Design of induction motor speed observer based on long short-term memory

Ilten, Erdem; Calgan, Haris; Demirtas, Metin

doi:10.1007/s00521-022-07458-0

Design of induction motor speed observer based on long short-term memory

Original Article
Published: 22 June 2022

Volume 34, pages 18703–18723, (2022)
Cite this article

Neural Computing and Applications Aims and scope Submit manuscript

371 Accesses
4 Citations
1 Altmetric
Explore all metrics

Abstract

This paper presents a machine learning regression algorithm based on speed estimation for sensorless control of an induction motor. Long short-term memory (LSTM) based on deep learning method is used to design the induction motor speed observer. The proposed LSTM observer utilizes only the measured stator currents and voltages. It estimates the motor speed in the presence of inherent dynamics and sensor noises. Although LSTM is one of the common deep learning methods, its implementation on speed estimation for induction motor has not been tackled in the literature. The estimation performance of proposed LSTM observer (LSTMO) is investigated using four common metrics: root relative squared error, mean absolute error, mean squared error and root mean squared error. Performance of the proposed method is well guaranteed for different operating speeds. The designed observer is compared with the traditional sliding mode observer in order to prove the validity. It can be deduced from experimental results that the proposed method estimates the actual speed value successfully. LSTMO tracks the speed accurately regardless of any changes in reference speed. It is shown that there is no chattering effect on the estimated speed as compared with SMO.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Investigation into LSTM Deep Learning for Induction Motor Fault Diagnosis

Intelligent Fault Detection of Rotating Machinery Using Long-Short-Term Memory (LSTM) Network

Real-time safety monitoring in the induction motor using deep hierarchic long short-term memory

Article 31 August 2018

References

Demirtas M, Ilten E, Calgan H (2019) Pareto-based multi-objective optimization for fractional order PIλ speed control of induction motor by using Elman neural network. Arab J Sci Eng 44:2165–2175
Article Google Scholar
Ilten E, Demirtas M (2019) Fractional order super-twisting sliding mode observer for sensorless control of induction motor. COMPEL Int J Comput Math Electr Electron Eng 38:878–892
Article Google Scholar
Bahloul M, Chrifi-Alaoui L, Drid S, Souissi M, Chaabane M (2018) Robust sensorless vector control of an induction machine using multiobjective adaptive fuzzy luenberger observer. ISA Trans 74:144–154
Article Google Scholar
Sun X, Chen L, Yang Z, Zhu H (2012) Speed-sensorless vector control of a bearingless induction motor with artificial neural network inverse speed observer. IEEE/ASME Trans Mechatron 18:1357–1366
Article Google Scholar
Purwahyudi B (2011) RNN based rotor flux and speed estimation of induction motor. Int J Power Electron Drive Syst 1:58
Google Scholar
Zhang Y, Yin Z, Zhang Y, Liu J, Tong X (2019) A novel sliding mode observer with optimized constant rate reaching law for sensorless control of induction motor. IEEE Trans Ind Electron 67:5867–5878
Article Google Scholar
Ammar A, Kheldoun A, Metidji B, Ameid T, Azzoug Y (2020) Feedback linearization based sensorless direct torque control using stator flux MRAS-sliding mode observer for induction motor drive. ISA Trans 98:382–392
Article Google Scholar
An Q, Zhang J, An Q, Liu X, Shamekov A, Bi K (2019) Frequency-adaptive complex-coefficient filter-based enhanced sliding mode observer for sensorless control of permanent magnet synchronous motor drives. IEEE Trans Ind Appl 56:335–343
Article Google Scholar
El Daoudi S, Lazrak L, Lafkih MA (2020) Upgraded sensorless direct torque control using MRAS-sliding mode observer for asynchronous motor. In: 2020 IEEE 6th international conference on optimization and applications. IEEE, pp 1–5
Zhao Z, Ruan Z, Meng D, Xue Y, Gu C (2019) Sliding mode observer based sensorless model predictive current control for induction motor. In: 2019 IEEE 2nd international conference on power energy applications. IEEE, pp 84–88
Gadoue SM, Giaouris D, Finch JW (2009) Sensorless control of induction motor drives at very low and zero speeds using neural network flux observers. IEEE Trans Ind Electron 56:3029–3039
Article Google Scholar
Brandstetter P, Kuchar M (2017) Sensorless control of variable speed induction motor drive using RBF neural network. J Appl Log 24:97–108
Article MathSciNet Google Scholar
Abdel-Nasser M, Mahmoud K (2019) Accurate photovoltaic power forecasting models using deep LSTM-RNN. Neural Comput Appl 31:2727–2740
Article Google Scholar
Souza RM, Nascimento EGS, Miranda UA, Silva WJD, Lepikson HA (2021) Deep learning for diagnosis and classification of faults in industrial rotating machinery. Comput Ind Eng 153:107060
Article Google Scholar
Song Z, Yang J, Mei X, Tao T, Xu M (2021) Deep reinforcement learning for permanent magnet synchronous motor speed control systems. Neural Comput Appl 33:5409–5418
Article Google Scholar
Cipollini F, Oneto L, Coraddu A, Savio S (2019) Unsupervised deep learning for induction motor bearings monitoring. Data Enabled Discov Appl 3:1–13
Article Google Scholar
Qi X (2018) Rotor resistance and excitation inductance estimation of an induction motor using deep-Q-learning algorithm. Eng Appl Artif Intell 72:67–79
Article Google Scholar
Shao S, Yan R, Lu Y, Wang P, Gao RX (2019) DCNN-based multi-signal induction motor fault diagnosis. IEEE Trans Instrum Meas 69:2658–2669
Article Google Scholar
Mejia J, Avelar-Sosa L, Mederos B, Ramírez ES, Roman JDD (2021) Prediction of time series using an analysis filter bank of LSTM units. Comput Ind Eng 157:107371
Article Google Scholar
Livieris IE, Pintelas E, Pintelas P (2020) A CNN–LSTM model for gold price time-series forecasting. Neural Comput Appl 32:17351–17360
Article Google Scholar
Yang F, Zhang S, Li W, Miao Q (2020) State-of-charge estimation of lithium-ion batteries using LSTM and UKF. Energy 201:117664
Article Google Scholar
Günel K, Ekti AR (2019) Exploiting machine learning applications for smart grids. In: 2019 16th international multi-conference systems and signals devices. IEEE, pp 679–685
Aydogmus O, Boztas G (2019) Deep learning-based approach for speed estimation of a PMa-SynRM. In: 2019 11th international conference on electrical and electronics engineering. IEEE, pp 172–176
Acikgoz H, Korkmaz D (2021) Long short-term memory network-based speed estimation model of an asynchronous motor. In: 2021 12th international symposium on advanced topics in electrical engineering. IEEE, pp 1–6
Kerboua A, Metatla A, Kelaiaia R, Batouche M (2018) Real-time safety monitoring in the induction motor using deep hierarchic long short-term memory. Int J Adv Manuf Technol 99:2245–2255
Article Google Scholar
Yan Z, Utkin V (2002) Sliding mode observers for electric machines-an overview. In: IEEE 2002 28th annual conference of the IEEE industrial electronics society. IECON 02, vol 3. IEEE, pp 1842–1847
Wang J, Li J, Wang X, Wang J, Huang M (2021) Air quality prediction using CT-LSTM. Neural Comput Appl 33:4779–4792
Article Google Scholar

Download references

Author information

Authors and Affiliations

Department of Electrical-Electronics Engineering, Balikesir University, Balikesir, 10145, Turkey
Erdem Ilten, Haris Calgan & Metin Demirtas

Authors

Erdem Ilten
View author publications
You can also search for this author in PubMed Google Scholar
Haris Calgan
View author publications
You can also search for this author in PubMed Google Scholar
Metin Demirtas
View author publications
You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Erdem Ilten.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendix 1

LSTM training configurations (ADAM)
Gradient decay factor	0.9000
Squared gradient decay factor	0.9990
Epsilon	1.0000e-08
Initial learn rate	1.0000e-03
Learn rate schedule	‘piecewise’
Learn rate drop factor	1
Learn rate drop period	5
L2 regularization	1.0000e−4
Gradient threshold method	‘l2norm’
Gradient threshold	Inf
Max epochs	20,000
Mini batch size	64
Verbose	1
Verbose frequency	50
Validation data	[]
Validation frequency	50
Validation patience	Inf
Shuffle	‘once’
Checkpoint path	‘’
Execution environment	‘auto’
Worker load	[]
Output Fcn	[]
Plots	‘training-progress’
Sequence length	‘longest’
Sequence padding value	0
Sequence padding direction	‘right’
Dispatch In background	0
Reset input normalization	1
Batch normalization statistics	‘population’

Appendix 2

Training						Testing
Runs	Metrics	LSTMO_RRSE	LSTMO_MAE	LSTMO_MSE	LSTMO_RMSE	Runs	Metrics	LSTMO_RRSE	LSTMO_MAE	LSTMO_MSE	LSTMO_RMSE
1	RRSE	9.418848038	3.526246071	17.49655724	3.246854782	1	RRSE	2.668583632	13.68160915	10.0595665	0.017718811
	MAE	0.006260031	0.004349939	0.010593898	0.004778219		MAE	0.007071496	0.012227926	0.010117421	0.007035259
	MSE	5.51E-05	3.03E-05	0.000148169	4.83E-05		MSE	0.000180098	0.000262202	0.00019763	0.000136089
	RMSE	0.007421944	0.005507178	0.012172464	0.00695064		RMSE	0.013420048	0.016192665	0.014058078	0.011665709
2	RRSE	9.149031639	3.324883938	18.5030098	3.176984072	2	RRSE	5.580521107	10.32260132	7.826035023	0.658511817
	MAE	0.006378506	0.004222007	0.011313778	0.005228935		MAE	0.007056737	0.009973672	0.008047258	0.007427121
	MSE	5.78E-05	2.65E-05	0.000167483	5.67E-05		MSE	0.000165052	0.000178353	0.000155643	0.000132479
	RMSE	0.00760504	0.005152079	0.012941515	0.007526683		RMSE	0.012847264	0.013354871	0.012475694	0.011509959
3	RRSE	9.39336586	3.290128946	19.59127998	3.127569437	3	RRSE	6.922595501	7.627953053	12.81419659	2.412278414
	MAE	0.006350711	0.004242572	0.01181056	0.005086933		MAE	0.00718584	0.008176859	0.011219737	0.006660185
	MSE	5.73971E-05	3.0552E-05	0.000179937	5.09104E-05		MSE	0.000168162	0.000153822	0.000224967	0.000126699
	RMSE	0.007576089	0.005527387	0.013414076	0.00713515		RMSE	0.01296771	0.012402512	0.014998907	0.011256046
4	RRSE	1.306487322	20.99702835	1.50126946	5.446084023	4	RRSE	6.630444527	7.587314606	11.55204391	2.09450841
	MAE	0.003635295	0.012531962	0.005000455	0.005549603		MAE	0.006991637	0.007991162	0.010374757	0.007069815
	MSE	2.00E-05	0.00016857	4.65E-05	5.44E-05		MSE	0.000164314	0.00014906	0.000205795	0.0001333
	RMSE	0.004470969	0.012983467	0.006821549	0.00737336		RMSE	0.012818511	0.012208994	0.014345541	0.011545583
5	RRSE	3.04867053	17.50133324	3.858956099	3.503109932	5	RRSE	7.307052612	6.952277184	10.96157265	2.71931839
	MAE	0.003962351	0.01045765	0.005059151	0.005358941		MAE	0.007134117	0.007527955	0.010137635	0.007265371
	MSE	2.59E-05	0.000125065	4.98E-05	5.21E-05		MSE	0.000164486	0.000133014	0.00020216	0.000155114
	RMSE	0.005086054	0.011183232	0.007057874	0.007220299		RMSE	0.012825198	0.011533155	0.014218311	0.012454473
6	RRSE	4.306676388	15.37772083	6.632499218	2.285447359	6	RRSE	7.482122898	6.440505028	11.28944683	3.063552141
	MAE	0.004474522	0.009267899	0.005748326	0.005145377		MAE	0.007331906	0.007166887	0.010321706	0.007350747
	MSE	3.09E-05	0.000102578	5.74E-05	5.18E-05		MSE	0.000172519	0.000132214	0.000204912	0.000157098
	RMSE	0.005559922	0.010128069	0.007577162	0.007196878		RMSE	0.013134649	0.011498431	0.014314743	0.012533883
7	RRSE	5.286098003	13.52388287	8.251178741	1.121043921	7	RRSE	7.246935844	4.619747162	12.89699554	3.810185432
	MAE	0.004487365	0.008280195	0.006391491	0.004864099		MAE	0.007125809	0.006744046	0.011263018	0.006657805
	MSE	3.24E-05	8.51E-05	7.35E-05	4.48E-05		MSE	0.000162235	0.000126699	0.000233945	0.000150451
	RMSE	0.005691004	0.009225348	0.008575831	0.006691532		RMSE	0.012737154	0.011256078	0.015295245	0.012265846
8	RRSE	6.705172062	10.57586956	11.5995779	0.30301404	8	RRSE	7.543101788	3.805944681	13.91415882	4.528122425
	MAE	0.005004418	0.006831058	0.007624794	0.004667386		MAE	0.007346611	0.006808578	0.011829331	0.006614024
	MSE	3.79E-05	6.20E-05	8.73E-05	4.60E-05		MSE	0.000169251	0.000129216	0.000244983	0.000152715
	RMSE	0.0061569	0.007876472	0.0093429	0.006783974		RMSE	0.013009667	0.01136733	0.015651928	0.012357794
9	RRSE	7.161473274	9.925579071	12.65333652	0.68126756	9	RRSE	6.629994392	4.343562603	16.27892303	4.894608021
	MAE	0.005405077	0.006369478	0.008168098	0.004881911		MAE	0.00724201	0.007542234	0.013223928	0.006704318
	MSE	5.36E-05	5.66E-05	0.000102979	4.39E-05		MSE	0.000173858	0.000190672	0.000281014	0.000154519
	RMSE	0.007321612	0.007520807	0.010147859	0.006624342		RMSE	0.013185541	0.013808408	0.016763484	0.012430552
10	RRSE	7.730611324	8.111246109	13.72068405	1.340061426	10	RRSE	8.399152756	2.521861792	15.76922607	4.48237133
	MAE	0.005301708	0.005846383	0.008881926	0.004472319		MAE	0.008260184	0.006941829	0.01321882	0.007105742
	MSE	4.11E-05	5.14E-05	0.000116789	4.18E-05		MSE	0.000179354	0.000141171	0.000282715	0.000141207
	RMSE	0.006411572	0.007166377	0.010806899	0.00646449		RMSE	0.013392327	0.011881541	0.016814124	0.011883047
11	RRSE	8.246351242	7.128528118	14.67404652	2.161147118	11	RRSE	8.564740181	2.460358858	14.69442654	4.974498272
	MAE	0.005568364	0.005312016	0.009154497	0.004745898		MAE	0.008203689	0.006491726	0.012558551	0.007406249
	MSE	4.67E-05	4.20E-05	0.000119662	4.33E-05		MSE	0.000179176	0.000118808	0.000266613	0.000159853
	RMSE	0.00683275	0.006477964	0.010938994	0.006580677		RMSE	0.013385655	0.0108999	0.016328281	0.012643311
12	RRSE	8.01764679	7.367462635	13.81046486	1.822310686	12	RRSE	7.992843628	3.103095293	17.28656578	5.937756062
	MAE	0.00563979	0.005385101	0.008747359	0.004925379		MAE	0.007859158	0.006905321	0.013597504	0.007215901
	MSE	4.72E-05	4.41E-05	0.000109174	5.06E-05		MSE	0.000179588	0.000128628	0.000292011	0.000166077
	RMSE	0.006867181	0.006640861	0.010448653	0.007109851		RMSE	0.013401036	0.011341426	0.01708832	0.012887081
13	RRSE	8.04128933	6.333078384	14.07639599	2.18533349	13	RRSE	9.172445297	1.139784575	16.91308212	5.492619991
	MAE	0.005637942	0.005151529	0.008829397	0.004801015		MAE	0.008500945	0.00705429	0.014018349	0.007201904
	MSE	4.65E-05	4.00E-05	0.000115587	4.85E-05		MSE	0.000187962	0.000136562	0.000306731	0.000135102
	RMSE	0.006820661	0.00632637	0.010751128	0.006966119		RMSE	0.013709915	0.011685953	0.01751373	0.011623331
14	RRSE	8.396392822	5.321415901	13.93141174	2.552544355	14	RRSE	8.368747711	1.923480272	19.48267174	6.174377918
	MAE	0.005794688	0.004741536	0.008701168	0.004685224		MAE	0.008357272	0.006711199	0.015602195	0.007307443
	MSE	4.82E-05	3.50E-05	0.000106328	4.88E-05		MSE	0.000196764	0.000145363	0.000348578	0.000143308
	RMSE	0.006945137	0.005918995	0.01031155	0.006985215		RMSE	0.014027272	0.012056658	0.018670231	0.011971114
15	RRSE	9.787680626	3.385415077	15.2611208	3.927855015	15	RRSE	9.889588356	1.128131509	18.83555984	6.182326794
	MAE	0.006162158	0.004430962	0.009431798	0.004787944		MAE	0.008918705	0.007161868	0.014807743	0.007991103
	MSE	5.47E-05	3.22E-05	0.000127544	4.82E-05		MSE	0.000200284	0.000165147	0.000331715	0.000169912
	RMSE	0.007398812	0.005670188	0.01129352	0.006939294		RMSE	0.01415218	0.012850969	0.018213047	0.013035043
16	RRSE	9.092707634	3.223680735	14.40806007	3.484260082	16	RRSE	6.326579571	6.522587776	6.347493172	2.398679256
	MAE	0.00600011	0.004416592	0.009048891	0.004757599		MAE	0.006652007	0.007400653	0.00741112	0.007136225
	MSE	5.17E-05	3.17E-05	0.000120915	4.57E-05		MSE	0.000172418	0.000143762	0.000159777	0.000132709
	RMSE	0.007191082	0.005631145	0.010996114	0.006759215		RMSE	0.013130791	0.011990085	0.012640292	0.011519928
17	RRSE	9.177042007	2.960017443	14.49669743	3.630592823	17	RRSE	7.975327492	3.953770399	10.1101017	3.556468725
	MAE	0.006081981	0.004323687	0.009015884	0.00476124		MAE	0.00788285	0.006161991	0.009607174	0.007641668
	MSE	5.23E-05	3.05E-05	0.000115905	5.02E-05		MSE	0.000175428	0.000114669	0.00019217	0.000165876
	RMSE	0.007234795	0.005518392	0.010765895	0.007084363		RMSE	0.013244913	0.010708384	0.013862554	0.012879279
18	RRSE	10.35882568	2.431340456	18.7802639	4.28304863	18	RRSE	8.080028534	3.792222738	10.40210152	3.636235476
	MAE	0.006523961	0.004284566	0.011312958	0.005037513		MAE	0.00788418	0.006277016	0.009809324	0.007533209
	MSE	5.91E-05	3.03E-05	0.000166722	4.79E-05		MSE	0.000174075	0.000114196	0.000187731	0.0001597
	RMSE	0.007687051	0.005503376	0.012912076	0.006919891		RMSE	0.013193735	0.010686262	0.013701498	0.012637227
19	RRSE	9.391844749	3.055666208	18.41030502	3.468268871	19	RRSE	8.450791359	3.210067749	12.01174068	3.708900928
	MAE	0.006257656	0.004298432	0.011184405	0.00491498		MAE	0.007938721	0.006489959	0.01096543	0.007347065
	MSE	5.55E-05	2.82E-05	0.000162764	5.18E-05		MSE	0.000176986	0.000153514	0.000227903	0.000149616
	RMSE	0.007447345	0.005306832	0.012757903	0.007194906		RMSE	0.013303599	0.012390064	0.015096473	0.012231751
20	RRSE	9.791671753	1.946482897	17.99656677	3.912195444	20	RRSE	8.685555458	2.690992594	12.47299862	4.039010525
	MAE	0.006417119	0.003980397	0.010874598	0.004969217		MAE	0.00829056	0.006095721	0.011194387	0.007367417
	MSE	5.73E-05	2.72E-05	0.000154625	5.11E-05		MSE	0.00018472	0.000126111	0.000222807	0.00014258
	RMSE	0.007569712	0.005210802	0.01243483	0.00714579		RMSE	0.013591187	0.011229934	0.014926734	0.011940689
21	RRSE	1.151005626	20.93393326	1.61465919	5.179502964	21	RRSE	7.993913174	1.405203223	19.3386631	7.281675816
	MAE	0.003587903	0.012515613	0.005088875	0.005359588		MAE	0.007644069	0.007409093	0.015308117	0.007373263
	MSE	1.96E-05	0.000170084	4.76E-05	4.89E-05		MSE	0.000202084	0.000159089	0.000352705	0.000152411
	RMSE	0.004426551	0.013041624	0.006895991	0.006993357		RMSE	0.014215617	0.012613068	0.018780429	0.012345501
22	RRSE	4.721087933	14.08647251	6.070676804	1.577996492	22	RRSE	8.472633362	0.225629628	20.53218079	7.597074986
	MAE	0.004394084	0.008656065	0.005749199	0.004748845		MAE	0.007918749	0.007607555	0.016108934	0.007331847
	MSE	3.86E-05	9.37E-05	6.28E-05	4.27E-05		MSE	0.000188463	0.0001879	0.000367236	0.000162931
	RMSE	0.006209368	0.009679062	0.007927103	0.006535403		RMSE	0.013728196	0.013707652	0.019163411	0.012764459
23	RRSE	5.285715103	11.88545322	8.465101242	0.688143492	23	RRSE	8.188530922	0.563410342	19.73656082	7.096270084
	MAE	0.00438732	0.007356174	0.00627473	0.004475981		MAE	0.007690742	0.007577449	0.015667846	0.006979452
	MSE	2.97E-05	6.99E-05	6.57E-05	3.89E-05		MSE	0.000183972	0.000159939	0.000348788	0.000139854
	RMSE	0.005447874	0.00835795	0.008106377	0.006234538		RMSE	0.013563617	0.012646681	0.018675879	0.011825983
24	RRSE	5.591560364	10.78257179	7.95010519	0.100517347	24	RRSE	8.479554176	0.3343952	19.55312538	7.812271118
	MAE	0.004569247	0.006905103	0.006298932	0.004612876		MAE	0.00785411	0.00737749	0.015416115	0.007326439
	MSE	3.42E-05	6.40E-05	6.87E-05	4.36E-05		MSE	0.000185844	0.000145844	0.000342492	0.000164227
	RMSE	0.005849355	0.008000671	0.00828966	0.006605408		RMSE	0.013632474	0.012076573	0.018506553	0.01281512
25	RRSE	6.128604889	9.206692696	11.60713482	0.241750702	25	RRSE	8.478050232	0.189988986	20.16418266	7.571714401
	MAE	0.004802908	0.006051816	0.00768233	0.00450154		MAE	0.007806574	0.007595241	0.015954887	0.007335765
	MSE	3.47E-05	5.40E-05	8.91E-05	4.06E-05		MSE	0.000188637	0.000160383	0.000360854	0.000143826
	RMSE	0.005889174	0.007350211	0.00944042	0.006371219		RMSE	0.013734516	0.012664231	0.018996162	0.01199274
26	RRSE	6.608845234	8.158085823	10.97660351	0.910784304	26	RRSE	8.011313438	0.675485849	19.97354317	7.072063446
	MAE	0.0048871	0.005741586	0.007257248	0.004320623		MAE	0.007612485	0.007474384	0.015624346	0.007152535
	MSE	3.47E-05	4.81E-05	8.52E-05	4.25E-05		MSE	0.000185275	0.000162225	0.000354367	0.000143339
	RMSE	0.005892995	0.006938844	0.009232687	0.006516813		RMSE	0.013611582	0.012736746	0.018824633	0.011972437
27	RRSE	6.861320019	7.324820995	11.7957716	1.249208212	27	RRSE	7.363449574	1.936250687	18.89953041	6.708554745
	MAE	0.005151983	0.005319409	0.007621985	0.004468231		MAE	0.007156076	0.007303722	0.01484952	0.007077089
	MSE	3.86E-05	4.07E-05	8.60E-05	4.14E-05		MSE	0.000186322	0.000163241	0.000330344	0.000140859
	RMSE	0.006212273	0.006383425	0.009272109	0.006433568		RMSE	0.013649969	0.01277659	0.018175358	0.011868417
28	RRSE	1.832819104	15.83655167	1.937633395	3.438581228	28	RRSE	7.875720024	1.502499938	19.51660728	7.346045017
	MAE	0.003238135	0.009563868	0.004983363	0.004544165		MAE	0.00752382	0.007286938	0.015171056	0.007363629
	MSE	1.69E-05	0.000107957	4.59E-05	3.66E-05		MSE	0.000185235	0.000152857	0.00033945	0.000164746
	RMSE	0.004113377	0.010390242	0.006775156	0.006046682		RMSE	0.013610103	0.012363521	0.01842417	0.012835339
29	RRSE	4.576643467	10.6365633	4.561273098	0.605561078	29	RRSE	7.811802387	1.443646312	20.17746735	6.97763586
	MAE	0.003889236	0.006661592	0.005336394	0.004231307		MAE	0.007355128	0.007327405	0.015786301	0.007033275
	MSE	2.37E-05	5.72E-05	5.18E-05	3.93E-05		MSE	0.000185986	0.000158743	0.000357127	0.000139749
	RMSE	0.004867573	0.00756449	0.007197705	0.006271651		RMSE	0.01363767	0.012599338	0.018897794	0.011821568
30	RRSE	6.382016659	8.093851089	6.727919102	0.788435638	30	RRSE	7.714351177	1.679606795	18.38054085	7.332436085
	MAE	0.004423352	0.006003464	0.005904355	0.004270176		MAE	0.007328041	0.007183528	0.01456661	0.007315627
	MSE	3.05E-05	6.71E-05	6.22E-05	3.60E-05		MSE	0.000186598	0.000142306	0.000318098	0.000163966
	RMSE	0.005522259	0.00819318	0.007884932	0.006000633		RMSE	0.013660084	0.011929211	0.017835295	0.012804924
31	RRSE	6.276622295	6.276304722	7.292142868	1.405661106	31	RRSE	8.191814423	1.085845709	19.35712051	7.4741745
	MAE	0.004670341	0.004952581	0.005844653	0.004297324		MAE	0.007819866	0.007054044	0.015345143	0.007461767
	MSE	3.33E-05	3.78E-05	6.05E-05	4.30E-05		MSE	0.00018647	0.000133681	0.000337538	0.000169426
	RMSE	0.005770518	0.006144757	0.007780995	0.006558882		RMSE	0.013655415	0.01156204	0.018372212	0.013016392
32	RRSE	6.714302063	5.087916374	9.897346497	1.620143533	32	RRSE	7.729020119	1.191905379	20.40231323	6.876341343
	MAE	0.00465186	0.004559014	0.006775913	0.004132907		MAE	0.007682878	0.007166218	0.015977206	0.007051782
	MSE	3.32E-05	3.37E-05	7.53E-05	3.33E-05		MSE	0.000185591	0.000163839	0.000354442	0.000142478
	RMSE	0.005763428	0.005808932	0.008676073	0.005774904		RMSE	0.013623194	0.012799968	0.018826623	0.0119364
33	RRSE	7.406809807	3.814402819	10.1796999	2.496333361	33	RRSE	7.835498333	1.422548771	19.65023232	7.421327591
	MAE	0.00512172	0.004324336	0.006888068	0.004312552		MAE	0.007526658	0.007397214	0.015524383	0.00724483
	MSE	3.83E-05	3.10E-05	8.16E-05	3.83E-05		MSE	0.000197118	0.000150653	0.000347086	0.000146072
	RMSE	0.006190902	0.005565836	0.009033924	0.006186175		RMSE	0.014039864	0.012274075	0.018630248	0.012086023
34	RRSE	7.399498463	3.353266239	10.45517349	2.380333185	34	RRSE	7.812380791	1.569856167	19.31220245	7.450750351
	MAE	0.005109637	0.004311424	0.007086303	0.0044443		MAE	0.007335482	0.007233674	0.015125544	0.007228965
	MSE	3.90E-05	3.12E-05	8.50E-05	3.93E-05		MSE	0.000176977	0.000145313	0.000334656	0.000165314
	RMSE	0.006241206	0.005583348	0.009217535	0.006271425		RMSE	0.013303279	0.012054599	0.01829361	0.012857459
35	RRSE	8.238182068	2.257633924	12.91383839	3.009449959	35	RRSE	8.139739037	1.791327	21.93042183	7.602011681
	MAE	0.005366476	0.003734543	0.008134623	0.004271665		MAE	0.007451959	0.007794598	0.016633315	0.007348958
	MSE	4.18E-05	2.54E-05	9.80E-05	3.49E-05		MSE	0.000188724	0.000167315	0.000383303	0.000146047
	RMSE	0.006462176	0.005035311	0.009901814	0.005905249		RMSE	0.013737672	0.01293503	0.019578135	0.012085009
36	RRSE	8.604465485	1.274289727	12.1039772	3.788179874	36	RRSE	7.931909561	1.235551	18.92589378	7.692430019
	MAE	0.005501057	0.004173941	0.007757239	0.004335421		MAE	0.00765868	0.007249773	0.014952833	0.007526848
	MSE	4.31E-05	3.01E-05	9.71E-05	3.87E-05		MSE	0.0001586	0.000121556	0.000328603	0.000148128
	RMSE	0.006565338	0.005484293	0.009853259	0.006219626		RMSE	0.012593656	0.01102524	0.018127402	0.012170776
37	RRSE	9.111460686	1.011760473	14.76052475	4.005013466	37	RRSE	7.910579681	1.526494384	19.22528458	7.427342892
	MAE	0.005772948	0.00405997	0.009111213	0.004466235		MAE	0.007403136	0.007380349	0.015017303	0.007202365
	MSE	4.59E-05	2.78E-05	0.00011862	3.76E-05		MSE	0.000189521	0.000150182	0.000339669	0.000149624
	RMSE	0.006778528	0.005273215	0.010891263	0.00613579		RMSE	0.013766674	0.012254872	0.018430114	0.012232099
38	RRSE	9.252702713	1.21647346	14.64553928	4.036224842	38	RRSE	7.486089706	1.818207145	19.62262917	7.877697468
	MAE	0.006009937	0.004259036	0.009099979	0.004589162		MAE	0.007133023	0.007035055	0.01519981	0.007992134
	MSE	5.01E-05	3.16E-05	0.000122099	4.25E-05		MSE	0.000197008	0.00015039	0.000346896	0.000163652
	RMSE	0.007079761	0.005621814	0.01104984	0.006516162		RMSE	0.014035956	0.012263369	0.018625151	0.012792641
39	RRSE	8.706567764	1.158379793	14.28929806	3.659450054	39	RRSE	7.781282425	2.251657009	18.4135437	7.317749023
	MAE	0.005840024	0.003902864	0.008861193	0.00455858		MAE	0.007202005	0.008148436	0.014493564	0.007183693
	MSE	4.92E-05	2.69E-05	0.000113961	3.91E-05		MSE	0.00018974	0.0001652	0.000327626	0.000143165
	RMSE	0.007015065	0.00519067	0.01067527	0.006252967		RMSE	0.013774601	0.012853005	0.018100448	0.011965175
40	RRSE	9.25455761	0.267809063	15.61623859	4.121153355	40	RRSE	7.029219151	2.792447329	19.35932732	6.570281506
	MAE	0.006009383	0.003940254	0.009588476	0.004630211		MAE	0.006883624	0.007529828	0.015036232	0.00724387
	MSE	4.98E-05	2.80E-05	0.000129308	4.15E-05		MSE	0.000188094	0.000167881	0.000337763	0.000143063
	RMSE	0.007057134	0.005291339	0.011371358	0.006445138		RMSE	0.013714748	0.012956879	0.018378334	0.011960912
41	RRSE	10.11128521	1.136354804	17.86570549	4.975209236	41	RRSE	8.175927162	1.923269987	20.2292614	8.05198288
	MAE	0.006325124	0.004159327	0.010795362	0.004738116		MAE	0.007492046	0.007333628	0.01567021	0.007663357
	MSE	5.36E-05	3.05E-05	0.000155025	4.25E-05		MSE	0.000190717	0.000147727	0.000349662	0.000175051
	RMSE	0.007323223	0.005524328	0.01245092	0.006517296		RMSE	0.013810023	0.012154279	0.018699246	0.013230701
42	RRSE	10.23351765	0.32144013	18.88076782	5.131510735	42	RRSE	7.640318394	1.992036819	19.28205872	7.438173771
	MAE	0.006641489	0.004071428	0.011272075	0.004806296		MAE	0.00732991	0.007462173	0.015077786	0.007454067
	MSE	5.93E-05	2.89E-05	0.000161025	4.40E-05		MSE	0.000188626	0.000152298	0.000340758	0.0001669
	RMSE	0.007701404	0.00538042	0.012689564	0.006636936		RMSE	0.013734116	0.012340907	0.01845964	0.012918961
43	RRSE	9.837866783	0.256581545	18.66327858	4.766049862	43	RRSE	7.735900879	2.022973061	20.55413055	7.258568287
	MAE	0.00621024	0.00409312	0.011020721	0.00455153		MAE	0.007292325	0.007459333	0.015947167	0.007314213
	MSE	5.32E-05	2.96E-05	0.000157153	4.16E-05		MSE	0.000191644	0.000164718	0.000364617	0.00014681
	RMSE	0.007290758	0.005438351	0.012536085	0.006450916		RMSE	0.013843538	0.012834235	0.019094948	0.012116535
44	RRSE	10.21303368	0.800672352	18.11089516	5.121080399	44	RRSE	7.844963551	1.902891994	20.23511314	7.552832127
	MAE	0.006374944	0.004135238	0.010895703	0.004766957		MAE	0.007345116	0.007310798	0.015747491	0.007340153
	MSE	5.56E-05	2.83E-05	0.000153706	4.77E-05		MSE	0.000189333	0.000147766	0.000360335	0.000149164
	RMSE	0.007457202	0.005316389	0.012397833	0.006907908		RMSE	0.013759839	0.012155887	0.018982487	0.012213256
45	RRSE	10.45437813	0.651390254	19.24680138	5.191915035	45	RRSE	8.155870438	1.507307529	22.59509087	7.66785717
	MAE	0.006592077	0.003863183	0.011521724	0.004941925		MAE	0.007575543	0.007452206	0.017352792	0.007620564
	MSE	5.81E-05	2.68E-05	0.000168328	4.53E-05		MSE	0.000188691	0.000170676	0.000405739	0.000154215
	RMSE	0.007621816	0.005178796	0.012974112	0.006730032		RMSE	0.013736469	0.01306429	0.020142958	0.012418327
46	RRSE	10.61807728	1.233188391	19.46906662	5.218859673	46	RRSE	7.501655579	2.184672356	21.69430161	6.992140293
	MAE	0.006685753	0.003987074	0.011659158	0.005082067		MAE	0.007213502	0.007383095	0.016747108	0.007192067
	MSE	5.99E-05	2.96E-05	0.000176384	4.58E-05		MSE	0.000186151	0.000156935	0.000390109	0.000141276
	RMSE	0.007738289	0.005438189	0.013280966	0.006768197		RMSE	0.013643734	0.012527368	0.019751189	0.01188594
47	RRSE	9.759709358	0.827094018	16.87990952	4.776286602	47	RRSE	7.559007168	2.398530483	20.96367645	7.329694271
	MAE	0.006323101	0.004230344	0.010144193	0.004519139		MAE	0.007169228	0.007043203	0.01611859	0.007584359
	MSE	5.43E-05	3.37E-05	0.000139485	4.03E-05		MSE	0.000165541	0.000124824	0.000355144	0.000141277
	RMSE	0.007367926	0.005805864	0.011810397	0.006344758		RMSE	0.012866286	0.01117248	0.018845253	0.011885989
48	RRSE	10.06562519	1.142641068	17.21339226	5.197535992	48	RRSE	8.001426697	1.666833878	21.05992889	7.729929924
	MAE	0.006451075	0.004057381	0.010296236	0.004906729		MAE	0.007475972	0.007163189	0.01631864	0.007709148
	MSE	5.75E-05	3.09E-05	0.000145904	4.70E-05		MSE	0.000189832	0.000145353	0.000376599	0.000173954
	RMSE	0.00758173	0.00555834	0.012079089	0.006859277		RMSE	0.01377795	0.012056232	0.019406157	0.013189157
49	RRSE	9.89395237	1.163902521	19.32448006	4.780901432	49	RRSE	7.424761772	2.185619831	20.06874275	7.429775238
	MAE	0.006421661	0.003922783	0.011622668	0.004716931		MAE	0.006954729	0.007167548	0.01556653	0.007249736
	MSE	5.52E-05	2.94E-05	0.000170134	4.13E-05		MSE	0.000141296	0.000115186	0.000351289	0.000135532
	RMSE	0.007431708	0.00541775	0.013043545	0.006426529		RMSE	0.011886783	0.010732458	0.018742692	0.011641831
50	RRSE	10.33056927	1.113586426	19.15169334	5.128182888	50	RRSE	7.693232059	1.633349657	20.70928001	7.254265308
	MAE	0.006474213	0.003927531	0.011500327	0.004832438		MAE	0.007279074	0.007565951	0.016206015	0.007194425
	MSE	5.80E-05	2.80E-05	0.000168874	4.67E-05		MSE	0.000186376	0.000190344	0.000366936	0.000156744
	RMSE	0.007617989	0.005293685	0.01299517	0.006831192		RMSE	0.013651974	0.013796519	0.01915556	0.012519758

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ilten, E., Calgan, H. & Demirtas, M. Design of induction motor speed observer based on long short-term memory. Neural Comput & Applic 34, 18703–18723 (2022). https://doi.org/10.1007/s00521-022-07458-0

Download citation

Received: 30 November 2021
Accepted: 22 May 2022
Published: 22 June 2022
Issue Date: November 2022
DOI: https://doi.org/10.1007/s00521-022-07458-0

Keywords

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Design of induction motor speed observer based on long short-term memory

Abstract

Access this article

Similar content being viewed by others

Investigation into LSTM Deep Learning for Induction Motor Fault Diagnosis

Intelligent Fault Detection of Rotating Machinery Using Long-Short-Term Memory (LSTM) Network

Real-time safety monitoring in the induction motor using deep hierarchic long short-term memory

References

Author information

Authors and Affiliations

Corresponding author

Ethics declarations

Conflict of interest

Additional information

Publisher's Note

Appendices

Appendix 1

Appendix 2

Rights and permissions

About this article

Cite this article

Keywords

Navigation

Design of induction motor speed observer based on long short-term memory

Abstract

Access this article

Similar content being viewed by others

Investigation into LSTM Deep Learning for Induction Motor Fault Diagnosis

Intelligent Fault Detection of Rotating Machinery Using Long-Short-Term Memory (LSTM) Network

Real-time safety monitoring in the induction motor using deep hierarchic long short-term memory

References

Author information

Authors and Affiliations

Corresponding author

Ethics declarations

Conflict of interest

Additional information

Publisher's Note

Appendices

Appendix 1

Appendix 2

Rights and permissions

About this article

Cite this article

Share this article

Keywords

Search

Navigation