https://github.com/ashishpatel26/predictive_maintenance_using_machine-learning_microsoft_casestudy

Predictive_Maintenance_using_Machine-Learning_Microsoft_Casestudy
https://github.com/ashishpatel26/predictive_maintenance_using_machine-learning_microsoft_casestudy

case-study cortana-intelligence-gallery learning machine maintenance microsoft-cortana predictive predictive-maintenance

Last synced: 24 days ago
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Predictive_Maintenance_using_Machine-Learning_Microsoft_Casestudy

Host: GitHub
URL: https://github.com/ashishpatel26/predictive_maintenance_using_machine-learning_microsoft_casestudy
Owner: ashishpatel26
Created: 2018-04-05T10:15:35.000Z (about 7 years ago)
Default Branch: master
Last Pushed: 2018-04-05T10:54:20.000Z (about 7 years ago)
Last Synced: 2025-05-07T03:38:22.083Z (about 1 month ago)
Topics: case-study, cortana-intelligence-gallery, learning, machine, maintenance, microsoft-cortana, predictive, predictive-maintenance
Language: Jupyter Notebook
Size: 30.6 MB
Stars: 121
Watchers: 3
Forks: 92
Open Issues: 3
Metadata Files:
- Readme: Readme.md

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README

# Problem Description

A major problem faced by businesses in asset-heavy industries such as manufacturing is the significant costs that are associated with delays in the production process due to mechanical problems. Most of these businesses are interested in predicting these problems in advance so that they can proactively prevent the problems before they occur which will reduce the costly impact caused by downtime. Please refer to the playbook for predictive maintenance for a detailed explanation of common use cases in predictive maintenance and modelling approaches.

In this notebook, we follow the ideas from the playbook referenced above and aim to provide the steps of implementing a predictive model for a scenario which is based on a synthesis of multiple real-world business problems. This example brings together common data elements observed among many predictive maintenance use cases and the data itself is created by data simulation methods.

The business problem for this example is about predicting problems caused by component failures such that the question "What is the probability that a machine will fail in the near future due to a failure of a certain component?" can be answered. The problem is formatted as a multi-class classification problem and a machine learning algorithm is used to create the predictive model that learns from historical data collected from machines. In the following sections, we go through the steps of implementing such a model which are feature engineering, label construction, training and evaluation. First, we start by explaining the data sources in the next section.
# Data Sources

Common data sources for predictive maintenance problems are :

* **Failure history:** The failure history of a machine or component within the machine.
* **Maintenance history:** The repair history of a machine, e.g. error codes, previous maintenance activities or component replacements.
* **Machine conditions and usage:** The operating conditions of a machine e.g. data collected from sensors.
* **Machine features:** The features of a machine, e.g. engine size, make and model, location.
* **Operator features:** The features of the operator, e.g. gender, past experience
The data for this example comes from 4 different sources which are real-time telemetry data collected from machines, error messages, historical maintenance records that include failures and machine information such as type and age.

```python
import pandas as pd

telemetry = pd.read_csv('PdM_telemetry.csv')
errors = pd.read_csv('PdM_errors.csv')
maint = pd.read_csv('PdM_maint.csv')
failures = pd.read_csv('PdM_failures.csv')
machines = pd.read_csv('PdM_machines.csv')
```

```python
# format datetime field which comes in as string
telemetry['datetime'] = pd.to_datetime(telemetry['datetime'], format="%Y-%m-%d %H:%M:%S")

print("Total number of telemetry records: %d" % len(telemetry.index))
print(telemetry.head())
telemetry.describe()
```

Total number of telemetry records: 876100
datetime machineID volt rotate pressure \
0 2015-01-01 06:00:00 1 176.217853 418.504078 113.077935
1 2015-01-01 07:00:00 1 162.879223 402.747490 95.460525
2 2015-01-01 08:00:00 1 170.989902 527.349825 75.237905
3 2015-01-01 09:00:00 1 162.462833 346.149335 109.248561
4 2015-01-01 10:00:00 1 157.610021 435.376873 111.886648

vibration
0 45.087686
1 43.413973
2 34.178847
3 41.122144
4 25.990511

machineID
volt
rotate
pressure
vibration

count
876100.000000
876100.000000
876100.000000
876100.000000
876100.000000

mean
50.500000
170.777736
446.605119
100.858668
40.385007

std
28.866087
15.509114
52.673886
11.048679
5.370361

min
1.000000
97.333604
138.432075
51.237106
14.877054

25%
25.750000
160.304927
412.305714
93.498181
36.777299

50%
50.500000
170.607338
447.558150
100.425559
40.237247

75%
75.250000
181.004493
482.176600
107.555231
43.784938

max
100.000000
255.124717
695.020984
185.951998
76.791072

#### **Telemetry**
The first data source is the telemetry time-series data which consists of **voltage, rotation, pressure, and vibration** measurements collected from 100 machines in **real time averaged over every hour collected during the year 2015**. Below, we display the first 10 records in the dataset. A summary of the whole dataset is also provided.

```python
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns

plot_df = telemetry.loc[(telemetry['machineID'] == 1) &
(telemetry['datetime'] > pd.to_datetime('2015-01-01')) &
(telemetry['datetime']

![png](output_4_1.png)

#### **Errors**
The second major data source is the error logs. These are **non-breaking errors thrown while the machine is still operational and do not constitute as failures.** The **error date and times** are rounded to the closest hour since the telemetry data is collected at an hourly rate.

```python
# format of datetime field which comes in as string
errors['datetime'] = pd.to_datetime(errors['datetime'],format = '%Y-%m-%d %H:%M:%S')
errors['errorID'] = errors['errorID'].astype('category')
print("Total Number of error records: %d" %len(errors.index))
errors.head()
```

Total Number of error records: 3919

datetime
machineID
errorID

0
2015-01-03 07:00:00
1
error1

1
2015-01-03 20:00:00
1
error3

2
2015-01-04 06:00:00
1
error5

3
2015-01-10 15:00:00
1
error4

4
2015-01-22 10:00:00
1
error4

```python
sns.set_style("darkgrid")
plt.figure(figsize=(20, 8))
errors['errorID'].value_counts().plot(kind='bar')
plt.ylabel('Count')
errors['errorID'].value_counts()
```

error1 1010
error2 988
error3 838
error4 727
error5 356
Name: errorID, dtype: int64

![png](output_7_1.png)

#### **Maintenance**
These are the **scheduled and unscheduled** maintenance records which correspond to both **regular inspection of components as well as failures.** A **record is generated if a component is replaced during the scheduled inspection or replaced due to a breakdown.** The **records that are created due to breakdowns will be called failures** which is explained in the later sections. Maintenance data has both 2014 and 2015 records.

```python
maint['datetime'] = pd.to_datetime(maint['datetime'], format='%Y-%m-%d %H:%M:%S')
maint['comp'] = maint['comp'].astype('category')
print("Total Number of maintenance Records: %d" %len(maint.index))
maint.head()
```

Total Number of maintenance Records: 3286

datetime
machineID
comp

0
2014-06-01 06:00:00
1
comp2

1
2014-07-16 06:00:00
1
comp4

2
2014-07-31 06:00:00
1
comp3

3
2014-12-13 06:00:00
1
comp1

4
2015-01-05 06:00:00
1
comp4

```python
sns.set_style("darkgrid")
plt.figure(figsize=(10, 4))
maint['comp'].value_counts().plot(kind='bar')
plt.ylabel('Count')
maint['comp'].value_counts()
```

comp2 863
comp4 811
comp3 808
comp1 804
Name: comp, dtype: int64

![png](output_10_1.png)

#### **Machines**
This data set includes some information about the machines: model type and age (years in service).

```python
machines['model'] = machines['model'].astype('category')

print("Total number of machines: %d" % len(machines.index))
machines.head()
```

Total number of machines: 100

machineID
model
age

0
1
model3
18

1
2
model4
7

2
3
model3
8

3
4
model3
7

4
5
model3
2

```python
sns.set_style("darkgrid")
plt.figure(figsize=(15, 6))
_, bins, _ = plt.hist([machines.loc[machines['model'] == 'model1', 'age'],
machines.loc[machines['model'] == 'model2', 'age'],
machines.loc[machines['model'] == 'model3', 'age'],
machines.loc[machines['model'] == 'model4', 'age']],
20, stacked=True, label=['model1', 'model2', 'model3', 'model4'])
plt.xlabel('Age (yrs)')
plt.ylabel('Count')
plt.legend()
```

![png](output_13_1.png)

#### **Failures**
These are the records of component replacements **due to failures.** Each record has a **date and time, machine ID, and failed component type.**

```python
# format datetime field which comes in as string
failures['datetime'] = pd.to_datetime(failures['datetime'], format="%Y-%m-%d %H:%M:%S")
failures['failure'] = failures['failure'].astype('category')

print("Total number of failures: %d" % len(failures.index))
failures.head()
```

Total number of failures: 761

datetime
machineID
failure

0
2015-01-05 06:00:00
1
comp4

1
2015-03-06 06:00:00
1
comp1

2
2015-04-20 06:00:00
1
comp2

3
2015-06-19 06:00:00
1
comp4

4
2015-09-02 06:00:00
1
comp4

```python
sns.set_style("darkgrid")
plt.figure(figsize=(15, 4))
failures['failure'].value_counts().plot(kind='bar')
plt.ylabel('Count')
failures['failure'].value_counts()
```

comp2 259
comp1 192
comp4 179
comp3 131
Name: failure, dtype: int64

![png](output_16_1.png)

## Feature Engineering
The first step in predictive maintenance applications is feature engineering which requires bringing the different data sources together to create features that best describe a machines's health condition at a given point in time. In the next sections, several feature engineering methods are used to create features based on the properties of each data source.

### Lag Features from Telemetry
Telemetry data almost always comes with time-stamps which makes it suitable for calculating lagging features. A common method is to pick a window size for the lag features to be created and compute rolling aggregate measures such as mean, standard deviation, minimum, maximum, etc. to represent the short term history of the telemetry over the lag window. In the following, rolling mean and standard deviation of the telemetry data over the last 3 hour lag window is calculated for every 3 hours.

```python
# Calculate mean values for telemetry features
temp = []
fields = ['volt', 'rotate', 'pressure', 'vibration']
for col in fields:
temp.append(pd.pivot_table(telemetry,
index='datetime',
columns='machineID',
values=col).resample('3H', closed='left', label='right', how='mean').unstack())
telemetry_mean_3h = pd.concat(temp, axis=1)
telemetry_mean_3h.columns = [i + 'mean_3h' for i in fields]
telemetry_mean_3h.reset_index(inplace=True)
```

C:\Program Files\Microsoft\ML Server\PYTHON_SERVER\lib\site-packages\ipykernel_launcher.py:8: FutureWarning: how in .resample() is deprecated
the new syntax is .resample(...).mean()

# repeat for standard deviation
temp = []
for col in fields:
temp.append(pd.pivot_table(telemetry,
index='datetime',
columns='machineID',
values=col).resample('3H', closed='left', label='right', how='std').unstack())
telemetry_sd_3h = pd.concat(temp, axis=1)
telemetry_sd_3h.columns = [i + 'sd_3h' for i in fields]
telemetry_sd_3h.reset_index(inplace=True)

telemetry_mean_3h.head()
```

C:\Program Files\Microsoft\ML Server\PYTHON_SERVER\lib\site-packages\ipykernel_launcher.py:8: FutureWarning: how in .resample() is deprecated
the new syntax is .resample(...).mean()

C:\Program Files\Microsoft\ML Server\PYTHON_SERVER\lib\site-packages\ipykernel_launcher.py:19: FutureWarning: how in .resample() is deprecated
the new syntax is .resample(...).std()

machineID
datetime
voltmean_3h
rotatemean_3h
pressuremean_3h
vibrationmean_3h

0
1
2015-01-01 09:00:00
170.028993
449.533798
94.592122
40.893502

1
1
2015-01-01 12:00:00
164.192565
403.949857
105.687417
34.255891

2
1
2015-01-01 15:00:00
168.134445
435.781707
107.793709
41.239405

3
1
2015-01-01 18:00:00
165.514453
430.472823
101.703289
40.373739

4
1
2015-01-01 21:00:00
168.809347
437.111120
90.911060
41.738542

For capturing a longer term effect, 24 hour lag features are also calculated as below.

```python
temp = []
fields = ['volt', 'rotate', 'pressure', 'vibration']
for col in fields:
temp.append(pd.rolling_mean(pd.pivot_table(telemetry,
index='datetime',
columns='machineID',
values=col), window=24).resample('3H',
closed='left',
label='right',
how='first').unstack())
telemetry_mean_24h = pd.concat(temp, axis=1)
telemetry_mean_24h.columns = [i + 'mean_24h' for i in fields]
telemetry_mean_24h.reset_index(inplace=True)
telemetry_mean_24h = telemetry_mean_24h.loc[-telemetry_mean_24h['voltmean_24h'].isnull()]

# repeat for standard deviation
temp = []
fields = ['volt', 'rotate', 'pressure', 'vibration']
for col in fields:
temp.append(pd.rolling_std(pd.pivot_table(telemetry,
index='datetime',
columns='machineID',
values=col), window=24).resample('3H',
closed='left',
label='right',
how='first').unstack())
telemetry_sd_24h = pd.concat(temp, axis=1)
telemetry_sd_24h.columns = [i + 'sd_24h' for i in fields]
telemetry_sd_24h = telemetry_sd_24h.loc[-telemetry_sd_24h['voltsd_24h'].isnull()]
telemetry_sd_24h.reset_index(inplace=True)

# Notice that a 24h rolling average is not available at the earliest timepoints
telemetry_mean_24h.head(10)
```

C:\Program Files\Microsoft\ML Server\PYTHON_SERVER\lib\site-packages\ipykernel_launcher.py:7: FutureWarning: pd.rolling_mean is deprecated for DataFrame and will be removed in a future version, replace with
DataFrame.rolling(window=24,center=False).mean()
import sys
C:\Program Files\Microsoft\ML Server\PYTHON_SERVER\lib\site-packages\ipykernel_launcher.py:10: FutureWarning: how in .resample() is deprecated
the new syntax is .resample(...).first()
# Remove the CWD from sys.path while we load stuff.
C:\Program Files\Microsoft\ML Server\PYTHON_SERVER\lib\site-packages\ipykernel_launcher.py:23: FutureWarning: pd.rolling_std is deprecated for DataFrame and will be removed in a future version, replace with
DataFrame.rolling(window=24,center=False).std()
C:\Program Files\Microsoft\ML Server\PYTHON_SERVER\lib\site-packages\ipykernel_launcher.py:26: FutureWarning: how in .resample() is deprecated
the new syntax is .resample(...).first()

machineID
datetime
voltmean_24h
rotatemean_24h
pressuremean_24h
vibrationmean_24h

7
1
2015-01-02 06:00:00
169.733809
445.179865
96.797113
40.385160

8
1
2015-01-02 09:00:00
170.614862
446.364859
96.849785
39.736826

9
1
2015-01-02 12:00:00
169.893965
447.009407
97.715600
39.498374

10
1
2015-01-02 15:00:00
171.243444
444.233563
96.666060
40.229370

11
1
2015-01-02 18:00:00
170.792486
448.440437
95.766838
40.055214

12
1
2015-01-02 21:00:00
170.556674
452.267095
98.065860
40.033247

13
1
2015-01-03 00:00:00
168.460525
451.031783
99.273286
38.903462

14
1
2015-01-03 03:00:00
169.772951
447.502464
99.005946
39.389725

15
1
2015-01-03 06:00:00
170.900562
453.864597
100.877342
38.696225

16
1
2015-01-03 09:00:00
169.533156
454.785072
100.050567
39.449734

Next, the columns of the feature datasets created earlier are merged to create the final feature set from telemetry.

```python
# merge columns of feature sets created earlier
telemetry_feat = pd.concat([telemetry_mean_3h,
telemetry_sd_3h.ix[:, 2:6],
telemetry_mean_24h.ix[:, 2:6],
telemetry_sd_24h.ix[:, 2:6]], axis=1).dropna()
telemetry_feat.describe()
```

machineID
voltmean_3h
rotatemean_3h
pressuremean_3h
vibrationmean_3h
voltsd_3h
rotatesd_3h
pressuresd_3h
vibrationsd_3h
voltmean_24h
rotatemean_24h
pressuremean_24h
vibrationmean_24h
voltsd_24h
rotatesd_24h
pressuresd_24h
vibrationsd_24h

count
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000

mean
50.380935
170.774427
446.609386
100.858340
40.383609
13.300173
44.453951
8.885780
4.440575
170.775661
446.609874
100.857574
40.383881
14.919452
49.950788
10.046380
5.002089

std
28.798424
9.498824
33.119738
7.411701
3.475512
6.966389
23.214291
4.656364
2.319989
4.720237
18.070458
4.737293
2.058059
2.261097
7.684305
1.713206
0.799599

min
1.000000
125.532506
211.811184
72.118639
26.569635
0.025509
0.078991
0.027417
0.015278
155.812721
266.010419
91.057429
35.060087
6.380619
18.385248
4.145308
2.144863

25%
25.000000
164.447794
427.564793
96.239534
38.147458
8.028675
26.906319
5.369959
2.684556
168.072275
441.542561
98.669734
39.354077
13.359069
44.669022
8.924165
4.460675

50%
50.000000
170.432407
448.380260
100.235357
40.145874
12.495542
41.793798
8.345801
4.173704
170.212704
449.206885
100.099533
40.072618
14.854186
49.617459
9.921332
4.958793

75%
75.000000
176.610017
468.443933
104.406534
42.226898
17.688520
59.092354
11.789358
5.898512
172.462228
456.366349
101.613047
40.833112
16.395372
54.826993
10.980250
5.484430

max
100.000000
241.420717
586.682904
162.309656
69.311324
58.444332
179.903039
35.659369
18.305595
220.782618
499.096975
152.310351
61.932124
27.664538
103.819404
28.654103
12.325783

```python
telemetry_feat.head()
```

### Lag Features from Errors
Like telemetry data, errors come with timestamps. An important difference is that the **error IDs are categorical values** and **should not be averaged over time intervals like the telemetry measurements.** Instead, we count the number of errors of each type in a **lagging window. We begin by reformatting the error data** to have one entry per machine per time at which at least one error occurred:

```python
errors
```

datetime
machineID
errorID

0
2015-01-03 07:00:00
1
error1

1
2015-01-03 20:00:00
1
error3

2
2015-01-04 06:00:00
1
error5

3
2015-01-10 15:00:00
1
error4

4
2015-01-22 10:00:00
1
error4

5
2015-01-25 15:00:00
1
error4

6
2015-01-27 04:00:00
1
error1

7
2015-03-03 22:00:00
1
error2

8
2015-03-05 06:00:00
1
error1

9
2015-03-20 18:00:00
1
error1

10
2015-03-26 01:00:00
1
error2

11
2015-03-31 23:00:00
1
error1

12
2015-04-19 06:00:00
1
error2

13
2015-04-19 06:00:00
1
error3

14
2015-04-29 19:00:00
1
error4

15
2015-05-04 23:00:00
1
error2

16
2015-05-12 09:00:00
1
error1

17
2015-05-21 07:00:00
1
error4

18
2015-05-24 02:00:00
1
error3

19
2015-05-25 05:00:00
1
error1

20
2015-06-09 06:00:00
1
error3

21
2015-06-18 06:00:00
1
error5

22
2015-06-23 10:00:00
1
error3

23
2015-08-23 19:00:00
1
error1

24
2015-08-30 01:00:00
1
error3

25
2015-09-01 06:00:00
1
error5

26
2015-09-13 17:00:00
1
error2

27
2015-09-15 06:00:00
1
error1

28
2015-10-01 23:00:00
1
error1

29
2015-10-15 05:00:00
1
error1

...
...
...
...

3889
2015-01-16 00:00:00
100
error4

3890
2015-02-01 10:00:00
100
error1

3891
2015-02-11 06:00:00
100
error1

3892
2015-02-12 21:00:00
100
error1

3893
2015-03-08 15:00:00
100
error1

3894
2015-04-27 04:00:00
100
error4

3895
2015-04-27 22:00:00
100
error5

3896
2015-05-16 23:00:00
100
error2

3897
2015-05-17 13:00:00
100
error2

3898
2015-05-22 02:00:00
100
error3

3899
2015-07-05 16:00:00
100
error3

3900
2015-07-19 01:00:00
100
error2

3901
2015-08-14 16:00:00
100
error4

3902
2015-08-30 15:00:00
100
error4

3903
2015-09-09 06:00:00
100
error1

3904
2015-09-14 23:00:00
100
error3

3905
2015-10-03 05:00:00
100
error3

3906
2015-10-09 07:00:00
100
error1

3907
2015-10-17 02:00:00
100
error3

3908
2015-10-17 12:00:00
100
error1

3909
2015-10-24 23:00:00
100
error1

3910
2015-10-27 21:00:00
100
error2

3911
2015-11-05 02:00:00
100
error3

3912
2015-11-07 17:00:00
100
error1

3913
2015-11-12 01:00:00
100
error1

3914
2015-11-21 08:00:00
100
error2

3915
2015-12-04 02:00:00
100
error1

3916
2015-12-08 06:00:00
100
error2

3917
2015-12-08 06:00:00
100
error3

3918
2015-12-22 03:00:00
100
error3

3919 rows × 3 columns

```python
# create a column for each error type
error_count = pd.get_dummies(errors.set_index('datetime')).reset_index()
error_count
error_count.columns = ['datetime', 'machineID', 'error1', 'error2', 'error3', 'error4', 'error5']
error_count.head(13)
```

datetime
machineID
error1
error2
error3
error4
error5

0
2015-01-03 07:00:00
1
1
0
0
0
0

1
2015-01-03 20:00:00
1
0
0
1
0
0

2
2015-01-04 06:00:00
1
0
0
0
0
1

3
2015-01-10 15:00:00
1
0
0
0
1
0

4
2015-01-22 10:00:00
1
0
0
0
1
0

5
2015-01-25 15:00:00
1
0
0
0
1
0

6
2015-01-27 04:00:00
1
1
0
0
0
0

7
2015-03-03 22:00:00
1
0
1
0
0
0

8
2015-03-05 06:00:00
1
1
0
0
0
0

9
2015-03-20 18:00:00
1
1
0
0
0
0

10
2015-03-26 01:00:00
1
0
1
0
0
0

11
2015-03-31 23:00:00
1
1
0
0
0
0

12
2015-04-19 06:00:00
1
0
1
0
0
0

```python
# combine errors for a given machine in a given hour
error_count = error_count.groupby(['machineID','datetime']).sum().reset_index()
error_count.head(13)
```

machineID
datetime
error1
error2
error3
error4
error5

0
1
2015-01-03 07:00:00
1
0
0
0
0

1
1
2015-01-03 20:00:00
0
0
1
0
0

2
1
2015-01-04 06:00:00
0
0
0
0
1

3
1
2015-01-10 15:00:00
0
0
0
1
0

4
1
2015-01-22 10:00:00
0
0
0
1
0

5
1
2015-01-25 15:00:00
0
0
0
1
0

6
1
2015-01-27 04:00:00
1
0
0
0
0

7
1
2015-03-03 22:00:00
0
1
0
0
0

8
1
2015-03-05 06:00:00
1
0
0
0
0

9
1
2015-03-20 18:00:00
1
0
0
0
0

10
1
2015-03-26 01:00:00
0
1
0
0
0

11
1
2015-03-31 23:00:00
1
0
0
0
0

12
1
2015-04-19 06:00:00
0
1
1
0
0

```python
error_count = telemetry[['datetime', 'machineID']].merge(error_count, on=['machineID', 'datetime'], how='left').fillna(0.0)
error_count.describe()
```

machineID
error1
error2
error3
error4
error5

count
876100.000000
876100.000000
876100.000000
876100.000000
876100.000000
876100.000000

mean
50.500000
0.001153
0.001128
0.000957
0.000830
0.000406

std
28.866087
0.033934
0.033563
0.030913
0.028795
0.020154

min
1.000000
0.000000
0.000000
0.000000
0.000000
0.000000

25%
25.750000
0.000000
0.000000
0.000000
0.000000
0.000000

50%
50.500000
0.000000
0.000000
0.000000
0.000000
0.000000

75%
75.250000
0.000000
0.000000
0.000000
0.000000
0.000000

max
100.000000
1.000000
1.000000
1.000000
1.000000
1.000000

Finally, we can compute the total number of errors of each type over the last 24 hours, for timepoints taken every three hours:

```python
temp = []
fields = ['error%d' % i for i in range(1,6)]
for col in fields:
temp.append(pd.rolling_sum(pd.pivot_table(error_count,
index='datetime',
columns='machineID',
values=col), window=24).resample('3H',
closed='left',
label='right',
how='first').unstack())
error_count = pd.concat(temp, axis=1)
error_count.columns = [i + 'count' for i in fields]
error_count.reset_index(inplace=True)
error_count = error_count.dropna()
error_count.describe()
```

C:\Program Files\Microsoft\ML Server\PYTHON_SERVER\lib\site-packages\ipykernel_launcher.py:7: FutureWarning: pd.rolling_sum is deprecated for DataFrame and will be removed in a future version, replace with
DataFrame.rolling(window=24,center=False).sum()
import sys
C:\Program Files\Microsoft\ML Server\PYTHON_SERVER\lib\site-packages\ipykernel_launcher.py:10: FutureWarning: how in .resample() is deprecated
the new syntax is .resample(...).first()
# Remove the CWD from sys.path while we load stuff.

machineID
error1count
error2count
error3count
error4count
error5count

count
291400.00000
291400.000000
291400.000000
291400.000000
291400.000000
291400.000000

mean
50.50000
0.027649
0.027069
0.022907
0.019904
0.009753

std
28.86612
0.166273
0.164429
0.151453
0.140820
0.098797

min
1.00000
0.000000
0.000000
0.000000
0.000000
0.000000

25%
25.75000
0.000000
0.000000
0.000000
0.000000
0.000000

50%
50.50000
0.000000
0.000000
0.000000
0.000000
0.000000

75%
75.25000
0.000000
0.000000
0.000000
0.000000
0.000000

max
100.00000
2.000000
2.000000
2.000000
2.000000
2.000000

```python
error_count.head()
```

machineID
datetime
error1count
error2count
error3count
error4count
error5count

7
1
2015-01-02 06:00:00
0.0
0.0
0.0
0.0
0.0

8
1
2015-01-02 09:00:00
0.0
0.0
0.0
0.0
0.0

9
1
2015-01-02 12:00:00
0.0
0.0
0.0
0.0
0.0

10
1
2015-01-02 15:00:00
0.0
0.0
0.0
0.0
0.0

11
1
2015-01-02 18:00:00
0.0
0.0
0.0
0.0
0.0

### Days Since Last Replacement from Maintenance
A crucial data set in this example is the maintenance records which contain the information of component replacement records. Possible features from this data set can be, for example, the number of replacements of each component in the last 3 months to incorporate the frequency of replacements. However, more relevent information would be to calculate how long it has been since a component is last replaced as that would be expected to correlate better with component failures since the longer a component is used, the more degradation should be expected.

As a side note, creating lagging features from maintenance data is not as straightforward as for telemetry and errors, so the features from this data are generated in a more custom way. This type of ad-hoc feature engineering is very common in predictive maintenance since domain knowledge plays a big role in understanding the predictors of a problem. In the following, the days since last component replacement are calculated for each component type as features from the maintenance data.

```python
import numpy as np

# create a column for each error type
comp_rep = pd.get_dummies(maint.set_index('datetime')).reset_index()
comp_rep.columns = ['datetime', 'machineID', 'comp1', 'comp2', 'comp3', 'comp4']

# combine repairs for a given machine in a given hour
comp_rep = comp_rep.groupby(['machineID', 'datetime']).sum().reset_index()

# add timepoints where no components were replaced
comp_rep = telemetry[['datetime', 'machineID']].merge(comp_rep,
on=['datetime', 'machineID'],
how='outer').fillna(0).sort_values(by=['machineID', 'datetime'])

components = ['comp1', 'comp2', 'comp3', 'comp4']
for comp in components:
# convert indicator to most recent date of component change
comp_rep.loc[comp_rep[comp] < 1, comp] = None
comp_rep.loc[-comp_rep[comp].isnull(), comp] = comp_rep.loc[-comp_rep[comp].isnull(), 'datetime']

# forward-fill the most-recent date of component change
comp_rep[comp] = comp_rep[comp].fillna(method='ffill')

# remove dates in 2014 (may have NaN or future component change dates)
comp_rep = comp_rep.loc[comp_rep['datetime'] > pd.to_datetime('2015-01-01')]

# replace dates of most recent component change with days since most recent component change
for comp in components:
comp_rep[comp] = (comp_rep['datetime'] - comp_rep[comp]) / np.timedelta64(1, 'D')

comp_rep.describe()
```

machineID
comp1
comp2
comp3
comp4

count
876100.000000
876100.000000
876100.000000
876100.000000
876100.000000

mean
50.500000
53.525185
51.540806
52.725962
53.834191

std
28.866087
62.491679
59.269254
58.873114
59.707978

min
1.000000
0.000000
0.000000
0.000000
0.000000

25%
25.750000
13.291667
12.125000
13.125000
13.000000

50%
50.500000
32.791667
29.666667
32.291667
32.500000

75%
75.250000
68.708333
66.541667
67.333333
70.458333

max
100.000000
491.958333
348.958333
370.958333
394.958333

```python
comp_rep.head()
```

datetime
machineID
comp1
comp2
comp3
comp4

0
2015-01-01 06:00:00
1
19.000000
214.000000
154.000000
169.000000

1
2015-01-01 07:00:00
1
19.041667
214.041667
154.041667
169.041667

2
2015-01-01 08:00:00
1
19.083333
214.083333
154.083333
169.083333

3
2015-01-01 09:00:00
1
19.125000
214.125000
154.125000
169.125000

4
2015-01-01 10:00:00
1
19.166667
214.166667
154.166667
169.166667

## Machine Features
The machine features can be used without further modification. These include descriptive information about the type of each machine and its age (number of years in service). If the age information had been recorded as a "first use date" for each machine, a transformation would have been necessary to turn those into a numeric values indicating the years in service.

Lastly, we merge all the feature data sets we created earlier to get the final feature matrix.

```python

```

```python
telemetry_feat
```

machineID
datetime
voltmean_3h
rotatemean_3h
pressuremean_3h
vibrationmean_3h
voltsd_3h
rotatesd_3h
pressuresd_3h
vibrationsd_3h
voltmean_24h
rotatemean_24h
pressuremean_24h
vibrationmean_24h
voltsd_24h
rotatesd_24h
pressuresd_24h
vibrationsd_24h

7
1
2015-01-02 06:00:00
180.133784
440.608320
94.137969
41.551544
21.322735
48.770512
2.135684
10.037208
169.733809
445.179865
96.797113
40.385160
15.726970
39.648116
11.904700
5.601191

8
1
2015-01-02 09:00:00
176.364293
439.349655
101.553209
36.105580
18.952210
51.329636
13.789279
6.737739
170.614862
446.364859
96.849785
39.736826
15.635083
41.828592
11.326412
5.583521

9
1
2015-01-02 12:00:00
160.384568
424.385316
99.598722
36.094637
13.047080
13.702496
9.988609
1.639962
169.893965
447.009407
97.715600
39.498374
13.995465
40.843882
11.036546
5.561553

10
1
2015-01-02 15:00:00
170.472461
442.933997
102.380586
40.483002
16.642354
56.290447
3.305739
8.854145
171.243444
444.233563
96.666060
40.229370
13.100364
43.409841
10.972862
6.068674

11
1
2015-01-02 18:00:00
163.263806
468.937558
102.726648
40.921802
17.424688
38.680380
9.105775
3.060781
170.792486
448.440437
95.766838
40.055214
13.808489
43.742304
10.988704
7.286129

12
1
2015-01-02 21:00:00
163.278466
446.493166
104.387585
38.068116
21.580492
41.380958
20.725597
6.932127
170.556674
452.267095
98.065860
40.033247
14.187985
40.676672
11.942227
8.723238

13
1
2015-01-03 00:00:00
172.191198
434.214692
93.747282
39.716482
16.369836
14.636041
18.817326
3.426997
168.460525
451.031783
99.273286
38.903462
13.707794
40.509184
10.141026
8.634082

14
1
2015-01-03 03:00:00
175.210027
504.845430
108.512153
37.763933
5.991921
16.062702
6.382608
3.449468
169.772951
447.502464
99.005946
39.389725
11.818603
44.468516
9.444955
8.332673

15
1
2015-01-03 06:00:00
181.690108
472.783187
93.395164
38.621099
11.514450
47.880443
2.177029
7.670520
170.900562
453.864597
100.877342
38.696225
12.069391
46.669661
8.609526
8.089348

16
1
2015-01-03 09:00:00
172.382935
505.141261
98.524373
49.965572
7.065150
56.849540
5.230039
2.687565
169.533156
454.785072
100.050567
39.449734
12.755234
44.016114
9.893704
7.013132

17
1
2015-01-03 12:00:00
174.303858
436.182686
94.092681
50.999589
19.017196
26.420163
7.661944
3.516734
170.866013
463.871291
99.360632
40.766639
12.848646
45.090576
9.846662
5.888262

18
1
2015-01-03 15:00:00
176.246348
451.646684
98.102389
59.198241
12.572504
31.574383
15.559351
6.562087
171.041651
463.701291
98.965877
42.396850
14.968351
37.088898
10.133452
5.702356

19
1
2015-01-03 18:00:00
158.433533
453.900213
98.878129
46.851925
5.136952
21.216569
11.400650
2.688559
171.244533
464.320613
98.853189
44.608814
17.058217
36.617908
9.867174
5.743753

20
1
2015-01-03 21:00:00
162.387954
454.140377
92.651129
54.261635
4.563331
57.747656
4.754203
5.118076
171.385039
459.937314
97.292157
45.284751
18.405763
35.819938
9.743769
5.246435

21
1
2015-01-04 00:00:00
174.243192
394.998095
99.829845
46.930738
6.268730
29.167663
10.564287
6.822855
171.880633
461.437128
96.786742
47.311018
18.249831
42.055638
10.961128
5.093464

22
1
2015-01-04 03:00:00
176.443361
459.528820
111.855296
55.296056
16.330285
20.602657
7.064583
4.651468
172.513202
456.429165
97.742700
48.416442
19.141287
37.018824
10.642956
4.618287

23
1
2015-01-04 06:00:00
186.092896
451.641253
107.989359
55.308074
13.489090
62.185045
5.118176
4.904365
172.686245
453.387589
99.304019
51.158654
18.887033
36.997459
11.042775
5.195423

24
1
2015-01-04 09:00:00
166.281848
453.787824
106.187582
51.990080
24.276228
23.621315
11.176731
3.394073
172.042428
450.418764
100.284484
52.153213
20.837993
34.051825
9.654971
5.066388

25
1
2015-01-04 12:00:00
175.412103
445.450581
100.887363
54.251534
34.918687
11.001625
10.580336
2.921501
171.219623
443.802134
102.358897
52.854420
21.298322
36.054002
9.885781
5.246894

26
1
2015-01-04 15:00:00
157.347716
451.882075
101.289380
48.602686
24.617739
28.950883
9.966729
2.356486
172.013443
444.882018
102.578580
52.789794
21.200183
38.544116
10.429692
7.192434

27
1
2015-01-04 18:00:00
176.450550
446.033068
84.521555
47.638836
8.071400
76.511343
2.636879
4.108621
170.176321
445.069594
102.359939
51.518719
18.814679
40.547527
11.133170
7.556313

28
1
2015-01-04 21:00:00
190.325814
422.692565
107.393234
49.552856
8.390777
7.176553
4.262645
7.598552
172.932248
444.618018
101.425508
52.135905
16.762469
49.373445
10.443534
8.545739

29
1
2015-01-05 00:00:00
169.985134
458.929418
91.494362
54.882021
9.451483
12.052752
3.685906
6.621183
175.121131
443.916392
102.130179
51.653294
17.435946
43.819375
10.830449
8.809530

30
1
2015-01-05 03:00:00
149.082619
412.180336
93.509785
54.386079
19.075952
30.715081
3.090266
6.530610
173.407255
446.265950
100.874614
52.529450
16.661364
47.266846
11.225440
9.068824

31
1
2015-01-05 06:00:00
185.782709
439.531288
99.413660
51.558082
14.495664
45.663743
4.289212
7.330397
170.757841
440.958228
98.716746
51.746749
17.863934
44.895080
10.675981
7.475304

32
1
2015-01-05 09:00:00
169.084809
463.433785
107.678774
41.710336
12.245544
61.759107
4.400233
9.750017
171.929104
443.448775
98.675590
51.780445
15.139300
45.766081
10.959268
6.855778

33
1
2015-01-05 12:00:00
165.518790
449.743255
110.377851
38.952082
23.170638
45.762142
14.009473
0.797364
170.908522
443.069042
98.830333
49.679550
13.985517
42.542001
11.050133
4.842842

34
1
2015-01-05 15:00:00
175.989642
419.863490
112.571146
41.514254
4.028327
20.148499
5.862629
9.702498
170.416326
443.555122
100.221328
48.481038
13.344630
39.327146
10.268539
4.884344

35
1
2015-01-05 18:00:00
188.576444
487.336742
88.967297
36.571052
8.278605
76.534023
11.892088
1.945849
173.315167
444.049581
101.633306
47.279992
15.793146
42.984028
10.006300
4.637101

36
1
2015-01-05 21:00:00
166.681364
481.685320
104.154110
38.662638
11.957697
25.052743
11.999161
4.804263
173.743459
446.505202
100.540356
45.527290
16.132288
40.754154
9.744855
4.591048

...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...

291370
100
2015-10-02 06:00:00
165.259415
432.364050
96.793097
38.697882
16.715588
9.197585
11.016730
9.167743
169.115085
459.202414
99.099044
39.342719
12.889019
60.409151
11.549081
5.671215

291371
100
2015-10-02 09:00:00
185.907346
465.062411
94.161434
36.156060
22.822289
64.351154
6.469484
1.656610
168.838507
455.101759
98.960206
38.277576
13.917591
56.810848
11.118412
6.061118

291372
100
2015-10-02 12:00:00
167.546991
448.203119
99.383591
39.659572
2.573507
84.299208
2.490792
2.252574
169.223690
463.630715
99.296474
38.406915
14.611939
56.534099
8.553177
5.893650

291373
100
2015-10-02 15:00:00
175.468904
441.861941
105.814802
38.788653
9.104554
48.615069
6.004070
3.244295
172.163049
458.787617
100.063674
38.458947
15.232866
49.321412
8.345687
5.292801

291374
100
2015-10-02 18:00:00
157.401371
459.332121
93.247465
42.236723
14.711827
45.268580
5.590642
2.204472
173.119397
456.196849
100.114215
39.063775
15.920072
48.742610
7.909495
5.249418

291375
100
2015-10-02 21:00:00
168.651510
430.056138
104.487324
35.735005
16.328969
45.108180
9.103806
6.093867
168.410263
448.519301
100.049480
39.083797
14.635941
50.313046
7.582133
5.108806

291376
100
2015-10-03 00:00:00
168.623762
497.504580
100.682235
40.610939
12.914771
25.775781
11.444951
3.359673
168.849711
450.330382
100.243957
38.469840
14.915283
50.148100
7.928488
5.518228

291377
100
2015-10-03 03:00:00
168.537058
441.837105
87.893111
40.076219
23.866338
36.817201
16.820180
0.482728
171.513651
452.462106
98.514174
38.626944
14.750503
44.620373
8.348839
5.182752

291378
100
2015-10-03 06:00:00
161.436752
401.579802
90.792431
35.624101
14.429283
85.801834
16.225371
1.396074
169.625319
451.508453
97.368816
38.762103
16.055332
49.218444
9.546008
5.020598

291379
100
2015-10-03 09:00:00
188.559785
491.929571
102.821662
40.034460
12.668164
41.768856
9.448383
8.454640
167.950194
453.659486
97.292065
38.635159
15.942467
59.763569
9.431896
4.476863

291380
100
2015-10-03 12:00:00
164.149847
466.463280
100.447025
40.694147
16.460088
31.589198
10.188202
5.086589
168.530246
448.103742
97.730594
39.228047
16.122100
57.394487
9.171658
4.866485

291381
100
2015-10-03 15:00:00
184.727094
487.140570
100.860907
36.430834
12.401664
57.508894
18.394116
7.153156
169.765458
458.759394
98.775532
38.935773
16.994700
55.665652
9.630112
4.896106

291382
100
2015-10-03 18:00:00
171.585447
479.021432
101.846824
49.115340
13.318878
40.471453
10.951704
0.649491
169.818254
460.880691
97.926823
39.295892
15.077105
56.097762
9.818266
4.919802

291383
100
2015-10-03 21:00:00
162.144446
404.865418
98.384468
35.389856
22.516178
36.216388
11.492089
7.269283
172.199254
459.599763
98.365107
39.964091
14.414241
59.222526
10.569736
4.693342

291384
100
2015-10-04 00:00:00
166.584930
437.980304
104.019479
43.766793
22.109109
65.256390
12.621841
1.793100
170.812061
453.681180
98.994157
40.013985
13.522301
61.197614
10.103349
4.286568

291385
100
2015-10-04 03:00:00
173.182209
452.585928
106.572235
40.534601
16.930726
38.788180
10.747137
6.510290
170.439828
455.036021
99.830401
40.129183
14.551122
65.430315
9.389132
4.484563

291386
100
2015-10-04 06:00:00
155.554082
464.175866
102.615428
36.003311
7.678204
24.248612
6.064152
5.007039
172.264492
453.800429
102.163329
40.050108
13.103400
62.190761
9.128160
4.502950

291387
100
2015-10-04 09:00:00
163.814555
433.614467
114.798438
36.454615
5.259901
40.947023
10.677648
8.252193
170.243198
455.333806
102.290708
40.197103
13.120654
57.910021
9.238228
4.803393

291388
100
2015-10-04 12:00:00
169.196188
403.488184
94.199431
39.189491
22.977467
27.176467
9.430194
13.841831
167.765844
451.355029
103.465520
40.252524
13.315211
59.466979
9.471171
4.442337

291389
100
2015-10-04 15:00:00
165.814250
446.765824
99.334107
44.464271
1.457549
58.086715
1.622380
3.173978
167.312650
439.435929
102.009695
40.435349
11.768963
60.646198
9.136786
5.149517

291390
100
2015-10-04 18:00:00
167.848340
438.393471
90.054937
40.301288
15.958412
40.168662
11.238292
3.633503
166.963446
438.276090
101.637723
40.172602
14.141910
58.372646
8.463179
5.221115

291391
100
2015-10-04 21:00:00
173.508300
439.917848
93.063793
38.750136
7.633479
44.399657
11.019912
4.952713
165.979125
435.138421
102.005617
39.497908
14.000620
59.820047
6.856021
5.392136

291392
100
2015-10-05 00:00:00
182.432617
497.264899
95.443869
40.594815
9.940475
77.558997
4.707020
3.106529
168.142646
447.915202
99.620102
39.635003
14.372707
59.563942
7.988174
5.256284

291393
100
2015-10-05 03:00:00
158.783988
438.405164
100.420803
40.153025
10.849108
72.556330
2.576581
4.504970
168.398872
448.148851
99.351099
39.518646
15.763140
57.682117
8.088214
5.301986

291394
100
2015-10-05 06:00:00
183.150826
426.209117
98.880399
34.418557
20.539063
29.605169
13.588936
7.168643
168.651040
446.075986
98.741443
39.840623
15.331755
60.839923
7.891711
5.269038

291395
100
2015-10-05 09:00:00
188.267556
407.256175
108.931184
36.553233
9.599915
40.722980
1.639521
5.724500
171.826650
441.278667
98.311919
39.196175
16.429023
62.147934
7.475540
5.448962

291396
100
2015-10-05 12:00:00
167.859576
465.992407
107.953155
42.708899
14.190347
92.277799
9.577243
0.735339
174.657123
444.147310
98.520388
38.820190
17.019808
64.730136
8.961444
5.833191

291397
100
2015-10-05 15:00:00
170.348099
434.234744
104.514343
38.607950
10.232598
49.524471
12.445345
2.596743
173.787879
448.842085
100.028549
39.375067
17.096392
64.718132
9.420879
5.738756

291398
100
2015-10-05 18:00:00
152.265370
459.557611
103.536524
40.718426
6.758667
27.051145
12.824247
2.752883
172.496791
442.086577
100.361794
38.943434
15.119775
65.929509
8.836617
6.139142

291399
100
2015-10-05 21:00:00
162.887965
481.415205
96.687092
37.162591
20.541773
55.057460
11.713728
3.539798
170.782713
448.188498
100.794970
38.980896
15.573014
61.859239
9.942610
6.191276

290601 rows × 18 columns

```python
final_feat = telemetry_feat.merge(error_count, on=['datetime', 'machineID'], how='left')
final_feat = final_feat.merge(comp_rep, on=['datetime', 'machineID'], how='left')
final_feat = final_feat.merge(machines, on=['machineID'], how='left')

print(final_feat.head())
final_feat.describe()
```

machineID datetime voltmean_3h rotatemean_3h pressuremean_3h \
0 1 2015-01-02 06:00:00 180.133784 440.608320 94.137969
1 1 2015-01-02 09:00:00 176.364293 439.349655 101.553209
2 1 2015-01-02 12:00:00 160.384568 424.385316 99.598722
3 1 2015-01-02 15:00:00 170.472461 442.933997 102.380586
4 1 2015-01-02 18:00:00 163.263806 468.937558 102.726648

vibrationmean_3h voltsd_3h rotatesd_3h pressuresd_3h vibrationsd_3h \
0 41.551544 21.322735 48.770512 2.135684 10.037208
1 36.105580 18.952210 51.329636 13.789279 6.737739
2 36.094637 13.047080 13.702496 9.988609 1.639962
3 40.483002 16.642354 56.290447 3.305739 8.854145
4 40.921802 17.424688 38.680380 9.105775 3.060781

... error2count error3count error4count error5count comp1 comp2 \
0 ... 0.0 0.0 0.0 0.0 20.000 215.000
1 ... 0.0 0.0 0.0 0.0 20.125 215.125
2 ... 0.0 0.0 0.0 0.0 20.250 215.250
3 ... 0.0 0.0 0.0 0.0 20.375 215.375
4 ... 0.0 0.0 0.0 0.0 20.500 215.500

comp3 comp4 model age
0 155.000 170.000 model3 18
1 155.125 170.125 model3 18
2 155.250 170.250 model3 18
3 155.375 170.375 model3 18
4 155.500 170.500 model3 18

[5 rows x 29 columns]

machineID
voltmean_3h
rotatemean_3h
pressuremean_3h
vibrationmean_3h
voltsd_3h
rotatesd_3h
pressuresd_3h
vibrationsd_3h
voltmean_24h
...
error1count
error2count
error3count
error4count
error5count
comp1
comp2
comp3
comp4
age

count
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
...
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000
290601.000000

mean
50.380935
170.774427
446.609386
100.858340
40.383609
13.300173
44.453951
8.885780
4.440575
170.775661
...
0.027560
0.027058
0.022846
0.019955
0.009780
53.382610
51.256589
52.536687
53.679601
11.345226

std
28.798424
9.498824
33.119738
7.411701
3.475512
6.966389
23.214291
4.656364
2.319989
4.720237
...
0.166026
0.164401
0.151266
0.140998
0.098931
62.478424
59.156008
58.822946
59.658975
5.826345

min
1.000000
125.532506
211.811184
72.118639
26.569635
0.025509
0.078991
0.027417
0.015278
155.812721
...
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000

25%
25.000000
164.447794
427.564793
96.239534
38.147458
8.028675
26.906319
5.369959
2.684556
168.072275
...
0.000000
0.000000
0.000000
0.000000
0.000000
13.250000
12.000000
13.000000
12.875000
7.000000

50%
50.000000
170.432407
448.380260
100.235357
40.145874
12.495542
41.793798
8.345801
4.173704
170.212704
...
0.000000
0.000000
0.000000
0.000000
0.000000
32.625000
29.500000
32.125000
32.375000
12.000000

75%
75.000000
176.610017
468.443933
104.406534
42.226898
17.688520
59.092354
11.789358
5.898512
172.462228
...
0.000000
0.000000
0.000000
0.000000
0.000000
68.500000
65.875000
67.125000
70.250000
16.000000

max
100.000000
241.420717
586.682904
162.309656
69.311324
58.444332
179.903039
35.659369
18.305595
220.782618
...
2.000000
2.000000
2.000000
2.000000
2.000000
491.875000
348.875000
370.875000
394.875000
20.000000

8 rows × 27 columns

# Label Construction
When using multi-class classification for predicting failure due to a problem, labelling is done by taking a time window prior to the failure of an asset and labelling the feature records that fall into that window as "about to fail due to a problem" while labelling all other records as "Â€Âœnormal." This time window should be picked according to the business case: in some situations it may be enough to predict failures hours in advance, while in others days or weeks may be needed to allow e.g. for arrival of replacement parts.

The prediction problem for this example scenerio is to estimate the probability that a machine will fail in the near future due to a failure of a certain component. More specifically, the goal is to compute the probability that a machine will fail in the next 24 hours due to a certain component failure (component 1, 2, 3, or 4). Below, a categorical failure feature is created to serve as the label. All records within a 24 hour window before a failure of component 1 have failure=comp1, and so on for components 2, 3, and 4; all records not within 24 hours of a component failure have failure=none.

```python
labeled_features = final_feat.merge(failures, on=['datetime', 'machineID'], how='left')
labeled_features = labeled_features.fillna(method='bfill', limit=7) # fill backward up to 24h
labeled_features = labeled_features.fillna('none')
labeled_features.head()
```

5 rows × 30 columns

Below is an example of records that are labeled as failure=comp4 in the failure column. Notice that the first 8 records all occur in the 24-hour window before the first recorded failure of component 4. The next 8 records are within the 24 hour window before another failure of component 4.

```python
labeled_features.loc[labeled_features['failure'] == 'comp4'][:16]
```

machineID
datetime
voltmean_3h
rotatemean_3h
pressuremean_3h
vibrationmean_3h
voltsd_3h
rotatesd_3h
pressuresd_3h
vibrationsd_3h
...
error3count
error4count
error5count
comp1
comp2
comp3
comp4
model
age
failure

17
1
2015-01-04 09:00:00
166.281848
453.787824
106.187582
51.990080
24.276228
23.621315
11.176731
3.394073
...
1.0
0.0
1.0
22.125
217.125
157.125
172.125
model3
18
comp4

18
1
2015-01-04 12:00:00
175.412103
445.450581
100.887363
54.251534
34.918687
11.001625
10.580336
2.921501
...
1.0
0.0
1.0
22.250
217.250
157.250
172.250
model3
18
comp4

19
1
2015-01-04 15:00:00
157.347716
451.882075
101.289380
48.602686
24.617739
28.950883
9.966729
2.356486
...
1.0
0.0
1.0
22.375
217.375
157.375
172.375
model3
18
comp4

20
1
2015-01-04 18:00:00
176.450550
446.033068
84.521555
47.638836
8.071400
76.511343
2.636879
4.108621
...
1.0
0.0
1.0
22.500
217.500
157.500
172.500
model3
18
comp4

21
1
2015-01-04 21:00:00
190.325814
422.692565
107.393234
49.552856
8.390777
7.176553
4.262645
7.598552
...
1.0
0.0
1.0
22.625
217.625
157.625
172.625
model3
18
comp4

22
1
2015-01-05 00:00:00
169.985134
458.929418
91.494362
54.882021
9.451483
12.052752
3.685906
6.621183
...
0.0
0.0
1.0
22.750
217.750
157.750
172.750
model3
18
comp4

23
1
2015-01-05 03:00:00
149.082619
412.180336
93.509785
54.386079
19.075952
30.715081
3.090266
6.530610
...
0.0
0.0
1.0
22.875
217.875
157.875
172.875
model3
18
comp4

24
1
2015-01-05 06:00:00
185.782709
439.531288
99.413660
51.558082
14.495664
45.663743
4.289212
7.330397
...
0.0
0.0
1.0
0.000
218.000
158.000
0.000
model3
18
comp4

1337
1
2015-06-18 09:00:00
169.324639
453.923471
101.313249
53.092274
28.155693
42.557599
7.688674
2.488851
...
0.0
0.0
1.0
89.125
29.125
14.125
134.125
model3
18
comp4

1338
1
2015-06-18 12:00:00
190.691297
441.577271
97.192512
44.025425
6.296827
47.271008
7.577957
4.648336
...
0.0
0.0
1.0
89.250
29.250
14.250
134.250
model3
18
comp4

1339
1
2015-06-18 15:00:00
163.602957
433.781185
93.173047
43.051368
18.147449
30.242516
10.870615
2.740922
...
0.0
0.0
1.0
89.375
29.375
14.375
134.375
model3
18
comp4

1340
1
2015-06-18 18:00:00
178.587550
427.300815
118.643186
50.958609
2.229649
17.168087
15.714144
5.669003
...
0.0
0.0
1.0
89.500
29.500
14.500
134.500
model3
18
comp4

1341
1
2015-06-18 21:00:00
158.851795
520.113831
101.974559
44.156671
14.554854
77.101968
4.788908
5.468742
...
0.0
0.0
1.0
89.625
29.625
14.625
134.625
model3
18
comp4

1342
1
2015-06-19 00:00:00
162.191516
453.545010
101.521779
49.136659
12.553190
33.332139
5.983913
1.893250
...
0.0
0.0
1.0
89.750
29.750
14.750
134.750
model3
18
comp4

1343
1
2015-06-19 03:00:00
166.732741
485.036994
100.284288
44.587560
11.099161
57.308864
3.052958
3.062215
...
0.0
0.0
1.0
89.875
29.875
14.875
134.875
model3
18
comp4

1344
1
2015-06-19 06:00:00
172.059069
463.242610
96.905050
53.701413
14.757880
55.874000
3.204981
2.329615
...
0.0
0.0
1.0
0.000
30.000
15.000
0.000
model3
18
comp4

16 rows × 30 columns

# Modelling
After the feature engineering and labelling steps, either Azure Machine Learning Studio or this notebook can be used to create a predictive model. The recommend Azure Machine Learning Studio experiment can be found in the Cortana Intelligence Gallery: Predictive Maintenance Modelling Guide Experiment. Below, we describe the modelling process and provide an example Python model.

# Training, Validation and Testing
When working with time-stamped data as in this example, record partitioning into training, validation, and test sets should be performed carefully to prevent overestimating the performance of the models. In predictive maintenance, the features are usually generated using lagging aggregates: records in the same time window will likely have identical labels and similar feature values. These correlations can give a model an "unfair advantage" when predicting on a test set record that shares its time window with a training set record. We therefore partition records into training, validation, and test sets in large chunks, to minimize the number of time intervals shared between them.

Predictive models have no advance knowledge of future chronological trends: in practice, such trends are likely to exist and to adversely impact the model's performance. To obtain an accurate assessment of a predictive model's performance, we recommend training on older records and validating/testing using newer records.

For both of these reasons, a time-dependent record splitting strategy is an excellent choice for predictive maintenace models. The split is effected by choosing a point in time based on the desired size of the training and test sets: all records before the timepoint are used for training the model, and all remaining records are used for testing. (If desired, the timeline could be further divided to create validation sets for parameter selection.) To prevent any records in the training set from sharing time windows with the records in the test set, we remove any records at the boundary -- in this case, by ignoring 24 hours' worth of data prior to the timepoint.

```python
from sklearn.ensemble import GradientBoostingClassifier

# make test and training splits
threshold_dates = [[pd.to_datetime('2015-07-31 01:00:00'), pd.to_datetime('2015-08-01 01:00:00')],
[pd.to_datetime('2015-08-31 01:00:00'), pd.to_datetime('2015-09-01 01:00:00')],
[pd.to_datetime('2015-09-30 01:00:00'), pd.to_datetime('2015-10-01 01:00:00')]]

test_results = []
models = []
for last_train_date, first_test_date in threshold_dates:
# split out training and test data
train_y = labeled_features.loc[labeled_features['datetime'] < last_train_date, 'failure']
train_X = pd.get_dummies(labeled_features.loc[labeled_features['datetime'] < last_train_date].drop(['datetime',
'machineID',
'failure'], 1))
test_X = pd.get_dummies(labeled_features.loc[labeled_features['datetime'] > first_test_date].drop(['datetime',
'machineID',
'failure'], 1))
# train and predict using the model, storing results for later
my_model = GradientBoostingClassifier(random_state=42)
my_model.fit(train_X, train_y)
test_result = pd.DataFrame(labeled_features.loc[labeled_features['datetime'] > first_test_date])
test_result['predicted_failure'] = my_model.predict(test_X)
test_results.append(test_result)
models.append(my_model)
```

```python
sns.set_style("darkgrid")
plt.figure(figsize=(10, 6))
labels, importances = zip(*sorted(zip(test_X.columns, models[0].feature_importances_), reverse=True, key=lambda x: x[1]))
plt.xticks(range(len(labels)), labels)
_, labels = plt.xticks()
plt.setp(labels, rotation=90)
plt.bar(range(len(importances)), importances)
plt.ylabel('Importance')
```

![png](output_47_1.png)

# Evaluation
In predictive maintenance, machine failures are usually rare occurrences in the lifetime of the assets compared to normal operation. This causes an imbalance in the label distribution which usually causes poor performance as algorithms tend to classify majority class examples better at the expense of minority class examples as the total misclassification error is much improved when majority class is labeled correctly. This causes low recall rates although accuracy can be high and becomes a larger problem when the cost of false alarms to the business is very high. To help with this problem, sampling techniques such as oversampling of the minority examples are usually used along with more sophisticated techniques which are not covered in this notebook.

```python
sns.set_style("darkgrid")
plt.figure(figsize=(8, 4))
labeled_features['failure'].value_counts().plot(kind='bar')
plt.xlabel('Component failing')
plt.ylabel('Count')
```

![png](output_49_1.png)

Also, due to the class imbalance problem, it is important to look at evaluation metrics other than accuracy alone and compare those metrics to the baseline metrics which are computed when random chance is used to make predictions rather than a machine learning model. The comparison will bring out the value and benefits of using a machine learning model better.

In the following, we use an evaluation function that computes many important evaluation metrics along with baseline metrics for classification problems. For a detailed explanation of the metrics, please refer to the scikit-learn documentation and a companion blog post (with examples in R, not Python),

```python
from sklearn.metrics import confusion_matrix, recall_score, accuracy_score, precision_score

def Evaluate(predicted, actual, labels):
output_labels = []
output = []

# Calculate and display confusion matrix
cm = confusion_matrix(actual, predicted, labels=labels)
print('Confusion matrix\n- x-axis is true labels (none, comp1, etc.)\n- y-axis is predicted labels')
print(cm)

# Calculate precision, recall, and F1 score
accuracy = np.array([float(np.trace(cm)) / np.sum(cm)] * len(labels))
precision = precision_score(actual, predicted, average=None, labels=labels)
recall = recall_score(actual, predicted, average=None, labels=labels)
f1 = 2 * precision * recall / (precision + recall)
output.extend([accuracy.tolist(), precision.tolist(), recall.tolist(), f1.tolist()])
output_labels.extend(['accuracy', 'precision', 'recall', 'F1'])

# Calculate the macro versions of these metrics
output.extend([[np.mean(precision)] * len(labels),
[np.mean(recall)] * len(labels),
[np.mean(f1)] * len(labels)])
output_labels.extend(['macro precision', 'macro recall', 'macro F1'])

# Find the one-vs.-all confusion matrix
cm_row_sums = cm.sum(axis = 1)
cm_col_sums = cm.sum(axis = 0)
s = np.zeros((2, 2))
for i in range(len(labels)):
v = np.array([[cm[i, i],
cm_row_sums[i] - cm[i, i]],
[cm_col_sums[i] - cm[i, i],
np.sum(cm) + cm[i, i] - (cm_row_sums[i] + cm_col_sums[i])]])
s += v
s_row_sums = s.sum(axis = 1)

# Add average accuracy and micro-averaged precision/recall/F1
avg_accuracy = [np.trace(s) / np.sum(s)] * len(labels)
micro_prf = [float(s[0,0]) / s_row_sums[0]] * len(labels)
output.extend([avg_accuracy, micro_prf])
output_labels.extend(['average accuracy',
'micro-averaged precision/recall/F1'])

# Compute metrics for the majority classifier
mc_index = np.where(cm_row_sums == np.max(cm_row_sums))[0][0]
cm_row_dist = cm_row_sums / float(np.sum(cm))
mc_accuracy = 0 * cm_row_dist; mc_accuracy[mc_index] = cm_row_dist[mc_index]
mc_recall = 0 * cm_row_dist; mc_recall[mc_index] = 1
mc_precision = 0 * cm_row_dist
mc_precision[mc_index] = cm_row_dist[mc_index]
mc_F1 = 0 * cm_row_dist;
mc_F1[mc_index] = 2 * mc_precision[mc_index] / (mc_precision[mc_index] + 1)
output.extend([mc_accuracy.tolist(), mc_recall.tolist(),
mc_precision.tolist(), mc_F1.tolist()])
output_labels.extend(['majority class accuracy', 'majority class recall',
'majority class precision', 'majority class F1'])

# Random accuracy and kappa
cm_col_dist = cm_col_sums / float(np.sum(cm))
exp_accuracy = np.array([np.sum(cm_row_dist * cm_col_dist)] * len(labels))
kappa = (accuracy - exp_accuracy) / (1 - exp_accuracy)
output.extend([exp_accuracy.tolist(), kappa.tolist()])
output_labels.extend(['expected accuracy', 'kappa'])

# Random guess
rg_accuracy = np.ones(len(labels)) / float(len(labels))
rg_precision = cm_row_dist
rg_recall = np.ones(len(labels)) / float(len(labels))
rg_F1 = 2 * cm_row_dist / (len(labels) * cm_row_dist + 1)
output.extend([rg_accuracy.tolist(), rg_precision.tolist(),
rg_recall.tolist(), rg_F1.tolist()])
output_labels.extend(['random guess accuracy', 'random guess precision',
'random guess recall', 'random guess F1'])

# Random weighted guess
rwg_accuracy = np.ones(len(labels)) * sum(cm_row_dist**2)
rwg_precision = cm_row_dist
rwg_recall = cm_row_dist
rwg_F1 = cm_row_dist
output.extend([rwg_accuracy.tolist(), rwg_precision.tolist(),
rwg_recall.tolist(), rwg_F1.tolist()])
output_labels.extend(['random weighted guess accuracy',
'random weighted guess precision',
'random weighted guess recall',
'random weighted guess F1'])

output_df = pd.DataFrame(output, columns=labels)
output_df.index = output_labels

return output_df
```

```python
evaluation_results = []
for i, test_result in enumerate(test_results):
print('\nSplit %d:' % (i+1))
evaluation_result = Evaluate(actual = test_result['failure'],
predicted = test_result['predicted_failure'],
labels = ['none', 'comp1', 'comp2', 'comp3', 'comp4'])
evaluation_results.append(evaluation_result)
evaluation_results[0] # show full results for first split only
```

Split 1:
Confusion matrix
- x-axis is true labels (none, comp1, etc.)
- y-axis is predicted labels
[[119594 21 0 4 3]
[ 18 515 3 5 1]
[ 0 0 860 0 1]
[ 13 0 2 372 1]
[ 2 2 6 0 497]]

Split 2:
Confusion matrix
- x-axis is true labels (none, comp1, etc.)
- y-axis is predicted labels
[[95266 13 0 4 3]
[ 19 399 2 1 1]
[ 0 0 700 0 0]
[ 12 0 2 291 1]
[ 2 2 4 0 392]]

Split 3:
Confusion matrix
- x-axis is true labels (none, comp1, etc.)
- y-axis is predicted labels
[[71724 7 0 4 3]
[ 17 300 1 1 1]
[ 0 1 547 0 0]
[ 11 0 0 212 1]
[ 2 1 3 0 274]]

none
comp1
comp2
comp3
comp4

accuracy
0.999327
0.999327
0.999327
0.999327
0.999327

precision
0.999724
0.957249
0.987371
0.976378
0.988072

recall
0.999766
0.950185
0.998839
0.958763
0.980276

F1
0.999745
0.953704
0.993072
0.967490
0.984158

macro precision
0.981759
0.981759
0.981759
0.981759
0.981759

macro recall
0.977566
0.977566
0.977566
0.977566
0.977566

macro F1
0.979634
0.979634
0.979634
0.979634
0.979634

average accuracy
0.999731
0.999731
0.999731
0.999731
0.999731

micro-averaged precision/recall/F1
0.999327
0.999327
0.999327
0.999327
0.999327

majority class accuracy
0.981152
0.000000
0.000000
0.000000
0.000000

majority class recall
1.000000
0.000000
0.000000
0.000000
0.000000

majority class precision
0.981152
0.000000
0.000000
0.000000
0.000000

majority class F1
0.990486
0.000000
0.000000
0.000000
0.000000

expected accuracy
0.962796
0.962796
0.962796
0.962796
0.962796

kappa
0.981922
0.981922
0.981922
0.981922
0.981922

random guess accuracy
0.200000
0.200000
0.200000
0.200000
0.200000

random guess precision
0.981152
0.004446
0.007062
0.003182
0.004158

random guess recall
0.200000
0.200000
0.200000
0.200000
0.200000

random guess F1
0.332269
0.008698
0.013642
0.006265
0.008148

random weighted guess accuracy
0.962755
0.962755
0.962755
0.962755
0.962755

random weighted guess precision
0.981152
0.004446
0.007062
0.003182
0.004158

random weighted guess recall
0.981152
0.004446
0.007062
0.003182
0.004158

random weighted guess F1
0.981152
0.004446
0.007062
0.003182
0.004158

```python

```

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