Main Content

Multi-Class Fault Detection Using Simulated Data

This example shows how to use a Simulink model to generate fault and healthy data. The data is used to develop a multi-class classifier to detect different combinations of faults. The example uses a triplex reciprocating pump model and includes leak, blocking, and bearing faults.

Setup the Model

This example uses many supporting files that are stored in a zip file. Unzip the file to get access to the supporting files, load the model parameters, and create the reciprocating pump library.

if ~exist('+mech_hydro_forcesPS','dir')
    unzip('pdmRecipPump_supportingfiles.zip')
end

% Load Parameters
pdmRecipPump_Parameters %Pump
CAT_Pump_1051_DataFile_imported %CAD

% Create Simscape library if needed
if exist('mech_hydro_forcesPS_Lib','file')~=4
    ssc_build mech_hydro_forcesPS
end
Generating Simulink library 'mech_hydro_forcesPS_lib' in the current directory 'C:\Users\anagar\OneDrive - MathWorks\Desktop\Predictive Project\RUL using DL\MultiFaultDetectionExample\ExampleManager\anagar.doc2\predmaint-ex92746726' ...

Reciprocating Pump Model

The reciprocating pump consists of an electric motor, the pump housing, pump crank and pump plungers.

mdl = 'pdmRecipPump';
open_system(mdl)

open_system([mdl,'/Pump'])

The pump model is configured to model three types of faults; cylinder leaks, blocked inlet, and increased bearing friction. These faults are parameterized as workspace variables and configured through the pump block dialog.

Simulating Fault and Healthy Data

For each of the three fault types create an array of values that represent the fault severity, ranging from no fault to a significant fault.

% Define fault parameter variations
numParValues = 10;
leak_area_set_factor = linspace(0.00,0.036,numParValues);
leak_area_set = leak_area_set_factor*TRP_Par.Check_Valve.In.Max_Area;
leak_area_set = max(leak_area_set,1e-9); % Leakage area cannot be 0
blockinfactor_set = linspace(0.8,0.53,numParValues);
bearingfactor_set = linspace(0,6e-4,numParValues);

The pump model is configured to include noise, thus running the model with the same fault parameter values will result in different simulation outputs. This is useful for developing a classifier as it means there can be multiple simulation results for the same fault condition and severity. To configure simulations for such results, create vectors of fault parameter values where the values represent no faults, a single fault, combinations of two faults, and combinations of three faults. For each group (no fault, single fault, etc.) create 125 combinations of fault values from the fault parameter values defined above. This gives a total of 1000 combinations of fault parameter values. Note that running these 1000 simulations in parallel takes around an hour on a standard desktop and generates around 620MB of data. To reduce simulation time, reduce the number of fault combinations to 20 by changing runAll = true to runAll = false. Note that a larger dataset results in a more robust classifier.

% Set number of elements in each fault group
runAll = true; 
if runAll
    % Create a large dataset to build a robust classifier
    nPerGroup = 100; 
else
    % Create a smaller dataset to reduce simulation time
    nPerGroup = 20; %#ok<UNRCH> 
end

rng('default');    % Feed default seed to rng (Random number generator)

% No fault simulations
leakArea = repmat(leak_area_set(1),nPerGroup,1);
blockingFactor = repmat(blockinfactor_set(1),nPerGroup,1);
bearingFactor = repmat(bearingfactor_set(1),nPerGroup,1);

% Single fault simulations
idx = ceil(10*rand(nPerGroup,1));
leakArea = [leakArea; leak_area_set(idx)'];
blockingFactor = [blockingFactor;repmat(blockinfactor_set(1),nPerGroup,1)];
bearingFactor = [bearingFactor;repmat(bearingfactor_set(1),nPerGroup,1)];
idx = ceil(10*rand(nPerGroup,1));
leakArea = [leakArea; repmat(leak_area_set(1),nPerGroup,1)];
blockingFactor = [blockingFactor;blockinfactor_set(idx)'];
bearingFactor = [bearingFactor;repmat(bearingfactor_set(1),nPerGroup,1)];
idx = ceil(10*rand(nPerGroup,1));
leakArea = [leakArea; repmat(leak_area_set(1),nPerGroup,1)];
blockingFactor = [blockingFactor;repmat(blockinfactor_set(1),nPerGroup,1)];
bearingFactor = [bearingFactor;bearingfactor_set(idx)'];

% Double fault simulations
idxA = ceil(10*rand(nPerGroup,1));
idxB = ceil(10*rand(nPerGroup,1));
leakArea = [leakArea; leak_area_set(idxA)'];
blockingFactor = [blockingFactor;blockinfactor_set(idxB)'];
bearingFactor = [bearingFactor;repmat(bearingfactor_set(1),nPerGroup,1)];
idxA = ceil(10*rand(nPerGroup,1));
idxB = ceil(10*rand(nPerGroup,1));
leakArea = [leakArea; leak_area_set(idxA)'];
blockingFactor = [blockingFactor;repmat(blockinfactor_set(1),nPerGroup,1)];
bearingFactor = [bearingFactor;bearingfactor_set(idxB)'];
idxA = ceil(10*rand(nPerGroup,1));
idxB = ceil(10*rand(nPerGroup,1));
leakArea = [leakArea; repmat(leak_area_set(1),nPerGroup,1)];
blockingFactor = [blockingFactor;blockinfactor_set(idxA)'];
bearingFactor = [bearingFactor;bearingfactor_set(idxB)'];

% Triple fault simulations
idxA = ceil(10*rand(nPerGroup,1));
idxB = ceil(10*rand(nPerGroup,1));
idxC = ceil(10*rand(nPerGroup,1));
leakArea = [leakArea; leak_area_set(idxA)'];
blockingFactor = [blockingFactor;blockinfactor_set(idxB)'];
bearingFactor = [bearingFactor;bearingfactor_set(idxC)'];

Use the fault parameter combinations to create Simulink.SimulationInput objects. For each simulation input ensure that the random seed is set differently to generate different results.

for ct = numel(leakArea):-1:1
    simInput(ct) = Simulink.SimulationInput(mdl);
    simInput(ct) = setVariable(simInput(ct),'leak_cyl_area_WKSP',leakArea(ct));
    simInput(ct) = setVariable(simInput(ct),'block_in_factor_WKSP',blockingFactor(ct));
    simInput(ct) = setVariable(simInput(ct),'bearing_fault_frict_WKSP',bearingFactor(ct));
    simInput(ct) = setVariable(simInput(ct),'noise_seed_offset_WKSP',ct-1);
end

Use the generateSimulationEnsemble function to run the simulations defined by the Simulink.SimulationInput objects defined above and store the results in a local sub-folder. Then create a simulationEnsembleDatastore from the stored results.

% Run the simulation and create an ensemble to manage the simulation
% results

if isfolder('./Data')
    % Delete existing mat files
    delete('./Data/*.mat')
end   

[ok,e] = generateSimulationEnsemble(simInput,fullfile('.','Data'),'UseParallel',true);
[28-Jun-2021 13:38:31] Checking for availability of parallel pool...
Starting parallel pool (parpool) using the 'local' profile ...
Preserving jobs with IDs: 1 because they contain crash dump files.
You can use 'delete(myCluster.Jobs)' to remove all jobs created with profile local. To create 'myCluster' use 'myCluster = parcluster('local')'.
Connected to the parallel pool (number of workers: 6).
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[28-Jun-2021 13:41:17] Configuring simulation cache folder on parallel workers...
[28-Jun-2021 13:41:18] Transferring base workspace variables used in the model to parallel workers...
[28-Jun-2021 13:41:19] Loading model on parallel workers...
[28-Jun-2021 13:41:43] Running simulations...
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[28-Jun-2021 14:01:14] Completed 272 of 800 simulation runs
[28-Jun-2021 14:01:18] Completed 273 of 800 simulation runs
[28-Jun-2021 14:01:19] Completed 274 of 800 simulation runs
[28-Jun-2021 14:01:20] Completed 275 of 800 simulation runs
[28-Jun-2021 14:01:21] Completed 276 of 800 simulation runs
[28-Jun-2021 14:01:39] Completed 277 of 800 simulation runs
[28-Jun-2021 14:01:40] Completed 278 of 800 simulation runs
[28-Jun-2021 14:01:41] Completed 279 of 800 simulation runs
[28-Jun-2021 14:01:42] Completed 280 of 800 simulation runs
[28-Jun-2021 14:01:43] Completed 281 of 800 simulation runs
[28-Jun-2021 14:01:44] Completed 282 of 800 simulation runs
[28-Jun-2021 14:02:05] Completed 283 of 800 simulation runs
[28-Jun-2021 14:02:06] Completed 284 of 800 simulation runs
[28-Jun-2021 14:02:07] Completed 285 of 800 simulation runs
[28-Jun-2021 14:02:08] Completed 286 of 800 simulation runs
[28-Jun-2021 14:02:09] Completed 287 of 800 simulation runs
[28-Jun-2021 14:02:10] Completed 288 of 800 simulation runs
[28-Jun-2021 14:02:28] Completed 289 of 800 simulation runs
[28-Jun-2021 14:02:29] Completed 290 of 800 simulation runs
[28-Jun-2021 14:02:30] Completed 291 of 800 simulation runs
[28-Jun-2021 14:02:32] Completed 292 of 800 simulation runs
[28-Jun-2021 14:02:33] Completed 293 of 800 simulation runs
[28-Jun-2021 14:02:34] Completed 294 of 800 simulation runs
[28-Jun-2021 14:02:51] Completed 295 of 800 simulation runs
[28-Jun-2021 14:02:52] Completed 296 of 800 simulation runs
[28-Jun-2021 14:02:53] Completed 297 of 800 simulation runs
[28-Jun-2021 14:02:54] Completed 298 of 800 simulation runs
[28-Jun-2021 14:02:56] Completed 299 of 800 simulation runs
[28-Jun-2021 14:02:57] Completed 300 of 800 simulation runs
[28-Jun-2021 14:03:07] Completed 301 of 800 simulation runs
[28-Jun-2021 14:03:10] Completed 302 of 800 simulation runs
[28-Jun-2021 14:03:10] Completed 303 of 800 simulation runs
[28-Jun-2021 14:03:11] Completed 304 of 800 simulation runs
[28-Jun-2021 14:03:13] Completed 305 of 800 simulation runs
[28-Jun-2021 14:03:14] Completed 306 of 800 simulation runs
[28-Jun-2021 14:03:21] Completed 307 of 800 simulation runs
[28-Jun-2021 14:03:23] Completed 308 of 800 simulation runs
[28-Jun-2021 14:03:24] Completed 309 of 800 simulation runs
[28-Jun-2021 14:03:25] Completed 310 of 800 simulation runs
[28-Jun-2021 14:03:28] Completed 311 of 800 simulation runs
[28-Jun-2021 14:03:30] Completed 312 of 800 simulation runs
[28-Jun-2021 14:03:38] Completed 313 of 800 simulation runs
[28-Jun-2021 14:03:41] Completed 314 of 800 simulation runs
[28-Jun-2021 14:03:42] Completed 315 of 800 simulation runs
[28-Jun-2021 14:03:45] Completed 316 of 800 simulation runs
[28-Jun-2021 14:03:46] Completed 317 of 800 simulation runs
[28-Jun-2021 14:03:51] Completed 318 of 800 simulation runs
[28-Jun-2021 14:03:57] Completed 319 of 800 simulation runs
[28-Jun-2021 14:03:58] Completed 320 of 800 simulation runs
[28-Jun-2021 14:03:59] Completed 321 of 800 simulation runs
[28-Jun-2021 14:04:00] Completed 322 of 800 simulation runs
[28-Jun-2021 14:04:02] Completed 323 of 800 simulation runs
[28-Jun-2021 14:04:12] Completed 324 of 800 simulation runs
[28-Jun-2021 14:04:13] Completed 325 of 800 simulation runs
[28-Jun-2021 14:04:14] Completed 326 of 800 simulation runs
[28-Jun-2021 14:04:15] Completed 327 of 800 simulation runs
[28-Jun-2021 14:04:19] Completed 328 of 800 simulation runs
[28-Jun-2021 14:04:20] Completed 329 of 800 simulation runs
[28-Jun-2021 14:04:23] Completed 330 of 800 simulation runs
[28-Jun-2021 14:04:26] Completed 331 of 800 simulation runs
[28-Jun-2021 14:04:30] Completed 332 of 800 simulation runs
[28-Jun-2021 14:04:31] Completed 333 of 800 simulation runs
[28-Jun-2021 14:04:33] Completed 334 of 800 simulation runs
[28-Jun-2021 14:04:38] Completed 335 of 800 simulation runs
[28-Jun-2021 14:04:44] Completed 336 of 800 simulation runs
[28-Jun-2021 14:04:45] Completed 337 of 800 simulation runs
[28-Jun-2021 14:04:47] Completed 338 of 800 simulation runs
[28-Jun-2021 14:04:48] Completed 339 of 800 simulation runs
[28-Jun-2021 14:04:49] Completed 340 of 800 simulation runs
[28-Jun-2021 14:05:01] Completed 341 of 800 simulation runs
[28-Jun-2021 14:05:03] Completed 342 of 800 simulation runs
[28-Jun-2021 14:05:04] Completed 343 of 800 simulation runs
[28-Jun-2021 14:05:09] Completed 344 of 800 simulation runs
[28-Jun-2021 14:05:11] Completed 345 of 800 simulation runs
[28-Jun-2021 14:05:12] Completed 346 of 800 simulation runs
[28-Jun-2021 14:05:14] Completed 347 of 800 simulation runs
[28-Jun-2021 14:05:16] Completed 348 of 800 simulation runs
[28-Jun-2021 14:05:19] Completed 349 of 800 simulation runs
[28-Jun-2021 14:05:21] Completed 350 of 800 simulation runs
[28-Jun-2021 14:05:22] Completed 351 of 800 simulation runs
[28-Jun-2021 14:05:25] Completed 352 of 800 simulation runs
[28-Jun-2021 14:05:30] Completed 353 of 800 simulation runs
[28-Jun-2021 14:05:33] Completed 354 of 800 simulation runs
[28-Jun-2021 14:05:35] Completed 355 of 800 simulation runs
[28-Jun-2021 14:05:36] Completed 356 of 800 simulation runs
[28-Jun-2021 14:05:37] Completed 357 of 800 simulation runs
[28-Jun-2021 14:05:43] Completed 358 of 800 simulation runs
[28-Jun-2021 14:05:47] Completed 359 of 800 simulation runs
[28-Jun-2021 14:05:49] Completed 360 of 800 simulation runs
[28-Jun-2021 14:05:56] Completed 361 of 800 simulation runs
[28-Jun-2021 14:05:57] Completed 362 of 800 simulation runs
[28-Jun-2021 14:05:58] Completed 363 of 800 simulation runs
[28-Jun-2021 14:05:59] Completed 364 of 800 simulation runs
[28-Jun-2021 14:06:08] Completed 365 of 800 simulation runs
[28-Jun-2021 14:06:09] Completed 366 of 800 simulation runs
[28-Jun-2021 14:06:11] Completed 367 of 800 simulation runs
[28-Jun-2021 14:06:12] Completed 368 of 800 simulation runs
[28-Jun-2021 14:06:16] Completed 369 of 800 simulation runs
[28-Jun-2021 14:06:18] Completed 370 of 800 simulation runs
[28-Jun-2021 14:06:23] Completed 371 of 800 simulation runs
[28-Jun-2021 14:06:24] Completed 372 of 800 simulation runs
[28-Jun-2021 14:06:25] Completed 373 of 800 simulation runs
[28-Jun-2021 14:06:27] Completed 374 of 800 simulation runs
[28-Jun-2021 14:06:28] Completed 375 of 800 simulation runs
[28-Jun-2021 14:06:30] Completed 376 of 800 simulation runs
[28-Jun-2021 14:06:33] Completed 377 of 800 simulation runs
[28-Jun-2021 14:06:37] Completed 378 of 800 simulation runs
[28-Jun-2021 14:06:39] Completed 379 of 800 simulation runs
[28-Jun-2021 14:06:43] Completed 380 of 800 simulation runs
[28-Jun-2021 14:06:50] Completed 381 of 800 simulation runs
[28-Jun-2021 14:06:51] Completed 382 of 800 simulation runs
[28-Jun-2021 14:06:53] Completed 383 of 800 simulation runs
[28-Jun-2021 14:06:54] Completed 384 of 800 simulation runs
[28-Jun-2021 14:06:56] Completed 385 of 800 simulation runs
[28-Jun-2021 14:06:59] Completed 386 of 800 simulation runs
[28-Jun-2021 14:07:00] Completed 387 of 800 simulation runs
[28-Jun-2021 14:07:03] Completed 388 of 800 simulation runs
[28-Jun-2021 14:07:04] Completed 389 of 800 simulation runs
[28-Jun-2021 14:07:07] Completed 390 of 800 simulation runs
[28-Jun-2021 14:07:15] Completed 391 of 800 simulation runs
[28-Jun-2021 14:07:18] Completed 392 of 800 simulation runs
[28-Jun-2021 14:07:19] Completed 393 of 800 simulation runs
[28-Jun-2021 14:07:27] Completed 394 of 800 simulation runs
[28-Jun-2021 14:07:29] Completed 395 of 800 simulation runs
[28-Jun-2021 14:07:31] Completed 396 of 800 simulation runs
[28-Jun-2021 14:07:32] Completed 397 of 800 simulation runs
[28-Jun-2021 14:07:36] Completed 398 of 800 simulation runs
[28-Jun-2021 14:07:38] Completed 399 of 800 simulation runs
[28-Jun-2021 14:07:39] Completed 400 of 800 simulation runs
[28-Jun-2021 14:07:53] Completed 401 of 800 simulation runs
[28-Jun-2021 14:07:55] Completed 402 of 800 simulation runs
[28-Jun-2021 14:07:57] Completed 403 of 800 simulation runs
[28-Jun-2021 14:07:59] Completed 404 of 800 simulation runs
[28-Jun-2021 14:08:01] Completed 405 of 800 simulation runs
[28-Jun-2021 14:08:06] Completed 406 of 800 simulation runs
[28-Jun-2021 14:08:18] Completed 407 of 800 simulation runs
[28-Jun-2021 14:08:20] Completed 408 of 800 simulation runs
[28-Jun-2021 14:08:22] Completed 409 of 800 simulation runs
[28-Jun-2021 14:08:24] Completed 410 of 800 simulation runs
[28-Jun-2021 14:08:27] Completed 411 of 800 simulation runs
[28-Jun-2021 14:08:31] Completed 412 of 800 simulation runs
[28-Jun-2021 14:08:42] Completed 413 of 800 simulation runs
[28-Jun-2021 14:08:44] Completed 414 of 800 simulation runs
[28-Jun-2021 14:08:46] Completed 415 of 800 simulation runs
[28-Jun-2021 14:08:48] Completed 416 of 800 simulation runs
[28-Jun-2021 14:08:52] Completed 417 of 800 simulation runs
[28-Jun-2021 14:08:55] Completed 418 of 800 simulation runs
[28-Jun-2021 14:09:06] Completed 419 of 800 simulation runs
[28-Jun-2021 14:09:09] Completed 420 of 800 simulation runs
[28-Jun-2021 14:09:11] Completed 421 of 800 simulation runs
[28-Jun-2021 14:09:13] Completed 422 of 800 simulation runs
[28-Jun-2021 14:09:15] Completed 423 of 800 simulation runs
[28-Jun-2021 14:09:19] Completed 424 of 800 simulation runs
[28-Jun-2021 14:09:31] Completed 425 of 800 simulation runs
[28-Jun-2021 14:09:33] Completed 426 of 800 simulation runs
[28-Jun-2021 14:09:35] Completed 427 of 800 simulation runs
[28-Jun-2021 14:09:38] Completed 428 of 800 simulation runs
[28-Jun-2021 14:09:40] Completed 429 of 800 simulation runs
[28-Jun-2021 14:09:45] Completed 430 of 800 simulation runs
[28-Jun-2021 14:09:57] Completed 431 of 800 simulation runs
[28-Jun-2021 14:10:00] Completed 432 of 800 simulation runs
[28-Jun-2021 14:10:02] Completed 433 of 800 simulation runs
[28-Jun-2021 14:10:05] Completed 434 of 800 simulation runs
[28-Jun-2021 14:10:07] Completed 435 of 800 simulation runs
[28-Jun-2021 14:10:12] Completed 436 of 800 simulation runs
[28-Jun-2021 14:10:21] Completed 437 of 800 simulation runs
[28-Jun-2021 14:10:25] Completed 438 of 800 simulation runs
[28-Jun-2021 14:10:27] Completed 439 of 800 simulation runs
[28-Jun-2021 14:10:29] Completed 440 of 800 simulation runs
[28-Jun-2021 14:10:31] Completed 441 of 800 simulation runs
[28-Jun-2021 14:10:35] Completed 442 of 800 simulation runs
[28-Jun-2021 14:10:47] Completed 443 of 800 simulation runs
[28-Jun-2021 14:10:51] Completed 444 of 800 simulation runs
[28-Jun-2021 14:10:53] Completed 445 of 800 simulation runs
[28-Jun-2021 14:10:55] Completed 446 of 800 simulation runs
[28-Jun-2021 14:10:57] Completed 447 of 800 simulation runs
[28-Jun-2021 14:10:59] Completed 448 of 800 simulation runs
[28-Jun-2021 14:11:13] Completed 449 of 800 simulation runs
[28-Jun-2021 14:11:15] Completed 450 of 800 simulation runs
[28-Jun-2021 14:11:18] Completed 451 of 800 simulation runs
[28-Jun-2021 14:11:20] Completed 452 of 800 simulation runs
[28-Jun-2021 14:11:22] Completed 453 of 800 simulation runs
[28-Jun-2021 14:11:24] Completed 454 of 800 simulation runs
[28-Jun-2021 14:11:40] Completed 455 of 800 simulation runs
[28-Jun-2021 14:11:42] Completed 456 of 800 simulation runs
[28-Jun-2021 14:11:44] Completed 457 of 800 simulation runs
[28-Jun-2021 14:11:46] Completed 458 of 800 simulation runs
[28-Jun-2021 14:11:48] Completed 459 of 800 simulation runs
[28-Jun-2021 14:11:50] Completed 460 of 800 simulation runs
[28-Jun-2021 14:12:05] Completed 461 of 800 simulation runs
[28-Jun-2021 14:12:06] Completed 462 of 800 simulation runs
[28-Jun-2021 14:12:08] Completed 463 of 800 simulation runs
[28-Jun-2021 14:12:10] Completed 464 of 800 simulation runs
[28-Jun-2021 14:12:12] Completed 465 of 800 simulation runs
[28-Jun-2021 14:12:15] Completed 466 of 800 simulation runs
[28-Jun-2021 14:12:29] Completed 467 of 800 simulation runs
[28-Jun-2021 14:12:31] Completed 468 of 800 simulation runs
[28-Jun-2021 14:12:33] Completed 469 of 800 simulation runs
[28-Jun-2021 14:12:35] Completed 470 of 800 simulation runs
[28-Jun-2021 14:12:37] Completed 471 of 800 simulation runs
[28-Jun-2021 14:12:41] Completed 472 of 800 simulation runs
[28-Jun-2021 14:12:53] Completed 473 of 800 simulation runs
[28-Jun-2021 14:12:55] Completed 474 of 800 simulation runs
[28-Jun-2021 14:12:58] Completed 475 of 800 simulation runs
[28-Jun-2021 14:13:00] Completed 476 of 800 simulation runs
[28-Jun-2021 14:13:02] Completed 477 of 800 simulation runs
[28-Jun-2021 14:13:07] Completed 478 of 800 simulation runs
[28-Jun-2021 14:13:19] Completed 479 of 800 simulation runs
[28-Jun-2021 14:13:21] Completed 480 of 800 simulation runs
[28-Jun-2021 14:13:23] Completed 481 of 800 simulation runs
[28-Jun-2021 14:13:26] Completed 482 of 800 simulation runs
[28-Jun-2021 14:13:28] Completed 483 of 800 simulation runs
[28-Jun-2021 14:13:35] Completed 484 of 800 simulation runs
[28-Jun-2021 14:13:44] Completed 485 of 800 simulation runs
[28-Jun-2021 14:13:46] Completed 486 of 800 simulation runs
[28-Jun-2021 14:13:48] Completed 487 of 800 simulation runs
[28-Jun-2021 14:13:50] Completed 488 of 800 simulation runs
[28-Jun-2021 14:13:52] Completed 489 of 800 simulation runs
[28-Jun-2021 14:14:01] Completed 490 of 800 simulation runs
[28-Jun-2021 14:14:08] Completed 491 of 800 simulation runs
[28-Jun-2021 14:14:10] Completed 492 of 800 simulation runs
[28-Jun-2021 14:14:12] Completed 493 of 800 simulation runs
[28-Jun-2021 14:14:14] Completed 494 of 800 simulation runs
[28-Jun-2021 14:14:16] Completed 495 of 800 simulation runs
[28-Jun-2021 14:14:27] Completed 496 of 800 simulation runs
[28-Jun-2021 14:14:35] Completed 497 of 800 simulation runs
[28-Jun-2021 14:14:37] Completed 498 of 800 simulation runs
[28-Jun-2021 14:14:39] Completed 499 of 800 simulation runs
[28-Jun-2021 14:14:41] Completed 500 of 800 simulation runs
[28-Jun-2021 14:14:43] Completed 501 of 800 simulation runs
[28-Jun-2021 14:14:45] Completed 502 of 800 simulation runs
[28-Jun-2021 14:14:46] Completed 503 of 800 simulation runs
[28-Jun-2021 14:14:50] Completed 504 of 800 simulation runs
[28-Jun-2021 14:14:51] Completed 505 of 800 simulation runs
[28-Jun-2021 14:14:53] Completed 506 of 800 simulation runs
[28-Jun-2021 14:14:54] Completed 507 of 800 simulation runs
[28-Jun-2021 14:14:55] Completed 508 of 800 simulation runs
[28-Jun-2021 14:15:06] Completed 509 of 800 simulation runs
[28-Jun-2021 14:15:08] Completed 510 of 800 simulation runs
[28-Jun-2021 14:15:10] Completed 511 of 800 simulation runs
[28-Jun-2021 14:15:11] Completed 512 of 800 simulation runs
[28-Jun-2021 14:15:13] Completed 513 of 800 simulation runs
[28-Jun-2021 14:15:15] Completed 514 of 800 simulation runs
[28-Jun-2021 14:15:18] Completed 515 of 800 simulation runs
[28-Jun-2021 14:15:23] Completed 516 of 800 simulation runs
[28-Jun-2021 14:15:25] Completed 517 of 800 simulation runs
[28-Jun-2021 14:15:27] Completed 518 of 800 simulation runs
[28-Jun-2021 14:15:29] Completed 519 of 800 simulation runs
[28-Jun-2021 14:15:30] Completed 520 of 800 simulation runs
[28-Jun-2021 14:15:33] Completed 521 of 800 simulation runs
[28-Jun-2021 14:15:35] Completed 522 of 800 simulation runs
[28-Jun-2021 14:15:40] Completed 523 of 800 simulation runs
[28-Jun-2021 14:15:42] Completed 524 of 800 simulation runs
[28-Jun-2021 14:15:46] Completed 525 of 800 simulation runs
[28-Jun-2021 14:15:48] Completed 526 of 800 simulation runs
[28-Jun-2021 14:15:50] Completed 527 of 800 simulation runs
[28-Jun-2021 14:15:51] Completed 528 of 800 simulation runs
[28-Jun-2021 14:15:53] Completed 529 of 800 simulation runs
[28-Jun-2021 14:15:54] Completed 530 of 800 simulation runs
[28-Jun-2021 14:15:57] Completed 531 of 800 simulation runs
[28-Jun-2021 14:16:02] Completed 532 of 800 simulation runs
[28-Jun-2021 14:16:04] Completed 533 of 800 simulation runs
[28-Jun-2021 14:16:05] Completed 534 of 800 simulation runs
[28-Jun-2021 14:16:15] Completed 535 of 800 simulation runs
[28-Jun-2021 14:16:17] Completed 536 of 800 simulation runs
[28-Jun-2021 14:16:19] Completed 537 of 800 simulation runs
[28-Jun-2021 14:16:21] Completed 538 of 800 simulation runs
[28-Jun-2021 14:16:23] Completed 539 of 800 simulation runs
[28-Jun-2021 14:16:25] Completed 540 of 800 simulation runs
[28-Jun-2021 14:16:28] Completed 541 of 800 simulation runs
[28-Jun-2021 14:16:30] Completed 542 of 800 simulation runs
[28-Jun-2021 14:16:39] Completed 543 of 800 simulation runs
[28-Jun-2021 14:16:42] Completed 544 of 800 simulation runs
[28-Jun-2021 14:16:44] Completed 545 of 800 simulation runs
[28-Jun-2021 14:16:48] Completed 546 of 800 simulation runs
[28-Jun-2021 14:16:50] Completed 547 of 800 simulation runs
[28-Jun-2021 14:16:52] Completed 548 of 800 simulation runs
[28-Jun-2021 14:16:55] Completed 549 of 800 simulation runs
[28-Jun-2021 14:16:57] Completed 550 of 800 simulation runs
[28-Jun-2021 14:17:00] Completed 551 of 800 simulation runs
[28-Jun-2021 14:17:06] Completed 552 of 800 simulation runs
[28-Jun-2021 14:17:12] Completed 553 of 800 simulation runs
[28-Jun-2021 14:17:14] Completed 554 of 800 simulation runs
[28-Jun-2021 14:17:16] Completed 555 of 800 simulation runs
[28-Jun-2021 14:17:18] Completed 556 of 800 simulation runs
[28-Jun-2021 14:17:20] Completed 557 of 800 simulation runs
[28-Jun-2021 14:17:23] Completed 558 of 800 simulation runs
[28-Jun-2021 14:17:25] Completed 559 of 800 simulation runs
[28-Jun-2021 14:17:28] Completed 560 of 800 simulation runs
[28-Jun-2021 14:17:31] Completed 561 of 800 simulation runs
[28-Jun-2021 14:17:34] Completed 562 of 800 simulation runs
[28-Jun-2021 14:17:36] Completed 563 of 800 simulation runs
[28-Jun-2021 14:17:37] Completed 564 of 800 simulation runs
[28-Jun-2021 14:17:42] Completed 565 of 800 simulation runs
[28-Jun-2021 14:17:46] Completed 566 of 800 simulation runs
[28-Jun-2021 14:17:48] Completed 567 of 800 simulation runs
[28-Jun-2021 14:17:50] Completed 568 of 800 simulation runs
[28-Jun-2021 14:17:52] Completed 569 of 800 simulation runs
[28-Jun-2021 14:17:57] Completed 570 of 800 simulation runs
[28-Jun-2021 14:17:59] Completed 571 of 800 simulation runs
[28-Jun-2021 14:18:07] Completed 572 of 800 simulation runs
[28-Jun-2021 14:18:09] Completed 573 of 800 simulation runs
[28-Jun-2021 14:18:11] Completed 574 of 800 simulation runs
[28-Jun-2021 14:18:13] Completed 575 of 800 simulation runs
[28-Jun-2021 14:18:15] Completed 576 of 800 simulation runs
[28-Jun-2021 14:18:17] Completed 577 of 800 simulation runs
[28-Jun-2021 14:18:30] Completed 578 of 800 simulation runs
[28-Jun-2021 14:18:32] Completed 579 of 800 simulation runs
[28-Jun-2021 14:18:34] Completed 580 of 800 simulation runs
[28-Jun-2021 14:18:35] Completed 581 of 800 simulation runs
[28-Jun-2021 14:18:38] Completed 582 of 800 simulation runs
[28-Jun-2021 14:18:40] Completed 583 of 800 simulation runs
[28-Jun-2021 14:18:42] Completed 584 of 800 simulation runs
[28-Jun-2021 14:18:44] Completed 585 of 800 simulation runs
[28-Jun-2021 14:18:45] Completed 586 of 800 simulation runs
[28-Jun-2021 14:18:47] Completed 587 of 800 simulation runs
[28-Jun-2021 14:18:49] Completed 588 of 800 simulation runs
[28-Jun-2021 14:18:56] Completed 589 of 800 simulation runs
[28-Jun-2021 14:18:58] Completed 590 of 800 simulation runs
[28-Jun-2021 14:19:00] Completed 591 of 800 simulation runs
[28-Jun-2021 14:19:03] Completed 592 of 800 simulation runs
[28-Jun-2021 14:19:05] Completed 593 of 800 simulation runs
[28-Jun-2021 14:19:07] Completed 594 of 800 simulation runs
[28-Jun-2021 14:19:12] Completed 595 of 800 simulation runs
[28-Jun-2021 14:19:14] Completed 596 of 800 simulation runs
[28-Jun-2021 14:19:16] Completed 597 of 800 simulation runs
[28-Jun-2021 14:19:18] Completed 598 of 800 simulation runs
[28-Jun-2021 14:19:24] Completed 599 of 800 simulation runs
[28-Jun-2021 14:19:27] Completed 600 of 800 simulation runs
[28-Jun-2021 14:19:29] Completed 601 of 800 simulation runs
[28-Jun-2021 14:19:37] Completed 602 of 800 simulation runs
[28-Jun-2021 14:19:39] Completed 603 of 800 simulation runs
[28-Jun-2021 14:19:41] Completed 604 of 800 simulation runs
[28-Jun-2021 14:19:44] Completed 605 of 800 simulation runs
[28-Jun-2021 14:19:46] Completed 606 of 800 simulation runs
[28-Jun-2021 14:19:48] Completed 607 of 800 simulation runs
[28-Jun-2021 14:19:51] Completed 608 of 800 simulation runs
[28-Jun-2021 14:19:53] Completed 609 of 800 simulation runs
[28-Jun-2021 14:19:55] Completed 610 of 800 simulation runs
[28-Jun-2021 14:19:57] Completed 611 of 800 simulation runs
[28-Jun-2021 14:20:01] Completed 612 of 800 simulation runs
[28-Jun-2021 14:20:04] Completed 613 of 800 simulation runs
[28-Jun-2021 14:20:05] Completed 614 of 800 simulation runs
[28-Jun-2021 14:20:07] Completed 615 of 800 simulation runs
[28-Jun-2021 14:20:18] Completed 616 of 800 simulation runs
[28-Jun-2021 14:20:20] Completed 617 of 800 simulation runs
[28-Jun-2021 14:20:23] Completed 618 of 800 simulation runs
[28-Jun-2021 14:20:25] Completed 619 of 800 simulation runs
[28-Jun-2021 14:20:27] Completed 620 of 800 simulation runs
[28-Jun-2021 14:20:30] Completed 621 of 800 simulation runs
[28-Jun-2021 14:20:32] Completed 622 of 800 simulation runs
[28-Jun-2021 14:20:35] Completed 623 of 800 simulation runs
[28-Jun-2021 14:20:42] Completed 624 of 800 simulation runs
[28-Jun-2021 14:20:45] Completed 625 of 800 simulation runs
[28-Jun-2021 14:20:47] Completed 626 of 800 simulation runs
[28-Jun-2021 14:20:50] Completed 627 of 800 simulation runs
[28-Jun-2021 14:20:52] Completed 628 of 800 simulation runs
[28-Jun-2021 14:20:55] Completed 629 of 800 simulation runs
[28-Jun-2021 14:20:57] Completed 630 of 800 simulation runs
[28-Jun-2021 14:21:00] Completed 631 of 800 simulation runs
[28-Jun-2021 14:21:02] Completed 632 of 800 simulation runs
[28-Jun-2021 14:21:05] Completed 633 of 800 simulation runs
[28-Jun-2021 14:21:16] Completed 634 of 800 simulation runs
[28-Jun-2021 14:21:18] Completed 635 of 800 simulation runs
[28-Jun-2021 14:21:21] Completed 636 of 800 simulation runs
[28-Jun-2021 14:21:23] Completed 637 of 800 simulation runs
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ens = simulationEnsembleDatastore(fullfile('.','Data'));

Processing and Extracting Features from the Simulation Results

The model is configured to log the pump output pressure, output flow, motor speed and motor current.

ens.DataVariables
ans = 8×1 string
    "SimulationInput"
    "SimulationMetadata"
    "iMotor_meas"
    "pIn_meas"
    "pOut_meas"
    "qIn_meas"
    "qOut_meas"
    "wMotor_meas"

For each member in the ensemble preprocess the pump output flow and compute condition indicators based on the pump output flow. The condition indicators are later used for fault classification. For preprocessing remove the first 0.8 seconds of the output flow as this contains transients from simulation and pump startup. As part of the preprocessing compute the power spectrum of the output flow, and use the SimulationInput to return the values of the fault variables.

Configure the ensemble so that the read only returns the variables of interest and call the preprocess function that is defined at the end of this example.

ens.SelectedVariables = ["qOut_meas", "SimulationInput"];
reset(ens)
data = read(ens)
data=1×2 table
        qOut_meas                SimulationInput        
    __________________    ______________________________

    {2001×1 timetable}    {1×1 Simulink.SimulationInput}

[flow,flowP,flowF,faultValues] = preprocess(data);

Plot the flow and flow spectrum. The plotted data is for a fault free condition.

% Figure with nominal
subplot(211);
plot(flow.Time,flow.Data);
subplot(212);
semilogx(flowF,pow2db(flowP));
xlabel('Hz')

The flow spectrum reveals resonant peaks at expected frequencies. Specifically, the pump motor speed is 950 rpm, or 15.833 Hz, and since the pump has 3 cylinders the flow is expected to have a fundamental at 3*15.833 Hz, or 47.5 Hz, as well as harmonics at multiples of 47.5 Hz. The flow spectrum clearly shows the expected resonant peaks. Faults in one cylinder of the pump will result in resonances at the pump motor speed, 15.833 Hz and its harmonics.

The flow spectrum and slow signal gives some ideas of possible condition indicators. Specifically, common signal statistics such as mean, variance, etc. as well as spectrum characteristics. Spectrum condition indicators relating to the expected harmonics such as the frequency with the peak magnitude, energy around 15.833 Hz, energy around 47.5 Hz, energy above 100 Hz, are computed. The frequency of the spectral kurtosis peak is also computed.

Configure the ensemble with data variables for the condition indicators and condition variables for fault variable values. Then call the extractCI function to compute the features, and use the writeToLastMemberRead command to add the feature and fault variable values to the ensemble. The extractCI function is defined at the end of this example.

ens.DataVariables = [ens.DataVariables; ...
    "fPeak"; "pLow"; "pMid"; "pHigh"; "pKurtosis"; ...
    "qMean"; "qVar"; "qSkewness"; "qKurtosis"; ...
    "qPeak2Peak"; "qCrest"; "qRMS"; "qMAD"; "qCSRange"];
ens.ConditionVariables = ["LeakFault","BlockingFault","BearingFault"];

feat = extractCI(flow,flowP,flowF);
dataToWrite = [faultValues, feat];
writeToLastMemberRead(ens,dataToWrite{:})

The above code preprocesses and computes the condition indicators for the first member of the simulation ensemble. Repeat this for all the members in the ensemble using the ensemble hasdata command. To get an idea of the simulation results under different fault conditions plot every hundredth element of the ensemble.

%Figure with nominal and faults
figure,
subplot(211);
lFlow = plot(flow.Time,flow.Data,'LineWidth',2);
subplot(212);
lFlowP = semilogx(flowF,pow2db(flowP),'LineWidth',2);
xlabel('Hz')
ct = 1;
lColors = get(lFlow.Parent,'ColorOrder');
lIdx = 2;

% Loop over all members in the ensemble, preprocess 
% and compute the features for each member
while hasdata(ens)
    
    % Read member data
    data = read(ens);
    
    % Preprocess and extract features from the member data
    [flow,flowP,flowF,faultValues] = preprocess(data);
    feat = extractCI(flow,flowP,flowF);
    
    % Add the extracted feature values to the member data
    dataToWrite = [faultValues, feat];
    writeToLastMemberRead(ens,dataToWrite{:})
    
    % Plot member signal and spectrum for every 100th member
    if mod(ct,100) == 0
        line('Parent',lFlow.Parent,'XData',flow.Time,'YData',flow.Data, ...
            'Color', lColors(lIdx,:));
        line('Parent',lFlowP.Parent,'XData',flowF,'YData',pow2db(flowP), ...
            'Color', lColors(lIdx,:));
        if lIdx == size(lColors,1)
            lIdx = 1;
        else
            lIdx = lIdx+1;
        end
    end
    ct = ct + 1;
end

Note that under different fault conditions and severities the spectrum contains harmonics at the expected frequencies.

Detect and Classify Pump Faults

The previous section preprocessed and computed condition indicators from the flow signal for all the members of the simulation ensemble, which correspond to the simulation results for different fault combinations and severities. The condition indicators can be used to detect and classify pump faults from a pump flow signal.

Configure the simulation ensemble to read the condition indicators, and use the tall and gather commands to load all the condition indicators and fault variable values into memory

% Get data to design a classifier.
reset(ens)
ens.SelectedVariables = [...
    "fPeak","pLow","pMid","pHigh","pKurtosis",...
    "qMean","qVar","qSkewness","qKurtosis",...
    "qPeak2Peak","qCrest","qRMS","qMAD","qCSRange",...
    "LeakFault","BlockingFault","BearingFault"];
idxLastFeature = 14;

% Load the condition indicator data into memory
data = gather(tall(ens));
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: 0% complete
Evaluation 0% complete

- Pass 1 of 1: Completed in 37 sec
Evaluation completed in 37 sec
data(1:10,:)
ans=10×17 table
    fPeak      pLow       pMid     pHigh     pKurtosis    qMean      qVar     qSkewness    qKurtosis    qPeak2Peak    qCrest     qRMS      qMAD     qCSRange    LeakFault    BlockingFault    BearingFault
    ______    _______    ______    ______    _________    ______    ______    _________    _________    __________    ______    ______    ______    ________    _________    _____________    ____________

    43.909     0.8468    117.73    18.855     276.49      35.573    7.5235    -0.73064       2.778         13.86      1.1491    35.679    2.2319     42692         1e-09          0.8              0      
    43.909     0.4622    125.98    18.956     12.417      35.577    7.8766    -0.70939        2.63        13.336      1.1451    35.688    2.3235     42699         1e-09          0.8              0      
    43.909     1.1679    138.01     17.54     11.589      35.575    7.4403     -0.7229      2.7135         12.61      1.1394    35.679    2.2415     42696         1e-09          0.8              0      
    14.779     235.27    193.49    26.728     197.02      33.223    15.242    -0.24387      2.2772         18.69       1.232    33.451     3.256     39862       3.2e-06          0.8              0      
    14.779     287.41    198.79    25.321     487.58      32.955    17.606    -0.20213        2.22        19.064      1.2304    33.221    3.5482     39539       3.6e-06          0.8              0      
    43.848     4.3805    137.31    19.175     110.93      35.275    7.5471    -0.70987      2.7751        13.858      1.1586    35.382    2.2525     42335         4e-07          0.8              0      
    14.839     303.74    176.33    23.665     392.38      32.908    17.638    -0.19533       2.237        19.561      1.2376    33.175    3.5358     39484       3.6e-06          0.8              0      
    44.151     133.99    159.09    26.973      434.6       33.76    12.137    -0.37195      2.5289        16.849      1.1925    33.939    2.8477     40507       2.4e-06          0.8              0      
    43.848    0.43902    134.89    18.997     12.417      35.562    7.8636     -0.6853      2.6661         13.91      1.1502    35.673    2.3088     42682         1e-09          0.8              0      
    43.969     12.292    124.71    22.448     478.48      34.986    8.0954    -0.71245      2.9268        15.015      1.1585    35.101    2.2984     41987         8e-07          0.8              0      

The fault variable values for each ensemble member (row in the data table) can be converted to fault flags and the fault flags combined to single flag that captures the different fault status of each member.

% Convert the fault variable values to flags
data.LeakFlag = data.LeakFault > 1e-6;
data.BlockingFlag = data.BlockingFault < 0.8;
data.BearingFlag = data.BearingFault > 0; 
data.CombinedFlag = data.LeakFlag+2*data.BlockingFlag+4*data.BearingFlag;

Create a classifier that takes as input the condition indicators and returns the combined fault flag. Train a support vector machine that uses a 2nd order polynomial kernel. Use the cvpartition command to partition the ensemble members into a set for training and a set for validation.

rng('default') % for reproducibility
predictors = data(:,1:idxLastFeature); 
response = data.CombinedFlag;
cvp = cvpartition(size(predictors,1),'KFold',5);

% Create and train the classifier
template = templateSVM(...
    'KernelFunction', 'polynomial', ...
    'PolynomialOrder', 2, ...
    'KernelScale', 'auto', ...
    'BoxConstraint', 1, ...
    'Standardize', true);
combinedClassifier = fitcecoc(...
    predictors(cvp.training(1),:), ...
    response(cvp.training(1),:), ...
    'Learners', template, ...
    'Coding', 'onevsone', ...
    'ClassNames', [0; 1; 2; 3; 4; 5; 6; 7]);

Check the performance of the trained classifier using the validation data and plot the results on a confusion plot.

% Check performance by computing and plotting the confusion matrix
actualValue = response(cvp.test(1),:);
predictedValue = predict(combinedClassifier, predictors(cvp.test(1),:));
confdata = confusionmat(actualValue,predictedValue);
figure,
labels = {'None', 'Leak','Blocking', 'Leak & Blocking', 'Bearing', ...
    'Bearing & Leak', 'Bearing & Blocking', 'All'};
h = heatmap(confdata, ...
    'YLabel', 'Actual leak fault', ...
    'YDisplayLabels', labels, ...
    'XLabel', 'Predicted fault', ...
    'XDisplayLabels', labels, ...
    'ColorbarVisible','off');

The confusion plot shows for each combination of faults the number of times the fault combination was correctly predicted (the diagonal entries of the plot) and the number of times the fault combination was incorrectly predicted (the off-diagonal entries).

The confusion plot shows that the classifier did not correctly classify some fault conditions (the off diagonal terms). However, the no fault condition was correctly predicted. In a couple of places a no fault condition was predicted when there was a fault (the first column), otherwise a fault was predicted although it may not be exactly the correct fault condition. Overall the validation accuracy was 66% and the accuracy at predicting that there is a fault 94%.

% Compute the overall accuracy of the classifier
sum(diag(confdata))/sum(confdata(:))
ans = 0.6625
% Compute the accuracy of the classifier at predicting 
% that there is a fault
1-sum(confdata(2:end,1))/sum(confdata(:))
ans = 0.9375

Examine the cases where no fault was predicted but a fault did exist. First find cases in the validation data where the actual fault was a blocking fault but a no fault was predicted.

vData = data(cvp.test(1),:);
b1 = (actualValue==2) & (predictedValue==0);
fData = vData(b1,15:17)
fData=10×3 table
    LeakFault    BlockingFault    BearingFault
    _________    _____________    ____________

      1e-09          0.71              0      
      1e-09          0.77              0      
      1e-09          0.71              0      
      1e-09          0.77              0      
      1e-09          0.71              0      
      1e-09          0.77              0      
      1e-09          0.71              0      
      1e-09          0.74              0      
      1e-09          0.77              0      
      1e-09          0.77              0      

Find cases in the validation data where the actual fault was a bearing fault but a no fault was predicted.

b2 = (actualValue==4) & (predictedValue==0);
vData(b2,15:17)
ans =

  0×3 empty table

Examining the cases where no fault was predictive but a fault did exist reveals that they occur when the blocking fault value of 0.77 is close to its nominal value of 0.8, or the bearing fault value of 6.6e-5 is close to its nominal value of 0. Plotting the spectrum for the case with a small blocking fault value and comparing with a fault free condition reveals that spectra are very similar making detection difficult. Re-training the classifier but including a blocking value of 0.77 as a non fault condition would significantly improve the performance of the fault detector. Alternatively, using additional pump measurements could provide more information and improve the ability to detect small blocking faults.

% Configure the ensemble to only read the flow and fault variable values
ens.SelectedVariables = ["qOut_meas","LeakFault","BlockingFault","BearingFault"];
reset(ens)

% Load the ensemble member data into memory
data = gather(tall(ens));
Evaluating tall expression using the Parallel Pool 'local':
- Pass 1 of 1: 0% complete
Evaluation 0% complete

- Pass 1 of 1: Completed in 31 sec
Evaluation completed in 31 sec
% Look for the member that was incorrectly predicted, and 
% compute its power spectrum
idx = ...
    data.BlockingFault == fData.BlockingFault(1) & ...
    data.LeakFault == fData.LeakFault(1) & ...
    data.BearingFault == fData.BearingFault(1);
flow1 = data(idx,1);
flow1 = flow1.qOut_meas{1};
[flow1P,flow1F] = pspectrum(flow1);

% Look for a member that does not have any faults
idx = ...
    data.BlockingFault == 0.8 & ...
    data.LeakFault == 1e-9 & ...
    data.BearingFault == 0;
flow2 = data(idx,1);
flow2 = flow2.qOut_meas{1};
[flow2P,flow2F] = pspectrum(flow2);

% Plot the power spectra
semilogx(...
    flow1F,pow2db(flow1P),...
    flow2F,pow2db(flow2P));
xlabel('Hz')
legend('Small blocking fault','No fault')

Conclusion

This example showed how to use a Simulink model to model faults in a reciprocating pump, simulate the model under different fault combinations and severities, extract condition indicators from the pump output flow and use the condition indicators to train a classifier to detect pump faults. The example examined the performance of fault detection using the classifier and noted that small blocking faults are very similar to the no fault condition and cannot be reliably detected.

Supporting Functions

function [flow,flowSpectrum,flowFrequencies,faultValues] = preprocess(data)
% Helper function to preprocess the logged reciprocating pump data.

% Remove the 1st 0.8 seconds of the flow signal
tMin = seconds(0.8);
flow = data.qOut_meas{1};
flow = flow(flow.Time >= tMin,:);
flow.Time = flow.Time - flow.Time(1);

% Ensure the flow is sampled at a uniform sample rate
flow = retime(flow,'regular','linear','TimeStep',seconds(1e-3));

% Remove the mean from the flow and compute the flow spectrum
fA = flow;
fA.Data = fA.Data - mean(fA.Data);
[flowSpectrum,flowFrequencies] = pspectrum(fA,'FrequencyLimits',[2 250]);

% Find the values of the fault variables from the SimulationInput
simin = data.SimulationInput{1};
vars = {simin.Variables.Name};
idx = strcmp(vars,'leak_cyl_area_WKSP');
LeakFault = simin.Variables(idx).Value;
idx = strcmp(vars,'block_in_factor_WKSP');
BlockingFault = simin.Variables(idx).Value;
idx = strcmp(vars,'bearing_fault_frict_WKSP');
BearingFault = simin.Variables(idx).Value;

% Collect the fault values in a cell array
faultValues = {...
    'LeakFault', LeakFault, ...
    'BlockingFault', BlockingFault, ...
    'BearingFault', BearingFault};
end

function ci = extractCI(flow,flowP,flowF)
% Helper function to extract condition indicators from the flow signal 
% and spectrum.

% Find the frequency of the peak magnitude in the power spectrum.
pMax = max(flowP);
fPeak = flowF(flowP==pMax);

% Compute the power in the low frequency range 10-20 Hz.
fRange = flowF >= 10 & flowF <= 20;
pLow = sum(flowP(fRange));

% Compute the power in the mid frequency range 40-60 Hz.
fRange = flowF >= 40 & flowF <= 60;
pMid = sum(flowP(fRange));

% Compute the power in the high frequency range >100 Hz.
fRange = flowF >= 100;
pHigh = sum(flowP(fRange));

% Find the frequency of the spectral kurtosis peak
[pKur,fKur] = pkurtosis(flow);
pKur = fKur(pKur == max(pKur));

% Compute the flow cumulative sum range.
csFlow = cumsum(flow.Data);
csFlowRange = max(csFlow)-min(csFlow);

% Collect the feature and feature values in a cell array. 
% Add flow statistic (mean, variance, etc.) and common signal 
% characteristics (rms, peak2peak, etc.) to the cell array.
ci = {...
    'qMean', mean(flow.Data), ...
    'qVar',  var(flow.Data), ...
    'qSkewness', skewness(flow.Data), ...
    'qKurtosis', kurtosis(flow.Data), ...
    'qPeak2Peak', peak2peak(flow.Data), ...
    'qCrest', peak2rms(flow.Data), ...
    'qRMS', rms(flow.Data), ...
    'qMAD', mad(flow.Data), ...
    'qCSRange',csFlowRange, ...
    'fPeak', fPeak, ...
    'pLow', pLow, ...
    'pMid', pMid, ...
    'pHigh', pHigh, ...
    'pKurtosis', pKur(1)};
end 

See Also

Related Topics