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Estimating Lithium-ion Battery Health

Introduction

Lithium-based batteries - their cycles characteristics and aging

Lithium-ion (or Li-ion) batteries are rechargeable batteries used for a variety of electronic devices, which range from eletric vehicles, smartphones, and even satellites.

However, despite their wide adoption, research isn’t mature enough to avoid problems with battery health and safety, and given the ubiquity of consumer electronics using the technology, this has led to some poor outcomes that range from poor user-experience to public safety concerns (see, for example, the Samsung Galaxy Note 7 explosions from 2016).

Dataset

In this example of predictive maintenance, we propose a data-driven method to estimate the health of a battery using the Li-ion battery dataset released by NASA.

This dataset includes information on Li-ion batteries over several charge and discharge cycles at room temperature. Charging was at a constant current (CC) at 1.5A until the battery voltage reached 4.2V and then continued in a constant voltage (CV) mode until the charge current dropped to 20mA.

Discharge was at a constant current (CC) level of 2A until the battery voltage fell to 2.7V.

You can download the Jupyter Notebook of the study here.

The dataset includes the following:

• Voltage_measured: Battery’s terminal voltage (Volts) for charging and discharging cycles.

• Current_measured: Battery’s output current (Amps) for charging and discharging cycles.

• Temperature_measured: Battery temperature (degree Celsius).

• Current_charge: Current measured at charger for charging cycles and at load for discharging cycles (Amps).

• Voltage_charge: Voltage measured at charger for charging cycles and at load for discharging ones (Volts).

• Start_time: Starting time of the cycle.

• Time: Time in seconds after the starting time for the cycle (seconds).

• Capacity: Battery capacity (Ahr) for discharging until 2.7V. Battery capacity is the product of the current drawn from the battery (while the battery is able to supply the load) until its voltage drops lower than a certain value for each cell.

We will follow the data science cycle (Data Exploration - Data Preparation - Data Modeling - Model Evaluation - Model Deployment) to solve this problem.

Initialization

This example uses the following version of VerticaPy:

import verticapy as vp

vp.__version__
Out[2]: '1.1.0'

Connect to Vertica. This example uses an existing connection called VerticaDSN. For details on how to create a connection, see the Connection tutorial. You can skip the below cell if you already have an established connection.

vp.connect("VerticaDSN")

Before we import the data, we’ll drop any existing schemas of the same name.

vp.drop("battery_data", method="schema")
Out[3]: True

vp.create_schema("battery_data", True)
Out[4]: True

Let us now ingest the data.

battery5 = vp.read_csv("data/data.csv")

Warning

This example uses a sample dataset. For the full analysis, you should consider using the complete dataset.

Understanding the Data

Let’s examine our data. Here, we use head() to retrieve the first five rows of the dataset.

	123 Voltage_measured Float 100%	...	123 Current_measured Float 100%	123 Capacity Float 8%
1	2.66684542897547	...	-2.00971847365549	1.76231507040931
2	2.68499881852498	...	-2.01263017531067	1.81403112750839
3	2.69951692300468	...	-2.01819088625634	1.49084440504002
4	2.70742704244784	...	-2.01141689693154	1.3389145230207
5	2.80290487900751	...	-2.01245713079778	1.32902865651207
6	2.81015874386668	...	-2.01301807875465	1.3389145230207
7	2.86534003859311	...	-2.01112277845238	1.30779599469444
8	2.87532762204241	...	-2.01373897721455	1.43867093714806
9	2.87544665543895	...	-2.01381259402161	1.83464550821204
10	2.88060038984582	...	-2.0137387886831	1.76231507040931
11	2.88091852838522	...	-2.01120565508369	1.52852526297564
12	2.8898440837763	...	-2.01373483656512	1.30335735590382
13	2.89319852614925	...	-2.01145478051058	1.29788708064957
14	2.8997991086539	...	-2.01285501364142	1.3236741274999
15	2.90158446050215	...	-2.01164854386623	1.78844323353705
16	2.90322576197612	...	-2.01357019097282	1.52264732528438
17	2.90406473654365	...	-2.01117875087499	1.30341004386556
18	2.92177442536308	...	-2.01270005947885	1.30901536423074
19	2.93939223121491	...	-2.01072443794785	1.71053335113519
20	2.94061511365568	...	-2.01367148573802	1.31863389675329

Let’s perform a few aggregations with describe() to get a high-level overview of the dataset.

battery5.describe()

	...	approx_75%	max
"Voltage_measured"	...	4.20589540329895	4.98472045064886
"Current_measured"	...	1.22946886392836	1.5215190253818
"Temperature_measured"	...	27.3344916075796	41.2725661150757
"Current_charge"	...	1.498	1.9984
"Voltage_charge"	...	4.65	5.002
"Time"	...	7494.96635294118	10807.219
"ambient_temp"	...	24.0	24.0
"Capacity"	...	1.74175033925828	1.85648742081816

To get a better idea of the changes between each cycle, we look at an aggregation at their start time, duration, and voltage at the beginning and the end of each cycle.

battery5["start_time"].describe()

	value
name	"start_time"
dtype	timestamp
count	35288
min	2008-04-02 13:08:17.000920
max	2008-05-28 11:09:42.000045

To see how the voltage changes during the cycle, we extract the initial and final voltage measurements for each cycle.

battery5.analytic(
    func = "first_value",
    columns = "Voltage_measured",
    by = "start_time",
    order_by = {"Time": "asc"},
    name = "first_voltage_measured",
)
battery5.analytic(
    func = "first_value",
    columns = "Voltage_measured",
    by = "start_time",
    order_by = {"Time": "desc"},
    name = "last_voltage_measured",
)
cycling_info = battery5.groupby(
        columns = [
            "start_time",
            "type",
            "first_voltage_measured",
            "last_voltage_measured",
        ],
        expr = [
            "COUNT(*) AS nr_of_measurements",
            "MAX(Time) AS cycle_duration",
        ],
).sort("start_time")
cycling_info["cycle_id"] = "ROW_NUMBER() OVER(ORDER BY start_time)"
cycling_info.head(100)

	📅 start_time Timestamp(29) 100%	...	123 cycle_duration Float(22) 100%	123 cycle_id Integer 100%
1	2008-04-02 13:08:17.000920	...	7561.75	1
2	2008-04-02 15:25:41.000593	...	3072.859	2
3	2008-04-02 16:37:51.000984	...	10516.0	3
4	2008-04-02 19:43:48.000405	...	3509.61	4
5	2008-04-02 20:55:40.000811	...	10401.937	5
6	2008-04-03 00:01:06.000687	...	3651.641	6
7	2008-04-03 01:12:38.000670	...	10397.89	7
8	2008-04-03 04:16:37.000375	...	3309.719	8
9	2008-04-03 05:27:49.000125	...	10166.718	9
10	2008-04-03 08:33:25.000702	...	3507.391	10
11	2008-04-03 09:44:35.000078	...	10352.141	11
12	2008-04-03 12:55:10.000686	...	3530.0	12
13	2008-04-03 14:06:43.000234	...	10683.61	13
14	2008-04-03 17:17:16.000015	...	2917.359	14
15	2008-04-03 18:28:47.000125	...	9667.515	15
16	2008-04-03 21:28:14.000718	...	3531.75	16
17	2008-04-03 22:38:27.000452	...	9901.391	17
18	2008-04-04 01:38:15.000217	...	3429.047	18
19	2008-04-04 02:48:06.000155	...	9370.672	19
20	2008-04-04 05:48:08.000609	...	3231.25	20
21	2008-04-04 06:58:00.000296	...	9491.344	21
22	2008-04-04 09:57:19.000765	...	3231.25	22
23	2008-04-04 11:06:50.000375	...	9969.688	23
24	2008-04-04 15:05:59.000905	...	9525.25	24
25	2008-04-04 17:56:27.000609	...	3491.016	25
26	2008-04-04 19:05:19.000234	...	9738.64	26
27	2008-04-04 22:01:54.000670	...	3310.344	27
28	2008-04-04 23:10:25.000420	...	10629.89	28
29	2008-04-05 02:20:26.000702	...	2744.891	29
30	2008-04-05 03:28:57.000234	...	9606.453	30
31	2008-04-05 06:25:01.000890	...	3114.0	31
32	2008-04-05 07:33:12.000734	...	9978.516	32
33	2008-04-05 10:30:32.000311	...	2002.875	33
34	2008-04-05 11:38:22.000140	...	9293.968	34
35	2008-04-05 14:34:41.000468	...	3171.938	35
36	2008-04-05 15:42:11.000531	...	9649.344	36
37	2008-04-05 18:39:25.000217	...	3192.39	37
38	2008-04-05 19:46:36.000125	...	10138.625	38
39	2008-04-05 22:46:35.000484	...	3035.625	39
40	2008-04-18 17:34:22.000890	...	10049.844	40
41	2008-04-18 21:10:19.000795	...	3055.828	41
42	2008-04-18 22:53:58.000343	...	10181.281	42
43	2008-04-19 02:29:09	...	3430.813	43
44	2008-04-19 04:12:06.000343	...	10159.375	44
45	2008-04-19 07:47:15.000702	...	3351.016	45
46	2008-04-19 09:29:52.000703	...	9911.547	46
47	2008-04-19 13:01:42.000561	...	3154.875	47
48	2008-04-19 14:43:41.000265	...	10250.282	48
49	2008-04-19 18:27:29.000827	...	2687.719	49
50	2008-04-19 20:09:47.000750	...	9695.265	50
51	2008-04-19 23:41:55.000686	...	3233.07799999999	51
52	2008-04-20 01:22:53.000953	...	10018.812	52
53	2008-04-20 04:54:41.000734	...	3390.922	53
54	2008-04-20 06:35:39.000765	...	10265.531	54
55	2008-04-20 10:16:28.000859	...	3392.25	55
56	2008-04-20 11:57:08.000765	...	10192.688	56
57	2008-04-20 15:37:05.000280	...	3410.688	57
58	2008-04-20 17:17:44.000030	...	9938.359	58
59	2008-04-20 20:50:38.000920	...	2938.156	59
60	2008-04-20 22:31:18.000045	...	10660.578	60
61	2008-04-21 02:15:02.000921	...	3076.766	61
62	2008-04-21 17:51:26.000312	...	10361.016	62
63	2008-04-22 14:15:41.000186	...	1671.75	63
64	2008-04-22 15:33:49.000875	...	3422.125	64
65	2008-04-22 17:04:53.000218	...	10039.766	65
66	2008-04-22 20:26:18.000920	...	3214.187	66
67	2008-04-22 21:56:21.000405	...	10129.656	67
68	2008-04-23 01:18:11.000795	...	3110.969	68
69	2008-04-23 02:47:55.000453	...	10618.844	69
70	2008-04-23 06:18:19.000920	...	3337.219	70
71	2008-04-23 07:47:54.000718	...	9917.282	71
72	2008-04-23 11:08:00.000312	...	3329.14	72
73	2008-04-23 12:37:17.000515	...	10456.562	73
74	2008-04-23 16:06:25.000170	...	3338.922	74
75	2008-04-23 17:35:42.000828	...	10344.032	75
76	2008-04-23 21:02:58.000295	...	3185.875	76
77	2008-04-23 22:32:06.000671	...	9949.17200000001	77
78	2008-04-24 01:51:33.000890	...	3329.735	78
79	2008-04-24 03:20:23.000359	...	10539.406	79
80	2008-04-24 06:50:00.000031	...	2998.875	80
81	2008-04-24 08:18:41.000703	...	10629.657	81
82	2008-04-24 11:49:24.000280	...	3224.375	82
83	2008-04-24 13:17:56.000250	...	10482.89	83
84	2008-04-24 16:45:56.000015	...	3312.032	84
85	2008-04-24 18:14:28.000937	...	10233.109	85
86	2008-04-24 21:38:11.000077	...	3263.375	86
87	2008-04-24 23:06:34.000155	...	10111.484	87
88	2008-04-25 12:03:44.000093	...	3148.859	88
89	2008-04-25 17:02:35.000703	...	10804.922	89
90	2008-04-25 20:03:55.000920	...	3273.343	90
91	2008-04-25 21:32:20.000468	...	10758.985	91
92	2008-04-26 01:04:35.000718	...	2998.234	92
93	2008-04-26 02:32:41.000093	...	10257.328	93
94	2008-04-26 05:57:35.000140	...	3227.031	94
95	2008-04-26 07:25:23.000030	...	10751.062	95
96	2008-04-26 10:58:25.000843	...	3168.437	96
97	2008-04-28 17:20:47.000859	...	9940.907	97
98	2008-04-29 12:15:56.000953	...	3328.937	98
99	2008-04-29 13:44:46.000545	...	10060.813	99
100	2008-04-29 17:05:27.000780	...	3045.407	100

We can see from the “duration” column that charging seems to take a longer time than discharging.

Let’s visualize this trend with an animated graph.

cycling_info.animated_bar(
    ts = "start_time",
    columns = ["type", "cycle_duration"],
)

Once Loop Reflect

The animated graph below shows how the cycles change throughout time. Another way we can verify that charging cycles are longer than discharging cycles is by looking at the average duration of each type of cycle.

cycling_info.bar(
    ["type"],
    method = "avg",
    of = "cycle_duration",
)

In general, charging cycles are longer than discharging cycles.

Let’s examine how voltage changes between cycles and their transitions.

cycling_info = cycling_info.groupby(
    "type",
    [
        "MIN(first_voltage_measured) AS min_first_voltage",
        "AVG(first_voltage_measured) AS avg_first_voltage",
        "MAX(first_voltage_measured) AS max_first_voltage",
        "MIN(last_voltage_measured)  AS min_last_voltage",
        "AVG(last_voltage_measured)  AS avg_last_voltage",
        "MAX(last_voltage_measured)  AS max_last_voltage",
    ],
)
cycling_info.head(100)

	📅 start_time Timestamp(29) 100%	...	123 cycle_duration Float(22) 100%	123 cycle_id Integer 100%
1	2008-04-02 13:08:17.000920	...	7561.75	1
2	2008-04-02 15:25:41.000593	...	3072.859	2
3	2008-04-02 16:37:51.000984	...	10516.0	3
4	2008-04-02 19:43:48.000405	...	3509.61	4
5	2008-04-02 20:55:40.000811	...	10401.937	5
6	2008-04-03 00:01:06.000687	...	3651.641	6
7	2008-04-03 01:12:38.000670	...	10397.89	7
8	2008-04-03 04:16:37.000375	...	3309.719	8
9	2008-04-03 05:27:49.000125	...	10166.718	9
10	2008-04-03 08:33:25.000702	...	3507.391	10
11	2008-04-03 09:44:35.000078	...	10352.141	11
12	2008-04-03 12:55:10.000686	...	3530.0	12
13	2008-04-03 14:06:43.000234	...	10683.61	13
14	2008-04-03 17:17:16.000015	...	2917.359	14
15	2008-04-03 18:28:47.000125	...	9667.515	15
16	2008-04-03 21:28:14.000718	...	3531.75	16
17	2008-04-03 22:38:27.000452	...	9901.391	17
18	2008-04-04 01:38:15.000217	...	3429.047	18
19	2008-04-04 02:48:06.000155	...	9370.672	19
20	2008-04-04 05:48:08.000609	...	3231.25	20
21	2008-04-04 06:58:00.000296	...	9491.344	21
22	2008-04-04 09:57:19.000765	...	3231.25	22
23	2008-04-04 11:06:50.000375	...	9969.688	23
24	2008-04-04 15:05:59.000905	...	9525.25	24
25	2008-04-04 17:56:27.000609	...	3491.016	25
26	2008-04-04 19:05:19.000234	...	9738.64	26
27	2008-04-04 22:01:54.000670	...	3310.344	27
28	2008-04-04 23:10:25.000420	...	10629.89	28
29	2008-04-05 02:20:26.000702	...	2744.891	29
30	2008-04-05 03:28:57.000234	...	9606.453	30
31	2008-04-05 06:25:01.000890	...	3114.0	31
32	2008-04-05 07:33:12.000734	...	9978.516	32
33	2008-04-05 10:30:32.000311	...	2002.875	33
34	2008-04-05 11:38:22.000140	...	9293.968	34
35	2008-04-05 14:34:41.000468	...	3171.938	35
36	2008-04-05 15:42:11.000531	...	9649.344	36
37	2008-04-05 18:39:25.000217	...	3192.39	37
38	2008-04-05 19:46:36.000125	...	10138.625	38
39	2008-04-05 22:46:35.000484	...	3035.625	39
40	2008-04-18 17:34:22.000890	...	10049.844	40
41	2008-04-18 21:10:19.000795	...	3055.828	41
42	2008-04-18 22:53:58.000343	...	10181.281	42
43	2008-04-19 02:29:09	...	3430.813	43
44	2008-04-19 04:12:06.000343	...	10159.375	44
45	2008-04-19 07:47:15.000702	...	3351.016	45
46	2008-04-19 09:29:52.000703	...	9911.547	46
47	2008-04-19 13:01:42.000561	...	3154.875	47
48	2008-04-19 14:43:41.000265	...	10250.282	48
49	2008-04-19 18:27:29.000827	...	2687.719	49
50	2008-04-19 20:09:47.000750	...	9695.265	50
51	2008-04-19 23:41:55.000686	...	3233.07799999999	51
52	2008-04-20 01:22:53.000953	...	10018.812	52
53	2008-04-20 04:54:41.000734	...	3390.922	53
54	2008-04-20 06:35:39.000765	...	10265.531	54
55	2008-04-20 10:16:28.000859	...	3392.25	55
56	2008-04-20 11:57:08.000765	...	10192.688	56
57	2008-04-20 15:37:05.000280	...	3410.688	57
58	2008-04-20 17:17:44.000030	...	9938.359	58
59	2008-04-20 20:50:38.000920	...	2938.156	59
60	2008-04-20 22:31:18.000045	...	10660.578	60
61	2008-04-21 02:15:02.000921	...	3076.766	61
62	2008-04-21 17:51:26.000312	...	10361.016	62
63	2008-04-22 14:15:41.000186	...	1671.75	63
64	2008-04-22 15:33:49.000875	...	3422.125	64
65	2008-04-22 17:04:53.000218	...	10039.766	65
66	2008-04-22 20:26:18.000920	...	3214.187	66
67	2008-04-22 21:56:21.000405	...	10129.656	67
68	2008-04-23 01:18:11.000795	...	3110.969	68
69	2008-04-23 02:47:55.000453	...	10618.844	69
70	2008-04-23 06:18:19.000920	...	3337.219	70
71	2008-04-23 07:47:54.000718	...	9917.282	71
72	2008-04-23 11:08:00.000312	...	3329.14	72
73	2008-04-23 12:37:17.000515	...	10456.562	73
74	2008-04-23 16:06:25.000170	...	3338.922	74
75	2008-04-23 17:35:42.000828	...	10344.032	75
76	2008-04-23 21:02:58.000295	...	3185.875	76
77	2008-04-23 22:32:06.000671	...	9949.17200000001	77
78	2008-04-24 01:51:33.000890	...	3329.735	78
79	2008-04-24 03:20:23.000359	...	10539.406	79
80	2008-04-24 06:50:00.000031	...	2998.875	80
81	2008-04-24 08:18:41.000703	...	10629.657	81
82	2008-04-24 11:49:24.000280	...	3224.375	82
83	2008-04-24 13:17:56.000250	...	10482.89	83
84	2008-04-24 16:45:56.000015	...	3312.032	84
85	2008-04-24 18:14:28.000937	...	10233.109	85
86	2008-04-24 21:38:11.000077	...	3263.375	86
87	2008-04-24 23:06:34.000155	...	10111.484	87
88	2008-04-25 12:03:44.000093	...	3148.859	88
89	2008-04-25 17:02:35.000703	...	10804.922	89
90	2008-04-25 20:03:55.000920	...	3273.343	90
91	2008-04-25 21:32:20.000468	...	10758.985	91
92	2008-04-26 01:04:35.000718	...	2998.234	92
93	2008-04-26 02:32:41.000093	...	10257.328	93
94	2008-04-26 05:57:35.000140	...	3227.031	94
95	2008-04-26 07:25:23.000030	...	10751.062	95
96	2008-04-26 10:58:25.000843	...	3168.437	96
97	2008-04-28 17:20:47.000859	...	9940.907	97
98	2008-04-29 12:15:56.000953	...	3328.937	98
99	2008-04-29 13:44:46.000545	...	10060.813	99
100	2008-04-29 17:05:27.000780	...	3045.407	100

From this table, it looks like batteries are charged until they are almost full (4.2V) and discharging doesn’t begin until they are fully charged.

End-of-life (EOL) criteria for batteries is usually defined as when the battery capacity is lower than 70%-80% of its rated capacity. Since the rated capacity by the manufacturer for this battery is 2Ah, this battery is considered EOL when its capacity reaches 2Ah x 70% = 1.4Ah.

Let’s plot the capacity curve of the battery with its smoothed version and observe when it reaches the degradation criteria.

But first we need to perform some preprocessing.

discharging_data = battery5[battery5["type"] == "discharge"]
d_cap = discharging_data[["start_time", "Capacity"]].groupby(["start_time", "Capacity"])
d_cap["discharge_id"] = "ROW_NUMBER() OVER(ORDER BY start_time, Capacity)"
d_cap.rolling(
    func = "mean",
    columns = "capacity",
    window = (-100, -1),
    name = "smooth_capacity",
)

	📅 start_time Timestamp(29) 100%	...	123 Capacity Float(22) 100%	123 smooth_capacity Float(22) 99%
1	2008-05-26 20:21:04.000921	...	1.28745252213794	[null]
2	2008-05-26 15:30:43.000968	...	1.28800339261912	1.28745252213794
3	2008-05-26 10:44:38.000468	...	1.29346361384424	1.28772795737853
4	2008-05-26 01:13:02.000796	...	1.29788708064957	1.2896398428671
5	2008-05-26 06:01:08.000170	...	1.29807350569189	1.29170165231272
6	2008-05-25 10:51:37.000015	...	1.30303291864059	1.29297602298855
7	2008-05-25 15:37:08.000890	...	1.30335735590382	1.29465217226389
8	2008-05-25 20:23:04.000453	...	1.30341004386556	1.29589576992674
9	2008-05-25 05:57:17.000890	...	1.30779599469444	1.29683505416909
10	2008-05-27 15:52:41.000359	...	1.30901536423074	1.29805293644969
11	2008-05-25 01:06:49.000828	...	1.31320206344422	1.29914917922779
12	2008-05-24 20:21:13.000436	...	1.31347513213243	1.30042671415656
13	2008-05-22 11:23:22.000187	...	1.31816915884452	1.30151408232121
14	2008-05-22 20:59:50.000203	...	1.3182930401027	1.30279524205378
15	2008-05-22 16:17:58.000890	...	1.31846644366403	1.3039022276287
16	2008-05-24 15:31:10.000593	...	1.31863389675329	1.30487317536439
17	2008-05-22 06:32:40.000920	...	1.32317089922762	1.30573322045119
18	2008-05-24 10:42:50.000484	...	1.3236741274999	1.30675896626157
19	2008-05-23 12:13:16.000359	...	1.32387242224427	1.30769869744148
20	2008-05-27 20:45:42.000125	...	1.32507932864294	1.30854994611531

Now we can plot the graphs. In VerticaPy we have multiple options to plot the graphs with different syntax of customization. For a complete list of all the graphs and their options check out the Chart Gallery.

Now let’s first try to plot this using Matplotlib:

import matplotlib.pyplot as plt
from matplotlib.pyplot import axhline

# Switch the plotting library to Matplotlib
vp.set_option("plotting_lib", "matplotlib")

fig = plt.figure()
ax = d_cap.plot(ts = "discharge_id", columns = ["Capacity", "smooth_capacity"])
ax.axhline(y = 1.4, label = "End-of-life criteria")
ax.set_title("Capacity degradation curve of the battery, its smoothed version and its end-of-life threshold")
ax.legend()
plt.show()

import matplotlib.pyplot as plt

from matplotlib.pyplot import axhline

# Switch the plotting library to Matplotlib
vp.set_option("plotting_lib", "matplotlib")

fig = plt.figure()

ax = d_cap.plot(ts = "discharge_id", columns = ["Capacity", "smooth_capacity"])

ax.axhline(y = 1.4, label = "End-of-life criteria")
Out[10]: <matplotlib.lines.Line2D at 0x7fd387638b80>

ax.set_title("Capacity degradation curve of the battery, its smoothed version and its end-of-life threshold")
Out[11]: Text(0.5, 1.0, 'Capacity degradation curve of the battery, its smoothed version and its end-of-life threshold')

ax.legend()
Out[12]: <matplotlib.legend.Legend at 0x7fd3876e8670>

plt.show()

We can now try to plot it using Plotly. We can conveniently switch between the plotting libraries using:

# Switch the plotting library to Plotly
vp.set_option("plotting_lib", "plotly")

import plotly.graph_objects as go

plot = d_cap.plot(ts = "discharge_id", columns = ["Capacity", "smooth_capacity"], title = "Capacity degradation curve of the battery, its smoothed version and its end-of-life threshold")

# Add horizontal line
plot.add_hline(y = 1.4, line_width = 3, line_dash = "dash", line_color = "green")

# Add legend for the horizontal line
plot.add_trace(go.Scatter(x = [None], y = [None], mode = "lines", line = dict(color="green", width=3, dash="dash"), name = "End-of-life criteria"))

The sudden increases in battery capacity come from the self-charging property of Li-ion batteries. The smoothed graph makes the downward trend in the battery’s capacity very clear.

An important observation here is that the battery meets the EOL criteria around the 125th cycle.

Goal and Problem Modeling

Understanding battery health is important, but at the time of writing, there’s no direct way to measure it. In our case, we’ll create a degredation model to find the relationship between a battery’s overall health and the other properties in the dataset, which includes charge and discharge cycle duration, average voltage and current, etc.

One possible definition of the battery’s overall health (“state of health” or “SoH”) is the following:

Let \(Cap_{rate}\) be the rated capacity of the battery when it’s new (2Ah in our case), and \(Cap_{actual}\) be the actual capacity of the battery at a specific time. The state of health of the battery is defined as:

\[SoH = \frac{Cap_{actual}}{Cap_{rate}} \times 100\% = \frac{1}{2}Cap_{actual}\]

Data preparation

Outliet detection

Let’s start by finding and removing the global outliers from our dataset.

battery5.outliers(
    columns = [
        "Voltage_measured",
        "Current_measured",
        "Temperature_measured","Capacity",
    ],
    name = "global_outlier",
    threshold = 4.0,
)
battery5.filter("global_outlier = 0").drop("global_outlier")

Feature engineering

Since measurements like voltage and temperature tend to differ within the different cycles, we’ll create some features that can describe those cycles.

sample_cycle = battery5[battery5["Capacity"] == "1.83514614292266"]
sample_cycle["Voltage_measured"].plot(ts = "Time")
sample_cycle["Temperature_measured"].plot(ts = "Time")

We’ll define new features that describe the minimum and maximum temperature during one cycle; the minimal voltage; and the time needed to reach minimum voltage and maximum temperature.

# filter for discharge cycles
discharging_data = battery5[battery5["type"] == "discharge"]

# define new features
discharge_cycle_metrics = discharging_data.groupby(
        columns = ["start_time"],
        expr = [
            "MIN(Temperature_measured) AS min_temp",
            "MAX(Temperature_measured) AS max_temp",
            "MIN(Voltage_measured) AS min_volt",
        ]
).join(
        discharging_data,
        how = "left",
        on = {"min_volt": "voltage_measured"},
        expr1 = ["*"],
        expr2 = ["Time AS time_to_reach_minvolt"],
).join(
        discharging_data,
        how = "left",
        on = {"max_temp": "temperature_measured"},
        expr1 = ["*"],
        expr2 = ["Time AS time_to_reach_maxtemp"],
)

# calculate values of SOH
discharging_data = discharging_data.groupby(["start_time", "Capacity"])
discharging_data["SOH"] = discharging_data["Capacity"] * 0.5

# define the final dataset and save it to db
final_df = discharge_cycle_metrics.join(
    discharging_data,
    on_interpolate = {"start_time": "start_time"},
    how = "left",
    expr1 = ["*"],
    expr2 = ["SOH AS SOH"],
)

# normalize the features
final_df.normalize(
    method = "minmax",
    columns = [
        "min_temp",
        "max_temp",
        "min_volt",
        "time_to_reach_minvolt",
        "time_to_reach_maxtemp",
    ],
)

# save it to db
final_df.to_db(name = "battery_data.finaldata_battery_5")

Machine Learning

AutoML tests several models and returns input scores for each. We can use this to find the best model for our dataset.

Note

We are only using the three algorithms, but you can change the estimator parameter to try all the native algorithms: ``estimator = ‘native’ ``

from verticapy.machine_learning.vertica.automl import AutoML
from verticapy.machine_learning.vertica import LinearRegression, RandomForestRegressor, Ridge

model = AutoML(
    "battery_data.battery_autoML",
    estimator = [
        RandomForestRegressor(),
        LinearRegression(),
        Ridge(),
    ],
    estimator_type = "regressor"
)
model.fit(
    "battery_data.finaldata_battery_5",
    X = [
        "min_temp",
        "max_temp",
        "min_volt",
        "time_to_reach_minvolt",
        "time_to_reach_maxtemp",
    ],
    y = "SOH",
)

We can visualize the performance and efficency differences of each model with a plot.

model.plot()

# take the best model and its parameters
best_model = model.best_model_

params = best_model.get_params()

print(best_model._model_type)
LinearRegression

We can now define the model using those hyperparameters and train it.

# define a regression model based on the selected parameters
model_rf = LinearRegression(name = "btr_lr1", **params)
model_rf.fit(
    final_df,
    X = [
        "min_temp",
        "max_temp",
        "min_volt",
        "time_to_reach_minvolt",
        "time_to_reach_maxtemp",
    ],
    y = "SOH",
)

model_rf.regression_report()

	value
explained_variance	0.96333884685611
max_error	0.0826358574982834
median_absolute_error	0.00811763379847186
mean_absolute_error	0.0125867357193153
mean_squared_error	0.000330328059204944
root_mean_squared_error	0.0181749294140292
r2	0.96333884685611
r2_adj	0.962207329783768
aic	-1333.62233469026
bic	-1315.84749491322

The predictive power of our model looks pretty good. Let’s use our model to predict the SoH of the battery. We can visualize our prediction with a plot against the true values.

# take the predicted values and the plot them along the true ones
result = model_rf.predict(
    final_df,
    name = "SOH_estimates",
)
result.plot(
    ts = "start_time",
    columns = ["SOH", "SOH_estimates"],
)

Conclusion

We successfully defined a battery degradation model that can make accurate predictions about the health of a Li-ion battery. This model could be used to, for example, accurately send warnings to users when their batteries meet the EOL criteria.