 Your HTML code for the FuzzyLogic Waveform Detector web page is well structured and covers a range of functionalities. It includes meta tags for SEO, links to external star sheets and scripts, a header section with navigation, and a main content area with various controls and informational sections. Here are a few suggestions for improvement. Relative Parts Ensure that the relative parts, like Slash Barnacaos underscore images slash fuzzylogic.jpg, are correctly pointing to the resources. If your website is hosted in a different environment, like a server, relative parts might need adjustment. Accessibility Make sure that all interactive elements are accessible. For instance, for the select and input elements, ensure they are fully accessible to users with disabilities, possibly by adding more descriptive labels or ARIA attributes. Optimization Consider deferring non-critical JavaScript to reduce the initial load time. For scripts that aren't essential for the initial rendering, use the async or defer attributes. Validation It's always good practice to validate your HTML to ensure there are no syntax errors. You can use the W3C validation service for this. Comments and documentation Your comment at the end indicates that there is a main.js file linked to this page. Make sure that this script is correctly linked and functioning as intended. Also, ensure your code is well documented for future maintenance or updates. Responsive Design Ensure your website is responsive and provides a good user experience on various devices. This can be achieved through responsive design techniques in CSS. CO and metadata Consider enhancing your less-than-meta greater-than-tags for better CO. For example, adding a less... For example, adding a less-than-meta... Just remember to test across different browsers and devices. The main.js file for your fuzzy logic application is comprehensive and well-structured. It primarily handles the interaction with the user interface elements, fetching data from the server, and updating the UI based on the response. Here are some key points and suggestions. Of endlessness, the script correctly adds of endlessness to UI elements in good wave and noise amplitude to trigger the Analyze Waveform function when the user interacts with these elements. Fetching data, the Analyze Waveform function sends a post request to the Analyze endpoint with the selected Waveform and Noise Ampitude. This is a good approach for dynamic data processing. Data Visualization The script uses plot later plot various graphs. This is a powerful library for creating interactive charts. Error Handling The use of catch for error handling in fetch requests and error logging in case of invalid data is a good practice. DOM Manipulation The script updates the DOM elements with the response data effectively. Fuzzy Logic Visualization The plot fuzzy logic parameters function creates detailed visualizations for different aspects of the fuzzy logic data, which is great for an educational tool. Optimization and Organization Consider separating the graph plotting logic into separate functions for better readability and maintenance. You may want to refactor repeated code, like the creation of trace objects into a utility function. Comments and Documentation Add more comments explaining the purpose of functions and complex logic. This will be helpful for future maintenance or for other developers reviewing your code. Robustness Make sure to handle scenarios where the server might not respond or return an unexpected response format. Loading Indicators Since there are network requests involved, implementing a loading indicator or disabling the input elements during the request can improve user experience. Overall, the JavaScript code appears to be well thought out and should provide a solid functionality for your web application. Just ensure to test across different browsers for compatibility. Your Flask application for the fuzzy logic waveform detector seems well structured and functionally rich. It incorporates fuzzy logic for waveform analysis and provides a detailed response to the client. Here are some observations and potential areas for improvement. Error Handling Your code includes a tri-except block in the Analyze route, which is good for handling unexpected errors. Make sure that all possible exceptions are being caught and handled properly. Input Validation You're checking if input underscore wave underscore value is none, which is good. It might be beneficial to also validate the type and range of noise underscore amplitude underscore value to ensure it's within expected bounds. Fuzzy Logic Implementation The implementation of fuzzy logic with SK fuzzy looks correct. You are creating membership functions, applying fuzzy rules and defuzzifying the output. Ensure that these fuzzy sets and rules accurately represent the logic you intend to model. Global Variables for History You're using global variables, detection underscore error underscore history and unknown underscore percentage underscore history, the store historical data. While this works, consider that in a production environment with multiple users, this will make all users histories together. A session-based or request-specific approach might be more suitable. Your implementation of fuzzy logic using the SK fuzzy library appears to be on the right track. Here are some key points to ensure your fuzzy logic model is implemented effectively. Membership Functions You've defined trapezoidal membership functions, Fuzz, TrapMF, for both symmetry and peak underscore sharpness. This is a common choice for fuzzy sets. Make sure the parameters of these functions, like 0, 0, 0.1, 0.2, for MF underscore symmetry underscore low, accurately represent the linguistic variables you're modeling, like low, medium and high symmetry. The choice of trapezoidal membership functions, using Fuzz, TrapMF, for both symmetry and peak underscore sharpness in your fuzzy logic implementation is appropriate for many applications, including waveform analysis. Here are some considerations to ensure the effectiveness of these membership functions. Representation of Linguistic Variables Trapezoidal membership functions are versatile for representing linguistic variables like low, medium and high. Ensure that the parameters of these functions, e.g., 0, 0, 0.1, 0.2, for MF underscore symmetry underscore low, appropriately capture the essence of these terms. For instance, low should cover the range of values that you consider to be definitively low, and not encroach significantly into the medium range. Medium typically represents a transition phase between low and high and should be set accordingly. High should similarly be distinct from medium and cover the upper range of values. Overlap between functions, there should be an appropriate amount of overlap between adjacent membership functions, e.g., between MF underscore symmetry underscore low and MF underscore symmetry underscore mid. This overlap allows for smooth transitions and represents the uncertainty and fuzziness inherent in these linguistic terms. Coverage of the entire range, ensure that the entire range of possible values for symmetry and peak underscore sharpness is covered by the membership functions. There should be no value that falls outside all to define membership functions. Ensuring complete coverage of the entire range of possible values for symmetry and peak underscore sharpness with your membership functions is crucial in fuzzy logic. This ensures that for any possible input value, the system has a defined response. Here's how you can ensure this in your fuzzy logic implementation. Range of input values. First, identify the complete range of possible values for symmetry and peak underscore sharpness. This range should be based on the theoretical or empirical limits of these parameters in the context of your application. Low, medium, high membership functions. Design the low, medium, and high membership functions so that they span the entire range of symmetry and peak underscore sharpness. For example, the low membership function should start at the minimum possible value. Overlap, ensure that there's sufficient overlap between adjacent membership functions so that any value in the range belongs to at least one membership function. Visualize membership functions. Plot these membership functions to visually confirm that they cover the entire range of values. This will help you see if there are any gaps or overly narrow coverage in certain areas. Validation. Test the membership functions with input values spanning the entire range. Ensure that for every input value, the fuzzy logic system produces a meaningful output. This means that each input value should activate at least one membership function to send a degree. Adjustments based on testing. If you find any gaps or issues during testing, adjust the parameters of the membership functions. The goal is to achieve a balance where the system is sensitive enough to differentiate between different levels of symmetry and peak underscore sharpness, but not so sensitive that it produces erratic or nonsensical outputs. Consistent with theoretical understanding, the coverage should be consistent with your theoretical understanding of symmetry and peak underscore sharpness in the context of waveforms. If certain values are more likely or significant in practical scenarios, the membership functions should reflect that in their coverage. Creating a style.css file to ensure that the plots fit the whole screen involves defining CSS rules that target the plot elements in your HTML structure. Here's a basic template to get you started. To create a style.css that ensures plots fit the entire screen and includes all necessary classes with a specified color theme, you can use the following CSS. This CSS will be structured to make sure your plots take full advantage of the available screen space, while also incorporating the color theme variables you've provided. This CSS file defines a basic layout with your color theme variables. It ensures that plot containers, graph gas, take the full width of the screen. Each section, panel, statistics, etc., has its own styling, with margins and paddings for better readability. Navigation and other text elements are styled to match your color theme. To create a style.css file that ensures all plots fit the screen without scrolling and includes the specified classes with the provided color theme, follow these guidelines. General layout and sizing. Ensure that elements resize responsibly to fit various screen sizes. Set a maximum width for the plots to prevent horizontal scrolling. Color theme. Utilize the provided color variables for consistency across the design. Specific classes. Style the control, statistics, stat item, graphs, fuzzy logic parameters, and content section classes according to your layout requirements. Here's a basic template for your style.css. CSS. Copy code. Root. Murders 1. Number 0477BF. Murders 2. Number 04BF68. Murders 3. Hashtag F2C641. Murders 4. Hashtag F25835. Murders 5. Number 0D0D. Body. And responsive design. You can expand upon this by adding more specific styling rules for other elements, text sizes, button styles, etc., as needed for your application. Remember to test the layout on different devices and screen sizes to ensure that the plots and other elements render properly without the need for scrolling. To modify your style.css to include multiple charts horizontally when the window size is wide enough, you can use CSS Flexbox or CSS Grid. Flexbox is a good choice for this scenario as it allows for a flexible layout that adjusts based on the size of the container. Here's how you could update the CSS to include this feature. Use Flexbox for the graphs. Make the, graphs and, fuzzy logic parameters containers flex containers. Allow the child elements, individual graphs, to wrap as needed. Responsive design. Set a media query for larger screens where you want the graphs to be displayed side by side. For smaller screens, the graphs can stack vertically. Here's the updated CSS. Ensuring complete coverage of the entire range of possible values for symmetry and peak underscore sharpness with your membership functions is crucial in fuzzy logic. This ensures that for any possible input value, the system has a defined response. Here's how you can ensure this in your fuzzy logic implementation. Range of Input values. First, identify the complete range of possible values for symmetry and peak underscore sharpness. This range should be based on the theoretical or empirical limits of these parameters in the context of your application. Design membership functions to cover the full range. Low, medium, high membership functions. Design the low, medium, and high membership functions so that they span the entire range of symmetry and peak underscore sharpness. For example, the low membership function should start at the minimum possible value. The high membership function should extend to the maximum possible value. The medium membership function bridges the gap between low and high. Overlap. Ensure that there's sufficient overlap between adjacent membership functions so that any value in the range belongs to at least one membership function. Visualize membership functions. Plot these membership functions to visually confirm that they cover the entire range of values. This will help you see if there are any gaps or overly narrow coverage in certain areas. Validation. Test the membership functions with input values spanning the entire range. Ensure that for every input value, the fuzzy logic system produces a meaningful output. This means that each input value should activate at least one membership function to send a degree. Adjustments based on testing. If you find any gaps or issues during testing, adjust the parameters of the membership functions accordingly. The goal is to achieve a balance where the system is sensitive enough to differentiate between different levels of symmetry and peak underscore sharpness, but not so sensitive that it produces erratic or nonsensical outputs. Consistent with theoretical understanding, the coverage should be consistent with your theoretical understanding of symmetry and peak underscore sharpness in the context of waveforms. If certain values are more likely or significant in practical scenarios, the membership functions should reflect that in their coverage. By carefully designing your membership functions to cover the entire range of symmetry and peak underscore sharpness, you ensure that your fuzzy logic system can handle any input within the expected domain, leading to more reliable and accurate outputs. If your fuzzy logic system is incorrectly identifying a square waveform input as a triangle waveform, there are several aspects of the system you may need to review and adjust. Membership function parameters. Re-examine the parameters of your membership functions for symmetry and peak sharpness. The parameters might not be accurately representing the characteristics of a square wave. Adjust these parameters so that the system can more accurately differentiate between square and triangle waves. To address the issue of the system incorrectly identifying a square waveform as a triangle waveform and enhance the functionality of your application, you might want to include the display of output characteristics of the input signal. Here's how you can proceed to both diagnose the problem and enhance your code. Diagnostic visualization. It's important to visualize the characteristics of the input signal that are being evaluated by the fuzzy logic system. This might include the symmetry and sharpness measures that your system uses to classify the waveform. By adding graphs that show the input signal's calculated symmetry and sharpness, you can visually inspect whether these measures are being calculated as expected. Fixing the fuzzy logic classification. Adjust the membership functions if the calculated symmetry and sharpness do not align with the expected values for a square wave. Check the rule activations in your fuzzy logic system. The rule activation graph should clearly show the highest activation for the square rule where a square wave is input. Ensure the centroid calculation in the aggregated output fuzzy set with centroid, graph is correctly finding the balance point of the aggregated fuzzy set. Updating the front end. To display the output characteristics, you would add additional elements to your front end to show the calculated symmetry and sharpness. You can modify your JavaScript to include additional plotly graphs that outdated similarly to the existing graphs. Back end adjustments. Ensure your flash back end sends the necessary data for the new characteristics you want to display. This includes the symmetry and sharpness arrays and any other relevant data. Adjust the analyze route to include this additional information in the JSON response. JavaScript code. Update your main JS or equivalent front end script to handle the new data for symmetry and sharpness. Use this data to populate new plotly graphs, which you will add to the HTML of your application. Here is a simplified example of how you might modify your JavaScript to add a new plot for the symmetry characteristic. For this to work, you would need to add an element with id equals, symmetry graph div, to your HTML, and your back end would need to supply symmetry array as part of the JSON response. If there is no data, symmetry array being sent from the flash back end, you need to modify the back end to calculate and send this data to the front end. Apologies for the confusion. Let's align with the data structure that your flash back end is expected to return based on a provided Python code. According to your Python code, the fuzzy data should contain a structure with symmetry and sharpness information, each containing an array for x and values for low, mid, and high membership functions. To display the symmetry characteristic of the input signal on the front end, you will need to add a new graph to your JavaScript code that handles the plotting of the symmetry data contained within the fuzzy data object of the JSON response. Here is how you might modify your main. JS to add a new plot for the symmetry characteristic using the data from the fuzzy data object. Make sure you add a corresponding div element to your HTML file where this graph should be displayed. By updating the JavaScript and HTML code with the above changes, the front end will be able to display the symmetry characteristics based on the fuzzy data returned by the back end. This visualization will help you diagnose why a square wave input might be misclassified as a triangle wave by giving you insight into the fuzzy logic system's internal workings. If the symmetry characteristic is not being calculated or interpreted correctly, it can lead to incorrect classification, which you can now investigate incorrect. Yes, having a sharpness graph is equally important because it represents another key feature that your fuzzy logic system uses to classify waveforms. If the sharpness characteristic is not as expected for a square wave, this calls to contribute to the misclassification issue. Here's how you can add a sharpness graph similar to the symmetry graph in your main, JS. The symmetry membership function and the sharpness graph represent two different characteristics of the input signal and how these characteristics are interpreted by the fuzzy logic system. Symmetry membership function. The symmetry membership function graphically represents how much a given signal's symmetry characteristic, calculated from a signal, matches with predefined fuzzy sets labeled as low, mid, and high symmetry. These membership functions are used by the fuzzy logic system to determine the degree to which the symmetry of the input signal conforms to these fuzzy sets. In waveform analysis, symmetry refers to how mirror like a signal is about a central axis. A high symmetry score would indicate that the waveform looks similar on both sides of the axis. Sharpness graph. The sharpness graph would represent the calculated sharpness of the input signal over time or across samples. Sharpness typically refers to how abrupt or steep the changes in the signal are. In the context of waveforms, sharpness might indicate the presence of peaks or edges. If you were to graph the sharpness, it would show the actual calculated sharpness values of a signal, not the membership degrees. For example, it might show where the signal has sharp transitions or peaks, which is characteristic of square waves. In the context of the fuzzy logic system, you would also have sharpness membership functions similar to symmetry membership functions. Sharpness membership function. Similar to symmetry, sharpness membership functions will show how much the calculated sharpness measures the low, mid, and high fuzzy sets for sharpness. This helps the fuzzy logic system decide to what degree the signal's sharpness fits into each category and is crucial for classifying waveforms with sharp features like square waves. In summary, symmetry membership function deals with the fuzzy categorization of the signal's symmetry characteristic. Sharpness graph could represent either the actual calculated sharpness values across the signal or, if referring to membership functions, the fuzzy categorization of the signal's sharpness characteristic. When creating visualizations for these, you will be plotting the degree to which the calculated characteristics, symmetry, and sharpness of a signal match predefined fuzzy categories. This is essential for tuning and debugging your fuzzy logic system, especially if you're encountering misclassification issues. You're correct. The plot fuzzy logic parameters function in your JavaScript code is indeed intended to plot the fuzzy logic parameters, including the membership functions for symmetry and sharpness, based on the fuzzy data received from the back end. It plots the membership functions and the degree of activation for each fuzzy rule, e.g., square, triangle, trapezoid. Here's how the plot fuzzy logic parameters function operates, based on the provided code. Symmetry membership functions plot. This creates a plot showing the low, mid, and high symmetry membership functions along with the degree of activation for each. The x-axis is the range of possible symmetry values, and the y-axis is the degree to which the input symmetry is considered low, mid, or high. Sharpness membership functions plot. Similar to symmetry, this plot visualizes the membership functions for the sharpness characteristic of the input signal. The degree of activation for low, mid, and high sharpness is displayed, showing how the input sharpness is categorized by the fuzzy system. Rule activation plot. This shows the degree to which each fuzzy rule is activated based on the input's characteristics. For instance, it will show how much the input signal activates the, square, rule versus the, triangle, or trapezoid, rule. Aggregated output fuzzy set with centroid. This plot visualizes the aggregated result of all the fuzzy rules applied in the calculated centroid that is used for defuzzification, which ultimately determines the classified waveform. To display these plots on your front end, make sure the developments for each plot are present in your HTML, and call plot fuzzy logic parameters, data, fuzzy data, within your JavaScript code where data is the JSON response from the server. If you need to troubleshoot why a square wave is being misclassified as a triangle, you can use these plots to examine the fuzzy logic systems internal decision-making process. You should check. If the activation levels for the symmetry and sharpness characteristics are as expected for a square wave. If the activation levels for the symmetry and sharpness characteristics are as expected for a square wave. If the rule activations correctly reflect a higher activation for, square, rule when a square wave is input. Whether the centroid calculation on the aggregated fuzzy set accurately represents the balance point, leading to the correct classification. Whether the centroid calculation on the aggregated fuzzy set accurately represents the balance point, leading to the correct classification. Based on the new screenshot you've provided, it appears that the system is experiencing a 100% detection error, which means the classification is entirely incorrect for the input given. Here's a step-by-step approach to diagnose and potentially resolve the issue. Examine the inward waveform graph to ensure that the signal being analyzed is indeed a square wave. Noise is present, so ensure the noise level is not so high that it fundamentally changes the shape of the waveform. Check the rule activation graph. In a correctly functioning system, the square rule should have the highest activation when the input is a square wave. However, the graph indicates significant activation for the triangle rule instead. This suggests that either the features extracted from the inverse signal, symmetry and sharpness, are not accurate, while a membership function parameters and rules are not correctly tuned for the characteristics of a square wave. The aggregated output fuzzy set with centroid graph shows the aggregated membership function and the resulting centroid, which is used to decide on the classification. The centroid appears to be placed in a position that, according to the system's logic, corresponds more closely to a triangle wave rather than a square wave. Feature extraction ensure that the features, symmetry and sharpness are extracted in a way that is resilient to noise and accurately reflects the characteristics of square waves. The calculation membership function tuning adjusts the parameters of the membership functions. If the noise level is typical for your use case, the membership functions should account for that noise when differentiating between waveforms. Rule refinement, revisit the fuzzy rules. The rules may need to be adjusted to ensure that the correct waveform classification is triggered based on the features extracted from the signal. The defuzzification strategy, confirm that the defuzzification strategy and centroid calculation are correctly implemented. The centroid should accurately reflect center of mass of the aggregated fuzzy set. Noise handling, if noise is a significant factor, consider implementing a pre-processing step to reduce the noise or a post-processing step to correct for noise induced errors in feature extraction. The issue you're encountering, where the system identifies the input as a triangle wave, despite the rule activation and centroid indicating a square wave, could be due to several reasons. Centroid calculation issue, the centroid appears to be correctly located within the range that should indicate a square wave as per the aggregated output fuzzy set with centroid, graph. However, the final classification output is a triangle wave. This suggests there might be a problem with how the centroid value is being interpreted or mapped to the output classification. Defuzzification process, the defuzzification process translates the fuzzy values into a single crisp output. There could be a bug or logical error in the defuzzification code that interprets the centroid value. Output classification logic, the logic that takes the centroid value and determines the output wave classification might be incorrectly implemented. It's possible that the thresholds for classifying the centroid value into a square, triangle or trapezoid wave are not set correctly. Front end back end mismatch, there might be a mismatch between the back end processing and the front end display. It's essential to ensure that the front end correctly receives and interprets the back end's response. Given the provided centroid value of 0.53 in the classification logic, the output wave should indeed be classified as a triangle, because 0.53 is less than two-thirds but greater than one-third. The classification logic seems to be functioning as programmed according to the conditions you set up. However, if the visualizations in your understanding of the system indicate that the waveform should be classified as a square, rather than a triangle, then you may need to adjust your classification thresholds based on the centroid value. The current thresholds might not be correctly aligned with the characteristics of the waveforms you are analyzing. Here are some steps you can take. Re-evaluate thresholds, reconsider the centroid thresholds for classifying waveforms. It might be that the boundary is too strict or too lenient. You may need to analyze a variety of waveforms and see where the centroid's usually lied to adjust these thresholds better. Waveform feature analysis, analyze the features of your waveforms, especially the symmetry and sharpness values that contribute to the centroid calculation. The features that lead to the centroid being calculated as 0.53 for a square wave might need to be investigated to ensure they're being calculated correctly. Visualizations, use the visualizations to confirm the centroid calculation is consistent with the rule activations. If the rule activation clearly shows a higher activation for the square rule, yet the centroid is in the triangle range, you might want to adjust how the centroid is calculated or reconsider the definition of your membership functions. Adjust membership functions, if the square waveform consistently results in a centroid indicative of a triangle, it may be necessary to adjust the membership functions themselves so that the centroid calculation more accurately reflects the activation levels. Testing and calibration, test with various known waveforms and calibrate your system accordingly. By doing so, you'll be able to refine the thresholds of the centroid values to ensure that the output classifications are accurate. Refine fuzzy logic system, consider the possibility that your fuzzy logic system may need more fine tuning. The membership functions, rules, or even the method for aggregating the rules might need to be adjusted to better reflect the characteristics of the input waveforms. After making adjustments, test the system again with the same square waveform and check if the centroid value and the classification are now aligned with the expected outcome. If the system still classifies the waveform incorrectly, continue to iterate on the fuzzy logic parameters and thresholds until the system performs as intended. To overlay the current waveform parameters on top of the symmetry and sharpness membership function plots, you need to monitor-