_mean = sraw_mean;
}
fn mox_model_process(&mut self, sraw: f32) -> f32 {
match self.algorithm_type {
AlgorithmType::Nox => (sraw - self.mox_model_sraw_mean) / 2000.0 * self.index_gain,
AlgorithmType::Voc => {
(sraw - self.mox_model_sraw_mean) / (-1.0 * (self.mox_model_sraw_std + 220.0))
* self.index_gain
}
}
}
fn sigmoid_scaled_set_parameters(&mut self, x0: f32, k: f32, offset_default: f32) {
self.sigmoid_scaled_k = k;
self.sigmoid_scaled_x0 = x0;
self.sigmoid_scaled_offset_default = offset_default;
}
fn sigmoid_scaled_process(&mut self, sample: f32) -> f32 {
let x = self.sigmoid_scaled_k * (sample - self.sigmoid_scaled_x0);
if x < -50.0 {
500.0
} else if x > 50.0 {
0.0
} else if sample >= 0.0 {
let shift = if self.sigmoid_scaled_offset_default == 1.0 {
500.0 / 499.0 * (1.0 - self.index_offset)
} else {
(500.0 - 5.0 * self.index_offset) / 4.0
};
(500.0 + shift) / (1.0 + expf(x)) - shift
} else {
self.index_offset / self.sigmoid_scaled_offset_default * (500.0 / (1.0 + expf(x)))
}
}
fn adaptive_lowpass_set_parameters(&mut self) {
self.adaptive_lowpass_a1 = self.sampling_interval / (20.0 + self.sampling_interval);
self.adaptive_lowpass_a2 = self.sampling_interval / (500.0 + self.sampling_interval);
self.adaptive_lowpass_initialized = false;
}
fn adaptive_lowpass_process(&mut self, sample: f32) -> f32 {
if !self.adaptive_lowpass_initialized {
self.adaptive_lowpass_x1 = sample;
self.adaptive_lowpass_x2 = sample;
self.adaptive_lowpass_x3 = sample;
self.adaptive_lowpass_initialized = true;
}
self.adaptive_lowpass_x1 = (1.0 - self.adaptive_lowpass_a1) * self.adaptive_lowpass_x1
+ self.adaptive_lowpass_a1 * sample;
self.adaptive_lowpass_x2 = (1.0 - self.adaptive_lowpass_a2) * self.adaptive_lowpass_x2
+ self.adaptive_lowpass_a2 * sample;
let mut abs_delta = self.adaptive_lowpass_x1 - self.adaptive_lowpass_x2;
if abs_delta < 0.0 {
abs_delta *= -1.0;
}
let f1 = expf(-0.2f32 * abs_delta);
let tau_a = (500.0 - 20.0) * f1 + 20.0;
let a3 = self.sampling_interval / (self.sampling_interval + tau_a);
self.adaptive_lowpass_x3 = (1.0 - a3) * self.adaptive_lowpass_x3 + a3 * sample;
self.adaptive_lowpass_x3
}
}
fn expf(value: f32) -> f32 {
F32Ext::exp(value)
}
fn sqrtf(value: f32) -> f32 {
F32Ext::sqrt(value)
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn voc_reaches_mean() {
let mut algo = GasIndexAlgorithm::new(AlgorithmType::Voc, 1.0);
for _ in 0..200 {
let _ = algo.process(1337);
}
assert_eq!(algo.process(1337), 100);
}
#[test]
fn nox_reaches_mean() {
let mut algo = GasIndexAlgorithm::new(AlgorithmType::Nox, 1.0);
for _ in 0..200 {
let _ = algo.process(1337);
}
assert_eq!(algo.process(1337), 1);
}
}