26 Feature Scaling Lab: Preprocessing Workflow

26.1 Start With the Decision

This section: Start With the Decision — Start with one saved copy of the raw data.

Start with one saved copy of the raw data. Mark which rows belong to training and which belong to the final test.

26.2 Route Overview

This section: Route Overview — This is part 1 of 2.

This is part 1 of 2. Continue with Feature Scaling Lab: Statistical Analysis.

26.3 Part Objectives

This section: Part Objectives

• Test normalization preprocessing check with a concrete scenario and pass criteria.
• Validate step 6: experiment with filtering with a concrete scenario and pass criteria.

26.4 Start With the Story

This section: Start With the Story

26.5 Learning Objectives

This section: Learning Objectives

By the end of this chapter, you will be able to:

• Apply Normalization Techniques: Implement min-max scaling, Z-score normalization, and robust scaling for multi-sensor data fusion
• Compare Normalization Methods: Evaluate which scaling approach suits each downstream use case (neural networks, clustering, visualization)
• Implement a Complete Pipeline: Build and test an end-to-end data quality system on an ESP32 microcontroller
• Assess Data Quality Metrics: Calculate and interpret validation rates, outlier counts, and imputation statistics

26.6 Normalization Preprocessing Check

This section: Normalization Preprocessing Check — The mathematical gist.

The mathematical gist. The simulator’s 10000 * (4095/adc - 1) is the voltage-divider equation solved backward. At ADC code 2048 it gives 9,995 ohms, close to the 10 kΩ balance point; this corrects the old box’s 9,990-ohm arithmetic slip. The same 12-bit, 3.3 V converter has a 0.806 mV code step and 0.233 mV RMS rounding noise. Its 200 ms loop samples at 5.00 Hz, so 2.50 Hz is the fastest safe input; an illustrative 3.00 Hz cycle folds to 2.00 Hz before normalization starts.

Math Bridge · guided foundationsWhat does 4095 / adc - 1 recover?Let Data Dora invert the thermistor divider, then audit its ADC and sampling limits. Learn the maths

26.7 Prerequisites

This section: Prerequisites

Before diving into this chapter, you should be familiar with:

• Data Validation and Outlier Detection: Understanding validation as the first stage of data quality
• Missing Value Imputation and Noise Filtering: Handling gaps and noise in sensor data
• Edge Data Acquisition: Understanding how sensor data is collected at the edge

26.8 Data Normalization and Scaling

This section: Data Normalization and Scaling — First stop: the scalers themselves.

First stop: the scalers themselves. Before the lab code mixes temperature, light, drift, and quality flags, you need to know what each transformation preserves and what it can distort.

26.9 Min-Max Scaling

This section: Min-Max Scaling

Scales data to a fixed range (typically 0-1):

class MinMaxScaler:
    def __init__(self, feature_range=(0, 1)):
        self.min_val = None
        self.max_val = None
        self.feature_min, self.feature_max = feature_range

    def fit(self, data):
        """Learn min/max from training data"""
        self.min_val = min(data)
        self.max_val = max(data)

    def transform(self, value):
        """Scale a single value"""
        if self.max_val == self.min_val:
            return self.feature_min

        scaled = (value - self.min_val) / (self.max_val - self.min_val)
        return scaled * (self.feature_max - self.feature_min) + self.feature_min

    def inverse_transform(self, scaled_value):
        """Convert back to original scale"""
        original = (scaled_value - self.feature_min) / (self.feature_max - self.feature_min)
        return original * (self.max_val - self.min_val) + self.min_val

26.10 Z-Score Normalization (Standardization)

This section: Z-Score Normalization (Standardization)

Centers data around mean with unit variance:

class ZScoreNormalizer:
    def __init__(self):
        self.mean = None
        self.std = None

    def fit(self, data):
        """Learn mean and std from training data"""
        import numpy as np
        self.mean = np.mean(data)
        self.std = np.std(data)

    def transform(self, value):
        """Normalize a single value"""
        if self.std == 0:
            return 0.0
        return (value - self.mean) / self.std

    def inverse_transform(self, normalized_value):
        """Convert back to original scale"""
        return normalized_value * self.std + self.mean

26.11 Robust Scaling

This section: Robust Scaling

Uses median and IQR, robust to outliers:

class RobustScaler:
    def __init__(self):
        self.median = None
        self.iqr = None

    def fit(self, data):
        """Learn median and IQR from training data"""
        import numpy as np
        self.median = np.median(data)
        q1 = np.percentile(data, 25)
        q3 = np.percentile(data, 75)
        self.iqr = q3 - q1

    def transform(self, value):
        """Scale using median and IQR"""
        if self.iqr == 0:
            return 0.0
        return (value - self.median) / self.iqr

    def inverse_transform(self, scaled_value):
        """Convert back to original scale"""
        return scaled_value * self.iqr + self.median

26.12 When to Use Each Method

This section: When to Use Each Method

Min-Max

• Use case: Neural networks and bounded outputs
• Preserves: Distribution shape
• Sensitive to: Outliers

Z-Score

• Use case: SVM, K-means, PCA, and other scale-sensitive methods
• Preserves: Relative distances
• Sensitive to: Outliers that shift the mean or standard deviation

Robust Scaling

• Use case: Datasets where outliers should not dominate the scaling range
• Preserves: Median-based relationships
• Sensitive to: Extremely sparse data

Log Transform

• Use case: Right-skewed data such as power measurements or event counts
• Preserves: Multiplicative relationships
• Sensitive to: Zero or negative values

26.13 Interactive Normalization Calculator

This section: Interactive Normalization Calculator

Try different sensor values and see how each normalization method transforms them:

26.14 Data Quality Lab: ESP32 Wokwi Simulation

This section: Data Quality Lab: ESP32 Wokwi Simulation — Now apply those scalers inside a streaming edge pipeline.

Now apply those scalers inside a streaming edge pipeline. The goal is not just to compute a normalized value; it is to know which validation, filtering, and imputation decisions produced that value.

26.15 Lab Overview

This section: Lab Overview — In this hands-on lab, you will implement a complete data quality preprocessing pipeline on an ESP32 microcontroller.

In this hands-on lab, you will implement a complete data quality preprocessing pipeline on an ESP32 microcontroller. The simulation demonstrates real-world techniques for handling sensor data problems including outliers, missing values, noise, and the need for normalization.

What You Will Learn:

1. Sensor Data Validation: Implementing range checks and rate-of-change validation
2. Outlier Detection: Using Z-score and IQR methods to identify anomalous readings
3. Missing Value Handling: Forward-fill and interpolation techniques for gap handling
4. Noise Filtering: Moving average, median filter, and exponential smoothing
5. Data Normalization: Min-max scaling and Z-score normalization for multi-sensor fusion

Skills Practiced:

• Real-time data processing on embedded systems
• Statistical calculations with limited memory
• Circular buffer implementations
• Streaming algorithm design

26.16 Lab Components

This section: Lab Components

Range Validation

• Implementation: Physical bounds checking
• Visual indicator: Red LED on violation

Z-Score Outliers

• Implementation: Rolling statistics
• Visual indicator: Yellow LED on outlier

Median Filter

• Implementation: 5-sample sliding window
• Visual indicator: Smoothed output in serial

Moving Average

• Implementation: 10-sample window
• Visual indicator: Trend visualization

Normalization

• Implementation: 0-1 scaling
• Visual indicator: Percentage output

26.17 Wokwi Simulator

This section: Wokwi Simulator — Use the simulator launch link below to build your data quality preprocessing system while keeping the lab instructions open in this chapter.

Use the simulator launch link below to build your data quality preprocessing system while keeping the lab instructions open in this chapter.

26.18 Circuit Setup

This section: Circuit Setup

Connect the sensors and indicators to the ESP32:

Add this diagram.json configuration in Wokwi:

{
  "version": 1,
  "author": "IoT Class - Data Quality Lab",
  "editor": "wokwi",
  "parts": [
    { "type": "wokwi-esp32-devkit-v1", "id": "esp", "top": 0, "left": 0 },
    { "type": "wokwi-ntc-temperature-sensor", "id": "temp1", "top": -120, "left": 80 },
    { "type": "wokwi-photoresistor-sensor", "id": "ldr1", "top": -120, "left": 180 },
    { "type": "wokwi-potentiometer", "id": "pot1", "top": -120, "left": 280 },
    { "type": "wokwi-led", "id": "led_red", "top": 180, "left": 80, "attrs": { "color": "red" } },
    { "type": "wokwi-led", "id": "led_yellow", "top": 180, "left": 130, "attrs": { "color": "yellow" } },
    { "type": "wokwi-led", "id": "led_green", "top": 180, "left": 180, "attrs": { "color": "green" } },
    { "type": "wokwi-led", "id": "led_blue", "top": 180, "left": 230, "attrs": { "color": "blue" } },
    { "type": "wokwi-resistor", "id": "r1", "top": 230, "left": 80, "attrs": { "value": "220" } },
    { "type": "wokwi-resistor", "id": "r2", "top": 230, "left": 130, "attrs": { "value": "220" } },
    { "type": "wokwi-resistor", "id": "r3", "top": 230, "left": 180, "attrs": { "value": "220" } },
    { "type": "wokwi-resistor", "id": "r4", "top": 230, "left": 230, "attrs": { "value": "220" } }
  ],
  "connections": [
    ["esp:GND.1", "temp1:GND", "black", ["h0"]],
    ["esp:3V3", "temp1:VCC", "red", ["h0"]],
    ["esp:34", "temp1:OUT", "green", ["h0"]],
    ["esp:GND.1", "ldr1:GND", "black", ["h0"]],
    ["esp:3V3", "ldr1:VCC", "red", ["h0"]],
    ["esp:35", "ldr1:OUT", "orange", ["h0"]],
    ["esp:GND.1", "pot1:GND", "black", ["h0"]],
    ["esp:3V3", "pot1:VCC", "red", ["h0"]],
    ["esp:32", "pot1:SIG", "purple", ["h0"]],
    ["esp:18", "led_red:A", "red", ["h0"]],
    ["led_red:C", "r1:1", "black", ["h0"]],
    ["r1:2", "esp:GND.1", "black", ["h0"]],
    ["esp:19", "led_yellow:A", "yellow", ["h0"]],
    ["led_yellow:C", "r2:1", "black", ["h0"]],
    ["r2:2", "esp:GND.1", "black", ["h0"]],
    ["esp:21", "led_green:A", "green", ["h0"]],
    ["led_green:C", "r3:1", "black", ["h0"]],
    ["r3:2", "esp:GND.1", "black", ["h0"]],
    ["esp:22", "led_blue:A", "blue", ["h0"]],
    ["led_blue:C", "r4:1", "black", ["h0"]],
    ["r4:2", "esp:GND.1", "black", ["h0"]]
  ]
}

26.19 Complete Arduino Code

This section: Complete Arduino Code

Copy this code into the Wokwi editor:

// ============================================================================
// DATA QUALITY LAB: Comprehensive IoT Data Preprocessing Pipeline
// ============================================================================
// Demonstrates: Validation, Outlier Detection, Missing Value Handling,
//               Noise Filtering, Normalization, and Data Scaling
// ============================================================================

#include <Arduino.h>
#include <math.h>

// ====================== PIN DEFINITIONS ======================
const int TEMP_PIN = 34;        // Temperature sensor (NTC)
const int LIGHT_PIN = 35;       // Light sensor (LDR)
const int DRIFT_PIN = 32;       // Potentiometer for drift simulation

const int LED_RED = 18;         // Range violation indicator
const int LED_YELLOW = 19;      // Outlier detection indicator
const int LED_GREEN = 21;       // Valid data indicator
const int LED_BLUE = 22;        // Missing data indicator

// ====================== SAMPLING PARAMETERS ======================
const int SAMPLE_INTERVAL_MS = 200;        // 5 Hz sampling rate
const int VALIDATION_WINDOW = 50;          // Samples for statistics
const int FILTER_WINDOW_MEDIAN = 5;        // Median filter window
const int FILTER_WINDOW_MA = 10;           // Moving average window
const float EXP_SMOOTHING_ALPHA = 0.3;     // Exponential smoothing factor

// ====================== VALIDATION THRESHOLDS ======================
// Temperature sensor valid range (Celsius after conversion)
const float TEMP_MIN_VALID = -10.0;
const float TEMP_MAX_VALID = 60.0;
const float TEMP_MAX_RATE = 2.0;           // Max 2C change per second

// Light sensor valid range (0-4095 ADC, 0-100000 lux mapped)
const float LIGHT_MIN_VALID = 0.0;
const float LIGHT_MAX_VALID = 100000.0;

// Outlier detection thresholds
const float ZSCORE_THRESHOLD = 3.0;        // Standard deviations
const float IQR_MULTIPLIER = 1.5;          // IQR outlier multiplier
const float MAD_THRESHOLD = 3.5;           // Modified Z-score threshold

// Missing data parameters
const int MAX_MISSING_SAMPLES = 10;        // Max consecutive missing allowed
const float MISSING_PROBABILITY = 0.05;    // Simulate 5% missing data

// ====================== DATA STRUCTURES ======================

// Circular buffer for streaming statistics
template<int SIZE>
struct CircularBuffer {
    float data[SIZE];
    int head;
    int count;

    CircularBuffer() : head(0), count(0) {
        for (int i = 0; i < SIZE; i++) data[i] = 0;
    }

    void push(float value) {
        data[head] = value;
        head = (head + 1) % SIZE;
        if (count < SIZE) count++;
    }

    float get(int index) const {
        // Get value at index (0 = oldest)
        int actual = (head - count + index + SIZE) % SIZE;
        return data[actual];
    }

    bool isFull() const { return count == SIZE; }
    int size() const { return count; }
};

// Statistics calculator for streaming data
struct StreamingStats {
    float sum;
    float sumSq;
    int count;
    float min_val;
    float max_val;

    StreamingStats() : sum(0), sumSq(0), count(0),
                       min_val(INFINITY), max_val(-INFINITY) {}

    void reset() {
        sum = sumSq = 0;
        count = 0;
        min_val = INFINITY;
        max_val = -INFINITY;
    }

    void add(float value) {
        sum += value;
        sumSq += value * value;
        count++;
        if (value < min_val) min_val = value;
        if (value > max_val) max_val = value;
    }

    float mean() const { return count > 0 ? sum / count : 0; }

    float variance() const {
        if (count < 2) return 0;
        return (sumSq - sum * sum / count) / (count - 1);
    }

    float stdDev() const { return sqrt(variance()); }
};

// Sensor reading with quality metadata
struct SensorReading {
    float rawValue;
    float cleanedValue;
    float normalizedValue;
    unsigned long timestamp;
    bool isValid;
    bool isOutlier;
    bool isMissing;
    bool isImputed;
    String qualityFlags;
};

// ====================== GLOBAL STATE ======================

// Circular buffers for different processing stages
CircularBuffer<VALIDATION_WINDOW> tempRawBuffer;
CircularBuffer<VALIDATION_WINDOW> tempCleanBuffer;
CircularBuffer<FILTER_WINDOW_MEDIAN> tempMedianBuffer;
CircularBuffer<FILTER_WINDOW_MA> tempMABuffer;

CircularBuffer<VALIDATION_WINDOW> lightRawBuffer;
CircularBuffer<VALIDATION_WINDOW> lightCleanBuffer;

// Streaming statistics
StreamingStats tempStats;
StreamingStats lightStats;

// For rate-of-change validation
float lastValidTemp = NAN;
unsigned long lastValidTempTime = 0;
float lastValidLight = NAN;
unsigned long lastValidLightTime = 0;

// For exponential smoothing
float expSmoothedTemp = NAN;
float expSmoothedLight = NAN;

// For missing data handling
int consecutiveMissingTemp = 0;
int consecutiveMissingLight = 0;
float lastImputedTemp = NAN;
float lastImputedLight = NAN;

// Normalization parameters (learned from data)
float tempMinSeen = INFINITY;
float tempMaxSeen = -INFINITY;
float lightMinSeen = INFINITY;
float lightMaxSeen = -INFINITY;

// Statistics counters
unsigned long totalSamples = 0;
unsigned long validSamples = 0;
unsigned long outlierSamples = 0;
unsigned long missingSamples = 0;
unsigned long imputedSamples = 0;
unsigned long rangeViolations = 0;
unsigned long rateViolations = 0;

// ====================== HELPER FUNCTIONS ======================

// Convert ADC reading to temperature (NTC thermistor approximation)
float adcToTemperature(int adcValue) {
    if (adcValue == 0) return -INFINITY;
    if (adcValue >= 4095) return INFINITY;

    // Simplified Steinhart-Hart approximation for 10K NTC
    float resistance = 10000.0 * (4095.0 / adcValue - 1.0);
    float steinhart = resistance / 10000.0;
    steinhart = log(steinhart);
    steinhart /= 3950.0;
    steinhart += 1.0 / (25.0 + 273.15);
    steinhart = 1.0 / steinhart;
    steinhart -= 273.15;

    return steinhart;
}

// Convert ADC reading to light level (LDR approximation)
float adcToLight(int adcValue) {
    // Map ADC to approximate lux (logarithmic)
    if (adcValue < 10) return 0;
    float lux = 100000.0 * pow((float)adcValue / 4095.0, 2);
    return lux;
}

// ====================== VALIDATION FUNCTIONS ======================

// Range validation - check if value is within physical bounds
bool validateRange(float value, float minValid, float maxValid, String& errorMsg) {
    if (isnan(value) || isinf(value)) {
        errorMsg = "NaN/Inf";
        return false;
    }
    if (value < minValid) {
        errorMsg = "Below min (" + String(minValid) + ")";
        return false;
    }
    if (value > maxValid) {
        errorMsg = "Above max (" + String(maxValid) + ")";
        return false;
    }
    errorMsg = "OK";
    return true;
}

// Rate-of-change validation - detect impossible jumps
bool validateRateOfChange(float currentValue, float lastValue,
                          unsigned long currentTime, unsigned long lastTime,
                          float maxRate, String& errorMsg) {
    if (isnan(lastValue) || lastTime == 0) {
        errorMsg = "First reading";
        return true;
    }

    float timeDelta = (currentTime - lastTime) / 1000.0;  // seconds
    if (timeDelta <= 0) {
        errorMsg = "Invalid timestamp";
        return false;
    }

    float rate = abs(currentValue - lastValue) / timeDelta;
    if (rate > maxRate) {
        errorMsg = "Rate " + String(rate, 2) + " exceeds max " + String(maxRate);
        return false;
    }

    errorMsg = "Rate OK (" + String(rate, 2) + ")";
    return true;
}

// ====================== OUTLIER DETECTION ======================

// Z-Score outlier detection
bool detectOutlierZScore(float value, float mean, float stdDev,
                         float threshold, float& zScore) {
    if (stdDev == 0) {
        zScore = 0;
        return false;
    }

    zScore = abs((value - mean) / stdDev);
    return zScore > threshold;
}

// IQR outlier detection (requires sorted buffer)
bool detectOutlierIQR(CircularBuffer<VALIDATION_WINDOW>& buffer, float value,
                      float multiplier, float& lowerBound, float& upperBound) {
    if (buffer.size() < 10) return false;

    // Copy to temporary array for sorting
    float sorted[VALIDATION_WINDOW];
    int n = buffer.size();
    for (int i = 0; i < n; i++) {
        sorted[i] = buffer.get(i);
    }

    // Simple bubble sort (OK for small buffers)
    for (int i = 0; i < n - 1; i++) {
        for (int j = 0; j < n - i - 1; j++) {
            if (sorted[j] > sorted[j + 1]) {
                float temp = sorted[j];
                sorted[j] = sorted[j + 1];
                sorted[j + 1] = temp;
            }
        }
    }

    // Calculate quartiles
    int q1Idx = n / 4;
    int q3Idx = 3 * n / 4;
    float q1 = sorted[q1Idx];
    float q3 = sorted[q3Idx];
    float iqr = q3 - q1;

    lowerBound = q1 - multiplier * iqr;
    upperBound = q3 + multiplier * iqr;

    return (value < lowerBound) || (value > upperBound);
}

// ====================== NOISE FILTERING ======================

// Moving average filter
float filterMovingAverage(CircularBuffer<FILTER_WINDOW_MA>& buffer, float newValue) {
    buffer.push(newValue);

    float sum = 0;
    for (int i = 0; i < buffer.size(); i++) {
        sum += buffer.get(i);
    }

    return sum / buffer.size();
}

// Median filter (excellent for spike removal)
float filterMedian(CircularBuffer<FILTER_WINDOW_MEDIAN>& buffer, float newValue) {
    buffer.push(newValue);

    // Copy and sort
    float sorted[FILTER_WINDOW_MEDIAN];
    int n = buffer.size();
    for (int i = 0; i < n; i++) {
        sorted[i] = buffer.get(i);
    }

    for (int i = 0; i < n - 1; i++) {
        for (int j = 0; j < n - i - 1; j++) {
            if (sorted[j] > sorted[j + 1]) {
                float temp = sorted[j];
                sorted[j] = sorted[j + 1];
                sorted[j + 1] = temp;
            }
        }
    }

    if (n % 2 == 0) {
        return (sorted[n/2 - 1] + sorted[n/2]) / 2.0;
    }
    return sorted[n / 2];
}

// Exponential smoothing filter
float filterExponentialSmoothing(float& smoothed, float newValue, float alpha) {
    if (isnan(smoothed)) {
        smoothed = newValue;
    } else {
        smoothed = alpha * newValue + (1 - alpha) * smoothed;
    }
    return smoothed;
}

// ====================== MISSING VALUE HANDLING ======================

// Simulate missing data (for demonstration)
bool simulateMissingData() {
    return random(1000) < (MISSING_PROBABILITY * 1000);
}

// Forward-fill imputation with limit
float imputeForwardFill(float lastValidValue, int& consecutiveMissing,
                        int maxMissing, bool& wasImputed) {
    consecutiveMissing++;

    if (consecutiveMissing > maxMissing || isnan(lastValidValue)) {
        wasImputed = false;
        return NAN;
    }

    wasImputed = true;
    return lastValidValue;
}

// ====================== NORMALIZATION ======================

// Min-Max scaling to 0-1 range
float normalizeMinMax(float value, float minSeen, float maxSeen) {
    if (maxSeen == minSeen) return 0.5;
    return (value - minSeen) / (maxSeen - minSeen);
}

// Z-Score normalization (standardization)
float normalizeZScore(float value, float mean, float stdDev) {
    if (stdDev == 0) return 0;
    return (value - mean) / stdDev;
}

// Update normalization parameters
void updateNormalizationParams(float value, float& minSeen, float& maxSeen) {
    if (value < minSeen) minSeen = value;
    if (value > maxSeen) maxSeen = value;
}

// ====================== MAIN PROCESSING FUNCTION ======================

SensorReading processTemperature(int adcValue, unsigned long timestamp) {
    SensorReading reading;
    reading.timestamp = timestamp;
    reading.isValid = true;
    reading.isOutlier = false;
    reading.isMissing = false;
    reading.isImputed = false;
    reading.qualityFlags = "";

    // Step 0: Check for simulated missing data
    if (simulateMissingData()) {
        reading.isMissing = true;
        missingSamples++;

        // Try forward-fill imputation
        bool wasImputed;
        float imputed = imputeForwardFill(lastValidTemp, consecutiveMissingTemp,
                                          MAX_MISSING_SAMPLES, wasImputed);

        if (wasImputed) {
            reading.rawValue = NAN;
            reading.cleanedValue = imputed;
            reading.isImputed = true;
            reading.qualityFlags += "IMPUTED_FFILL ";
            imputedSamples++;
            lastImputedTemp = imputed;
        } else {
            reading.rawValue = NAN;
            reading.cleanedValue = NAN;
            reading.normalizedValue = NAN;
            reading.qualityFlags += "MISSING_NO_IMPUTE ";
            return reading;
        }
    } else {
        consecutiveMissingTemp = 0;

        // Step 1: Convert ADC to temperature
        reading.rawValue = adcToTemperature(adcValue);

        // Step 2: Range validation
        String rangeError;
        if (!validateRange(reading.rawValue, TEMP_MIN_VALID, TEMP_MAX_VALID, rangeError)) {
            reading.isValid = false;
            reading.qualityFlags += "RANGE_VIOLATION(" + rangeError + ") ";
            rangeViolations++;
        }

        // Step 3: Rate-of-change validation
        String rateError;
        if (!validateRateOfChange(reading.rawValue, lastValidTemp,
                                  timestamp, lastValidTempTime,
                                  TEMP_MAX_RATE, rateError)) {
            reading.isValid = false;
            reading.qualityFlags += "RATE_VIOLATION(" + rateError + ") ";
            rateViolations++;
        }

        // Step 4: Outlier detection (only if range-valid)
        if (reading.isValid && tempStats.count > 20) {
            float zScore;
            if (detectOutlierZScore(reading.rawValue, tempStats.mean(),
                                    tempStats.stdDev(), ZSCORE_THRESHOLD, zScore)) {
                reading.isOutlier = true;
                reading.qualityFlags += "ZSCORE_OUTLIER(z=" + String(zScore, 2) + ") ";
                outlierSamples++;
            }

            float lowerBound, upperBound;
            if (detectOutlierIQR(tempRawBuffer, reading.rawValue,
                                 IQR_MULTIPLIER, lowerBound, upperBound)) {
                reading.isOutlier = true;
                reading.qualityFlags += "IQR_OUTLIER ";
            }
        }

        // Step 5: Apply noise filtering
        if (reading.isValid && !reading.isOutlier) {
            // Median filter first (removes spikes)
            float medianFiltered = filterMedian(tempMedianBuffer, reading.rawValue);

            // Then moving average (smooths remaining noise)
            float maFiltered = filterMovingAverage(tempMABuffer, medianFiltered);

            // Exponential smoothing for final output
            reading.cleanedValue = filterExponentialSmoothing(expSmoothedTemp,
                                                              maFiltered,
                                                              EXP_SMOOTHING_ALPHA);

            // Update statistics with valid data
            tempStats.add(reading.rawValue);
            tempRawBuffer.push(reading.rawValue);
            tempCleanBuffer.push(reading.cleanedValue);

            // Update last valid
            lastValidTemp = reading.rawValue;
            lastValidTempTime = timestamp;
            validSamples++;
        } else if (reading.isOutlier) {
            // Use median of recent values for outlier replacement
            reading.cleanedValue = filterMedian(tempMedianBuffer,
                                                tempMedianBuffer.get(tempMedianBuffer.size() - 1));
            reading.qualityFlags += "OUTLIER_REPLACED ";
        } else {
            // Range/rate violation - use last valid with flag
            if (!isnan(lastValidTemp)) {
                reading.cleanedValue = lastValidTemp;
                reading.qualityFlags += "USING_LAST_VALID ";
            } else {
                reading.cleanedValue = NAN;
            }
        }
    }

    // Step 6: Normalization
    if (!isnan(reading.cleanedValue)) {
        updateNormalizationParams(reading.cleanedValue, tempMinSeen, tempMaxSeen);
        reading.normalizedValue = normalizeMinMax(reading.cleanedValue,
                                                   tempMinSeen, tempMaxSeen);
    } else {
        reading.normalizedValue = NAN;
    }

    if (reading.qualityFlags == "") {
        reading.qualityFlags = "CLEAN";
    }

    totalSamples++;
    return reading;
}

SensorReading processLight(int adcValue, unsigned long timestamp) {
    SensorReading reading;
    reading.timestamp = timestamp;
    reading.isValid = true;
    reading.isOutlier = false;
    reading.isMissing = false;
    reading.isImputed = false;
    reading.qualityFlags = "";

    // Similar processing as temperature (abbreviated for space)
    if (simulateMissingData()) {
        reading.isMissing = true;
        missingSamples++;

        bool wasImputed;
        float imputed = imputeForwardFill(lastValidLight, consecutiveMissingLight,
                                          MAX_MISSING_SAMPLES, wasImputed);

        if (wasImputed) {
            reading.rawValue = NAN;
            reading.cleanedValue = imputed;
            reading.isImputed = true;
            reading.qualityFlags = "IMPUTED_FFILL";
            imputedSamples++;
        } else {
            reading.rawValue = NAN;
            reading.cleanedValue = NAN;
            reading.normalizedValue = NAN;
            reading.qualityFlags = "MISSING_NO_IMPUTE";
            return reading;
        }
    } else {
        consecutiveMissingLight = 0;
        reading.rawValue = adcToLight(adcValue);

        // Simplified processing for light sensor
        String rangeError;
        if (!validateRange(reading.rawValue, LIGHT_MIN_VALID, LIGHT_MAX_VALID, rangeError)) {
            reading.isValid = false;
            reading.qualityFlags = "RANGE_VIOLATION";
            rangeViolations++;
        }

        if (reading.isValid) {
            reading.cleanedValue = filterExponentialSmoothing(expSmoothedLight,
                                                              reading.rawValue,
                                                              EXP_SMOOTHING_ALPHA);
            lightStats.add(reading.rawValue);
            lightRawBuffer.push(reading.rawValue);
            lastValidLight = reading.rawValue;
            lastValidLightTime = timestamp;
            validSamples++;
        } else {
            reading.cleanedValue = lastValidLight;
        }
    }

    // Normalization
    if (!isnan(reading.cleanedValue)) {
        updateNormalizationParams(reading.cleanedValue, lightMinSeen, lightMaxSeen);
        reading.normalizedValue = normalizeMinMax(reading.cleanedValue,
                                                   lightMinSeen, lightMaxSeen);
    }

    if (reading.qualityFlags == "") {
        reading.qualityFlags = "CLEAN";
    }

    totalSamples++;
    return reading;
}

// ====================== LED INDICATOR CONTROL ======================

void updateLEDs(const SensorReading& tempReading, const SensorReading& lightReading) {
    // Red LED: Range violation
    if (!tempReading.isValid || !lightReading.isValid) {
        digitalWrite(LED_RED, HIGH);
    } else {
        digitalWrite(LED_RED, LOW);
    }

    // Yellow LED: Outlier detected
    if (tempReading.isOutlier || lightReading.isOutlier) {
        digitalWrite(LED_YELLOW, HIGH);
    } else {
        digitalWrite(LED_YELLOW, LOW);
    }

    // Green LED: Clean valid data
    if (tempReading.qualityFlags == "CLEAN" && lightReading.qualityFlags == "CLEAN") {
        digitalWrite(LED_GREEN, HIGH);
    } else {
        digitalWrite(LED_GREEN, LOW);
    }

    // Blue LED: Missing/imputed data
    if (tempReading.isMissing || tempReading.isImputed ||
        lightReading.isMissing || lightReading.isImputed) {
        digitalWrite(LED_BLUE, HIGH);
    } else {
        digitalWrite(LED_BLUE, LOW);
    }
}

// ====================== SERIAL OUTPUT ======================

void printSensorReading(const char* sensorName, const SensorReading& reading) {
    Serial.print(sensorName);
    Serial.print(": Raw=");
    if (isnan(reading.rawValue)) {
        Serial.print("NaN");
    } else {
        Serial.print(reading.rawValue, 2);
    }

    Serial.print(", Clean=");
    if (isnan(reading.cleanedValue)) {
        Serial.print("NaN");
    } else {
        Serial.print(reading.cleanedValue, 2);
    }

    Serial.print(", Norm=");
    if (isnan(reading.normalizedValue)) {
        Serial.print("NaN");
    } else {
        Serial.print(reading.normalizedValue, 3);
    }

    Serial.print(" [");
    Serial.print(reading.qualityFlags);
    Serial.println("]");
}

void printStatistics() {
    Serial.println("\n========== DATA QUALITY STATISTICS ==========");
    Serial.print("Total Samples: ");
    Serial.println(totalSamples);
    Serial.print("Valid Samples: ");
    Serial.print(validSamples);
    Serial.print(" (");
    Serial.print(100.0 * validSamples / max(totalSamples, 1UL), 1);
    Serial.println("%)");
    Serial.print("Outliers Detected: ");
    Serial.print(outlierSamples);
    Serial.print(" (");
    Serial.print(100.0 * outlierSamples / max(totalSamples, 1UL), 1);
    Serial.println("%)");
    Serial.print("Missing Values: ");
    Serial.print(missingSamples);
    Serial.print(" (");
    Serial.print(100.0 * missingSamples / max(totalSamples, 1UL), 1);
    Serial.println("%)");
    Serial.print("Imputed Values: ");
    Serial.print(imputedSamples);
    Serial.println();
    Serial.print("Range Violations: ");
    Serial.println(rangeViolations);
    Serial.print("Rate Violations: ");
    Serial.println(rateViolations);

    Serial.println("\n--- Temperature Statistics ---");
    Serial.print("Mean: ");
    Serial.print(tempStats.mean(), 2);
    Serial.print(" C, StdDev: ");
    Serial.print(tempStats.stdDev(), 2);
    Serial.print(" C, Range: [");
    Serial.print(tempMinSeen, 1);
    Serial.print(", ");
    Serial.print(tempMaxSeen, 1);
    Serial.println("] C");

    Serial.println("\n--- Light Statistics ---");
    Serial.print("Mean: ");
    Serial.print(lightStats.mean(), 0);
    Serial.print(" lux, StdDev: ");
    Serial.print(lightStats.stdDev(), 0);
    Serial.print(" lux, Range: [");
    Serial.print(lightMinSeen, 0);
    Serial.print(", ");
    Serial.print(lightMaxSeen, 0);
    Serial.println("] lux");
    Serial.println("==============================================\n");
}

// ====================== SETUP AND LOOP ======================

void setup() {
    Serial.begin(115200);
    delay(1000);

    // Initialize pins
    pinMode(TEMP_PIN, INPUT);
    pinMode(LIGHT_PIN, INPUT);
    pinMode(DRIFT_PIN, INPUT);

    pinMode(LED_RED, OUTPUT);
    pinMode(LED_YELLOW, OUTPUT);
    pinMode(LED_GREEN, OUTPUT);
    pinMode(LED_BLUE, OUTPUT);

    // All LEDs off initially
    digitalWrite(LED_RED, LOW);
    digitalWrite(LED_YELLOW, LOW);
    digitalWrite(LED_GREEN, LOW);
    digitalWrite(LED_BLUE, LOW);

    // Seed random for missing data simulation
    randomSeed(analogRead(0));

    Serial.println("============================================");
    Serial.println("  DATA QUALITY LAB: IoT Preprocessing Demo  ");
    Serial.println("============================================");
    Serial.println("Features demonstrated:");
    Serial.println("  - Range validation (physical bounds)");
    Serial.println("  - Rate-of-change validation");
    Serial.println("  - Z-Score outlier detection");
    Serial.println("  - IQR outlier detection");
    Serial.println("  - Median filter (spike removal)");
    Serial.println("  - Moving average filter (smoothing)");
    Serial.println("  - Exponential smoothing");
    Serial.println("  - Missing value imputation (forward-fill)");
    Serial.println("  - Min-Max normalization (0-1 scaling)");
    Serial.println("============================================");
    Serial.println("LED Indicators:");
    Serial.println("  RED: Range/Rate violation");
    Serial.println("  YELLOW: Outlier detected");
    Serial.println("  GREEN: Clean valid data");
    Serial.println("  BLUE: Missing/Imputed data");
    Serial.println("============================================\n");

    Serial.println("Starting data collection...\n");
}

unsigned long lastSampleTime = 0;
unsigned long lastStatsTime = 0;
const unsigned long STATS_INTERVAL_MS = 10000;  // Print stats every 10 seconds

void loop() {
    unsigned long currentTime = millis();

    // Sample at defined interval
    if (currentTime - lastSampleTime >= SAMPLE_INTERVAL_MS) {
        lastSampleTime = currentTime;

        // Read sensors
        int tempADC = analogRead(TEMP_PIN);
        int lightADC = analogRead(LIGHT_PIN);
        int driftADC = analogRead(DRIFT_PIN);

        // Add simulated drift from potentiometer (optional)
        float driftFactor = (driftADC - 2048) / 2048.0;  // -1 to +1
        tempADC = constrain(tempADC + (int)(driftFactor * 500), 0, 4095);

        // Process readings through data quality pipeline
        SensorReading tempReading = processTemperature(tempADC, currentTime);
        SensorReading lightReading = processLight(lightADC, currentTime);

        // Update LED indicators
        updateLEDs(tempReading, lightReading);

        // Print readings
        printSensorReading("TEMP", tempReading);
        printSensorReading("LIGHT", lightReading);
        Serial.println();
    }

    // Print statistics periodically
    if (currentTime - lastStatsTime >= STATS_INTERVAL_MS) {
        lastStatsTime = currentTime;
        printStatistics();
    }
}

26.20 Step-by-Step Instructions

This section: Step-by-Step Instructions — The Wokwi Serial Monitor is the source of evidence for the ESP32 sketch.

The Wokwi Serial Monitor is the source of evidence for the ESP32 sketch. The local Python calculation below checks only scaling arithmetic; it is not a Wokwi run or a substitute for the monitor trace. Record your own Wokwi readings when you run the browser simulation.

26.21 Step 1: Set Up the Simulator

This section: Step 1: Set Up the Simulator

• Open the Wokwi ESP32 workspace linked above and locate its diagram and sketch editor tabs.
• Paste this lab’s diagram.json into the diagram editor and the Arduino code into the sketch editor.
• Check the sensor and four LED connections against the Circuit Setup section before pressing Play.
• Open the Serial Monitor; the sketch’s start banner should identify the preprocessing demo and LED meanings.
• Save the project link or sketch revision with the trace, because a later rerun needs the same inputs.

26.22 Step 2: Run and Observe Validation

This section: Step 2: Run and Observe Validation

• Press Play, then watch the Serial Monitor for a temperature and light reading with its raw, clean, and normalized fields.
• Copy one complete CLEAN row with its timestamp; that flag means this reading passed the sketch’s checks.
• Keep the raw and clean fields together: the filter may move a valid value without making it invalid.
• Record a second row after changing a sensor control, so the input and observed response can be compared.
• If the monitor shows no row, check the sketch and circuit connections before claiming validation succeeded.

26.23 Step 3: Trigger Range Violations

This section: Step 3: Trigger Range Violations

• In the Wokwi sensor control, move the input beyond the sketch’s valid range or change it fast enough to exceed its rate limit.
• Watch the Serial Monitor for RANGE_VIOLATION or RATE_VIOLATION; copy the flagged row and the prior valid row.
• Compare the flagged raw value with the cleaned value; the sketch uses its last valid value when one is available.
• Check the red LED while the invalid reading is displayed, and note whether the next steady reading clears it.
• If the available sensor control cannot reach the configured limit, record that limitation instead of inventing a flag.

26.24 Step 4: Observe Outlier Detection

This section: Step 4: Observe Outlier Detection

• Let the Wokwi Serial Monitor collect more than 20 valid temperature samples before testing the statistical checks.
• Move the sensor sharply while remaining inside the valid range, then inspect the next flagged monitor row.
• Record whichever of ZSCORE_OUTLIER or IQR_OUTLIER actually appears; the sketch does not guarantee both on one input.
• Compare its raw value, OUTLIER_REPLACED flag, and cleaned value with the recent normal readings.
• A separate local Python arithmetic check used [20, 21, 22, 80] and returned median replacement 21.0; it does not claim the Wokwi sketch produced that row.

26.25 Step 5: Observe Missing Data Handling

This section: Step 5: Observe Missing Data Handling

• Leave the Wokwi simulation running; the sketch’s missing-data branch is random, so a short trace may show none.
• In the Serial Monitor, locate IMPUTED_FFILL and compare its clean value with the preceding valid reading.
• Check the blue LED while the missing or imputed row is displayed, and retain the flagged timestamp.
• If consecutive missing samples exceed the sketch’s limit, record MISSING_NO_IMPUTE and the absent normalized value.
• Report how many rows you observed and which flags appeared; do not infer a measured 5% rate from a short run.

26.26 Step 6: Experiment with Filtering

This section: Step 6: Experiment with Filtering

• Keep the Wokwi Serial Monitor open and change one sensor gradually; copy several consecutive raw and clean pairs.
• Mark which clean values lag or smooth the raw changes after the median, moving average, and exponential stages.
• Compare the normalized field only against the observed minimum and maximum for that same sensor.
• A real local Python arithmetic check for raw 20, 21, 22 gave (21 - 20) / (22 - 20) = 0.50.
• Do not treat that arithmetic result as serial output: quote the simulator’s own rows when assessing this ESP32 run.

26.27 Continue to the Next Part

This section: Continue to the Next Part — Carry this evidence into Feature Scaling Lab: Statistical Analysis, which begins with Step 7: Analyze Statistics.

Carry this evidence into Feature Scaling Lab: Statistical Analysis, which begins with Step 7: Analyze Statistics.