The safety and emotional well-being of companion animals, particularly pet dogs, have become significant concerns in recent years. Anxiety is a common issue among pet dogs, manifesting in behaviors such as excessive barking, pacing, trembling, and even destructive actions. These behaviors can profoundly affect both the dog's well-being and its owner's peace of mind. This research proposes a novel system that integrates deep learning (DL) algorithms with smart thin-film materials to monitor and regulate anxiety in dogs through a smart wearable solution. To analyze and detect anxiety regulation in pet dogs, a Tangent Search-driven Stacked Convolutional Neural Network (TS-StackedCNN) model is applied. Data is sorted into three levels of anxiety severity, where Level 1 is the lowest anxiety, Level 2 is moderate anxiety, and Level 3 is high anxiety. In the preparation of raw sensor data, a Gabor filter is applied during pre-processing to filter out noise and outliers so only the relevant data can be analyzed. Feature extraction was performed using Linear Discriminant Analysis (LDA) to find important features distinguishing each anxiety level. The TS-Stacked CNN model was able to reach a high level of accuracy after processing these features, where Level 1 had precision equal to 0.950, recall equal to 0.949, and F1-score equal to 0.948; Level 2 had precision equal to 0.946, recall equal to 0.889, and F1-score equal to 0.919; and Level 3 had precision equal to 0.864, recall equal to 0.868, and F1-score equal to 0.865. This interdisciplinary approach advances both animal behavioral science and functional smart materials, paving the way for real-world applications in pet care, veterinary monitoring, and stress intervention technologies.