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Multi-Channel Time Series Generation

Multi-channel generation allows you to create datasets with multiple independent or correlated signals sharing the same time axis. This is essential for simulating multi-sensor systems common in industrial environments.

What Are Multi-Channel Time Series?

Multi-channel time series have: - Single time axis - All channels share the same timestamps - Multiple data columns - Each channel has its own values - Independent or correlated - Channels can be statistically related

Single-Channel vs. Multi-Channel

Single-Channel:

Timestamp           Value
2024-01-01 00:00:00  100.5
2024-01-01 00:00:01  101.2
2024-01-01 00:00:02   99.8

Multi-Channel (3 channels):

Timestamp            X-Axis  Y-Axis  Z-Axis
2024-01-01 00:00:00   0.5     0.3    -0.2
2024-01-01 00:00:01   0.6     0.4    -0.1
2024-01-01 00:00:02   0.4     0.2    -0.3

When to Use Multi-Channel

Common Use Cases

Vibration Monitoring - 3 accelerometers (X, Y, Z axes) - Partially correlated (mechanical coupling) - Different vibration characteristics per axis

Temperature Arrays - Multiple temperature sensors in same environment - High positive correlation (similar ambient conditions) - Small variations due to local effects

Process Monitoring - Multiple process variables (temperature, pressure, flow) - Complex correlation patterns - Different units and scales per variable

Environmental Monitoring - Weather station (temp, humidity, pressure, wind speed) - Some correlation (temperature affects humidity) - Independent and dependent variables

Creating Your First Multi-Channel Time Series

Step 1: Add Channels

By default, Phoenix starts in single-channel mode. To enable multi-channel:

  1. Find the "Channels" section in the sidebar
  2. Click "Add Channel" button
  3. Phoenix creates "Channel 1" (your first channel)
  4. Click "Add Channel" again for more channels

You can add up to 10 channels total.

[Screenshot Required: Channel Tabs Interface] 1. After adding 3 channels 2. Capture: Channel tabs showing "Channel 1", "Channel 2", "Channel 3" with delete buttons 3. Purpose: Show the channel management interface

Step 2: Configure Channel Properties

Click on a channel tab to configure it. Each channel has:

Channel Identification

Channel Name (required) - Default: "Channel 1", "Channel 2", etc. - Customize to match your scenario: "X-Axis", "Temperature", "Pressure" - Appears in chart legend and data export

Unit (optional) - Measurement unit for this channel - Examples: "°C", "kPa", "m/s²", "V" - Used for documentation, not affecting calculations

Base Signal Configuration

Each channel independently has:

Mean Value - Baseline level for this channel - Can be different for each channel - Example: Temp1=20°C, Temp2=22°C, Temp3=19°C

Noise Amplitude - Random variation for this channel - Independent noise per channel (unless correlated) - Example: Clean sensor (noise=0.5), noisy sensor (noise=2)

Trend Slope (optional) - Linear drift for this channel - Independent trends per channel - Example: Sensor 1 drifting up, Sensor 2 stable

Oscillations

Each channel can have multiple oscillations:

  • Click "Add Oscillation" within the active channel
  • Configure frequency/period, amplitude, phase
  • Channels can have different oscillation characteristics
  • See Oscillations Guide for details

Step 3: Configure Multiple Channels

Switch between channel tabs to configure each one.

Example: 3-Axis Accelerometer

Channel 1: X-Axis - Name: "X-Axis" - Unit: "m/s²" - Mean: 0 - Noise: 0.1 - Oscillation: Frequency=30 Hz, Amplitude=2

Channel 2: Y-Axis - Name: "Y-Axis" - Unit: "m/s²" - Mean: 0 - Noise: 0.1 - Oscillation: Frequency=30 Hz, Amplitude=1.5

Channel 3: Z-Axis - Name: "Z-Axis" - Unit: "m/s²" - Mean: -9.81 (gravity) - Noise: 0.1 - Oscillation: Frequency=30 Hz, Amplitude=0.5

[Screenshot Required: Channel Configuration] 1. Configure 3 channels as above 2. Capture: Configuration panel for one channel showing all fields 3. Purpose: Show channel-specific settings

Step 4: Time Configuration

Time settings are shared across all channels:

  • All channels have the same duration
  • All channels use the same sampling frequency
  • All channels share timestamps

This ensures synchronized multi-channel data.

Step 5: Add Channel Correlations (Optional)

If your channels should be statistically related, add correlations.

See Channel Correlations Guide for comprehensive coverage.

Quick Setup: 1. Scroll to "Channel Correlations" section (appears when 2+ channels exist) 2. Click "Add Correlation" 3. Select two channels 4. Enter correlation coefficient (-1.0 to 1.0) 5. Repeat for other channel pairs as needed

[Screenshot Required: Channel Correlations Section] 1. Add correlation between Channel 1 and Channel 2 with value 0.7 2. Capture: Channel Correlations section showing correlation list 3. Purpose: Show correlation configuration interface

Step 6: Preview Multi-Channel Data

Click "Preview" to generate and visualize.

Multi-Channel Chart Features: - Multiple traces - One colored line per channel - Legend - Channel names with colors - Toggle visibility - Click legend items to hide/show channels - Independent scaling - Y-axis auto-scales to fit all channels

Multi-Channel Statistics: - Statistics shown per channel - Min, max, mean calculated independently - Total point count = points per channel × number of channels

[Screenshot Required: Multi-Channel Chart] 1. Generate 3-channel example from above 2. Capture: Chart showing 3 overlaid signals with legend 3. Purpose: Show what multi-channel visualization looks like

Step 7: Iterate and Refine

  • Switch between channel tabs to adjust individual channels
  • Preview after each change
  • Compare channel behaviors
  • Adjust correlations if needed

Step 8: Save or Export

Multi-channel data can be saved or exported just like single-channel:

CSV Export:

Timestamp,X-Axis,Y-Axis,Z-Axis
2024-01-01 00:00:00,0.5,0.3,-9.9
2024-01-01 00:00:01,0.6,0.4,-9.8

Excel/JSON: Includes all channels in structured format

See Export and Save Guide for details.

Channel Management

Adding Channels

  1. Click "Add Channel" button
  2. Channel appears as new tab
  3. Configure channel settings
  4. Maximum 10 channels

Removing Channels

  1. Click delete button (×) on channel tab
  2. Channel is immediately removed
  3. Correlations involving that channel are automatically deleted
  4. Cannot undo - re-add if needed

Renaming Channels

  1. Click on channel tab to activate it
  2. Find "Channel Name" field
  3. Enter new name
  4. Name appears in tab, chart legend, and exports

Reordering Channels

Channels appear in the order created. To reorder: 1. Delete unwanted channels 2. Add channels in desired order 3. Reconfigure settings

(Note: Future versions may add drag-to-reorder functionality)

Point Count Limits with Multi-Channel

Critical: Point limit applies to total points across all channels.

Calculation

Total Points = Points Per Channel × Number of Channels

Where:
Points Per Channel = Duration (seconds) × Sampling Frequency (Hz)

Examples

Example 1: 3 Channels at 1 Hz for 1 Hour

Duration: 1 hour = 3,600 seconds
Sampling: 1 Hz
Channels: 3
Points Per Channel: 3,600
Total Points: 3,600 × 3 = 10,800 ✗ EXCEEDS LIMIT (10,000)

Fix: Reduce sampling to 0.9 Hz

Points Per Channel: 3,600 × 0.9 = 3,240
Total Points: 3,240 × 3 = 9,720 ✓ Within limit

Example 2: 10 Channels at 0.1 Hz for 10 Minutes

Duration: 10 minutes = 600 seconds
Sampling: 0.1 Hz
Channels: 10
Points Per Channel: 600 × 0.1 = 60
Total Points: 60 × 10 = 600 ✓ Well within limit

Strategies for Staying Under Limit

  1. Reduce sampling frequency - Lower Hz value
  2. Reduce duration - Shorter time span
  3. Reduce channels - Fewer channels
  4. Optimize for use case:
  5. Fast events: High frequency, short duration, few channels
  6. Slow events: Low frequency, long duration, many channels

Common Multi-Channel Patterns

Temperature Sensor Array

Scenario: 4 temperature sensors in the same room

Configuration: - Channels: 4 - Names: "Sensor 1", "Sensor 2", "Sensor 3", "Sensor 4" - Unit: "°C" - Means: 20, 20.5, 19.5, 21 (slightly different locations) - Noise: All 0.3 (similar sensor quality) - Oscillation: All have Period=86400 (daily cycle), Amplitude=3 - Correlations: All pairs at 0.85-0.95 (high correlation)

[Screenshot Instructions: Temperature Array] 1. Configure 4 channels as above 2. Add correlations between all pairs (6 total): values 0.85-0.95 3. Duration: 2 days, Sampling: 0.001 Hz (1 sample per 16.67 minutes) 4. Preview 5. Capture: Chart showing 4 highly correlated temperature traces 6. Purpose: Demonstrate realistic multi-sensor scenario

3-Axis Vibration Monitor

Scenario: Accelerometer on rotating machinery

Configuration: - Channels: 3 - Names: "X-Axis", "Y-Axis", "Z-Axis" - Unit: "m/s²" - X-Axis: Mean=0, Noise=0.1, Oscillation=30 Hz/Amp=2 - Y-Axis: Mean=0, Noise=0.1, Oscillation=30 Hz/Amp=2 - Z-Axis: Mean=-9.81, Noise=0.1, Oscillation=30 Hz/Amp=0.5 (gravity + small vibration) - Correlations: X-Y at 0.3 (some mechanical coupling), others at 0.1 - Time: 10 seconds at 100 Hz

[Screenshot Instructions: Vibration Monitor] 1. Configure 3 channels as above 2. Duration: 10 seconds, Sampling: 100 Hz 3. Preview 4. Capture: Chart showing 3 axes with dominant 30 Hz vibrations 5. Purpose: Show high-frequency multi-axis data

Process Variables

Scenario: Chemical reactor with temperature, pressure, flow

Configuration: - Channel 1: Temperature - Name: "Reactor Temperature", Unit: "°C" - Mean: 85, Noise: 1, Trend: 0.01 (gradual increase)

  • Channel 2: Pressure
  • Name: "Reactor Pressure", Unit: "kPa"

  • Mean: 150, Noise: 2, Trend: 0.02 (increases with temperature)

  • Channel 3: Flow Rate

  • Name: "Inlet Flow", Unit: "L/min"

  • Mean: 50, Noise: 3, Trend: 0 (controlled)

  • Correlations:

  • Temp-Pressure: 0.8 (strong physical coupling)
  • Temp-Flow: -0.2 (slight inverse)
  • Pressure-Flow: -0.3 (inverse relationship)

Time: 1 hour, 0.1 Hz (1 sample every 10 seconds)

[Screenshot Instructions: Process Variables] 1. Configure 3 channels as above 2. Duration: 1 hour, Sampling: 0.1 Hz 3. Add correlations 4. Preview 5. Capture: Chart showing 3 different-scale variables trending upward 6. Purpose: Demonstrate process monitoring scenario

Tips for Multi-Channel Success

Channel Naming

Good Names: - Descriptive: "Front Left Temperature", "Motor Vibration X" - Include location: "Room 1 Temp", "Bearing 2 Accel" - Include axis/direction: "X-Axis", "Vertical"

Avoid: - Generic: "Channel 1", "Sensor A" - Abbreviations: "T1", "CH_A" (unless standard) - Too long: "Temperature Sensor Located in the Northwest Corner"

Setting Different Means

When channels measure the same phenomenon in the same conditions: - Use similar mean values (temp sensors in same room: 20°C, 20.5°C, 19.8°C)

When channels measure different phenomena: - Use appropriate scales (temperature: 20°C, pressure: 101 kPa)

Noise Levels

Same Sensor Type: Use similar noise amplitudes - 3 identical temperature sensors → all noise=0.3

Different Sensor Quality: Vary noise by quality - High-end sensor: noise=0.1 - Standard sensor: noise=0.5 - Low-quality sensor: noise=2.0

Oscillation Configuration

Same Source: Give channels similar or related frequencies - All axes vibrating at motor speed: 30 Hz

Different Sources: Use independent frequencies - Daily temp cycle: Period=86400 - Pump pulsation: Frequency=5 Hz

Using Correlations

When to Use: - Sensors measure related phenomena - Physical coupling exists - Shared environmental factors

When Not to Use: - Completely independent measurements - Different physical processes - Intentionally uncorrelated test data

See Channel Correlations Guide for detailed guidance.

Previewing Multi-Channel Data

Check Each Channel: - Use legend to toggle channels on/off - Verify each channel looks correct individually - Check relative amplitudes make sense

Check Correlations: - Correlated channels should move together - Uncorrelated channels should be independent - Zoom in to verify correlation patterns

Troubleshooting

"Data point limit exceeded" with multi-channel

Cause: Total points = points per channel × number of channels

Solutions: 1. Calculate current total: Duration × Frequency × Channels 2. Reduce any of the three factors: - Shorter duration - Lower sampling frequency - Fewer channels

Example:

Problem: 5 channels × 30 min × 1 Hz = 9,000 points ✓
Add 2 more channels: 7 channels × 30 min × 1 Hz = 12,600 points ✗

Solution: Reduce to 0.75 Hz
7 channels × 30 min × 0.75 Hz = 9,450 points ✓

Channel correlations section doesn't appear

Cause: Need at least 2 channels for correlations

Solution: Add a second channel (click "Add Channel")

Can't tell channels apart in chart

Solutions: 1. Use descriptive channel names (show in legend) 2. Toggle channels on/off using legend 3. Ensure channels have different amplitudes or means 4. Export to CSV and analyze separately

Channels look identical despite different configurations

Check: 1. Verify you're configuring the correct channel (check active tab) 2. Confirm you clicked "Preview" after making changes 3. Check that means/amplitudes are sufficiently different 4. If highly correlated (0.9+), channels will look very similar (expected)

Correlation validation fails

Error Message: "Correlation matrix is not valid"

Causes: 1. Impossible correlation combinations 2. Correlation values outside -1.0 to 1.0 range

Solution: See Channel Correlations Guide for troubleshooting

Wrong channel gets deleted

Prevention: - Pay attention to which channel tab has the × button - Delete buttons appear on each tab - No undo - be careful!

If It Happens: 1. Click "Add Channel" to re-create it 2. Reconfigure the channel settings 3. Re-add correlations if needed

Advanced Multi-Channel Scenarios

Harmonic Analysis

Create channels with harmonic relationships:

  • Fundamental: 10 Hz, Amplitude=5
  • 2nd Harmonic: 20 Hz, Amplitude=2
  • 3rd Harmonic: 30 Hz, Amplitude=1

Use high sampling (100 Hz) to capture all harmonics properly.

Phase-Shifted Channels

Use phase offset in oscillations to create phase-shifted signals:

  • Channel 1: Frequency=1 Hz, Phase=0
  • Channel 2: Frequency=1 Hz, Phase=π/2 (90° shift)
  • Channel 3: Frequency=1 Hz, Phase=π (180° shift)

Useful for simulating multi-phase systems (3-phase power, etc.)

Mixed Time Scales

Combine slow and fast phenomena:

  • Channel 1: Daily cycle (Period=86400, Amp=5)
  • Channel 2: Hourly fluctuation (Period=3600, Amp=2)
  • Channel 3: Fast vibration (Frequency=10 Hz, Amp=0.5)

Requires appropriate sampling frequency (2× fastest oscillation).

Next Steps

Master Correlations

Multi-channel data becomes powerful when channels are correlated: - Channel Correlations Guide - Learn to create realistic multi-sensor data

Understand Each Channel Component

Simulate Real-World Issues

Export and Use

Multi-channel generation opens up realistic simulations of complex multi-sensor systems. Practice with different channel configurations and correlation patterns to master this powerful Phoenix feature.