Shareholder rights law firm Johnson Fistel, LLP ( is investigating whether Amplitude, Inc. (NASDAQ:AMPL), any of its executive officers or others

AMPL SHAREHOLDER ALERT: Johnson Fistel Investigates Amplitude

InvestorPlace - Stock Market News, Stock Advice & Trading Tips Despite recent volatility, U.S. equities markets have had a much better year

3 Struggling Stocks to Sell in November Before They Implode

Endless Dungeon, the latest nugget from development studio Amplitude Studios, is shaping up to be a must-have for video game lovers! Published by publisher SEGA, the game awaits you on October 19, 2023 on PC, PS4, PS5, Xbox One, Xbox Series and Nintendo Switch, marking a new stage in the evolution of tactical roguelikes.

Endless Dungeon: our review of Amplitude Studios' new hit!

Pomerantz LLP is investigating claims on behalf of investors of Amplitude, Inc. ("Amplitude" or the "Company") (NASDAQ:AMPL). Such investors are advised to contact Robert

SHAREHOLDER ALERT: Pomerantz Law Firm Investigates Claims On Behalf of Investors of Amplitude, Inc. - AMPL

The sensitivity of LIGO has squeezed the quantum limit, meaning it can now detect merging black holes and neutron stars on smaller scales and at greater distances than ever before.

LIGO gravitational wave detector breaks 'quantum limit' to find deep universe black hole collisions

Sound energy travels in waves that are invisible and is measured in frequency and amplitude which is where the decibels are sensed and matter. I will define both of these words. Frequency is measured in the number of sound vibrations in one second.

What are these things called ‘decibels’ and why are they important?

The game’s presentation is excellent. Its art style is reminiscent of a refined comic book or visual novel – one moment you’re taking in a beautiful, plaintive scene, and the next moment – Boom! Bam! – is an action-packed spectacle. The soundtrack brings it all home, appropriately bouncing from soft electronic landscapes to pumping rock music.

Game On: Endless Dungeon offers a unique and exciting co-op experience

With the popularity of FWA (Fixed Wireless Access) devices among homes and enterprises, the pursuit of unleashing the potential of unlimited

Fibocom Debuts the Wi-Fi 7 Module WN170-GL at Broadband World Forum 2023

“Now that we have surpassed this quantum limit, we can do a lot more astronomy,” Lee McCuller, co-author and assistant professor of physics at Caltech, said in a press statement. “LIGO uses lasers and large mirrors to make its observations, but we are working at a level of sensitivity that means the device is affected by the quantum realm.”

The Quantum Limit Has Been Surpassed. That Seemed Impossible.

Gravitational wave facilities measure distortions in the fabric of spacetime down to 10 quadrillionths the width of a hair – small enough to hear interference from particles popping in and out of existence.

LIGO squeezes light to surpass quantum limit measuring spacetime ripples

Get the most recent info and news about Amplitude on HackerNoon, where 10k+ technologists publish stories for 4M+ monthly readers.

Amplitude Media is a full service creative agency specialising in film, photography, animation, and graphic design.

We pride ourselves on developing creative content that helps our clients communicate their message in exciting and interesting ways. Full service means we can manage the whole process, from concept creation to final delivery. Our marketing boffins can advise on the right strategic vision and delivery methods to meet your commercial objectives, then it's up to our project managers and creatives to knock it out of the park.

Sound good? Drop us a line. We'd love to chat.

Amplitude

It’s 10:15pm. The Amplify conference starts the next morning, and I just found out that I would be attending. I could not wait. I received a pass to Amplify because of the generosity of the Advancing Women in Product (AWIP) community — AWIP is a organization whose goal is to empower the next generation of women product leaders. So there I was on the morning of October 9th, nibbling on my mini breakfast croissant, bumping against the shoulders of product leaders, anticipating the start of a jam-packed, learning-rich, & Ritual Roasters coffee-filled day. If I think about the learnings I drew out of the conference, I’d say they weren’t necessarily profound nuggets of wisdom — they’re more like gentle reminders. Things I already know but tend to forget when building products. Here’s what I learned: Growth is more than a funnel. It’s a lot of different loops. I often break down products via the Pirate Funnel (Awareness, Acquisition, Activation, Retention, Revenue or AAARR for short). But Casey Winters, (VP Product at Eventbrite, formerly growth at Pinterest & Grubhub, among others), argues that that framework prioritizes feeding only into the top of the funnel. When in fact, our products are ongoing feedback mechanisms, aka Loops. Casey Winters interviewing Elena Verna Macro loops stitch our micro loops over time. We have 3 general types of loops: Viral loops are when users organically share or are incentivized to refer other friends back to your product. Content loops are classified based on the of content generated. These can be company (HubSpot, WebMD), user (Pinterest) or supply (Grubhub) generated. type Paid loops vary based on who does the work to distribute the product. These can be ads, sales teams or integrations via partnerships. These growth loops paint a better picture than a funnel, and when architected like this you’ll reap the best outcomes. We can make a difference when we look at products from the lens of social science. I love Dan Ariely (best-selling author of Predictably Irrational, behavioral economics professor at Duke University). I love behavioral economics. I love Dan Ariely’s talk on behavioral economics for products. Dan Ariely giving the keynote! Dan performed a research study in Kenya with the goal of finding ways to help Kenyans save money. He tried several tactics, with mediocre results: injecting friction to make it more difficult to take out money, sending guilt-filled reminders to save, and introducing loss aversion in saving. But the tactic that worked the best by far was so simple and effective: if they saved money that day then they could scratch that day off on a calendar using a coin. The coin method made them aware of their daily actions of saving, and also injected social accountability from their family members. A simple, yet effective change in habit that made the often invisible act of saving money, extremely visible everyday. Another great talk on behavior was from Tatyana Mamut. Her talk offered tactical advice in dealing with bad Internet behavior such as malicious accounts and fake news. As a company scales, entire departments are dedicated to taking down these bad actors before they infect the rest of the user base. These examples were simple yet powerful examples telling us, “hey, our users are humans, too.” We’ve got a lot to learn from a behavioral scientist’s lens. Data’s important, but use it in context. Quantitative data’s so hot these days. And why not? It gives great insights into WHAT our users are doing. But the WHY is also equally important — and we need to marry both quantitative and qualitative data. When initially measuring the success of a product, qualitative data might weigh more heavily. Sarah Tavel from Bessemer ventures emphasizes drawing from our First Principles and front loading user research. Our empathy skills in asking the right questions & observing raw human behavior comes first, until we can really couple the user research with data at scale. “Product managers are the owners of a unique definition of a problem worth solving.” I this definition of a PM from Eric Vishria (General Partner at Benchmark Capital). Let’s break that down. love This definition is great. We can read it and say “oh, yeah, of course.” But we forget to live its principle. We forget to take ownership when things don’t go as planned. We forget to clearly define our goals & problems for everyone else to act on. We forget we are not the solution creators but the conduit to unlock everyone else’s creative potentials. If we can remember this holistic definition, we become better product managers. Some friends from the conference The product leader can understand the systematic complexities of the products they build. I like the analogy that the partners at Benchmark Capital highlighted: We should not lose the forest for the trees. It’s easy to silo into that one northstar metric, or be hyperfocused in building out that one feature. But the best product leaders can look at the forest the complexities of what they’re building. The PM needs to ask themself, PMs need to understand the wider, not often thought of implications of the products they put out into the world. and Does it affect other product metrics? Will this negatively impact specific cultures? What are the ethical risks associated with this design change? As a bonus, my 6th takeaway is that Ritual Coffee Roasters is . (I had one too many cups.) the best Thank you, Advancing Women in Product for the opportunity to learn from all these amazing product minds. I’m already on the waitlist for next years Amplify conference. Congratulations to Amplitude for a successful conference!

Amplify Conference 2018

Authors:
(1) Dorian W. P. Amaral, Department of Physics and Astronomy, Rice University and These authors contributed approximately equally to this work;
(2) Mudit Jain, Department of Physics and Astronomy, Rice University, Theoretical Particle Physics and Cosmology, King’s College London and These authors contributed approximately equally to this work;
(3) Mustafa A. Amin, Department of Physics and Astronomy, Rice University;
(4) Christopher Tunnell, Department of Physics and Astronomy, Rice University. Table of Links Abstract and 1 Introduction 2 Calculating the Stochastic Wave Vector Dark Matter Signal 2.1 The Dark Photon Field 2.2 The Detector Signal 3 Statistical Analysis and 3.1 Signal Likelihood 3.2 Projected Exclusions 4 Application to Accelerometer Studies 4.1 Recasting Generalised Limits onto B − L Dark Matter 5 Future Directions 6 Conclusions, Acknowledgments, and References A Equipartition between Longitudinal and Transverse Modes B Derivation of Marginal Likelihood with Stochastic Field Amplitude C Covariance Matrix D The Case of the Gradient of a Scalar B Derivation of Marginal Likelihood with Stochastic Field Amplitude The full signal in time space is given by Using the series representation of the Bessel function, together with Gamma function identities, the 5 random variables can be integrated out analytically. We arrive at the following marginalized (and normalized) likelihood: where This likelihood can be split into three individual likelihoods for the sum/difference peaks and the Compton peak, as given in Eq. (3.2). The form of the likelihoods for the sum and difference peaks is equivalent. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Dorian W. P. Amaral, Department of Physics and Astronomy, Rice University and These authors contributed approximately equally to this work; (2) Mudit Jain, Department of Physics and Astronomy, Rice University, Theoretical Particle Physics and Cosmology, King’s College London and These authors contributed approximately equally to this work; (3) Mustafa A. Amin, Department of Physics and Astronomy, Rice University; (4) Christopher Tunnell, Department of Physics and Astronomy, Rice University. Authors: Authors: (1) Dorian W. P. Amaral, Department of Physics and Astronomy, Rice University and These authors contributed approximately equally to this work; (2) Mudit Jain, Department of Physics and Astronomy, Rice University, Theoretical Particle Physics and Cosmology, King’s College London and These authors contributed approximately equally to this work; (3) Mustafa A. Amin, Department of Physics and Astronomy, Rice University; (4) Christopher Tunnell, Department of Physics and Astronomy, Rice University. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Calculating the Stochastic Wave Vector Dark Matter Signal 2.1 The Dark Photon Field 2.1 The Dark Photon Field 2.2 The Detector Signal 2.2 The Detector Signal 3 Statistical Analysis and 3.1 Signal Likelihood 3 Statistical Analysis and 3.1 Signal Likelihood 3.2 Projected Exclusions 3.2 Projected Exclusions 4 Application to Accelerometer Studies 4 Application to Accelerometer Studies 4.1 Recasting Generalised Limits onto B − L Dark Matter 4.1 Recasting Generalised Limits onto B − L Dark Matter 5 Future Directions 5 Future Directions 6 Conclusions, Acknowledgments, and References 6 Conclusions, Acknowledgments, and References A Equipartition between Longitudinal and Transverse Modes A Equipartition between Longitudinal and Transverse Modes B Derivation of Marginal Likelihood with Stochastic Field Amplitude B Derivation of Marginal Likelihood with Stochastic Field Amplitude C Covariance Matrix C Covariance Matrix D The Case of the Gradient of a Scalar D The Case of the Gradient of a Scalar B Derivation of Marginal Likelihood with Stochastic Field Amplitude The full signal in time space is given by Using the series representation of the Bessel function, together with Gamma function identities, the 5 random variables can be integrated out analytically. We arrive at the following marginalized (and normalized) likelihood: where This likelihood can be split into three individual likelihoods for the sum/difference peaks and the Compton peak, as given in Eq. (3.2). The form of the likelihoods for the sum and difference peaks is equivalent. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Derivation of Marginal Likelihood with Stochastic Field Amplitude

Understanding the Monotonicity of the Sparsity Objective Function

Table of Links Abstract and 1. Introduction 2. Preliminaries and 2.1. Blind deconvolution 2.2. Quadratic neural networks 3. Methodology 3.1. Time domain quadratic convolutional filter 3.2. Superiority of cyclic features extraction by QCNN 3.3. Frequency domain linear filter with envelope spectrum objective function 3.4. Integral optimization with uncertainty-aware weighing scheme 4. Computational experiments 4.1. Experimental configurations 4.2. Case study 1: PU dataset 4.3. Case study 2: JNU dataset 4.4. Case study 3: HIT dataset 5. Computational experiments 5.1. Comparison of BD methods 5.2. Classification results on various noise conditions 5.3. Employing ClassBD to deep learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.5. Feature extraction ability of quadratic and conventional networks 5.6. Comparison of ClassBD filters 6. Conclusions Appendix and References 5.5. Feature extraction ability of quadratic and conventional networks Previously, we have theoretically demonstrated that quadratic networks possess superior cyclostationary feature extraction ability to conventional networks. It is also necessary to validate the performance in practice. Therefore, we construct two time-domain filters using quadratic convolutional layers and conventional convolutional layers with an identical structure and then evaluate their feature-extraction performance on the JNU dataset subjected to -10 dB noise. The signals are analyzed using the Fast-SC method [84]. The results, as depicted in Figure 8, clearly demonstrate that the quadratic network outperforms in terms of feature extraction capability. The bright lines in the spectral coherence, highlight the quadratic network can extract cyclic frequency across high and low frequency bands. Despite the severe attenuation of the signal amplitude due to the noise, the quadratic network effectively recovers the cyclic frequency of the signal. Remarkably, the amplitude of the initial few cyclic frequencies is even higher than that of the raw signal. Authors:
(1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China;
(3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China;
(4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Preliminaries and 2.1. Blind deconvolution 2. Preliminaries and 2.1. Blind deconvolution 2.2. Quadratic neural networks 2.2. Quadratic neural networks 3. Methodology 3. Methodology 3.1. Time domain quadratic convolutional filter 3.1. Time domain quadratic convolutional filter 3.2. Superiority of cyclic features extraction by QCNN 3.2. Superiority of cyclic features extraction by QCNN 3.3. Frequency domain linear filter with envelope spectrum objective function 3.3. Frequency domain linear filter with envelope spectrum objective function 3.4. Integral optimization with uncertainty-aware weighing scheme 3.4. Integral optimization with uncertainty-aware weighing scheme 4. Computational experiments 4.1. Experimental configurations 4.1. Experimental configurations 4.2. Case study 1: PU dataset 4.2. Case study 1: PU dataset 4.3. Case study 2: JNU dataset 4.3. Case study 2: JNU dataset 4.4. Case study 3: HIT dataset 4.4. Case study 3: HIT dataset 5. Computational experiments 5.1. Comparison of BD methods 5.1. Comparison of BD methods 5.2. Classification results on various noise conditions 5.2. Classification results on various noise conditions 5.3. Employing ClassBD to deep learning classifiers 5.3. Employing ClassBD to deep learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.5. Feature extraction ability of quadratic and conventional networks 5.5. Feature extraction ability of quadratic and conventional networks 5.6. Comparison of ClassBD filters 5.6. Comparison of ClassBD filters 6. Conclusions 6. Conclusions Appendix and References Appendix and References 5.5. Feature extraction ability of quadratic and conventional networks Previously, we have theoretically demonstrated that quadratic networks possess superior cyclostationary feature extraction ability to conventional networks. It is also necessary to validate the performance in practice. Therefore, we construct two time-domain filters using quadratic convolutional layers and conventional convolutional layers with an identical structure and then evaluate their feature-extraction performance on the JNU dataset subjected to -10 dB noise. The signals are analyzed using the Fast-SC method [84]. The results, as depicted in Figure 8, clearly demonstrate that the quadratic network outperforms in terms of feature extraction capability. The bright lines in the spectral coherence, highlight the quadratic network can extract cyclic frequency across high and low frequency bands. Despite the severe attenuation of the signal amplitude due to the noise, the quadratic network effectively recovers the cyclic frequency of the signal. Remarkably, the amplitude of the initial few cyclic frequencies is even higher than that of the raw signal. Authors: (1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China; (3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China; (4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. Authors: Authors: (1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China; (3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China; (4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv

Quadratic Networks Excel in Extracting Features Compared to Conventional Networks

Table of Links Abstract and 1. Introduction 2. Preliminaries and 2.1. Blind deconvolution 2.2. Quadratic neural networks 3. Methodology 3.1. Time domain quadratic convolutional filter 3.2. Superiority of cyclic features extraction by QCNN 3.3. Frequency domain linear filter with envelope spectrum objective function 3.4. Integral optimization with uncertainty-aware weighing scheme 4. Computational experiments 4.1. Experimental configurations 4.2. Case study 1: PU dataset 4.3. Case study 2: JNU dataset 4.4. Case study 3: HIT dataset 5. Computational experiments 5.1. Comparison of BD methods 5.2. Classification results on various noise conditions 5.3. Employing ClassBD to deep learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.5. Feature extraction ability of quadratic and conventional networks 5.6. Comparison of ClassBD filters 6. Conclusions Appendix and References 5. Computational experiments 5.1. Comparison of BD methods Despite the recent proposal of many BD methods, a few works have validated their fault diagnosis performance via the integration of classifiers. Initially, we assess the performance of these BD methods by employing WDCNN as the post-BD classifier. For comparative analysis, we utilize four prior-free BD methods: minimum entropy deconvolution (MED) [26], sparse maximum harmonics-to-noise-ratio Deconvolution (SMHD) [82], improved maximum correlated kurtosis deconvolution (IMCKD) [83], and multi-task neural network blind deconvolution (MNNBD) [31]. The metric employed for this evaluation is also the F1 score. The classification results of the three datasets are presented in Table 8. Collectively, our approach outperforms others on all three datasets, indicating that the classifier-guided optimization is more apt for fault diagnosis. This is because traditional BD methods employ unsupervised optimization, whereas our method implements supervised learning, which introduces class-aware information. Furthermore, our approach is a streamlined one-step pipeline. When compared to the combination of conventional BD and classifiers, our method demonstrates superior effectiveness under noise-affected conditions. On the other hand, it is imperative to validate the denoising performance of BD methods in the frequency domain, thereby demonstrating that these methods indeed extract fault-related features and provide interpretability. Therefore, we design a frequency domain metric called fault frequency index (FFI), which is defined as follows: Subsequently, we utilize the JNU dataset to demonstrate the feature extraction performance. The SNR is set to -10dB, and we apply BD methods to all faulty signals, and then calculate the FFI of the signals post-BD. The results are illustrated in Table 9. From these results, we can make several observations. Firstly, ClassBD is highly effective in extracting fault-related features, as evidenced by the highest FFIs across all signals, surpassing even the raw clean signals. Secondly, on average, all BD methods are capable of enhancing the fault characteristic frequencies. The FFIs are consistently higher than the noisy signals, with MNNBD ranking second-best, achieving an average improvement of 41% compared to the noisy signals. Finally, we present a comparison of the feature extraction performance on the B1000 signal using Fast-SC. As depicted in Figure 7, the bright lines in the spectral coherence suggest that the magnitudes of the cyclic frequencies 𝛼 and corresponding frequency bands are elevated. And the EES displays the intensity of the extracted cyclic frequencies of the signal post-BD. Several observations can be made from this. Firstly, the noise significantly attenuates the characteristics of the signal. A comparison between Figure 7 (a) and (b) reveals that the intensity of all frequency bands is suppressed, with the lower frequency bands being more severely drown out by the noise. Secondly, all BD methods are capable of enhancing the cyclic frequency characteristics of the signal, indicating the effectiveness of BD in extracting fault-related features from noisy signals. Specifically, MNNBD focuses on the fundamental cyclic frequency, resulting in the extraction of full frequency bands at the first cyclic frequency. While SHMD and MED enhance all cyclic frequency bands, the amplitude of the individual cyclic frequencies is lower. Lastly, ClassBD exhibits the best performance. It significantly enhances the cyclic frequency characteristics of the signal. More importantly, ClassBD can provide valuable interpretability in decision-making. Authors:
(1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China;
(3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China;
(4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Preliminaries and 2.1. Blind deconvolution 2. Preliminaries and 2.1. Blind deconvolution 2.2. Quadratic neural networks 2.2. Quadratic neural networks 3. Methodology 3. Methodology 3.1. Time domain quadratic convolutional filter 3.1. Time domain quadratic convolutional filter 3.2. Superiority of cyclic features extraction by QCNN 3.2. Superiority of cyclic features extraction by QCNN 3.3. Frequency domain linear filter with envelope spectrum objective function 3.3. Frequency domain linear filter with envelope spectrum objective function 3.4. Integral optimization with uncertainty-aware weighing scheme 3.4. Integral optimization with uncertainty-aware weighing scheme 4. Computational experiments 4.1. Experimental configurations 4.1. Experimental configurations 4.2. Case study 1: PU dataset 4.2. Case study 1: PU dataset 4.3. Case study 2: JNU dataset 4.3. Case study 2: JNU dataset 4.4. Case study 3: HIT dataset 4.4. Case study 3: HIT dataset 5. Computational experiments 5.1. Comparison of BD methods 5.1. Comparison of BD methods 5.2. Classification results on various noise conditions 5.2. Classification results on various noise conditions 5.3. Employing ClassBD to deep learning classifiers 5.3. Employing ClassBD to deep learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.5. Feature extraction ability of quadratic and conventional networks 5.5. Feature extraction ability of quadratic and conventional networks 5.6. Comparison of ClassBD filters 5.6. Comparison of ClassBD filters 6. Conclusions 6. Conclusions Appendix and References Appendix and References 5. Computational experiments 5.1. Comparison of BD methods Despite the recent proposal of many BD methods, a few works have validated their fault diagnosis performance via the integration of classifiers. Initially, we assess the performance of these BD methods by employing WDCNN as the post-BD classifier. For comparative analysis, we utilize four prior-free BD methods: minimum entropy deconvolution (MED) [26], sparse maximum harmonics-to-noise-ratio Deconvolution (SMHD) [82], improved maximum correlated kurtosis deconvolution (IMCKD) [83], and multi-task neural network blind deconvolution (MNNBD) [31]. The metric employed for this evaluation is also the F1 score. The classification results of the three datasets are presented in Table 8. Collectively, our approach outperforms others on all three datasets, indicating that the classifier-guided optimization is more apt for fault diagnosis. This is because traditional BD methods employ unsupervised optimization, whereas our method implements supervised learning, which introduces class-aware information. Furthermore, our approach is a streamlined one-step pipeline. When compared to the combination of conventional BD and classifiers, our method demonstrates superior effectiveness under noise-affected conditions. On the other hand, it is imperative to validate the denoising performance of BD methods in the frequency domain, thereby demonstrating that these methods indeed extract fault-related features and provide interpretability. Therefore, we design a frequency domain metric called fault frequency index (FFI), which is defined as follows: Subsequently, we utilize the JNU dataset to demonstrate the feature extraction performance. The SNR is set to -10dB, and we apply BD methods to all faulty signals, and then calculate the FFI of the signals post-BD. The results are illustrated in Table 9. From these results, we can make several observations. Firstly, ClassBD is highly effective in extracting fault-related features, as evidenced by the highest FFIs across all signals, surpassing even the raw clean signals. Secondly, on average, all BD methods are capable of enhancing the fault characteristic frequencies. The FFIs are consistently higher than the noisy signals, with MNNBD ranking second-best, achieving an average improvement of 41% compared to the noisy signals. Finally, we present a comparison of the feature extraction performance on the B1000 signal using Fast-SC. As depicted in Figure 7, the bright lines in the spectral coherence suggest that the magnitudes of the cyclic frequencies 𝛼 and corresponding frequency bands are elevated. And the EES displays the intensity of the extracted cyclic frequencies of the signal post-BD. Several observations can be made from this. Firstly, the noise significantly attenuates the characteristics of the signal. A comparison between Figure 7 (a) and (b) reveals that the intensity of all frequency bands is suppressed, with the lower frequency bands being more severely drown out by the noise. Secondly, all BD methods are capable of enhancing the cyclic frequency characteristics of the signal, indicating the effectiveness of BD in extracting fault-related features from noisy signals. Specifically, MNNBD focuses on the fundamental cyclic frequency, resulting in the extraction of full frequency bands at the first cyclic frequency. While SHMD and MED enhance all cyclic frequency bands, the amplitude of the individual cyclic frequencies is lower. Lastly, ClassBD exhibits the best performance. It significantly enhances the cyclic frequency characteristics of the signal. More importantly, ClassBD can provide valuable interpretability in decision-making. Authors: (1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China; (3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China; (4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. Authors: Authors: (1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China; (3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China; (4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv

AMPLITUDE

thisisamplitude.co.uk

1-10 employees

Since 2006

COMPANY RANKING

AMPLITUDE

EVERGREEN INDEX #145

Representing this company? Click here to claim and customize this page!

Amplitude WIKI

Apply to get your Tech Company News Page live on HackerNoon.com today!

AMPLITUDE

thisisamplitude.co.uk

1-10 employees

Since 2006

COMPANY RANKING

AMPLITUDE

EVERGREEN INDEX #145

RELATED COMPANIESRANK

STORIES ABOUT AMPLITUDE

Representing this company? Click here to claim and customize this page!

Amplitude WIKI

Apply to get your Tech Company News Page live on HackerNoon.com today!